THE LIBRARY

OF

THE UNIVERSITY
OF CALIFORNIA

LOS ANGELES

GIFT

From the Library of

Henry Goldman, Ph.D.

1886-1972

\

SYSTEM OF LOGIC

KATIOCINATIYE AND INDUCTIVE

VOL. I.

SYSTEM OF LOGIC

KATIOCINATIVE AND INDUCTIVE

BEING A CONNECTED VIEW OF THE
PRINCIPLES OF EVIDENCE

AND THE
METHODS OF SCIENTIFIC INVESTIGATION

BT

JOHN STUAET MILL

IN TWO VOLUMES
VOL. I.

EIGHTH EDITION

LONDON :
LONGMANS, GREEN, READER, AND DYER

1872.

<\\

PEEFACE TO THE FIRST EDITION.

THIS book makes no pretence of giving to the
world a new theory of the intellectual operations.
Its claim to attention, if it possess any, is grounded
on the fact that it is an attempt not to supersede, but
to embody and systematize, the best ideas which have
been either promulgated on its subject by speculative
writers, or conformed to by accurate thinkers in their
scientific inquiries.

To cement together the detached fragments of a
subject, never yet treated as a whole ; to harmonize
the true portions of discordant theories, by supplying
the links of thought necessary to connect them, and
by disentangling them from the errors with which
they are always more or less interwoven ; must
necessarily require a considerable amount of original
speculation. To other originality than this, the pre-
sent work lays no claim. In the existing state of
the cultivation of the sciences, there would be a very
strong presumption against any one who should
imagine that he had effected a revolution in the
theory of the investigation of truth, or added any
fundamentally new process to the practice of it.
The improvement which remains to be effected in
the methods of philosophizing (and the author be-
lieves that they have much need of improvement)
can only consist in performing, more systematically

b

VI PREFACE.

and accurately, operations with which, at least in
their elementary form, the human intellect in some
one or other of its employments is already familiar.

In the portion of the work which treats- of Eatio-
cination, the author has not deemed it necessary to
enter into technical details which may be obtained in
so perfect a shape from the existing treatises on what
is termed the Logic of the Schools. In the contempt
entertained by many modern philosophers for the
syllogistic art, it will be seen that he by no means
participates; though the scientific theory on which
its defence is usually rested appears to him erroneous :
and the view which he has suggested of the nature
and functions of the Syllogism may, perhaps, afford
the means of conciliating the principles of the art
with as much as is well grounded in the doctrines
and objections of its assailants.

The same abstinence from details could not be
observed in the First Book, on Names and Proposi-
tions ; because many useful principles and distinc-
tions which were contained in the old Logic, have
been gradually omitted from the writings of its later
teachers ; and it appeared desirable both to revive
these, and to reform and rationalize the philosophical
foundation on which they stood. The earlier chap-
ters of this preliminary Book will consequently
appear, to some readers, needlessly elementary and
scholastic. But those who know in what darkness
the nature of our knowledge, and of the processes by
which it is obtained, is often involved by a confused
apprehension of the import of the different classes of
Words and Assertions, will not regard these discus-
sions as either frivolous, or irrelevant to the topics
considered in the later Books.

PREFACE. Vll

On the subject of Induction, the task to be per-
formed was that of generalizing the modes of investi-
gating truth and estimating evidence, by which so
many important and recondite laws of nature have,
in the various sciences, been aggregated to the stock
of human knowledge. That this is not a task free
from difficulty may be presumed from the fact, that
even at a very recent period, eminent writers (among
whom it is sufficient to name Archbishop Whately,
and the author of a celebrated article on Bacon in
the Edinburgh Review] have not scrupled to pro-
nounce it impossible.* The author has endeavoured
to combat their theory in the manner in which
Diogenes confuted the sceptical reasonings against
the possibility of motion ; remembering that Dio-
genes' argument would have been equally conclusive,
though his individual perambulations might not have
extended beyond the circuit of his own tub.

Whatever may be the value of what the author
has succeeded in effecting on this branch of his sub-
ject, it is a duty to acknowledge that for much of it

* In the later editions of Archbishop Whateiy's Logic, he
states his meaning1 to be, not that " rules " for the ascertainment
of truths by inductive investigation cannot be laid down, or that
they may not be " of eminent service," but that they " must
always be comparatively vague and general, and incapable of
being built up into a regular demonstrative theory like that of
the Syllogism." (Book iv. ch. iv. § 3.) And he observes, that
to devise a system for this purpose, capable of being " brought
into a scientific form," would be an achievement which " he must
be more sanguine than scientific who expects." (Book iv. ch. ii.
§ 4.) To effect this, however, being the express object of the
portion of the present work which treats of Induction, the words
in the text are no overstatement of the difference of opinion be-
tween Archbishop Whately and me on the subject.

6 2

Vlll PREFACE.

lie has been indebted to several important treatises,
partly historical and partly philosophical, on the
generalities and processes of physical science, which
have been published within the last few years. To
these treatises, and to their authors, he has endea-
voured to do justice in the body of the work. But
as with one of these writers, Dr. Whewell, he has
occasion frequently to express differences of opinion,
it is more particularly incumbent on him in this
place to declare, that without the aid derived from
the facts and ideas contained in that gentleman's
History of the Inductive Sciences, the corresponding
portion of this work would probably not have been
written.

The concluding Book is an attempt to contribute
towards the solution of a question, which the decay
of old opinions, and the agitation that disturbs Euro-
pean society to its inmost depths, render as impor-
tant in the present day to the practical interests of
human life, as it must at all times be to the com-
pleteness of our speculative knowledge : viz. Whether
moral and social phenomena are really exceptions to
the general certainty and uniformity of the course of
nature ; and how far the methods, by which so many
of the laws of the physical world have been numbered
among truths irrevocably acquired and universally
assented to, can be made instrumental to the forma-
tion of a similar body of received doctrine in moral
and political science.

PfiEFACE TO THE THIED AND FOUETH
EDITIONS,

SEVERAL criticisms, of a more or less controversial
character, on this work, have appeared since the pub-
lication of the second edition ; and Dr. Whewell has
lately published a reply to those parts of it in which
some of his opinions were controverted.*

I have carefully reconsidered all the points on
which my conclusions have been assailed. But I
have not to announce a change of opinion on any
matter of importance. Such minor oversights as
have been detected, either by myself or by my
critics, I have, in general silently, corrected : but
it is not to be inferred that I agree with the objec-
tions which have been made to a passage, in every
instance in which I have altered or cancelled it. I
have often done so, merely that it might not remain
a stumbling-block, when the amount of discussion
necessary to place the matter in its true light would
have exceeded what was suitable to the occasion.

To several of the arguments which have been
urged against me, I have thought it useful to reply
with some degree of minuteness ; not from any taste
for controversy, but because the opportunity was
favourable for placing my own conclusions, and the
grounds of them, more clearly and completely before

* Now forming a chapter in his volume on The Philuso^hij <//'
Discovery.

PREFACE.

the reader. Truth on these subjects is militant,
and can only establish itself by means of conflict.
The most opposite opinions can make a plausible
show of evidence while each has the statement of its
own case ; and it is only possible to ascertain which
of them is in the right, after hearing and comparing
what each can say against the other, and what the
other can urge in its defence.

Even the criticisms from which I most dissent
have been of great service to me, by showing in what
places the exposition most needed to be improved, or
the argument strengthened. And I should have
been well pleased if the book had undergone a much
greater amount of attack ; as in that case I should
probably have been enabled to improve it still more
than I believe I have now done.

In the subsequent editions, the attempt to im-
prove the work by additions and corrections, suggested
by criticism or by thought, has been continued. The
additions and correction^ in the present (eighth)
edition, which are not very considerable, are chiefly
such as htive been suggested by Professor Bain's
" Logic," a book of great merit and value. Mr.
Bain's view of the science is essentially the same with
that taken in the present treatise, the differences of
opinion being few and unimportant compared with
the agreements ; and he has not only enriched the
exposition by many applications and illustrative de-
tails, but has appended to it a minute and very
valuable discussion of the logical principles specially
applicable to each of the sciences ; a task for which
the encyclopedical character of his knowledge pecu-

PREFACE.

liarly qualified him. I have in several instances
made use of his exposition to improve my own,
by adopting, and occasionally by controverting, matter
contained in his treatise,

The longest of the additions belongs to the
chapter on Causation, and is a discussion of the
question, how far, if at all, the ordinary mode of
stating the law of Cause and Effect requires modifica-
tion to adapt it to the new doctrine of the Con-
servation of Force : a point still more fully and
elaborately treated in Mr, Bain's work.

CONTENTS

OF

THE FIKST VOLUME.

INTRODUCTION.

PAGE

§ 1. A definition at the commencement of a subject must be
provisional ......

2. Is logic the art and science of reasoning ? . .2

3. Or the art and science of the pursuit of truth ? .3

4. Logic is concerned with inferences, not with intuitive truths 5

5. Relation of logic to the other sciences . . .8

6. Its utility, how shown . . . . .10

7. Definition of logic stated and illustrated . . .11

BOOK I.

OF NAMES AND PROPOSITIONS.

CHAPTER I. Of the Necessity of commencing with an Analysis of
Language.

§ 1. Theory of names, why a necessary part of logic . . 17

2. First step in the analysis of Propositions . . .18

3. Names must be studied before Things . . .21

CHAPTER II. Of Names.

§ 1. Names are names of things, not of our ideas . . 23

2. Words which are not names, but parts of names . . 24

3. General and Singular names . . . .26

4. Concrete and Abstract . . . . .29

5. Counotative and Non-connotative . . . .31

6. Positive and Negative . . . . .43

7. Relative and Absolute . . . . .44

8. Univocal and ^Equivocal . . . . .47

XIV CONTEXTS.

CHAPTER III. Of the Things denoted by Names.

PAGE

§ 1. Necessity of an enumeration of Nameable Things. The
Categories of Aristotle .

2. Ambiguity of the most general names

3. Feelings, or states of consciousness . . • .00

4. Feelings must be distinguished from their physical antece-

dents. Perceptions, what . .57

5. Volitions, and Actions, what

6. Substance and Attribute . . • • .60

7. Body -62

8. Mind ....

9. Qualities .....

10. Relations ......

11. Resemblance . . . . • .75

12. Quantity 78

13. All attributes of bodies are grounded on states of con-

sciousness . . . . . • . /9

14. So also all attributes of mind

15. Recapitulation ....

CHAPTER IV. Of Propositions.

§ 1. Nature and office of the copula . . . .85

2. Affirmative and Negative propositions . . .87

3. Simple and Complex . . . . .89

4. Universal, Particular, and Singular . . . .93

CHAPTER V. Of the Import of Propositions.

§ 1. Doctrine that a proposition is the expression of a relation

between two ideas . . . . . .96

2. Doctrine that it is the expression of a relation between the

meanings of two names . . . . .99

3. Doctrine that it consists in referring something to, or ex-

cluding something from, a class .... 103

4. What it really is . . . .108

5. It asserts (or denies) a sequence, a coexistence, a simple

existence, a causation . . . . .110

6. — or a resemblance . . . . . 113

7. Propositions of which the terms are abstract . .118

CONTENTS. XV

CHAPTEE VI. Of Propositions merely Verbal.

PAGB

§ 1. Essential and Accidental propositions . . . 122

2. All essential propositions are identical propositions . . 123

3. Individuals have no essences .... 127

4. Real propositions, how distinguished from verbal . .129

5. Two modes of representing the import of a Real proposition 130

CHAPTEE VII. Of the Nature of Classification, and the
Five Predicables.

§ 1. Classification, how connected with Naming . . . 132

2. The Predicates, what . . . . .134

3. Genus and Species ...... 134

4. Kinds have a real existence in nature . . . 137

5. Differentia ....... 142

6. Differentiae for general purposes, and differentiae for special

or technical purposes . . . . .144

7. Proprium . . . . . . .147

8. Accidens . . . . . . .149

CHAPTEE VIII. Of Definition.

§ 1. A definition, what . . . . . .151

2. Every name can be defined, whose meaning is susceptible of

analysis ....... 153

3. Complete, how distinguished from incomplete definitions . 155

4. — and from descriptions ..... 157

5. What are called definitions of Things, are definitions of Names

with an implied assumption of the existence of Things cor-
responding to them ..... 161

6. — even when such things do not in reality exist . . 169

7. Definitions, though of names only, must be grounded on

knowledge of the corresponding things . . . 171

XVI CONTEXTS.

BOOK II.

OF REASONING.

PAG«

CHAPTER I. Of Inference, or Reasoning, in general.

§ 1. Retrospect of the preceding book .... 179

2. Inferences improperly so called .... 181

3. Inferences proper, distinguished into inductions and ratioci-

nations ....... 185

CHAPTER II. Of Ratiocination, or Syllogism,

§ 1. Analysis of the Syllogism ..... 188

2. The dictum de omni not the foundation of reasoning, but a

mere identical proposition ..... 196

3. What is the really fundamental axiom of Ratiocination . 201

4. The other form of the axiom .... 204

CHAPTER III. Of the Functions, and Logical Value of the
Syllogism.

§ 1. Is the syllogism a pelitio principii ? 209

2. Insufficiency of the common theory .... 210

3. All inference is from particulars to particulars . . 212

4. General propositions are a record of such inferences, and the

rules of the syllogism are rules for the iuterpretation of the

record ....... 221

5. The syllogism not the type of reasoning, but a test of it . 225

6. The true type, what . . . . .229

7. Relation between Induction and Deduction . . . 232

8. Objections answered ..... 23-1

9. Of Formal Logic, and its relation to the Logic of Truth . 238

CHAPTER IV. Of Trains of Reasoning, and Deductive
Sciences.

§ 1. For what purpose trains of reasoning exist . . . 241

2. A train of reasoning is a series of inductive inferences . 241

3. — from particulars to particulars through marks of marks . 244

4. Why there are deductive sciences .... 247

5. Why other sciences still remain experimental . . 251

6. Experimental sciences may become deductive by the progress

of experiment ..... 253

7. In what manner this usually takes place . , . 254

CONTENTS. XVII

CHAPTER V. Of Demonstration, and Necessary Truths.

PAGE

§ 1. The Theorems of geometry are necessary truths only in the

sense of necessarily following from hypotheses . . 258

2. Those hypotheses are real facts with some of their circum-

stances exaggerated or omitted .... 262

3. Some of the first principles of geometry are axioms, and these

are not hypothetical ..... 264

4. — but are experimental truths .... 266

5. An objection answered ..... 268

6. Dr. Whewell's opinions on axioms examined . . 273

CHAPTEB VI. The same Subject continued,
§ 1. All deductive sciences are inductive . . . 290

2. The propositions of the science of number are not verbal, but

generalizations from experience .... 292

3. In what sense hypothetical ..... 297

4. The characteristic property of demonstrative science is to be

hypothetical ...... 298

5. Definition of demonstrative evidence . . . 300

CHAPTEE VII. Examination of some Opinions opposed to
the preceding doctrines.

§ 1. Doctrine of the Universal Postulate . . . 301

2. The test of inconceivability does not represent the aggregate

of past experience ...... 303

3. — nor is implied in every process of thought . . 306

4. Objections answei-ed ..... 314

5. Sir W. Hamilton's opinion on the Principles of Contradic-

tion and Excluded Middle ..... 319

BOOK III.

OF INDUCTION.
CniPTEB I. Preliminary Observations on Induction in general.

§. 1. Importance of an Inductive Logic .... 327
2. The logic of science is also that of business and life . . 328

CHAPTEE II. Of Inductions improperly so called.

§ 1. Inductions distinguished from verbal transformations . 333

2. — from inductions, falsely so called, in mathematics . 335

3. — and from descriptions ..... 337

4. Examination of Dr. Whewell's theory of Induction . . 340

5. Further illustration of the preceding remarks . . 350

XV111 CONTENTS.

CHAPTEB III. On the Ground of Induction.

PAGE

§ 1. Axiom of the uniformity of the course of nature . . 354

2. Not true in every sense. Induction per enumerationem

simplicem ....... 359

3. The question of Inductive Logic stated . . . 361

CHAPTEB IV. Of Laws of Nature.

§ 1. The general regularity in nature is a tissue of partial regu-
larities', called laws ..... 364

2. Scientific induction must be grounded on previous spon-

taneous inductions ...... 367

3. Are there any inductions fitted to be a test of all others? . 370

CHAPTER V. Of the Law of Universal Causation.
§ 1. The universal law of successive phenomena is the Law of

Causation ....... 373

2. — i.e. the law that every consequent has an invariable ante-

cedent ....... 376

3. The cause of a phenomenon is the assemblage of its condi-

tions ....... 378

4. The distinction of agent and patient illusory . . 386

5. Case in which the effect consists in giving a property to an

object ....... 388

6. The cause is not the invariable antecedent, but the uncondi-

tional invariable antecedent .... 300

7. Can a cause be simultaneous with its effect ? . . 395

8. Idea of a Permanent Cause, or original natural agent . 397

9. Uniformities of co-existence between effects of different per-

manent causes, are not laws .... 401

10. Theory of the Conservation of Force . . . 402

11. Doctrine that volition is an efficient cause, examined . 409

CHAPTEB VI. Of the Composition of Causes.
§ 1. Two modes of the conjunct action of causes, the mechanical

and the chemical . . . . . .427

2. The composition of causes the general rule; the other case

exceptional ...... 430

3. Are effects proportional to their causes ? . . 434

CHAPTEB VII. Of Observation and Experiment.

§ 1. The first step of inductive inquiry is a mental analysis of

complex phenomena into their elements . . . 437

2. The next is an actual separation of those elements . . 439

3. Advantages of experiment over observation . . . 440

4. Advantages of observation over experiment . . . 443

CONTENTS. XIX

CHAPTEB VIII. Of the Four Methods of Experimental
Inquiry.

FAOB

§ 1. Method of Agreement ..... 448

2. Method of Difference ..... 451

3. Mutual relation of these two methods . . . 452

4. Joint Method of Agreement and Difference . . . 456

5. Method of Residues ...... 459

6. Method of Concomitant Variations .... 460

7. Limitations of this last method .... 466

CHAPTEB IX. Miscellaneous Examples of the Four Methods.

§ 1. Liebig's theory of metallic poisons .... 472

2. Theory of induced electricity .... 476

3. Dr. Wells' theory of dew ..... 480

4. Dr. Brown-Stiquard's theory of cadaveric rigidity . . 488

5. Examples of the Method of Residues . . . 494

6. Dr. Whewell's objections to the Four Methods . . 498

CHAPTER X. Of Plurality of Causes; and of the Lderm'uclure
of Effects.

§ 1. One effect may have several causes .... 504

2. — which is the source of a characteristic imperfection of the

Method of Agreement ..... 505

3. Plurality of Causes, how ascertained . . . 510

4. Concurrence of Causes which do not compound their effects 511

5. Difficulties of the investigation, when causes compound their

effects ....... 514

6. Three modes of investigating the laws of complex effects . 519

7. The method of simple observation inapplicable . . 521

8. The purely experimental method inapplicable . . 522

CHAPTEB XI. Of the Deductive Method.

§ 1. First stage ; ascertainment of the laws of the separate causes

by direct induction ..... 529

2. Second stage ; ratiocination from the simple laws of the com-

plex cases ..... . 534

3. Third stage ; verification by specific experience . . 536

XX CONTENTS.

CHAPTER XII. Of the "Explanation of Laws of Nature.

PAGB

§ 1. Explanation defined ...... 540

2. First mode of explanation, by resolving the law of a complex

effect into the laws of the concurrent causes and the fact of
their coexistence . . ... . . 540

3. Second mode ; by the detection of an intermediate link in the

sequence ....... 541

4. Laws are always resolved into laws more general than them-

selves ....... 542

5. Third mode ; the subsumption of less general laws under a

more general one ...... 546

6. What the explanation of a law of nature amounts to . 548

CHAPTER XIII. Miscellaneous Examples of the Explanation of
Laws of Nature.

§ 1. The general theories of the sciences .... 551

2. Examples from chemical speculations . . . 553

3. Example from Dr. Brown-Sequard's researches on the

nervous system ...... 555

4. Examples of following newly-discovered laws into their

complex manifestations ..... 556

5. Examples of empirical generalizations, afterwards confirmed

and explained deductively ..... 558

6. Example from mental science .... 559

7. Tendency of all the sciences to become deductive . . 561

INTRODUCTION.

§ 1. THERE is as great diversity among authors in the
modes which they have adopted of defining logic, as in their
treatment of the details of it. This is what might naturally
be expected on any subject on which writers have availed them-
selves of the same language as a means of delivering different
ideas. Ethics and jurisprudence are liable to the remark in
ccmmon with logic. Almost every writer having taken a
different view of some of the particulars which these branches
of knowledge are usually understood to include ; each has so
framed his definition as to indicate beforehand his own peculiar
tenets, and sometimes to beg the question in their favour.

This diversity is not so much an evil to be complained of,
as an inevitable and in some degree a proper result of the
imperfect state of those sciences. It is not to be expected that
there should be agreement about the definition of anything,
until there is agreement about the thing itself. To define, is
to select from among all the properties of a thing, those
which shall be understood to be designated and declared
by its name ; and the properties must be well known to us
before we can be competent to determine which of them are
fittest to be chosen for this purpose. Accordingly, in the case
of so complex an aggregation of particulars as are compre-
hended in anything which can be called a science, the defini-
tion we set out with is seldom that which a more extensive
knowledge of the subject shows to be the most appropriate.
Until we know the particulars themselves, we cannot fix upon
the most correct and compact mode of circumscribing them by
a general description. It was not until after an extensive and
accurate acquaintance with the details of chemical phenomena,
VOL. i. 1

* INTRODUCTION.

that it was found possible to frame a rational definition of
chemistry ; and the definition of the science of life and orga-
nization is still a matter of dispute. So long as the sciences
are imperfect, the definitions must partake of their imperfec-
tion ; and if the former are progressive, the latter ought to be
so too. As much, therefore, as is to be expected from a defi-
nition placed at the commencement of a subject, is that it
should define the scope of our inquiries : and the definition
which I am about to offer of the science of logic, pretends to
nothing more, than to be a statement of the question which I
have put to myself, and which this book is an attempt to
resolve. The reader is at liberty to object to it as a definition
of logic ; but it is at all events a correct definition of the sub-
ject of these volumes.

§ 2. Logic has often been called the Art of Reasoning.
A writer* who has done more than any other person to restore
this study to the rank from which it had fallen in the esti-
mation of the cultivated class in our own country, has adopted
the above definition with an amendment; he has defined Logic
to be the Science, as well as the Art, of reasoning ; meaning
by the former term, the analysis of the mental process which
takes place whenever we reason, and by the latter, the rules,
grounded on that analysis, for conducting the process cor-
rectly. There can be no doubt as to the propriety of the
emendation. A right understanding of the mental process
itself, of the conditions it depends on, and the steps of which
it consists, is the only basis on which a system of rules, fitted
for the direction of the process, can possibly be founded. Art
necessarily presupposes knowledge ; art, in any but its infant
state, presupposes scientific knowledge : and if every art does
not bear the name of a science, it is only because several
sciences are often necessary to form the groundwork of a single
art. So complicated are the conditions which govern our prac-
tical agency, that to enable one thing to be done, it is often
requisite to knoiv the nature and properties of many things.

* Archbishop Whately.

DEFINITION AND PROVINCE OF LOGIC. O

Logic, then, comprises the science of reasoning, as well as
an art, founded on that science. But the word Reasoning,
again, like most other scientific terms in popular use, abounds
in ambiguities. In one of its acceptations, it means syllogizing ;
or the mode of inference which may be called (with sufficient
accuracy for the present purpose) concluding from generals to
particulars. In another of its senses, to reason is simply to
infer any assertion, from assertions already admitted : and in
this sense induction is as much entitled to be called reasoning
as the demonstrations of geometry.

Writers on logic have generally preferred the former accep-
tation of the term : the latter, and more extensive significa-
tion is that in which I mean to use it. I do this by virtue of
the right I claim for every author, to give whatever provi-
sional definition he pleases of his own subject. But sufficient
reasons will, I believe, unfold themselves as we advance, why
this should be not only the provisional but the final definition.
It involves, at all events, no arbitrary change in the meaning
of the word ; for, with the general usage of the English lan-
guage, the wider signification, I believe, accords better than
the more restricted one.

§ 3. But Reasoning, even in the widest sense of which
the word is susceptible, does not seem to comprehend all that
is included, either in the best, or even in the most current,
conception of the scope and province of our science. The
employment of the word Logic to denote the theory of Argu-
mentation, is derived from the Aristotelian, or, as they are
commonly termed, the scholastic, logicians. Yet even with
them, in their systematic treatises, Argumentation was the
subject only of the third part : the two former treated of
Terms, and of Propositions ; under one or other of which heads
were also included Definition and Division. By some, indeed,
these previous topics were professedly introduced only on
account of their connexion with reasoning, and as a prepara-^
tion for the doctrine and rules of the syllogism. Yet they-
were treated with greater minuteness, and dwelt on at greater
length, than was required for that purpose alone. More

1— -2

INTRODUCTION'.

writers on logic have generally understood the term as it was
employed hy the able author of the Port Royal Logic ; viz.
as equivalent to the Art of Thinking. Nor is this acceptation
confined to books, and scientific inquiries. Even in ordinary
conversation, the ideas connected with the word Logic include
at least precision of language, and accuracy of classification :
and we perhaps oftener hear persons speak of a logical arrange-
ment, or of expressions logically defined, than of conclusions
logically deduced from premises. Again, a man is often called
a great logician, or a man of powerful logic, not for the accu-
racy of his deductions, but for the extent of his command
over premises ; because the general propositions required for
explaining a difficulty or refuting a sophism, copiously and
promptly occur to him : because, in short, his knowledge,
besides being ample, is well under his command for argumen-
tative use. Whether, therefore, we conform to the practice of
those who have made the subject their particular study, or to
that of popular writers and common discourse, the province
of logic will include several operations of the intellect not
usually considered to fall within the meaning of the terms
Reasoning and Argumentation.

These various operations might be brought within the com-
pass of the science, and the additional advantage be obtained
of a very simple definition, if, by an extension of the term,
sanctioned by high authorities, we were to define logic as the
science which treats of the operations of the human under-
standing in the pursuit of truth. For to this ultimate end,
naming, classification, definition, and all other operations over
which logic has ever claimed jurisdiction, are essentially sub-
sidiary. They may all be regarded as contrivances for enabling
a person to know the truths which are needful to him, and to
know them at the precise moment at which they are needful.
Other purposes, indeed, are also served by these operations ;
for instance, that of imparting our knowledge to others. But,
viewed with regard to this purpose, they have never been con-
sidered as within the province of the logician. The sole object
of Logic is the guidance of one's own thoughts: the com-
munication of those thoughts to others falls under the con-

DEFINITION AND PROVINCE OF LOGIC. 5

sideration of Rhetoric, in the large sense in Avhich that art
was conceived by the ancients ; or of the still more extensive
art of Education. Logic takes cognizance of our intellectual
operations, only as they conduce to our own knowledge, and
to our command over that knowledge for our own uses. If
there were but one rational being in the universe, that being
might be a perfect logician ; and the science and art of logic
would be the same for that one person as for the whole
human race.

§ 4. But, if the definition which we formerly examined
included too little, that which is now suggested has the oppo-
site fault of including too much.

Truths are known to us in two ways : some are known
directly, and of themselves ; some through the medium of
other truths. The former are the subject of Intuition, or Con-
sciousness ; * the latter, of Inference. The truths known by
intuition are the original premises from which all others are
inferred. Our assent to the conclusion being grounded on the
truth of the premises, we never could arrive at any knowledge
by reasoning, unless something could be known antecedently
to all reasoning.

Examples of truths known to us by immediate conscious-
ness, are our own bodily sensations and mental feelings. I
know directly, and of my own knowledge, that I was vexed
yesterday, or that I am hungry to-day. Examples of truths
which we know only by way of inference, are occurrences
which took place while we were absent, the events recorded in
history, or the theorems of mathematics. The two former we
infer from the testimony adduced, or from the traces of those
past occurrences which still exist ; the latter, from the pre-
mises laid down in books of geometry, under the title of defi-
nitions and axioms. Whatever we are capable of knowing

* I use these terms indiscriminately, because, for the purpose in view, there
is no need for making any distinction between them. But metaphysicians
usually restrict the name Intuition to the direct knowledge we are supposed
to have of things external to our minds, and Consciousness to our knowledge of
our own mental phenomena.

6 INTRODUCTION.

must belong to the one class or to the other ; must be in the
number of the primitive data, or of the conclusions which can
be drawn from these.

With the original data, or ultimate premises of our know-
ledge; with their number or nature, the mode in which they
are obtained, or the tests by which they may be distinguished ;
logic, in a direct way at least, has, in the sense in which 1 con-
ceive the science, nothing to do. These questions are partly
not a subject of science at all, partly that of a very different
science.

Whatever is known to us by consciousness, is known be-
yond possibility of question. What one sees or feels, whether
bodily or mentally, one cannot but be sure that one sees or
feels. No science is required for the purpose of establishing
such truths ; no rules of art can render our knowledge of them
more certain than it is in itself. There is no logic for this
portion of our knowledge.

But we may fancy that we see or feel what we in reality
infer. A truth, or supposed truth, which is really the result
of a very rapid inference, may seem to be apprehended intui-
tively. It has long been agreed by thinkers of the most oppo-
site schools, that this mistake is actually made in so familiar
an instance as that of the eyesight. There is nothing of which
we appear to ourselves to be more directly conscious, than the
distance of an object from us. Yet it has long been ascertained,
that what is perceived by the eye, is at most nothing more
than a variously coloured surface ; that when we fancy we see
distance, all we really see is certain variations of apparent size,
and degrees of faintness of colour ; that our estimate of the
object's distance from us is the result partly of a rapid inference
from the muscular sensations accompanying the adjustment of
the focal distance of the eye to objects unequally remote from
us, and partly of a comparison (made with so much rapidity
that we are unconscious of making it) between the size and
colour of the object as they appear at the time, and the size
and colour of the same or of similar objects as they appeared
when close at hand, or when their degree of remoteness was
kuown by other evidence. The perception of distance by the

DEFINITION AND PROVINCE OF LOGIC. 7

eye, which seems so like intuition, is thus, in reality, an infe-
rence grounded on experience ; an inference, too, which we
learn to make ; and which we make with more and more cor-
rectness as our experience increases ; though in familiar cases
it takes place so rapidly as to appear exactly on a par with
those perceptions of sight which are really intuitive, our per-
ceptions of colour.*

Of the science, therefore, which expounds the operations of
the human understanding in the pursuit of truth, one essential
part is the inquiry : What are the facts which are the objects
of intuition or consciousness, and what are those which we
merely infer? But this inquiry has never been considered a
portion of logic. Its place is in another and a perfectly distinct
department of science, to which the name metaphysics more
particularly belongs : that portion of mental philosophy which
attempts to determine what part of the furniture of the mind
belongs to it originally, and what part is constructed out of
materials furnished to it from without. To this science apper-
tain the great and much debated questions of the existence of
matter ; the existence of spirit, and of a distinction between it
and matter ; the reality of time and space, as things without
the mind, and distinguishable from the objects which are said
to exist in them. For in the present state of the discussion on
these topics, it is almost universally allowed that the existence
of matter or of spirit, of spaee or of time, is in its nature un-
susceptible of being proved ; and that if anything is known of
them, it must be by immediate intuition. To the same science
belong the inquiries into the nature of Conception, Perception,
Memory, and Belief; all of which are operations of the under-
standing in the pursuit of truth ; but with which, as phenomena
of the mind, or with the possibility which may or may not
exist of analysing any of them into simpler phenomena, the

* This important theory has of late been called in question by a writer of
deserved reputation, Mr. Samuel Bailey; but I do not conceive that the grounds
on which it has been admitted as an established doctrine for a century past,
have been at all shaken by that gentleman's objections. I have elsewhere said
what appeared to me necessary in reply to his arguments. (Westminster Review
for October 1842 ; reprinted in Dissertations and Discussions, vol. ii.)

8 INTRODUCTION.

logician as such has no concern. To this science must also be
referred the following, and all analogous questions : To what
extent our intellectual faculties and our emotions are innate —
to what extent the result of association : Whether God, and
duty, are realities, the existence of which is manifest to us
a priori by the constitution of our rational faculty ; or whether
our ideas of them are acquired notions, the origin of which we
are able to trace and explain; and the reality of the objects
themselves a question not of consciousness or intuition, but of
evidence and reasoning.

The province of logic must be restricted to that portion of
our knowledge which consists of inferences from truths pre-
viously known ; whether those antecedent data be general pro-
positions, or particular observations and perceptions. Logic
is not the science of Belief, but the science of Proof, or Evi-
dence. In so far as belief professes to be founded on proof,
the office of logic is to supply a test for ascertaining whether
or not the belief is well grounded. With the claims which any
proposition has to belief on the evidence of consciousness, that
is, without evidence in the proper sense of the word, logic has
nothing to do.

§ 5. By far the greatest portion of our knowledge,
whether of general truths or of particular facts, being avowedly
matter of inference, nearly the whole, not only of science, but
of human conduct, is amenable to the authority of logic. To
draw inferences has been said to be the great business of life.
Every one has daily, hourly, and momentary need of ascer-
taining facts which he has not directly observed ; not from any
general purpose of adding to his stock of knowledge, but be-
cause the facts themselves are of importance to his interests
or to his occupations. The business of the magistrate, of the
military commander, of the navigator, of the physician, of the
agriculturist, is merely to judge of evidence, and to act accord-
ingly. They all have to ascertain certain facts, in order that
they may afterwards apply certain rules, either devised by
themselves, or prescribed for their guidance by others; and as
they do this well or ill, so they discharge well or ill the duties

DEFINITION AND PROVINCE OP LOGIC.

of their several callings. It is the only occupation in which
the mind never ceases to be engaged ; and is the subject, not
of logic, but of knowledge in general.

Logic, however, is not the same thing with knowledge,
though the field of logic is coextensive with the field of know-
ledge. Logic is the common judge and arbiter of all parti-
cular investigations. It does not undertake to find evidence,
but to determine whether it has been found. Logic neither
observes, nor invents, nor discovers ; but judges. It is no part
of the business of logic to inform the surgeon what appearances
are found to accompany a violent death. This he must learn
from his own experience and observation, or from that of
others, his predecessors in his peculiar pursuit. But logic sits
in judgment on the sufficiency of that observation and expe-
rience to justify his rules, and on the sufficiency of his rules
to justify his conduct. It does not give him proofs, but
teaches him what makes them proofs, and how he is to judge
of them. It does not teach that any particular fact proves
any other, but points out to what conditions all facts must
conform, in order that they may prove other facts. To decide
whether any given fact fulfils these conditions, or whether facts
can be found which fulfil them in a given case, belongs ex-
clusively to the particular art or science, or to our knowledge
of the particular subject.

It is in this sense that logic is, what it was so expressively
called by the schoolmen and by Bacon, ars artium ; the science
of science itself. All science consists of data and conclusions
from those data, of proofs and what they prove : now logic
points out what relations must subsist between data and what-
ever can be concluded from them, between proof and every-
thing which it can prove. If there be any such indispensable
relations, and if these can be precisely determined, every par-
ticular branch of science, as well as every individual in the
guidance of his conduct, is bound to conform to those rela-
tions, under the penalty of making false inferences — of drawing
conclusions which are not grounded in the realities of things.
Whatever has at any time been concluded justly, whatever
knowledge has been acquired otherwise than by immediate in-

10 INTRODUCTION.

tuition, depended on the observance of the laws which it is
the province of logic to investigate. If the conclusions are
just, and the knowledge real, those laws, whether known or
not, have been observed.

§ 6. We need not, therefore, seek any farther for a solu-
tion of the question, so often agitated, respecting the utility
of logic. If a science of logic exists, or is capable of existing,
it must be useful. If there be rules to which every mind con-
sciously or unconsciously conforms in every instance in which
it infers rightly, there seems little necessity for discussing
whether a person is more likely to observe those rules, when
he knows the rules, than when he is unacquainted with them.

A science may undoubtedly be brought to a certain, not
inconsiderable, stage of advancement, without the application
of any other logic to it than what all persons, who are said to
have a sound understanding, acquire empirically in the course
of their studies. Mankind judged of evidence, and often
correctly, before logic was a science, or they never could have
made it one. And they executed great mechanical works
before they understood the laws of mechanics. But there are
limits both to what mechanicians can do without principles of
mechanics, and to what thinkers can do without principles of
logic. A few individuals, by extraordinary genius, or by the
accidental acquisition of a good set of intellectual habits, may
work without principles in the same way, or nearly the same
way, in which they would have worked if they had been in
possession of principles. But the bulk of mankind require
either to understand the theory of what they are doing, or to
have rules laid down for them by those who have understood
the theory. In the progress of science from its easiest to its
more difficult problems, each great step in advance has usually
had either as its precursor, or as its accompaniment and neces-
sary condition, a corresponding improvement in the notions
and principles of logic received among the most advanced
thinkers. And if several of the more difficult sciences are
still in so defective a state ; if not only so little is proved, but
disputation has not terminated even about the little which

DEFINITION AND PROVINCE OF LOGIC. 11

seemed to be so; the reason perhaps is, that men's logical
notions have not yet acquired the degree of extension, or of
accuracy, requisite for the estimation of the evidence proper
to those particular departments of knowledge.

§ 7. Logic, then, is the science of the operations of the
understanding which are subservient to the estimation of
evidence : both the process itself of advancing from known
truths to unknown, and all other intellectual operations in so
far as auxiliary to this. It includes, therefore, the operation
of Naming ; for language is an instrument of thought, as well
as a means of communicating our thoughts. It includes, also,
Definition, and Classification. For, the use of these operations
(putting all other minds than one's own out of consideration)
is to serve not only for keeping our evidences and the conclu-
sions from them permanent and readily accessible in the
memory, but for so marshalling the facts which we may at
any time be engaged in investigating, as to enable us to
perceive more clearly what evidence there is, and to judge with
fewer chances of error whether it be sufficient. These, there-
fore, are operations specially instrumental to the estimation of
evidence, and, as such, are within the province of Logic.
There are other more elementary processes, concerned in all
thinking, such as Conception, Memory, and the like ; but of
these it is not necessary that Logic should take any peculiar
cognizance, since they have no special connexion with the
problem of Evidence, further than that, like all other problems
addressed to the understanding, it presupposes them.

Our object, then, will be, to attempt a correct analysis of
the intellectual process called Reasoning or Inference, and of
such other mental operations as are intended to facilitate this :
as well as, on the foundation of this analysis, and pari passu
with it, to bring together or frame a set of rules or canons for
testing the sufficiency of any given evidence to prove any
given proposition.

With respect to the first part of this undertaking, I do
not attempt to decompose the mental operations in question
into their ultimate elements. It is enough if the analysis as

INTRODUCTION.

far as it goes is correct, and if it goes far enough for the
practical purposes of logic considered as an art. The separa-
tion of a complicated phenomenon into its component parts is
not like a connected and interdependent chain of proof. If
one link of an argument breaks, the whole drops to the ground ;
but one step towards an analysis holds good and has an inde-
pendent value, though we should never be able to make a
second. The results which have been obtained by analytical
chemistry are not the less valuable, though it should be dis-
covered that all which we now call simple substances are really
compounds. All other things are at any rate compounded of
those elements : whether the elements themselves admit of
decomposition, is an important inquiry, but does not affect the
certainty of the science up to that point.

I shall, accordingly, attempt to analyse the process of
inference, and the processes subordinate to inference, so far
only as may be requisite for ascertaining the difference between
a correct and an incorrect performance of those processes.
The reason for thus limiting our design, is evident. It has
been said by objectors to logic, that we do not learn to use
our muscles by studying their anatomy. The fact is not quite
fairly stated ; for if the action of any of our muscles were
vitiated by local weakness, or other physical defect, a know-
ledge of their anatomy might be very necessary for effecting a
cure. But we should be justly liable to the criticism involved
in this objection, were we, in a treatise on logic, to carry the
analysis of the reasoning process beyond the point at which
any inaccuracy which may have crept into it must become
visible. In learning bodily exercises (to carry on the same
illustration) we do, and must, analyse the bodily motions so
far as is necessary for distinguishing those which ought to be
performed from those which ought not. To a similar extent,
and no further, it is necessary that the logician should analyse
the mental processes with which Logic is concerned. Logic
has no interest in carrying the analysis beyond the point at
which it becomes apparent whether the operations have in any
individual case been rightly or wrongly performed : in the
same manner as the science of music teaches us to discriminate

DEFINITION AND PROVINCE OF LOGIC. 13

between musical notes, and to know the combinations of which
they are susceptible, but not what number of vibrations in a
second correspond to each ; which, though useful to be known,
is useful for totally different purposes. The extension of
Logic as a Science is determined by its necessities as an Art :
whatever it does not need for its practical ends, it leaves to the
larger science which may be said to correspond, not to any
particular art, but to art in general ; the science which deals
with the constitution of the human faculties ; and to which, in
the part of our mental nature which concerns Logic, as well as
in all other parts, it belongs to decide what are ultimate facts,
and what are resolvable into other facts. And I believe it will
be found that most of the conclusions arrived at in this work
have no necessary connexion with any particular views re-
specting the ulterior analysis. Logic is common ground on
which the partisans of Hartley and of Reid, of Locke and of
Kant, may meet and join hands. Particular and detached
opinions of all these thinkers will no doubt occasionally be
controverted, since all of them were logicians as well as meta-
physicians ; but the field on which their principal battles have
been fought, lies beyond the boundaries of our science.

It cannot, indeed, be pretended that logical principles can
be altogether irrelevant to those more abstruse discussions ;
nor is it possible but that the view we are led to take of the
problem which logic proposes, must have a tendency favour-
able to the adoption of some one opinion, on these controverted
subjects, rather than another. For metaphysics, in endeavour-
ing to solve its own peculiar problem, must employ means, the
validity of which falls under the cognizance of logic. It pro-
ceeds, no doubt, as far as possible, merely by a closer and more
attentive interrogation of our consciousness, or more properly
speaking, of our memory ; and so far is not amenable to logic.
But wherever this method is insufficient to attain the end of
its inquiries, it must proceed, like other sciences, by means of
evidence. Now, the moment this science begins to draw in-
ferences from evidence, logic becomes the sovereign judge
whether its inferences are well grounded, or what other in-
ferences would be so.

14 INTRODUCTION.

This, however, constitutes no nearer or other relation be-
tween logic and metaphysics, than that which exists between
logic and every other science. And I can conscientiously
affirm, that no one proposition laid down in this work has
been adopted for the sake of establishing, or with any reference
to its fitness for being employed in establishing, preconceived
opinions in any department of knowledge or of inquiry on
which the speculative world is still undecided.*

* The view taken in the text, of the definition and purpose of Logic, stands
in marked opposition to that of the school of philosophy which, in this country,
is represented by the writings of Sir William Hamilton and of his numerous
pupils. Logic, as this school conceives it, is " the Science of the Formal Laws
of Thought" ; a definition framed for the express purpose of excluding, as irre-
levant to Logic, whatever relates to Belief and Disbelief, or to the pursuit of
truth as such, and restricting the science to that very limited portion of its
total province, which has reference to the conditions, not of Truth, but of Con-
sistency. What I have thought it useful to say in opposition to this limitation
of the field of Logic, has been said at some length in a separate work, first
published in 1865, and entitled An Examination of Sir William Hamilton's
Philosophy, and of the Principal Philosophical Questions discussed in his
Writings. For the purposes of the present Treatise, I am content that the
justification of the larger extension which I give to the domain of the science,
should rest on the sequel of the Treatise itself. Some remarks on the relation
which the Logic of Consistency bears to the Logic of Truth, and on the place
which that particular part occupies in the whole to which it belongs, will be
found in the present volume (Book II. chap. iii. § 9).

BOOK I.

OF NAMES AND PROPOSITIONS.

1 La scolastique, qui produisit dans la logique, comme dans la morale, et
dans une partie de la me'taphysique, une subtilite, une precision d'ide"es, dont
Phabitude inconnue aux anciens, a contribue* plus qu'on ne croit au progrfes
de la bonne philosophic.' — CONDOBCET, Vie de Turgot.

' To the schoolmen the vulgar languages are principally indebted for what
precision and analytic subtlety they possess.' — SIB W. HAMILTON, Discussions
in Philosophy.

CHAPTER I.

OF THE NECESSITY OF COMMENCING WITH AN
ANALYSIS OF LANGUAGE.

§ 1. IT is so much the established practice of writers on
logic to commence their treatises by a few general observations
(in most cases, it is true, rather meagre) on Terms and their
varieties, that it will, perhaps, scarcely be required from me in
merely following the common usage, to be as particular in
assigning my reasons, as it is usually expected that those
should be who deviate from it,

The practice, indeed, is recommended by considerations
far too obvious to require a formal justification. Logic is a
portion of the Art of Thinking: Language is evidently, and
by the admission of all philosophers, one of the principal in-
struments or helps of thought; and any imperfection in the
instrument, or in the mode of employing it, is confessedly
liable, still more than in almost any other art, to confuse and
impede the process, and destroy all ground of confidence in the
result. For a mind not previously versed in the meaning and
right use of the various kinds of words, to attempt the study
of methods of philosophizing, would be as if some one should
attempt to become an astronomical observer, having never
learned to adjust the focal distance of his optical instruments
so as to see distinctly.

Since Reasoning, or Inference, the principal subject of
logic, is an operation which usually takes place by means of
words, and in complicated cases can take place in no other
way ; those who have not a thorough insight into the signifi-
cation and purposes of words, will be under chances, amounting
almost to certainty, of reasoning or inferring incorrectly. And
logicians have generally felt that unless, in the very first stage,
they removed this source of error ; unless they taught their

VOL. i. 2

18 NAMES AND PROPOSITIONS,

pupil to put away the glasses which distort the ohject, and to
use those which are adapted to his purpose ID such a manner
as to assist, not perplex, his vision ; he would not he in a con-
dition to practise the remaining part of their discipline with
any prospect of advantage. Therefore it is that an inquiry
into language, so far as is needful to guard against the errors
to which it gives rise, has at all times heen deemed a necessary
preliminary to the study of logic.

But there is another reason, of a still more fundamental
nature, why the import of words should he the earliest subject
of the logician's consideration : because without it he cannot
examine into the import of Propositions. Now this is a
subject which stands on the very threshold of the science of
logic.

The object of logic, as defined in the Introductory Chapter,
is to ascertain how we come by that portion of our knowledge
(much the greatest portion) which is not intuitive : and by
what criterion we can, in matters not self-evident, distinguish
between things proved and things not proved, between what
is worthy and what is unworthy of belief. Of the various
questions which present themselves to our inquiring faculties,
some receive an answer from direct consciousness, others, if
resolved at all, can only be resolved by means of evidence.
Logic is concerned with these last. But before inquiring into
the mode of resolving questions, it is necessary to inquire what
are those which offer themselves ; what questions are conceiv-
able ; what inquiries are there, to which mankind have either
obtained, or heen able to imagine it possible that they should
obtain, an answer. This point is best ascertained by a survey
and analysis of Propositions.

§ 2. The answer to every question which it is possible to
frame, must be contained in a Proposition, or Assertion.
Whatever can be an object of belief, or even of disbelief, must,
when put into words, assume the form of a proposition. All
truth and all error lie in propositions. What, by a convenient
misapplication of an abstract term, we call a Truth, means
simply a True Proposition ; and errors are false propositions.

NECESSITY OF AN ANALYSIS OF NAMES. 19

To know the import of all possible propositions, would be to
know all questions which can be raised, all matters which are
susceptible of being either believed or disbelieved. How many
kinds of inquiries can be propounded ; how many kinds of
judgments can be made ; and how many kinds of propositions
it is possible to frame with a meaning ; are but different forms
of one and the same question. Since, then, the objects of all
Belief and of all Inquiry express themselves in propositions ;
a sufficient scrutiny of Propositions and of their varieties will
apprize us what questions mankind have actually asked of
themselves, and what, in the nature of answers to those
questions, they have actually thought they had grounds to
believe.

Now the first glance at a proposition shows that it is
formed by putting together two names. A proposition, ac^
cording to the common simple definition, which is sufficient
for our purpose, is, discourse, in which something is affirmed
or denied of something. Thus, in the proposition, Gold is
yellow, the quality yellow is affirmed of the substance gold.
In the proposition, Franklin was not born in England, the
fact expressed by the words born in England is denied of the
man Franklin.

Every proposition consists of three parts : the Subject, the
Predicate, and the Copula. The predicate is the name denoting
that which is affirmed or denied. The subject is the name de-
noting the person or thing which something is affirmed or denied
of. The copula is the sign denoting that there is an affirma-
tion or denial; and thereby enabling the hearer or reader to
distinguish a proposition from any other kind of discourse.
Thus, in the proposition, The earth is round, the Predicate is
the word round, which denotes the quality affirmed, or (as the
phrase is) predicated : the earth, words denoting the object
which that quality is affirmed of, compose the Subject; the
word is, which serves as the connecting mark between the sub-
ject and predicate, to show that one of them is affirmed of the
other, is called the Copula.

Dismissing, for the present, the copula, of which more will
be said hereafter, every proposition, then, consists of at least

2—2

20 NAMES AND PROPOSITIONS.

two names; brings together two names, in a particular manner.
This is already a first step towards what we are in quest of.
It appears from this, that for an act of belief, one object is not
sufficient; the simplest act of belief supposes, and has some-
thing to do with, two objects: two names, to say the least;
and (since the names must be names of something) two name-
able things. A large class of thinkers would cut the matter
short by saying, two ideas. They would say, that the subject
and predicate are both of them names of ideas ; the idea of
gold, for instance, and the idea of yellow ; and that what
takes place (or part of what takes place) in the act of belief,
consists in bringing (as it is often expressed) one of these
ideas under the other. But this we are not yet in a condition
to say : -whether such be the correct mode of describing the
phenomenon, is an after consideration. The result with which
for the present we must be contented, is, that in every act
of belief two objects are in some manner taken cognizance of;
that there can be no belief claimed, or question propounded,
which does not embrace two distinct (either material or intel-
lectual) subjects of thought; each of them capable, or not, of
being conceived by itself, but incapable of being believed by
itself.

I may say, for instance, " the sun." The word has a
meaning, and suggests that meaning to the mind of any one
who is listening to me. But suppose I ask him, Whether it
is true : whether he believes it ? He can give no answer.
There is as yet nothing to believe, or to disbelieve. Now,
however, let me make, of all possible assertions respecting the
sun, the one which involves the least of reference to any object
besides itself; let me say, " the sun exists." Here, at once, is
something which a person can say he believes. But here, in-
stead of only one, we find two distinct objects of conception :
the sun is one object; existence is another. Let it not be
said that this second conception, existence, is involved in the
first ; for the sun may be conceived as no longer existing.
" The sun" does not convey all the meaning that is conveyed
by "the sun exists:" " my father" does not include all the
meaning of " my father exists," for he may be dead ; :i a round

NECESSITY OF AN ANALYSIS OF NAMES. 21

square" does not include the meaning of " a round square
exists," for it does not and cannot exist. When I say " the
sun," " my father," or a " round square," I do not call upon
the hearer for any helief or disbelief, nor can either the one or
the other be afforded me ; but if I say, " the sun exists," " my
father exists," or "a round square exists," I call for belief;
and should, in the first of the three instances, meet with it ;
in the second, with belief or disbelief, as the case might be ; in
the third, with disbelief.

§ 3. This first step in the analysis of the object of belief,
which, though so obvious, will be found to be not unimportant,
is the only one which we shall find it practicable to make with-
out a preliminary survey of language. If we attempt to pro*
ceed further in the same path, that is, to analyse any further
the import of Propositions ; we find forced upon us, as a sub-
ject of previous consideration, the import of Names. For
every proposition consists of two names ; and every proposition
affirms or denies one of these names, of the other. Now what
we do, what passes in our mind, when we affirm or deny two
names of one another, must depend on what they are names
of; since it is with reference to that, and not to the mere
names themselves, that we make the affirmation or denial.
Here, therefore, we find a new reason why the signification of
names, and the relation generally between names and the
things signified by them, must occupy the preliminary stage
of the inquiry we are engaged in.

It may be objected that the meaning of names can guide
us at most only to the opinions, possibly the foolish and
groundless opinions, which mankind have formed concerning
things, and that as the object of philosophy is truth, not
opinion, the philosopher should dismiss words and look into
things themselves, to ascertain what questions can be asked
and answered in regard to them. This advice (which no one
has it in his power to follow) is in reality an exhortation to
discard the whole fruits of the labours of his predecessors, and
conduct himself as if he were the first person who had ever
turned an inquiring eye upon nature. What does any one's

NAMES AND PROPOSITIONS.

personal knowledge of Things amount to, after subtracting
all which he has acquired by means of the words of other
people ? Even after he has learned as much as people
usually do learn from others, will the notions of things con-
tained in his individual mind afford as sufficient a basis for a
catalogue raisonne as- the notions which are in the minds of
all mankind ?

In any enumeration and classification of Things, which
does not set out from their names, no varieties of things will
of course be comprehended but those recognised by the par-
ticular inquirer ; and it will still remain to be established, by
a subsequent examination of names, that the enumeration has
omitted nothing which ought to have been included. But if
we begin with names, and use them as our clue to the things,
we bring at once before us all the distinctions which have been
recognised, not by a single inquirer, but by all inquirers taken
together. It doubtless may, and I believe it will, be found,
that mankind have multiplied the varieties unnecessarily, and
have imagined distinctions among things, where there were
only distinctions in the manner of naming them. But we are
not entitled to assume this in the commencement. We must
begin by recognising the distinctions made by ordinary lan-
guage. If some of these appear, on a close examination, not
to be fundamental, the enumeration of the different kinds of
realities may be abridged accordingly. But to impose upon
the facts in the first instance the yoke of a theory, while the
grounds of the theory are reserved for discussion in a sub-
sequent stage, is not a course which a logician can reasonably
adopt.

CHAPTER II.

OF NAMES.

§ 1. "A NAME," says Hobbes,* " is a word taken at
pleasure to serve for a mark which may raise in our mind a
thought like to some thought we had before, and which being
pronounced to others, may be to them a sign of what thought
the speaker hadf before in his mind." This simple definition
of a name, as a word (or set of words) serving the double pur-
pose of a mark to recall to ourselves the likeness of a former
thought, and a sign to make it known to others, appears un-
exceptionable. Names, indeed, do much more than this ; but
whatever else they do, grows out of, and is the result of this :
as will appear in its proper place.

Are names more properly said to be the names of things,
or of our ideas of things ? The first is the expression in com-
mon use ; the last is that of some metaphysicians, who con-
ceived that in adopting it they were introducing a highly
important distinction. The eminent thinker, just quoted,
seems to countenance the latter opinion. "But seeing," he
continues, " names ordered in speech (as is defined) are signs
of our conceptions, it is manifest they are not signs of the
things themselves ; for that the sound of this word stone should
be the sign of a stone, cannot be understood in any sense but
this, that he that hears it collects that he that pronounces it
thinks of a stone."

If it be merely meant that the conception alone, and not
the thing itself, is recalled by the name, or imparted to the
hearer, this of course cannot be denied. Nevertheless, there
seems good reason for adhering to the common usage, and

* Computation or Logic, chap. ii.

t In the original "had, or had not." These last words, as involving a
subtlety foreign to our present purpose, I have forborne to quote.

24 NAMES AND PROPOSITIONS.

calling (as indeed Hobbes himself does in other places) the
word sun the name of the sun, and not the name of our idea
of the sun. For names are not intended only to make the
hearer conceive what we conceive, but also to inform him
what we believe. Now, when I use a name for the purpose
of expressing a belief, it is a belief concerning the thing itself,
not concerning my idea of it. When I say, "the sun is the
cause of day," I do not mean that my idea of the sun causes
or excites in me the idea of day ; or in other words, that
thinking of the sun makes me think of day. I mean, that a
certain physical fact, which is called the sun's presence (and
which, in the ultimate analysis, resolves itself into sensations,
not ideas) causes another physical fact, which is called day.
It seems proper to consider a word as the name of that which
we intend to be understood by it when we use it; of that
which any fact that we assert of it is to be understood of;
that, in short, concerning which, when we employ the word,
we intend to give information. Names, therefore, shall always
be spoken of in this work as the names of things themselves,
and not merely of our ideas of things.

But the question now arises, of what things ? and to
answer this it is necessary to take into consideration the
different kinds of names.

§ 2. It is usual, before examining the various classes into
which names are commonly divided, to begin by distinguishing
from names of every description, those words which are not
names, but only parts of names. Among such are reckoned
particles, as of, to, truly, often ; the inflected cases of nouns
substantive, as me, him, Johns ; and even adjectives, as large,
heavy. These words do not express things of which anything
can be affirmed or denied. We cannot say, Heavy fell, or A
heavy fell ; Truly, or A truly, was asserted ; Of, or An of, was
in the room. Unless, indeed, we are speaking of the mere
words themselves, as when we say, Truly is an English word,
or, Heavy is an adjective. In that case they are complete
names, viz. names of those particular sounds, or of those
particular collections of written characters. This employment

NAMES. 25

of a word to denote the mere letters and syllables of \vhich it
is composed, was termed by tbe schoolmen the suppositio
materialis of the word. In any other sense we cannot intro-
duce one of these words into the subject of a proposition,
unless in combination with other words ; as, A heavy body
fell, A truly important fact was asserted, A member of parlia-
ment was in the room.

An adjective, however, is capable of standing by itself as
the predicate of a proposition ; as when we say, Snow is white ;
and occasionally even as the subject, for we may say, White is
an agreeable colour. The adjective is often said to be so used
by a grammatical ellipsis : Snow is white, instead of Snow is
a white object ; White is an agreeable colour, instead of, A
white colour, or, The colour white, is agreeable. The Greeks
and Eomans were allowed, by the rules of their language, to
employ this ellipsis universally in the subject as well as in the
predicate of a proposition. In English this cannot, generally
speaking, be done. We may say, The earth is round ; but we
cannot say, Round is easily moved ; we must say, A round
object. This distinction, however, is rather grammatical than
logical. Since there is no difference of meaning between
round, and a round object, it is only custom which prescribes
that on any given occasion one shall be used, and not the
other. We shall, therefore, without scruple, speak of adjec-
tives as names, whether in their own right, or as representative
of the more circuitous forms of expression above exemplified.
The other classes of subsidiary words have no title whatever
to be considered as names. An adverb, or an accusative case,
cannot under any circumstances (except when their mere letters
and syllables are spoken of) figure as one of the terms of a
proposition.

Words which are not capable of being used as names, but
only as parts of names, were called by some of the schoolmen
Syncategorematic terms : from <ruv, with, and Karrjyoplw, to
predicate, because it was only ivith some other word that they
could be predicated. A word which could be used either as
the subject or predicate of a proposition without being accom-
panied by any other word, was termed by the same authorities

26 NAMES AND PROPOSITIONS.

a Categorematic term. A combination of one or more Cate-
gorematic, and one or more Syncategorematic words, as A
heavy body, or A court of justice, they sometimes called a
mixed term ; but this seems a needless multiplication of
technical expressions. A mixed term is, in the only useful
sense of the word, Categorematic. It belongs to the class of
what have been called many-worded names.

For, as one word is frequently not a name, but only part
of a name, so a number of words often compose one single
name, and no more. These words, " The place which the
wisdom or policy of antiquity had destined for the residence
of the Abyssinian princes," form in the estimation of the
logician only one name ; one Categorematic term. A mode
of determining whether any set of words makes only one
name, or more than one, is by pi-edicating something of it,
and observing whether, by this predication, we make only one
assertion or several. Thus, when we say, John Nokes, who
was the mayor of the town, died yesterday — by this predica-
tion we make but one assertion ; whence it appears that
" John Nokes, who was the mayor of the town," is no more
than one name. It is true that in this proposition, besides
the assertion that John Nokes died yesterday, there is included
another assertion, namely, that John Nokes was mayor of the
town. But this last assertion was already made : we did not
make it by adding the predicate, " died yesterday." Suppose,
however, that the words had been, John Nokes and the mayor
of the town, they would have formed two names instead of
one. For when we say, John Nokes and the mayor of the
town died yesterday, we make two assertions : one, that John
Nokes died yesterday ; the other, that the mayor of the town
died yesterday.

It being needless to illustrate at any greater length the
subject of many-worded names, we proceed to the distinctions
which have been established among names, not according to
the words they are composed of, but according to their
signification.

§ 3. All names are names of something, real or imagi-

NAMES. 27

nary ; but all things have not names appropriated to them
individually. For some individual objects we require, and
consequently have, separate distinguishing names ; there is a
name for every person, and for every remarkable place. Other
objects, of which we have not occasion to speak so frequently,
we do not designate by a name of their own ; but when the
necessity arises for naming them, we do so by putting together
several words, each of which, by itself, might be and is used
for an indefinite number of other objects ; as when I say, this
stone : " this " and " stone " being, each of them, names that
may be used of many other objects besides the particular one
meant, though the only object of which they can both be used
at the given moment, consistently with their signification, may
be the one of which I wish to speak.

Were this the sole purpose for which names, that are
common to more things than one, could be employed ; if they
only served, by mutually limiting each other, to afford a
designation for such individual objects as have no names of
their own : they could only be ranked among contrivances for
economizing the use of language. But it is evident that this
is not their sole function. It is by their means that we are
enabled to assert general propositions ; to affirm or deny any
predicate of an indefinite number of things at once. The
distinction, therefore, between general names, and individual
or singular names, is fundamental ; and may be considered as
the first grand division of names.

A general name is familiarly defined, a name which is
capable of being truly affirmed, in the same sense, of each of
an indefinite number of things. An individual or singular
name is a name which is only capable of being truly affirmed,
in the same sense, of one thing.

Thus, man is capable of being truly affirmed of John,
George, Mary, and other persons without assignable limit ;
and it is affirmed of all of them in the same sense ; for the
word man expresses certain qualities, and when we predicate
it of those persons, we assert that they all possess those
qualities. But John is only capable of being truly affirmed of
one single person, at least in the same sense. For, though

28 NAMES AND PROPOSITIONS.

there are many persons who bear that name, it is not conferred
upon them to indicate any qualities, or anything which be-
longs to them in common ; and cannot be said to be affirmed
of them in any sense at all, consequently not in the same
sense. " The king who succeeded William the Conqueror," is
also an individual name. For, that there cannot be more than
one person of whom it can be truly affirmed, is implied in the
meaning of the words. Even " the king," when the occasion
or the context defines the individual of whom it is to be
understood, may justly be regarded as an individual name.

It is not unusual, by way of explaining what is meant by
a general name, to say that it is the name of a class. But
this, though a convenient mode of expression for some pur-
poses, is objectionable as a definition, since it explains the
clearer of two things by the more obscure. It would be more
logical to reverse the proposition, and turn it into a definition
of the word class : " A class is the indefinite multitude of
individuals denoted by a general name."

It is necessary to distinguish general from collective
names. A general name is one which can be predicated of
each individual of a multitude ; a collective name cannot be
predicated of each separately, but only of all taken together.
" The 76th regiment of foot in the British army," which is a
collective name, is not a general but an individual name ; for
though it can be predicated of a multitude of individual
soldiers taken jointly, it cannot be predicated of them severally.
We may say, Jones is a soldier, and Thompson is a soldier,
and Smith is a soldier, but we cannot say, Jones is the 76th
regiment, end Thompson is the 76th regiment, and Smith is
the 76th regiment. We can only say, Jones, and Thompson,
and Smith, and Brown, and so forth (enumerating all the
soldiers), are the 76th regiment.

" The 76th regiment" is a collective name, but not a
general one : " a regiment" is both a collective and a general
name. General with respect to all individual regiments, of
each of which separately it can be affirmed : collective with
respect to the individual soldiers of whom any regiment is
composed.

NAMES. 29

§ 4. The second general division of names is into con-
crete and abstract. A concrete name is a name which stands
for a thing; an abstract name is a name which stands for an
attribute of a thing. Thus John, the sea, this table, are names
of things. White, also, is a name of a thing, or rather of
things. Whiteness, again, is the name of a quality or attri-
bute of those things. Man is a name of many things ;
humanity is a name of an attribute of those things. Old
is a name of things ; old age is a name of one of their at-
tributes.

I have used the words concrete and abstract in the sense
annexed to them by the schoolmen, who, notwithstanding the
imperfections of their philosophy, were unrivalled in the con-
struction of technical language, and whose definitions, in logic
at least, though they never went more than a little way into
the subject, have seldom, I think, been altered but to be
spoiled. A practice, however, has grown up in more modern
times, which, if not introduced by Locke, has gained currency
chiefly from his example, of applying the expression " abstract
name " to all names which are the result of abstraction or
generalization, and consequently to all general names, instead
of confining it to the names of attributes. The metaphysicians
of the Condillac school, — whose admiration of Locke, passing
over the profoundest speculations of that truly original genius,
usually fastens with peculiar eagerness upon his weakest
points, — have gone on imitating him in this abuse of language,
until there is now some difficulty in restoring the word to its
original signification. A more wanton alteration in the mean-
ing of a word is rarely to be met with ; for the expression
general name, the exact equivalent of which exists in all lan-
guages I am acquainted with, was already available for the
purpose to which abstract has been misappropriated, while the
misappropriation leaves that important class of words, the
names of attributes, without any compact distinctive appella-
tion. The old acceptation, however, has not gone so com-
pletely out of use, as to deprive those who still adhere to it of
all chance of being understood. By abstract, then, I shall
always, in Logic proper, mean the opposite of concrete ; by

30 NAMES AND PROPOSITIONS.

an abstract name, the name of an attribute ; by a concrete
name, the name of an object.

Do abstract names belong to the class of general, or to
that of singular names ? Some of them are certainly general.
I mean those which are names not of one single and definite
attribute, but of a class of attributes. Such is the word colour,
which is a name common to whiteness, redness, &c. Such is
even the word whiteness, in respect of the different shades of
whiteness to which it is applied in common : the word magni-
tude, in respect of the various degrees of magnitude and the
various dimensions of space ; the word weight, in respect of
the various degrees of weight. Such also is the word attribute
itself, the common name of all particular attributes. But
when only one attribute, neither variable in degree nor in
kind, is designated by the name ; asvisibleness ; tangibleness ;
equality ; squareness ; milkwhiteness ; then the name can
hardly be considered general ; for though it denotes an attri-
bute of many different objects, the attribute itself is always
conceived as one, not many.* To avoid needless logomachies,
the best course would probably be to consider these names as
neither general nor individual, and to place them in a class
apart.

It may be objected to our definition of an abstract name,
that not only the names which we have called abstract, but
adjectives, which we have placed in the concrete class, are
names of attributes ; that ivhite, for example, is as much the
came of the colour as ivhiteness is. But (as before remarked)
a word ought to be considered as the name of that which we
intend to be understood by it when we put it to its principal
use, that is, when we employ it in predication. When we say
snow is white, milk is white, linen is white, we do not mean
it to be understood that snow, or linen, or milk, is a colour.
We mean that they are things having the colour. The reverse
is the case with the word whiteness ; what we affirm to be
whiteness is not snow, but the colour of snow. Whiteness,
therefore, is the name of the colour exclusively : white is a

* Vide infra, note at the end of § 3, book ii. chap. ii.

NAMES. 31

name of all things whatever having the colour; a name, not of
the quality whiteness, but of every white object. It is true,
this name was given to all those various objects on account of
the quality ; and we may therefore say, without impropriety,
that the quality forms part of its signification ; but a name
can only be said to stand for, or to be a name of, the things of
which it can be predicated. We shall presently see that all
names which can be said to have any signification, all names
by applying which to an individual we give any information
respecting that individual, may be said to imply an attribute
of some sort ; but they are not names of the attribute ; it has
its own proper abstract name.

§ 5. This leads to the consideration of a third great
division of names, into connotative and non-connotative, the
latter sometimes, but improperly, called absolute. This is one
of the most important distinctions which we shall have occa-
sion to point out, and one of those which go deepest into the
nature of language.

A non-connotative term is one which signifies a subject
only, or an attribute only. A connotative term is one which
denotes a subject, and implies an attribute. By a subject is
here meant anything which possesses attributes. Thus John,
or London, or England, are names which signify a subject
only. Whiteness, length, virtue, signify an attribute only.
None of these names, therefore, are connotative. But ivhite,
long, virtuous, are connotative. The word white, denotes all
white things, as snow, paper, the foam of the sea, &c., and
implies, or in the language of the schoolmen, connotes,* the
attribute whiteness. The word white is not predicated of the
attribute, but of the subjects, snow, &c. ; but when we predi-
cate it of them, we convey the meaning that the attribute
whiteness belongs to them. The same may be said of the
other words above cited. Virtuous, for example, is the name of
a class, which includes Socrates, Howard, the Man of Eoss,

* Notare, to mark; connotare, to mark along with; to mark one thing with
or in addition to another.

32 NAMES AND PROPOSITIONS.

and an undefinable number of other individuals, past, present,
and to come. These individuals, collectively and severally,
can alone be said with propriety to be denoted by the word :
of them alone can it properly be said to be a name. But it is
a name applied to all of them in consequence of an attribute
which they are supposed to possess in common, the attribute
which has received the name of virtue. It is applied to all
beings that are considered to possess this attribute ; and to
none which are not so considered.

All concrete general names are connotative. The word
man, for example, denotes Peter, Jane, John, and an indefi-
nite number of other individuals, of whom, taken as a class, it
is the name. But it is applied to them, because they possess,
and to signify that they possess, certain attributes. These
seem to be, corporeity, animal life, rationality, and a certain
external form, which for distinction we call the human. Every
existing thing, which possessed all these attributes, would be
called a man; and anything which possessed none of them, or
only one, or two, or even three of them without the fourth,
would not be so called. For example, if in the interior of
Africa there were to be discovered a race of animals possess-
ing reason equal to that of human beings, but with the form
of 'an elephant, they would not be called men. Swift's Hou-
yhnhnms would not be so called. Or if such newly-discovered
beings possessed the form of man without any vestige of reason,
it is probable that some other name than that of man would be
found for them. How it happens that there can be any doubt
about the matter, will appear hereafter. The word man,
therefore, signifies all these attributes, and all subjects which
possess these attributes. But it can be predicated only of the
subjects. What we call men, are the subjects, the individual
Stiles and Nokes ; not the qualities by which their humanity
is constituted. The name, therefore, is said to signify the
subjects directly, the attributes indirectly ; it denotes the
subjects, and implies, or involves, or indicates, or as we shall
say henceforth connotes, the attributes. It is a connotative
name.

Connotative names have hence been also called denomina-

NAMES. 33

the, because the subject which they denote is denominated by,
or receives a name from the attribute which they connote.
Snow, and other objects, receive the name white, because they
possess the attribute which is called whiteness ; Peter, James,
and others receive the name man because they possess the
attributes which are considered to constitute humanity. The
attribute, or attributes, may therefore be said to denominate
those objects, or to give them a common name.*

It has been seen that all concrete general names are conno-
tative. Even abstract names, though the names only of attri-
butes, may in some instances be justly considered as connota-
tive ; for attributes themselves may have attributes ascribed to
them ; and a word which denotes attributes may connote an
attribute of those attributes. Of this description, for example,
is such a word as fault ; equivalent to bad or hurtful quality.
This word is a name common to many attributes, and connotes
hurtfulness, an attribute of those various attributes. When,
for example, we say that slowness, in a horse, is a fault, we
do not mean that the slow movement, the actual change of
place of the slow horse, is a bad thing, but that the property
or peculiarity of the horse, from which it derives that name,
the quality of being a slow mover, is an undesirable peculiarity.

In regard to those concrete names which are not general
but individual, a distinction must be made.

Proper names are not connotative : they denote the indi-
viduals who are called by them ; but they do not indicate or
imply any attributes as belonging to those individuals. When
we name a child by the name Paul, or a dog by the name
Ceesar, these names are simply marks used to enable those
individuals to be made subjects of discourse. It may be said
indeed, that we must have had some reason for giving them

* Archbishop Whately, who, in the later editions of his Elements of Logic,
aided in reviving the important distinction treated of in the text, proposes the
term " Attributive" as a substitute for "Connotative" (p. 22, 9th ed.) The
expression is, in itself, appropriate ; but as it has not the advantage of being
connected with any verb, of so markedly distinctive a character as " to connote,"
it is not, I think, fitted to supply the place of the word Connotative in scien-
tific use.

VOL. I. 3

34 NAMES AND PROPOSITIONS.

those names rather than any others ; and this is true ; but
the name, once given, is independent of the reason. A man
may have been named John, because that was the name of his
father; a town may have been named Dartmouth, because it
is situated at the mouth of the Dart. But it is no part of the
signification of the word John, that the father of the person so
called bore the same name ; nor even of the word Dartmouth,
to be situated at the mouth of the Dart. If sand should choke
up the mouth of the river, or an earthquake change its course,
and remove it to a distance from the town, the name of the
town would not necessarily be changed. That fact, therefore,
can form no part of the signification of the word ; for other-
wise, when the fact confessedly ceased to be true, no one would
any longer think of applying the name. Proper names are
attached to the objects themselves, and are not dependent on
the continuance of any attribute of the object.

But there is another kind of names, which, although they
are individual names, that is, predicable only of one object,
are really connotative. For, though we may give to an in-
dividual a name utterly unmeaning, which we call a proper
name, — a word which answers the purpose of showing what
thing it is we are talking about, but not of telling anything
about it; yet a name peculiar to an individual is not neces-
sarily of this description. It may be significant of some
attribute, or some union of attributes, which, being possessed
by no object but one, determines the name exclusively to that
individual. " The sun" is a name of this description ; " God,"
when used by a monotheist, is another. These, however, are
scarcely examples of what we are now attempting to illus-
trate, being, in strictness of language, general, not individual
names : for, however they may be in fact predicable only of
one object, there is nothing in the meaning of the words
themselves which implies this : and, accordingly, when we
are imagining and not affirming, we may speak of many suns ;
and the majority of mankind have believed, and still believe,
that there are many gods. But it is easy to produce words
which are real instances of connotative individual names. It
may be part of the meaning of the connotative name itself,

NAMES. 85

that there can exist but one individual possessing the attribute
which it connotes : as, for instance, " the only son of John
Stiles;" "the first emperor of Rome." Or the attribute con-
noted may be a connexion with some determinate event, and
the connexion may be of such a kind as only one individual
could have ; or may at least be such as only one individual
actually had; and this may be implied in the form of the
expression. "The father of Socrates" is an example of the
one kind (since Socrates could not have had two fathers) ;
" the author of the Iliad," "the murderer of Henri Quatre,"
of the second. For, though it is conceivable that more per-
sons than one might have participated in the authorship of
the Iliad, or in the murder of Henri Quatre, the employment
of the article the implies that, in fact, this was not the case.
What is here done by the word the, is done in other cases by
the context: thus, " Cesar's army" is an individual name, if
it appears from the context that the army meant is that which
Caesar commanded in a particular battle. The still more
general expressions, " the Roman army," or " the Christian
army," may be individualized in a similar manner. Another
case of frequent occurrence has already been noticed ; it is the
following. The name, being a many-worded one, may consist,
in the first place, of a general name, capable therefore in itself
of being affirmed of more things than one, but which is, in the
second place, so limited by other words joined with it, that the
entire expression can only be predicated of one object, consis-
tently with the meaning of the general term. This is exem-
plified in such an instance as the following : " the present
prime minister of England." Prime Minister of England is a
general name ; the attributes which it connotes may be pos-
sessed by an indefinite number of persons : in succession
however, not simultaneously ; since the meaning of the name
itself imports (among other things) that there can be only
one such person at a time. This being the case, and the
application of the name being afterwards limited by the article
and the word present, to such individuals as possess the attri-
butes at one indivisible point of time, it becomes applicable
only to one individual. And as this appears from the rneaii-

3—2

36 NAMES AND PROPOSITIONS.

ing of the name, without any extrinsic proof, it is strictly an
individual name.

From the preceding observations it will easily be collected,
that whenever the names given to objects convey any infor-
mation, that is, whenever they have properly any meaning,
the meaning resides not in what they denote, but in what they
connote. The only names of objects which connote nothing
are proper names ; and these have, strictly speaking, no signi-
fication.*

If, like the robber in the Arabian Nights, we make a mark
with chalk on a house to enable us to know it again, the mark
has a purpose, but it has not properly any meaning. The
chalk does not declare anything about the house ; it does not
mean, This is such a person's house, or This is a house which
contains booty. The object of making the mark is merely dis-
tinction. I say to myself, AH these houses are so nearly alike
that if I lose sight of them I shall not again be able to dis-
tinguish that which I am now looking at, from any of the
others; I must therefore contrive to make the appearance of
this one house unlike that of the others, that I may hereafter
know when I see the mark — not indeed any attribute of the
house — but simply that it is the same house which I am now
looking at. Morgiana chalked all the other houses in a
similar manner, and defeated the scheme : how ? simply by
obliterating the difference of appearance between that house
and the others. The chalk was still there, but it no longer
served the purpose of a distinctive mark.

When we impose a proper name, we perform an operation

* A writer who entitles his book Philosophy; or, the Science of Truth,
charges me in his very first page (referring at the foot of it to this passage)
with asserting that general names have properly no signification. And he
repeats this statement many times in the course of his volume, with comments,
not at all flattering, thereon. It is well to be now and then reminded to how
great a length perverse misquotation (for, strange as it appears, I do not be-
lieve that the writer is dishonest) can sometimes go. It is a warning to readers
when they see an author accused, with volume and page referred to, and the
apparent guarantee of inverted commas, of maintaining something more than
commonly absurd, not to give implicit credence to the assertion without veri-
fying the reference.

NAMES. 37

in some degree analogous to what the robber intended in
chalking the house. We put a mark, not indeed upon the
object itself, but, so to speak, upon the idea of the object. A
proper name is but an unmeaning mark which we connect in
our minds with the idea of the object, in order that whenever
the mark meets our eyes or occurs to our thoughts, we may
think of that individual object. Not being attached to the
thing itself, it does not, like the chalk, enable us to distin-
guish the object when we see it; but it enables us to distin-
guish it when it is spoken of, either in the records of our own
experience, or in the discourse of others ; to know that what
we find asserted in any proposition of which it is the subject,
is asserted of the individual thing with which we were pre-
viously acquainted.

When we predicate of anything its proper name ; when
we say, pointing to a man, this is Brown or Smith, or point-
ing to a city, that it is York, we do not, merely by so doing,
convey to the reader any information about them, except that
those are their names. By enabling him to identify the
individuals, we may connect them with information previously
possessed by him ; by saying, This is York, we may tell him
that it contains the Minster. But this is in virtue of what
he has previously heard concerning York; not by anything
implied in the name. It is otherwise when objects are spoken
of by counotative names. When we say, The town is built
of marble, we give the hearer what may be entirely new in-
formation, and this merely by the signification of the many-
worded connotative name, " built of marble." Such names
are not signs of the mere objects, invented because we have
occasion to think and speak of those objects individually ;
but signs which accompany an attribute : a kind of livery in
which the attribute clothes all objects which are recognised as
possessing it. They are not mere marks, but more, that is to
say, significant marks ; and the connotation is what constitutes
their significance.

As a proper name is said to be the name of the one indi-
vidual which it is predicated of, so (as well from the importance
of adhering to analogy, as for the other reasons formerly as-

38 NAMES AND PROPOSITIONS.

signed) a connotative name ought to be considered a name of
all the various individuals which it is predicable of, or in other
words denotes, and not of what it connotes. But by learning
what things it is a name of, we do not learn the meaning of
the name : for to the same thing we may, with equal propriety,
apply many names, not equivalent in meaning. Thus, I call
a certain man by the name Sophroniscus : I call him by
another name, The father of Socrates. Both these are names
of the same individual, but their meaning is altogether dif-
ferent; they are applied to that individual for two different
purposes : the one, merely to distinguish him from other per-
sons who are spoken of; the other to indicate a fact relating
to him, the fact that Socrates was his son. I further apply to
him these other expressions : a man, a Greek, an Athenian, a
sculptor, an old man, an honest man, a brave man. All these
are, or may be, names of Sophroniscus, not indeed of him
alone, but of him and each of an indefinite number of other
human beings. Each of these names is applied to Sophro-
niscus for a different reason, and by each whoever understands
its meaning is apprised of a distinct fact or number of facts
concerning him ; but those who knew nothing about the names
except that they were applicable to Sophroniscus, would be
altogether ignorant of their meaning. It is even possible that
I might know every single individual of whom a given name
could be with truth affirmed, and yet could not be said to know
the meaning of the name. A child knows who are its brothers
and sisters, long before it has any definite conception of the
nature of the facts which are involved in the -signification of
those words.

In some cases it is not easy to decide precisely how much
a particular word does or does not conn'ote ; that is, we do not
exactly know (the case not having arisen) what degree of dif-
ference in the object would occasion a difference in the name.
Thus, it is clear that the word man, besides animal life and
rationality, connotes also a certain external form ; but it would
be impossible to say precisely what form ; that is, to decide
how great a deviation from the form ordinarily found in the
beings whom we are accustomed to call men, would suffice in

NAMES. 39

a newly- discovered race to make us refuse them the name of
man. Rationality, also, being a quality which admits of de-
grees, it has never been settled what is the lowest degree of
that quality which would entitle any creature to he considered
a human being. In all such cases, the meaning of the general
name is so far unsettled and vague ; mankind have not come
to any positive agreement about the matter. When we come
to treat of Classification, we shall have occasion to show under
what conditions this vagueness may exist without practical
inconvenience ; and cases will appear in which the ends of
language are better promoted by it than by complete precision ;
in order that, in natural history for instance, individuals or
species of no very marked character may be ranged with those
more strongly characterized individuals or species to which,
in all their properties taken together, they bear the nearest
resemblance.

But this partial uncertainty in the connotation of names
can only be free from mischief when guarded by strict precau-
tions. One of the chief sources, indeed, of lax habits of thought,
is the custom of using connotative terms without a distinctly
ascertained connotation, and with no more precise notion of
their meaning than can be loosely collected from observing
what objects they are used to denote. It is in this manner
that we all acquire, and inevitably so, our first knowledge of
our vernacular language. A child learns the meaning of the
words man, or white, by hearing them applied to a variety of
individual objects, and finding out, by a process of generali-
zation and analysis which he could not himself describe, what
those different objects have in common. In the case of these
two words the process is so easy as to require no assistance
from culture ; the objects called human beings, and the ob-
jects called white, differing from all others by qualities of a
peculiarly definite and obvious character. But in many other
cases, objects bear a general resemblance to one another, which
leads to their being familiarly classed together under a com-
mon name, while, without more analytic habits than the gene-
rality of mankind possess, it is not immediately apparent what
are the particular attributes, upon the possession of which in

40 NAMES AND PROPOSITIONS.

common by them all, their general resemblance depends.
When this is the case, people use the name without any re-
cognised connotation, that is, without any precise meaning ;
they talk, and consequently think, vaguely, and remain con-
tented to attach only the same degree of significance to their
own words, which a child three years old attaches to the words
brother and sister. The child at least is seldom puzzled by
the starting up of new individuals, on whom he is ignorant
whether or not to confer the title ; because there is usually an
authority close at hand competent to solve all doubts. But a
similar resource does not exist in the generality of cases ;
and new objects are continually presenting themselves to men,
women, and children, which they are called upon to class
proprio motu. They, accordingly, do this on no other principle
than that of superficial similarity, giving to each new object
the name of that familiar object, the idea of which it most
readily recalls, or which, on a cursory inspection, it seems to
them most to resemble : as an unknown substance found in
the ground will be called, according to its texture, earth, sand,
or a stone. In this manner, names creep on from subject to
subject, until all traces of a common meaning sometimes dis-
appear, and the word comes to denote a number of things not
only independently of any common attribute, but which have
actually no attribute in common ; or none but what is shared
by other things to which the name is capriciously refused.*
Even scientific writers have aided in this perversion of general

* "Take the familiar term Stone. It is applied to mineral and rocky
materials, to the kernels of fruit, to the accumulations in the gall-bladder and
in the kidney ; while it is refused to polished minerals (called gems), to rocks
that have the cleavage suited for roofing (slates), and to baked clay (bricks),
It occurs in the designation of the magnetic oxide of iron (loadstone) and not
in speaking of other metallic ores. Such a term is wholly unfit for accurate
reasoning, unless hedged round on every occasion by other phrases ; as building
stone, precious stone, gall stone, &c. Moreover, the methods of definition are
baffled for want of sufficient community to ground upon. There is no quality
uniformly present in the cases where it is applied, and uniformly absent where
it is not applied ; hence the definer would have to employ largely the licence of
striking off existing applications, and taking in new ones." — BAIN, Loyic,
ii. 172.

NAMES. 41

language from its purpose ; sometimes because, like the vulgar,
they knew no better ; and sometimes in deference to that
aversion to admit new words, which induces mankind, on all
subjects not considered technical, to attempt to make the
original stock of names serve with but little augmentation to
express a constantly increasing number of objects and distinc-
tions, and, consequently, to express them in a manner pro-
gressively more and more imperfect.

To what a degree this loose mode of classing and denomi-
nating objects has rendered the vocabulary of mental and moral
philosophy unfit for the purposes of accurate thinking, is best
known to whoever has most meditated on the present condi-
tion of those branches of knowledge. Since, however, the
introduction of a new technical language as the vehicle of
speculations on subjects belonging to the domain of daily dis-
cussion, is extremely difficult to effeot, and would not be free
from inconvenience even if effected, the problem for the philo-
sopher, and one of the most difficult which he has to resolve,
is, in retaining the existing phraseology, how best to alleviate
its imperfections. This can only be accomplished by giving to
every general concrete name which there is frequent occasion
to predicate, a definite and fixed connotation ; in order that it
may be known what attributes, when we call an object by that
name, we really mean to predicate of the object. And the
question of most nicety is, how to give this fixed connotation
to a name, with the least possible change in the objects which
the name is habitually employed to denote ; with the least
possible disarrangement, either by adding or subtraction, of
the group of objects which, in however imperfect a manner, it
serves to circumscribe and hold together ; and with the least
vitiation of the truth of any propositions which are commonly
received as true.

This desirable purpose, of giving a fixed connotation where
it is wanting, is the end aimed at whenever any one attempts
to give a definition of a general name already in use ; every
definition of a connotative name being an attempt either
merely to declare, or to declare and analyse, the connotation of
the name. And the fact, that no questions which have arisen

42 NAMES AND PROPOSITION'S.

in the moral sciences have been subjects of keener controversy
than the definitions of almost all the leading expressions, is a
proof how great an extent the evil to which we have adverted
has attained.

Names with indeterminate connotation are not to he con-
founded with names which have more than one connotation,
that is to say, ambiguous words. A word may have several
meanings, but all of them fixed and recognised ones ; as the
vforft post, for example, or the word box, the various senses of
which it would be endless to enumerate. And the paucity of
existing names, in comparison with the demand for them, may
often render it advisable and even necessary to retain a name
in this multiplicity of acceptations, distinguishing these so
clearly as to prevent their being confounded with one another.
Such a word may be considered as two or more names, acci-
dentally written and spoken alike.*

* Before quitting the subject of connotative names, it is proper to observe,
that the first writer who, in our times, has adopted from the schoolmen the
word to connote, Mr. James Mill, in his Analysis of the Phenomena of the
Human Mind, employs it in a signification different from that in which it is
her« used. He uses the word in a sense coextensive with its etymology, apply-
ing it to every case in which a name, while pointing directly to one thing,
(which is consequently termed its signification,) includes also a tacit reference
to some other thing. In the case considered in the text, that of concrete
general names, his language and mine are the converse of one another. Con-
sidering (very justly) the signification of the name to lie in the attribute, he
speaks of the word as noting the attribute, and connoting the things possessing
the attribute. And he describes abstract names as being properly concrete
names with their connotation dropped : whereas, in my view, it is the denota-
tion which would be said to be dropped, what was previously connoted be-
coming the whole signification.

In adopting a phraseology at variance with that which so high an authority,
and one which I am less likely than any other person to undervalue, has deli-
berately sanctioned, I have been influenced by the urgent necessity for a term
exclusively appropriated to express the manner in which a concrete general
name serves to mark the attributes which are involved in its signification. This
necessity can scarcely be felt in its full force by any one who has not found by
experience how vain is the attempt to communicate clear ideas on the philo-
sophy of language without such a word. It is hardly an exaggeration to say,
that some of the most prevalent of the errors with which logic has been infected,
and a large part of the cloudiness and confusion of ideas which have enveloped
it, would, in all probability, have been avoided, if a term had been in common

NAMES. 43

§ 6. The fourth principal division of names, is into posi-
tive and negative. Positive, as man, tree, good ; negative, as
not-man, not-tree, not-good. To every positive concrete name,
a corresponding negative one might be framed. After giving
a name to any one thing, or to any plurality of things, we
might create a second name which should be a name of all
things whatever, except that particular thing or things. These
negative names are employed whenever we have occasion to
speak collectively of all things other than some thing or class
of things. When the positive name is connotative, the cor-
responding negative name is connotative likewise ; but in a
peculiar way, connoting not the presence but the absence of
an attribute. Thus, not-white denotes all things whatever
except white things ; and connotes the attribute of not possess-
ing whiteness. For the non-possession of any given attribute
is also an attribute, and may receive a name as such ; and thus
negative concrete names may obtain negative abstract names
to correspond to them.*

use to express exactly what I have signified by the term to connote. And the
schoolmen, to whom we are indebted for the greater part of our logical lan-
guage, gave us this also, and in. this very sense. For though some of their
general expressions countenance the use of the word in the more extensive and
vague acceptation in which it is taken by Mr. Mill, yet when they had to define
it specifically as a technical term, and to fix its meaning as such, with that
admirable precision which always characterizes their definitions, they clearly
explained that nothing was said to be connoted except forms, which word may
generally, in their writings, be understood as synonymous with attributes.

Now, if the word to connote, so well suited to the purpose to which they
applied it, be diverted from that purpose by being taken to fulfil another, for
which it does not seem to me to be at all required ; I am unable to find any
expression to replace it, but such as are commonly employed in a sense so much
more general, that it would be useless attempting to associate them peculiarly
with this precise idea. Such are the words, to involve, to imply, &c. By em-
ploying these, I should fail of attaining the object for which alone the name is
needed, namely, to distinguish this particular kind of involving and implying
from all other kinds, and to assure to it the degree of habitual attention which
its importance demands.

* Professor Bain (Logic, i. 56) thinks that negative names are not names
of all things whatever except those denoted by the correlative positive name,
but only for all things of some particular class : not-white, for instance, he
deems not to be a name for everything in nature except white things, but only
for every coloured thing other than white. In this case, however, as in all

44 NAMES AND PROPOSITIONS.

Names which are positive in form are often negative in
reality, and others are really positive though their form is
negative. The word inconvenient, for example, does not ex-
press the mere absence of convenience ; it expresses a positive
attribute, that of being the cause of discomfort or annoyance.
So the word unpleasant, notwithstanding its negative form,
does not connote the mere absence of pleasantness, but a less
degree of what is signified by the word painful, which, it is
hardly necessary to say, is^'positive. Idle, on the other hand,
is a word which, though positive in form, expresses nothing
but what would be signified either by the phrase not working,
or by the phrase not disposed to work ; and sober, either by
not drunk or by not drunken. .

There is a class of names called privative. A privative
name is equivalent in its signification to a positive and a nega-
tive name taken together ; being the name of something which
has once had a particular attribute, or for some other reason
might have been expected to have it, but which has it not.
Such is the word blind, which is not equivalent to not seeing,
or to not capable of seeing, for it would not, except by a poetical
or rhetorical figure, be applied to stocks and stones. A thing
is not usually said to be blind, unless the class to which it is
most familiarly referred, or to which it is referred on the par-
ticular occasion, be chiefly composed of things which can see
as in the case of a blind man, or a blind horse ; or unless it is
supposed for any reason that it ought to see ; as in saying of
a man, that he rushed blindly into an abyss, or of philosophers
or the clergy that the greater part of them are blind guides.
The names called privative, therefore, connote two things ; the
absence of certain attributes, and the presence of others, from
which the presence also of the former might naturally have
been expected.

§ 7. The fifth leading division of names is into relative

others, the test of what a name denotes is what it can be predicated of : and
we can certainly predicate of a sound, or a smell, that it is not white. The
affirmation and the negation of the same attribute cannot but divide the whole
field of predication between them.

NAMES. 45

and absolute, or let us rather say, relative and non-relative ;
for the word absolute is put upon much too hard duty in me-
taphysics, not to be willingly spared when its services can be
dispensed with. It resembles the word civil in the language
of jurisprudence, which stands for the opposite of criminal, the
opposite of ecclesiastical, the opposite of military, the opposite
of political — in short, the opposite of any positive word which
wants a negative.

Relative names are such as father, son; ruler, subject;
like ; equal ; unlike ; unequal ; longer, shorter ; cause, effect.
Their characteristic property is, that they are always given in
pairs. Every relative name which is predicated of an object,
supposes another object (or objects), of which we may predicate
either that same name or another relative name which is said
to be the correlative of the former. Thus, when we call any
person a son, we suppose other persons who must be called
parents. When we call any event a cause, we suppose another
event which is an effect. When we say of any distance that
it is longer, we suppose another distance which is shorter.
When we say of any object that it is like, we mean that it is
like some other object, which is also said to be like the first.
In this last case both objects receive the same name; the
relative term is it own correlative.

It is evident that these words, when concrete, are, like
other concrete general names, connotative ; they denote a sub-
ject, and connote an attribute ; and each of them has or might
have a corresponding abstract name, to denote the attribute
connoted by the concrete. Thus the concrete like has its
abstract likeness ; the concretes, father and son, have, or might
have, the abstracts, paternity, and filiety, or sonship. The
concrete name connotes an attribute, and the abstract name
which answers to it denotes that attribute. But of what
nature is the attribute ? Wherein consists the peculiarity in
the connotation of a relative name ?

The attribute signified by a relative name, say some, is a
relation ; and this they give, if not as a sufficient explanation,
at least as the only one attainable. If they are asked, What
then is a relation ? they do not profess to be able to tell. It

46 NAMES AIjJD PROPOSITIONS.

is generally regarded as something peculiarly recondite and
mysterious. I cannot, however, perceive in what respect it is
more so than any other attribute ; indeed, it appears to me to
be so in a somewhat less degree. I conceive rather, that it is
by examining into the signification of relative names, or, in
other words, into the nature of the attribute which they con-
note, that a clear insight may best be obtained into the nature
of all attributes : of all that is meant by an attribute.

It is obvious, in fact, that if we take any two correlative
names, father and son for instance, though the objects de-
noted by the names are different, they both, in a certain sense,
connote the same thing. They cannot, indeed, be said to
connote the same attribute : to be a father, is not the same
thing as to be a son. But when we call one man a father,
another a son, what we mean to affirm is a set of facts,
which are exactly the same in both cases. To predicate of A
that he is the father of B, and of B that he is the son of A,
is to assert one and the same fact in different words. The
two propositions are exactly equivalent : neither of them
asserts more or asserts less than the other. The paternity of
A and the filiety of B are not two facts, but two modes of
expressing the same fact. That fact, when analysed, consists
of a series of physical events or phenomena, in which both A
and B are parties concerned, and from which they both derive
names. What those names really connote, is this series of
events : that is the meaning, and the whole meaning, which
either of them is intended to convey. The series of events may
be said to constitute the relation ; the schoolmen called it the
foundation of the relation, fundamentum relationis.

In this manner any fact, or series of facts, in which two
different objects are implicated, and which is therefore pre-
dicable of both of them, may be either considered as consti-
tuting an attribute of the one, or an attribute of the other.
According as we consider it in the former, or in the latter
aspect, it is connoted by the one or the other of the two cor-
relative names. Father connotes the fact, regarded as consti-
tuting aa attribute of A ; son connotes the same fact, as con-
stituting an attribute of B. It may evidently be regarded

NAMES. 47

with equal propriety in either light. And all that appears
necessary to account for the existence of relative names, is,
that whenever there is a fact in which two individuals are con-
cerned, an attribute grounded on that fact may be ascribed to
either of these individuals.

A name, therefore, is said to be relative, when, over and
ahove the object which it denotes, it implies in its signification
the existence of another object, also deriving a denomination
from the same fact which is the ground of the first name. Or
(to express the same meaning in other words) a name is rela-
tive, when, being the name of one thing, its signification
cannot be explained but by mentioning another. Or we may
state it thus — when the name cannot be employed in discourse
so as to have a meaning, unless the name of some other thing
than what it is itself the name of, be either expressed or under-
stood. These definitions are all, at bottom, equivalent, being
modes of variously expressing this one distinctive circum-
stance— that every other attribute of an object might, without
any contradiction, be conceived still to exist if no object be-
sides that one had ever existed;* but those of its attributes
which are expressed by relative names, would on that suppo-
sition be swept away.

§ 8. Names have been further distinguished into univocal
and (equivocal : these, however, are not two kinds of names,
but two different modes of employing names. A name is
univocal, or applied univocally, with respect to all things of
which it can be predicated in the same sense ; it is equivocal,
or applied aequivocally, as respects those things of which it is
predicated in different senses. It is scarcely necessary to give
instances of a fact so familiar as the double meaning of a word.

* Or rather, all objects except itself and the percipient mind ; for, as we
shall see hereafter, to ascribe any attribute to an object, necessarily implies a
mind to perceive it.

The simple and clear explanation given in the text, of relation and relative
names, a subject so long the opprobrium of metaphysics, was given (as far as I
know) for the first time, by Mr. James Mill, in his Analysis of the Phenomena
of the Human Mind.

48 NAMES AND PROPOSITIONS.

In reality, as has been already observed, an sequivocal or am-
biguous word is not one name, but two names, accidentally
coinciding in sound. File meaning a steel instrument, and
file meaning a line of soldiers, have no more title to be con-
sidered one word, because written alike, than grease and Greece
have, because they are pronounced alike. They are one sound,
appropriated to form two different words.

An intermediate case is that of a name used analogically
or metaphorically ; that is, a name which is predicated of two
things, not univocally, or exactly in the same signification,
but in significations somewhat similar, and which being de-
rived one from the other, one of them may be considered the
primary, and the other a secondary signification. As when
we speak of a brilliant light and a brilliant achievement. The
word is not applied in the same sense to the light and to the
achievement ; but having been applied to the light in its
original sense, that of brightness to the eye, it is transferred
to the achievement in a derivative signification, supposed to
be somewhat like the primitive one. The word, however, is
just as properly two names instead of one, in this case, as in
that of the most perfect ambiguity. And one of the com-
monest forms of fallacious reasoning arising from ambiguity,
is that of arguing from a metaphorical expression as if it were
literal; that is, as if a word, when applied metaphorically,
were the same name as when taken in its original sense :
which will be seen more particularly in its place.

CHAPTER III.

OF THE THINGS DENOTED BY NAMES.

§ 1. LOOKING back now to the commencement of our
inquiry, let us attempt to measure how far it has advanced.
Logic, we found, is the Theory of Proof. But proof supposes
something provable, which must be a Proposition or Assertion ;
since nothing but a Proposition can be an object of belief, or
therefore of proof. A Proposition is, discourse which affirms
or denies something of some other thing. This is one step :
there must, it seems, be two things concerned in every act of
belief. But what are these Things ? They can be no other
than those signified by the two names, which being joined
together by a copula constitute the Proposition. If, therefore,
we knew what all names signify, we should know everything
which, in the existing state of human knowledge, is capable
either of being made a subject of affirmation or denial, or of
being itself affirmed or denied of a subject. We have accord-
ingly, in the preceding chapter, reviewed the various kinds of
Names, in order to ascertain what is signified by each of them.
And we have now carried this survey far enough to be able to
take an account of its results, and to exhibit an enumeration
of all kinds of Things which are capable of being made predi-
cates, or of having anything predicated of them : after which
to determine the import of Predication, that is, of Proposi-
tions, can be no arduous task.

The necessity of an enumeration of Existences, as the basis
of Logic, did not escape the attention of the schoolmen, and
of their master Aristotle, the most comprehensive, if not also
the most sagacious, of the ancient philosophers. The Cate-
gories, or Predicaments — the former a Greek word, the latter
its literal translation in the Latin language — were believed to
be an enumeration of all things capable of being named ; an

VOL. I. 4

50 'NAMES AND PROPOSITIONS.

enumeration by the summa genera, i.e. the most extensive
classes into which things could he distributed ; which, there-
fore, were so many highest Predicates, one or other of which was
supposed capable of being affirmed with truth of every name-
able thing whatsoever. The following are the classes into
which, according to this school of philosophy, Things in
general might be reduced : —

Ovffia, Substantla.

Tlocroj', Quantitas.

Tlowv, Qualitas.

ITpoc ri, Relatio.

Tloiftv, Actio.

TIa<TX«v, Passio.

Hot), Ubi.

HOTS, Quando.

KtTffflou, Situs.

"EXUV, Habitus.

The imperfections of this classification are too obvious to
require, and its merits are not sufficient to reward, a minute
examination. It is a mere catalogue of the distinctions rudely
marked out by the language of familiar life, with little or no
attempt to penetrate, by philosophic analysis, to the rationale
even of those common distinctions. Such an analysis, how-
ever superficially conducted, would have shown the enumera-
tion to be both redundant and defective. Some objects are
omitted, and others repeated several times under different
heads. It is like a division of animals into men, quadrupeds,
horses, asses, and ponies. That, for instance, could not be a
very comprehensive view of the nature of Relation which could
exclude action, passivity, and local situation from that cate-
gory. The same observation applies to the categories Quando
(or position in time), and Ubi (or position in space) ; while
the distinction between the latter and Situs is merely verbal.
The incongruity of erecting into a summwn genus the class
which forms the tenth category is manifest. On the other
hand, the enumeration takes no notice of anything besides
substances and attributes. In what category are we to place
sensations, or any other feelings and states of mind ; as hope,
joy, fear; sound, smell, taste; pain, pleasure; thought, judg-

THINGS DENOTED BY NAMES. 51

ment, conception, and the like ? Probably all these would
have been placed by the Aristotelian school in the categories
of actio and passio ; and the relation of such of them as are
active, to their objects, and of such of them as are passive, to
their causes, would rightly be so placed ; but the things
themselves, the feelings or states of mind, wrongly. Feelings,
or states of consciousness, are assuredly to be accounted among
realities, but they cannot be reckoned either among substances
or attributes.*

§ 2. Before recommencing, under better auspices, the
attempt made with such imperfect success by the early logi-

* On the preceding passage Professor Bain remarks (Logic, i. 265) : " The
Categories do not seam to have been intended as a classification of Nameable
Things, in the sense of 'an enumeration of all kinds of Things which are
capable of being made predicates, or of having anything predicated of them.'
They seem to have been rather intended as a generalization of predicates;
an analysis of the final import of predication. Viewed in this light, they are
not open to the objections offered by Mr. Mill. The proper question to ask is
not — In what Category are we to place sensations or other feelings or states of
mind ? but, Under what Categories can we predicate regarding states of mind ?
Take, for example, Hope. When we say that it is a state of rnind, we predi-
cate Substance : we may also describe how great it is (Quantity), what is the
quality of it, pleasurable or painful (Quality), what it has reference to (Rela-
tion). Aristotle seems to have framed the Categories on the plan — Here is an
individual ; what is the final analysis of all that we can predicate about him ?"

This is doubtless a true statement of the leading idea in the classification.
The Category Ovvla was certainly understood by Aristotle to be a general name
for all possible answers to the question Quid sit ? when asked respecting a con-
crete individual ; as the other Categories are names comprehending all possible
answers to the questions Quantum sit ? Quale sit ? &c. In Aristotle's con-
ception, therefore, the Categories may not have been a classification of
Things ; but they were soon converted into one by his Scholastic followers,
who certainly regarded and treated them as a classification of Things, and
carried them out as such, dividing down the Category Substance as a natur.ilist
might do, into the different classes of physical or metaphysical objects as
distinguished from attributes, and the other Categories into the principal
varieties of quantity, quality, relation, &c. It is, therefore, a just subject of
complaint against them, that they had no Category of Feeling. Feeling is
assuredly predicable as a summum genus, of every particular kind of feeling,
for instance, as in Mr. Bain's example, of Hope : but it cannot be brought
within any of the Categories as interpreted either by Aristotle or by his fol-
lowers.

4—2

52 NAMES AND PROPOSITIONS.

cians, we must take notice of an unfortunate ambiguity in all
the concrete names which correspond to the most general of
all abstract terms, the word Existence. When we have occa-
sion for a name which shall be capable of denoting whatever
exists, as contradistinguished from non-entity or Nothing,
there is hardly a word applicable to the purpose which is not
also, and even more familiarly, taken in a sense in which
it denotes only substances. But substances are not all that
exists; attributes, if such things are to be spoken of, must
be said to exist ; feelings certainly exist. Yet when we speak
of an object, or of a thing, we are almost always supposed
to mean a substance. There seems a kind of contradic-
tion in using such an expression as that one thing is merely
an attribute of another thing. And the announcement of a
Classification of Things would, I believe, prepare most readers
for an enumeration like those in natural history, beginning
with the great divisions of animal, vegetable, and mineral,
and subdividing them into classes and orders. If, rejecting
the word Thing, we endeavour to find another of a more
general import, or at least more exclusively confined to that
general import, a word denoting all that exists, and connoting
only simple existence ; no word might be presumed fitter for
such a purpose than being : originally the present participle
of a verb which in one of its meanings is exactly equivalent to
the verb exists ; and therefore suitable, even by its grammatical
formation, to be the concrete of the abstract existence. But this
word, strange as the fact may appear, is still more completely
spoiled for the purpose which it seemed expressly made for,
than the word Thing. Being is, by custom, exactly synony-
mous with substance ; except that it is free from a slight taint
of a second ambiguity; being applied impartially to matter
and to mind, while substance, though originally and in strict-
ness applicable to both, is apt to suggest in preference the idea
of matter. Attributes are never called Beings ; nor are feel-
ings. A Being is that which excites feelings, and which pos-
sesses attributes. The soul is called a Being ; God and angels
are called Beings ; but if we were to say, extension, colour,
wisdom, virtue, are beings, we should perhaps be suspected of

THINGS DENOTED BY NAMES. 53

thinking with some of the ancients, that the cardinal virtues
are animals ; or, at the least, of holding with the Platonic
school the doctrine of self-existent Ideas, or with the followers
of Epicurus that of Sensible Forms, which detach themselves
in every direction from bodies, and by coming in contact
with our organs, cause our perceptions. We should be sup-
posed, in short, to believe that Attributes are Substances.

In consequence of this perversion of the word Being, phi-
losophers looking about for something to supply its place, laid
their hands upon the word Entity, a piece of barbarous Latin,
invented by the schoolmen to be used as an abstract name, in
which class its grammatical form would seem to place it ; but
being seized by logicians in distress to stop a leak in their
terminology, it has ever since been used as a concrete name.
The kindred word essence, born at the same time and of the
same parents, scarcely underwent a more complete transforma-
tion when, from being the abstract of the verb to be, it came
to denote something sufficiently concrete to be enclosed in a
glass bottle. The word Entity, since it settled down into a
concrete name, has retained its universality of signification
somewhat less impaired than any of the names before men-
tioned. Yet the same gradual decay to which, after a certain
age, all the language of psychology seems liable, has been at
work even here. If you call virtue an entity, you are indeed
somewhat less strongly suspected of believing it to be a sub-
stance than if you called it a being ; but you are by no means
free from the suspicion. Every word which was originally in-
tended to connote mere existence, seems, after a time, to
enlarge its connotation to separate existence, or existence freed
from the condition of belonging to a substance ; which con-
dition being precisely what constitutes an attribute, attributes
are gradually shut out ; and along with them feelings, which
in ninety-nine cases out of a hundred have no other name than
that of the attribute which is grounded on them. Strange
that when the greatest embarrassment felt by all who have
any considerable number of thoughts to express, is to find a
sufficient variety of precise words fitted to express them, there
should be no practice to which even scientific thinkers are

54 NAMES AND PROPOSITIONS.

more addicted than that of taking valuable words to express
ideas which are sufficiently expressed by other words already
appropriated to them.

When it is impossible to obtain good tools, the next best
thing is to understand thoroughly the defects of those we have.
I have therefore warned the reader of the ambiguity of the
names which, for want of better, I am necessitated to employ.
It must now be the writer's endeavour so to employ them
as in no case to leave the meaning doubtful or obscure. No
one of the above terms being altogether unambiguous, I
shall not confine myself to any one, but shall employ on each
occasion the word which seems least likely in the particular
case to lead to misunderstanding ; nor do I pretend to use
either these or any other words with a rigorous adherence to
one single sense. To do so would often leave us without a
word to express what is signified by a known word in some
one or other of its senses : unless authors had an unlimited
licence to coin new words, together with (what it would
be more difficult to assume) unlimited power of making
readers understand them. Nor would it be wise in a writer,
on a subject involving so much of abstraction, to deny himself
the advantage derived from even an improper use of a term, when,
by means of it, some familiar association is called up which
brings the meaning home to the mind, as it were by a flash.

The difficulty both to the writer and reader, of the attempt
which must be made to use vague words so as to convey a pre-
cise meaning, is not wholly a matter of regret. It is not un-
fitting that logical treatises should afford an example of that,
to facilitate which is among the most important uses of logic.
Philosophical language will for a long time, and popular lan-
guage still longer, retain so much of vagueness and ambiguity,
that logic would be of little value if it did not, among its
other advantages, exercise the understanding in doing its work
neatly and correctly with these imperfect tools.

After this preamble it is time to proceed to our enumera-
tion. We shall commence with Feelings, the simplest class
of nameable things ; the term Feeling being of course under-
stood in its most enlarged sense.

THINGS DENOTED BY NAMES. 55

I. FEELINGS, OR STATES OF CONSCIOUSNESS.

§ 3. A Feeling and a State of Consciousness are, in the
language of philosophy, equivalent expressions : everything is
a feeling of which the mind is conscious ; everything which it
feels, or, in other words, which forms a part of its own sentient
existence. In popular language Feeling is not always synony-
mous with State of Consciousness ; heing often taken more
peculiarly for those states which are conceived as belonging to
the sensitive, or to the emotional, phasis of our nature, and
sometimes, with a still narrower restriction, to the emotional
alone, as distinguished from what are conceived as belonging
to the percipient or to the intellectual phasis. But .this is an
admitted departure from correctness of language ; just as, by a
popular perversion the exact converse of this, the word Mind is
withdrawn from its rightful generality of signification, and
restricted to the intellect. The still greater perversion by
which Feeling is sometimes confined not only to bodily sensa-
tions, but to the sensations of a single sense, that of touch,
needs not be more particularly adverted to.

Feeling, in the proper sense of the term, is a genus, of
which Sensation, Emotion, and Thought, are subordinate
species. Under the word Thought is here to be included what-
ever we are internally conscious of when we are said to think ;
from the consciousness we have when we think of a red colour
without having it before our eyes, to the most recondite
thoughts of a philosopher or poet. Be it remembered, how-
ever, that by a thought is to be understood what passes in the
mind itself, and not any object external to the mind, which the
person is commonly said to be thinking of. He may be think-
ing of the sun, or of God, but the sun and God are not
thoughts ; his mental image, however, of the sun, and his idea
of God, are thoughts ; states of his mind, not of the objects
themselves ; and so also is his belief of the existence of the sun,
or of God ; or his disbelief, if the case be so. Even imaginary
objects (which are said to exist only in our ideas) are to be
distinguished from our ideas of them. I may think of a
hobgoblin, as I may think of the loaf which was eaten yester-

56 NAMES AND PROPOSITIONS.

day, or of the flower which will hloom to-morrow. But the
hobgoblin which never existed is not the same thing with my
idea of a hobgoblin, any more than the loaf which once existed
is the same thing with my idea of a loaf, or the flower which
does not yet exist, but which will exist, is the same with my
idea of a flower. They are all, not thoughts, but objects of
thought ; though at the present time all the objects are alike
non-existent.

In like manner, a Sensation is to be carefully distinguished
from the object which causes the sensation ; our sensation of
white from a white object: nor is it less to be distinguished
from the attribute whiteness, which we ascribe to the object in
consequence of its exciting the sensation. Unfortunately for
clearness and due discrimination in considering these subjects,
our sensations seldom receive separate names. We have a name
for the objects which produce in us a certain sensation: the
word white. We have a name for the quality in those objects,
to which we ascribe the sensation : the name whiteness. But
when we speak of the sensation itself (as we have not occasion
to do this often except in our scientific speculations), language,
which adapts itself for the most part only to the common uses
of life, has provided us with no single-worded or immediate
designation ; we must employ a circumlocution, and say, The
sensation of white, or The sensation of whiteness ; we must
denominate the sensation either from the object, or from the
attribute, by which it is excited. Yet the sensation, though it
never does, might very well be conceived to exist, without any-
thing whatever to excite it. We can conceive it as arising
spontaneously in the mind. But if it so arose, we should have
no name to denote it which would not be a misnomer. In the
case of our sensations of hearing we are better provided ; we
have the word Sound, and a whole vocabulary of words to denote
the various kinds of sounds. For as we are often conscious of
these sensations in the absence of any perceptible object, we can
more easily conceive having them in the absence of any object
whatever. We need only shut our eyes and listen to music,
to have a conception of an universe with nothing in it except
sounds, and ourselves hearing them : and what is easily con-

THINGS DENOTED BY NAMES. 57

ceived separately, easily obtains a separate name. But in general
our names of sensations denote indiscriminately the sensation
and the attribute. Thus, colour stands for the sensations of
white, red, &c., but also for the quality in the coloured object.
We talk of the colours of things as among their properties.

§ 4. In the case of sensations, another distinction has also
to be kept in view, which is often confounded, and never with-
out mischievous consequences. This is, the distinction between
the sensation itself, and the state of the bodily organs which
precedes the sensation, and which constitutes the physical
agency by which it is produced. One of the sources of con-
fusion on this subject is the division commonly made of feelings
into Bodily and Mental. Philosophically speaking, there is no
foundation at all for this distinction : even sensations are states
of the sentient mind, not states of the body, as distinguished
from it. What I am conscious of when I see the colour blue,
is a feeling of blue colour, which is one thing ; the picture on
my retina, or the phenomenon of hitherto mysterious nature
which takes place in my optic nerve or in my brain, is another
thing, of which I am not at all conscious, and which scientific
investigation alone could have apprised me of. These are
states of ray body ; but the sensation of blue, which is the con-
sequence of these states of body, is not a state of body : that
which perceives and is conscious is called Mind. When sen-
sations are called bodily feelings, it is only as being the class
of feelings which are immediately occasioned by bodily states ;
whereas the other kinds of feelings, thoughts, for instance, or
emotions, are immediately excited not by anything acting upon
the bodily organs, but by sensations, or by previous thoughts.
This, however, is a distinction not in our feelings, but in the
agency which produces our feelings : all of them when actually
produced are states of mind.

Besides the affection of our bodily organs from without,
and the sensation thereby produced in our minds, many writers
admit a third link in the chain of phenomena, which they call
a Perception, and which consists in the recognition of an ex-
ternal object as the exciting cause of the sensation. This

58 NAMES AND PROPOSITIONS.

perception, they say, is an act of the mind, proceeding from
its own spontaneous activity ; while in a sensation the mind is
passive, being merely acted upon by the outward object. And
according to some metaphysicians, it is by an act of the mind,
similar to perception, except in not being preceded by any
sensation, that the existence of God, the soul, and other hyper-
physical objects is recognised.

These acts of what is termed perception, whatever be the
conclusion ultimately come to respecting their nature, must,
I conceive, take their place among the varieties of feelings or
states of mind. In so classing them, I have not the smallest
intention of declaring or insinuating any theory as to the law
of mind in which these mental processes may be supposed to
originate, or the conditions under which they may be legiti-
mate or the reverse. Far less do I mean (as Dr Whewell
seems to suppose must be meant in an analogous case*) to in-
dicate that as they are " merely states of mind," it is super-
fluous to inquire into their distinguishing peculiarities. I
abstain from the inquiry as irrelevant to the science of logic.
In these so-called perceptions, or direct recognitions by the
mind, of objects, whether physical or spiritual, which are ex-
ternal to itself, I can see only cases of belief; but of belief
which claims to be intuitive, or independent of external evi-
dence. When a stone lies before me, I am conscious of certain
sensations which I receive from it ; but if I say that these sen-
sations come to me from an external object which I perceive,
the meaning of these words is, that receiving the sensations, I
intuitively believe that an external cause of those sensations
exists. The laws of intuitive belief, and the conditions under
which it is legitimate, are a subject which, as we have already
so often remarked, belongs not to logic, but to the science of
the ultimate laws of the human mind.

To the same region of speculation belongs all that can be
said respecting the distinction which the German metaphy-
sicians and their French and English followers so elaborately
draw between the acts of the mind and its merely passive

* Philosophy of the Inductive Sciences, vol. i. p. 40.

THINGS DENOTED BY NAMES. 59

states ; between what it receives from, and what it gives to,
the crude materials of its experience. I am aware that with
reference to the view which those writers take of the primary
elements of thought and knowledge, this distinction is funda-
mental. But for the present purpose, which is to examine, not
the original groundwork of our knowledge, but how we come
by that portion of it which is not original ; the difference be-
tween active and passive states of mind is of secondary impor-
tance. For us, they all are states of mind, they all are feelings ;
by which, let it be said once more, I mean to imply nothing of
passivity, but simply that they are psychological facts, facts
which take place in the mind, and are to be carefully distin-
guished from the external or physical facts with which they
may be connected either as effects or as causes.

§ 5. Among active states of mind, there is, however, one
species which merits particular attention, because it forms a
principal part of the connotation of some important classes of
names. I mean volitions, or acts of the will. When we speak
of sentient beings by relative names, a large portion of the
connotation of the name usually consists of the actions of those
beings ; actions past, present, and possible or probable future.
Take, for instance, the words Sovereign and Subject. What
meaning do these words convey, but that of innumerable
actions, done or to be done by the sovereign and the subjects,
to or in regard to one another reciprocally ? So with the
words physician and patient, leader and follower, tutor and
pupil. In many cases the words also connote actions which
would be done under certain contingencies by persons other
than those denoted : as the words mortgagor and mortgagee,
obligor and obligee, and many other words expressive of legal
relation, which connote what a court of justice would do to
enforce the legal obligation if not fulfilled. There are also
words which connote actions previously done by persons other
than those denoted either by the name itself or by its correla-
tive ; as the word brother. From these instances, it may be
seen how large a portion of the connotation of names consists
of actions. Now what is an action ? Not one thing, but a

60 NAMES AND PROPOSITIONS.

series of two things : the state of mind called a volition, fol-
lowed by an effect. The volition or intention to produce the
effect, is one thing ; the effect produced in consequence of the
intention, is another thing ; the two together constitute the
action. I form the purpose of instantly moving my arm ; that
is a state of my mind : my arm (not being tied or paralytic)
moves in obedience to my purpose ; that is a physical fact,
consequent on a state of mind. The intention, followed by
the fact, or (if we prefer the expression) the fact when preceded
and caused by the intention, is called the action of moving
my arm.

§ 6. Of the first leading division of nameable things, viz.
Feelings or States of Consciousness, we began by recognising
three sub-divisions ; Sensations, Thoughts, and Emotions. The
first two of these we have illustrated at considerable length ;
the third, Emotions, not being perplexed by similar ambi-
guities, does not require similar exemplification. And, finally,
we have found it necessary to add to these three a fourth
species, commonly known by the name Volitions. We shall
now proceed to the two remaining classes of nameable things ;
all things which are regarded as external to the mind being
considered as belonging either to the class of Substances or to
that of Attributes.

II. SUBSTANCES.

Logicians have endeavoured to define Substance and Attri-
bute ; but their definitions are not so much attempts to draw
a distinction between the things themselves, as instructions
•what difference it is customary to make in the grammatical
structure of the sentence, according as we are speaking of sub-
stances or of attributes. Such definitions are rather lessons of
English, or of Greek, Latin, or German, than of mental philo-
sophy. An attribute, say the school logicians, must be the
attribute of something ; colour, for example, must be the colour
of something; goodness must be the goodness of something :
and if this something should cease to exist, or should cease to
be connected with the attribute, the existence of the attribute

THINGS DENOTED BY NAMES. 61

would be at an end. A substance, on the contrary, is self-
existent ; in speaking about it, we need not put of after its
name. A stone is not the stone of anything ; the moon is not
the moon of anything, but simply the moon. Unless, indeed,
the name which we choose to give to the substance be a re-
lative name; if so, it must be followed either by of, or by some
other particle, implying, as that preposition does, a reference
to something else : but then the other characteristic peculiarity
of an attribute would fail ; the something might be destroyed,
and the substance might still subsist. Thus, a father must be
the father of something, and so far resembles an attribute, in
being referred to something besides himself: if there were no
child, there would be no father : but this, when we look into
the matter, only means that we should not call him father.
The man called father might still exist though there were no
child, as he existed before there was a child : and there would
be no contradiction in supposing him to exist, though the
whole universe except himself were destroyed. But destroy
all white substances, and where would be the attribute white-
ness ? Whiteness, without any white thing, is a contradiction
in terms.

This is the nearest approach to a solution of the difficulty,
that will be found in the common treatises on logic. It will
scarcely be thought to be a satisfactory one. If an attribute
is distinguished from a substance by being the attribute of
something, it seems highly necessary to understand what is
meant by of; a particle which needs explanation too much
itself, to be placed in front of the explanation of anything
else. And as for the self-existence of substance, it is very
true that a substance may be conceived to exist without any
other substance, but so also may an attribute without any
other attribute: and we can no more imagine a substance
without attributes than we can imagine attributes without a
substance.

Metaphysicians, however, have probed the question deeper,
and given an account of Substance considerably more satis-
factory than this. Substances are usually distinguished as
Bodies or Minds. Of each of these, philosophers have at

62 NAMES AND PROPOSITIONS.

length provided us with a definition which seems unexcep-
tionable.

§ 7. A body, according to the received doctrine of mo-
dern metaphysicians, may be defined, the external cause to
which we ascribe our sensations. When I see and touch a
piece of gold, I am conscious of a sensation of yellow colour,
and sensations of hardness and weight ; and by varying the
mode of handling, I may add to these sensations many others
completely distinct from them. The sensations are all of
which I am directly conscious ; but I consider them as pro-
duced by something not only existing independently of my
will, but external to my bodily organs and to my mind. This
external something I call a body.

It may be asked, how come we to ascribe our sensations to
any external cause ? And is there sufficient ground for so
ascribing them ? It is known, that there are metaphysicians
who have raised a controversy on the point ; maintaining that
we are not warranted in referring our sensations to a cause
such as we understand by the word Body, or to any external
cause whatever. Though we have no concern here with this
controversy, nor with the metaphysical niceties on which it
turns, one of the best ways of showing what is meant by Sub-
stance is, to consider what position it is necessary to take up,
in order to maintain its existence against opponents.

It is certain, then, that a part of our notion of a body
consists of the notion of a number of sensations of our own, or
of other sentient beings, habitually occurring simultaneously.
My conception of the table at which I am writing is com-
pounded of its visible form and size, which are complex sensa-
tions of sight ; its tangible form and size, which are complex
sensations of our organs of touch and of our muscles ; its
weight, which is also a sensation of touch and of the muscles ;
its colour, which is a sensation of sight ; its hardness, which
is a sensation of the muscles ; its composition, which is another
word for all the varieties of sensation which we receive under
various circumstances from the wood of which it is made, and
so forth. All or most of these various sensations frequently

THINGS DENOTED BY NAMES. 63

are, and, as we learn by experience, always might be, expe-
rienced simultaneously, or in many different orders of succes-
sion at our own choice : and hence the thought of any one of
them makes us think of the others, and the whole becomes
mentally amalgamated into one mixed state of consciousness,
which, in the language of the school of Locke and Hartley, is
termed a Complex Idea.

Now, there are philosophers who have argued as follows.
If we conceive an orange to be divested of its natural colour
without acquiring any new one ; to lose its softness without
becoming hard, its roundness without becoming square or
pentagonal, or of any other regular or irregular figure what-
ever ; to be deprived of size, of weight, of taste, of smell ; to
lose all its mechanical and all its chemical properties, and
acquire no new ones ; to become, in short, invisible, intangible,
imperceptible not only by all our senses, but by the senses of
all other sentient beings, real or possible; nothing, say these
thinkers, would remain. For of what nature, they ask, could
be the residuum ? and by what token could it manifest its
presence ? To the unreflecting its existence seems to rest on the
evidence of the senses. But to the senses nothing is apparent
except the sensations. We know, indeed, that these sensations
are bound together by some law ; they do not come together
at random, but according to a systematic order, which is part
of the order established in the universe. When we experience
one of these sensations, we usually experience the others also,
or know that we have it in our power to experience them.
But a fixed law of connexion, making the sensations occur
together, does not, say these philosophers, necessarily require
what is called a substratum to support them. The conception
of a substratum is but one of many possible forms in which
that connexion presents itself to our imagination ; a mode of,
as it were, realizing the idea. If there be such a substratum,
suppose it at this instant miraculously annihilated, and let the
sensations continue to occur in the same order, and how would
the substratum be missed ? By what signs should we be able
to discover that its existence had terminated ? Should we not
have as much reason to believe that it still existed as we now

04 NAMES AND PROPOSITIONS.

have ? And if we should not then be warranted in believing
it, how can we be so now ? A body, therefore, according to
these metaphysicians, is not anything intrinsically different
from the sensations which the body is said to produce in us ;
it is, in short, a set of sensations, or rather, of possibilities of
sensation, joined together according to a fixed law.

The controversies to which these speculations have given
rise, and the doctrines which have been developed in the
attempt to find a conclusive answer to them, have been fruitful
of important consequences to the Science of Mind. The sensa-
tions (it was answered) which we are conscious of, and which
we receive, not at random, but joined together in a certain
uniform manner, imply not only a law or laws of connexion,
but a cause external to our mind, which cause, by its own
laws, determines the laws according to which the sensations
are connected and experienced. The schoolmen used to call
this external cause by the name we have already employed, a
substratum ; and its attributes (as they expressed themselves)
inhered, literally stuck, in it. To this substratum the name
Matter is usually given in philosophical discussions. It was
soon, however, acknowledged by all who reflected on the sub-
ject, that the existence of matter cannot be proved by extrinsic
evidence. The answer, therefore, now usually made to Berkeley
and his followers, is, that the belief is intuitive ; that mankind,
in all ages, have felt themselves compelled, by a necessity of
their nature, to refer their sensations to an external cause :
that even those who deny it in theory, yield to the necessity in
practice, and both in speech, thought, and feeling, do, equally
with the vulgar, acknowledge their sensations to be the effects
of something external to them : this knowledge, therefore, it
is affirmed, is as evidently intuitive as our knowledge of our
sensations themselves is intuitive. And here the question
merges in the fundamental problem of metaphysics properly
so called : to which science we leave it.

But although the extreme doctrine of the Idealist meta-
physicians, that objects are nothing but our sensations and
the laws which connect them, has not been generally adopted
by subsequent thinkers ; the point of most real importance is

THINGS DENOTED BY NAMES. 65

one on which those metaphysicians are now very generally
considered to have made out their case : viz., that all we know
of objects is the sensations which they give us, and the order
of the occurrence of those sensations. Kant himself, on this
point, is as explicit as Berkeley or Locke. However firmly
convinced that there exists an universe of " Things in them-
selves," totally distinct from the universe of phenomena, or of
things as they appear to our senses ; and even when bringing
into use a technical expression (Noumenon) to denote what the
thing is in itself, as contrasted with the representation of it in
our minds ; he allows that this representation (the matter
of which, he says, consists of our sensations, though the form
is given by the laws of the mind itself) is all we know of the
object: and that the real nature of the Thing is, and by
the constitution of our faculties ever must remain, at least in
the present state of existence, an impenetrable mystery to us.
" Of things absolutely or in themselves," says Sir William
Hamilton,* "be they external, be they internal, we know
nothing, or know them only as incognisable ; and become
aware of their incomprehensible existence, only as this is in-
directly and accidentally revealed to us, through certain quali-
ties related to our faculties of knowledge, and which qualities,
again, we cannot think as unconditioned, irrelative, existent
in and of themselves. All that we know is therefore phaeno-
menal, — phenomenal of the unknown. "f The same doctrine
is laid down in the clearest and strongest terms by M. Cousin,
whose observations on the subject are the more worthy of
attention, as, in consequence of the ultra-German and ontolo-
gical character of his philosophy in other respects, they may
be regarded as the admissions of an opponent.!

* Discussions on Philosophy, &c. Appendix I. pp. 643-4.

t It is to be regretted that Sir William Hamilton, though he often strenu-
ously insists on this doctrine, and though, in the passage quoted, he states it
with a comprehensiveness and force which leave nothing to be desired, did not
consistently adhere to his own doctrine, but maintained along with it opinions
with which it ia utterly irreconcilable. See the third and other chapters of
A n Examination of Sir William Hamilton's Philosophy.

J " Nous savons qu'il existe quelque chose hors de nous, parceque nous ne
pouvons expliquer nos perceptions sans les rattacher a des causes disttnctes de

VOL. I. 5

66 NAMES AND PROPOSITIONS.

There is not the slightest reason for believing that what
we call the sensible qualities of the object are a type of any-
thing inherent in itself, or bear any affinity to its own nature.
A cause does not, as such, resemble its effects ; an east wind
is not like the feeling of cold, nor heat like the steam of boil-
ing water. Why then should matter resemble our sensations ?
Why should the inmost nature of fire or water resemble the
impressions made by those objects upon our senses ?* Or on

nous m£mes ; nous savons de plus que ces causes, dont nous ne connaissons pas
d'ailleurs 1'essence, produisent les effets les plus variables, les plus divers, et
mSme les plus contraires, selon qu'elles rencontrent telle nature ou telle dis-
position du sujet. Mais savons-nous quelque chose de plus ? et nifime, vu le
caractere inde'termine' des causes que nous concevons dans les corps, y a-t-il
quelque chose de plus a savoir ? Y a-t-il lieu de nous enque"rir si nous per-

cevons les choses telles qu'elles sont ? Non e"videmment Je ne dis

pas que le probleme est insoluble, je dis qu'il est absurde et enferme une contra-
diction. Nous ne savons pas ce que ces causes sont en elles-me'mes, et la raison
nous deTend de chercher a le connaltre : mais il est bien Evident a priori, qu'elles
ne sont pas en elles-m.Sm.es ce qu'elles sont par rapport a nous, puisque la presence
du sujet modifie ne"cessairement leur action. Supprimez tout sujet sentant, il
est certain que ces causes agiraient encore puisqu'elles continueraient d'exister;
mais elles agiraient autrement ; elles seraient encore des qualite"s et des pro-
prie'te's, mais qui ne ressembleraient a rien de ce que nous connaissons. Le feu
ne manifesterait plus aucune des proprie'te's que nous lui connaissons : que
serait-il? C'est ce que nous ne saurons jamais. C'est d'ailleurs pent-fore un
probleme qui ne r&puynepas seulement a la nature de noire esprit, mais a I' essence
meme des choses. Quand meme en efFet on supprimerait par le pense"e tous les
sujets sentants, il faudrait encore adinettre que nul corps ne manifesterait ses
proprietes autrement qu'en relation avec un sujet quelconque, et dans ce cas
ses proprietes ne seraient encore que relatives: en sorte qu'il me paralt fort
raisonnable d'admettre que les propri6tes deterrainees des corps n'existent pas
independamrnent d'un sujet quelconque, et que quand on demande si les pro-
prietes de la matiere sont telles que nous les percevons, il faudrait voir aupara-
vant si elles sont en tant que de'termine'es, et dans quel sens il est vrai de dire
qu'elles sont." — Cours d'Histoire de la Philosophic Morale au ISme siecle, 8me
Ie9on.

* An attempt, indeed, has been made by Reid and others, to establish that
although some of the properties we ascribe to objects exist only in our sensa-
tions, others exist in the things themselves, being such as cannot possibly be
copies of any impression upon the senses ; and they ask, from what sensations
our notions of extension and figure have been derived ? The gauntlet thrown
down by Eeid was taken up by Brown, who, applying greater powers of ana-
lysis than had previously been applied to the notions of extension and figure,
pointed out that the sensations from which those notions are derived, are sensa-
tions of touch, combined with sensations of a class previously too little adverted

THINGS DENOTED BY NAMES. 67

what principle are we authorized to deduce from the effects,
anything concerning the cause, except that it is a cause ade-
quate to produce those effects ? It may, therefore, safely be
laid down as a truth both obvious in itself, and admitted by
all whom it is at present necessary to take into consideration,
that, of the outward world, we know and can know absolutely
nothing, except the sensations which we experience from it.*

to by metaphysicians, those which have their seat in our muscular frame. His
analysis, which was adopted and followed up by James Mill, has been further
and greatly improved upon in Professor Bain's profound work, The Senses and
the Intellect, and in the chapters on " Perception" of a work of eminent ana-
lytic power, Mr. Herbert Spencer's Principles of Psychology.

On this point M. Cousin may again be cited in favour of the better doctrine.
M. Cousin recognises, in opposition to Reid, the essential subjectivity of our
conceptions of what are called the primary qualities of matter, as extension,
solidity, &c., equally with those of colour, heat, and the remainder of the so-
called secondary qualities. — Cours, ut supra, 9me legon.

* This doctrine, which is the most complete form of the philosophical theory
known as the Relativity of Human Knowledge, has, since the recent revival in
this country of an active interest in metaphysical speculation, been the subject
of a greatly increased amount of discussion and controversy ; and dissentients
have manifested themselves in considerably greater number than I had any
knowledge of when the passage in the text was written. The doctrine has been
attacked from two sides. Some thinkers, among whom are the late Professor
Ferrier, in his Institutes of Metaphysic, and Professor John Grote, in his Explo-
ratio Philosophica, appear to deny altogether the reality of Noumena, or Things
in themselves — of an unknowable substratum or support for the sensations
which we experience, and which, according to the theory, constitute all our
knowledge of an external world. It seems to me, however, that in Professor
Grote's case at least, the denial of Noumena is only apparent, and that he does
not essentially differ from the other class of objectors, including Mr. Bailey in
his valuable Letters on the Philosoi^hy of the Human Mind, and (in spite of
the striking passage quoted in the text) also Sir William Hamilton, who can-
tend for a direct knowledge by the human mind of more than the sensations —
of certain attributes or properties as they exist not in us, but in the Things
themselves.

With the first of these opinions, that which denies Noumena, I have, as a
metaphysician, no quarrel ; but, whether it be Irue or false, it is irrelevant to
Logic. And since all the forms of language are in contradiction to it, nothing
but confusion could result from its unnecessary introduction into a treatise,
every essential doctrine of which could stand equally well with the opposite and
accredited opinion. The other and rival doctrine, that of a direct perception or
intuitive knowledge of the outward object as it is in itself, considered as distinct
from the sensations we receive from it, is of far greater practical momeut. But
even this question, depending on the nature and laws of Intuitive Knowledge,

5—2

68 NAMES AND PROPOSITIONS.

§ 8. Body having now been defined the external cause,
and (according to the more reasonable opinion) the unknown
external cause, to which \ve refer our sensations ; it remains
to frame a definition of Mind. Nor, after the preceding ob-
servations, will this be difficult. For, as our conception of a
body is that of an unknown exciting cause of sensations, so
our conception of a mind is that of an unknown recipient, or
percipient, of them ; and not of them alone, but of all our
other feelings. As body is understood to be the mysterious
something which excites the mind to feel, so mind is the
mysterious something which feels and thinks. It is unnecessary
to give in the case of mind, as we gave in the case of matter,
a particular statement of the sceptical system by which its
existence as a Thing in itself, distinct from the series of what
are denominated its states, is called in question. But it is
necessary to remark, that on the inmost nature (whatever be
meant by inmost nature) of the thinking principle, as well as
on the inmost nature of matter, we are, and with our faculties
mnst always remain, entirely in the dark. All which we are
aware of, even in our own minds, is (in the words of James
Mill) a certain " thread of consciousness ;" a series of feelings,
that is, of sensations, thoughts, emotions, and volitions, more
or less numerous and complicated. There is a something I call
Myself, or, by another form of expression, my mind, which I
consider as distinct from these sensations, thoughts, &c. ; a
something which I conceive to be not the thoughts, but the
being that has the thoughts, and which I can conceive as
existing for ever in a state of quiescence, without any thoughts
at all. But what this being is, though it is myself, I have no
knowledge, other than the series of its states of consciousness.
As bodies manifest themselves to me only through the sensa-
tions of which I regard them as the causes, so the thinking
principle, or mind, in my own nature, makes itself known to

is not within the province of Logic. For the grounds of my own opinion con-
cerning it, I must content myself with referring to a work already mentioned —
A n Examination of Sir William Hamilton's Philosophy ; several chapters of
which are devoted to a full discussion of the questions and theories relating to
the supposed direct perception of external objects.

THINGS DENOTED BY NAMES. 69

me only by the feelings of which it is conscious. I know
nothing about myself, save my capacities of feeling or being
conscious (including, of course, thinking and willing) : and
were I to learn anything new concerning my own nature, I
cannot with my present faculties conceive this new information
to be anything else, than that I have some additional capa-
cities, as yet unknown to me, of feeling, thinking, or willing.

Thus, then, as body is the unsentient cause to which we
are naturally prompted to refer a certain portion of our feel-
ings, so mind may be described as the sentient subject (in the
scholastic sense of the term) of all feelings ; that which has or
feels them. But of the nature of either body or mind, further
than the feelings which the former excites, and which the
latter experiences, we do not, according to the best existing
doctrine, know anything; and if anything, logic has nothing
to do with it, or with the manner in which the knowledge is
acquired. With this result we may conclude this portion of
our subject, and pass to the third and only remaining class or
division of Nameable Things.

III. ATTRIBUTES : AND, FIRST, QUALITIES.

§ 9. From what has already been said of Substance,
what is to be said of Attribute is easily deducible. For if we
know not, and cannot know, anything of bodies but the sensa-
tions which they excite in us or in others, those sensations
must be all that we can, at bottom, mean by their attributes ;
and the distinction which we verbally make between the pro-
perties of things and the sensations we receive from them,
must originate in the convenience of discourse rather than in
the nature of what is signified by the terms.

Attributes are usually distributed under the three heads of
Quality, Quantity, and Relation. We shall come to the two
latter presently : in the first place we shall confine ourselves
to the former.

Let us take, then, as our example, one of what are termed
the sensible qualities of objects, and let that example be white-
ness. When we ascribe whiteness to any substance, as, for

70 NAMES AND PROPOSITIONS.

instance, snow ; when we say that snow has the quality white-
ness, what do we really assert ? Simply, that when snow is
present to our organs, we have a particular sensation, which
we are accustomed to call the sensation of white. But how do
I know that snow is present ? Obviously by the sensations
which I derive from it, and not otherwise. I infer that the
object is present, because it gives me a certain assemblage or
series of sensations. And when I ascribe to it the attribute
whiteness, my meaning is only, that, of the sensations com-
posing this group or series, that which I call the sensation of
white colour is one.

This is one view which may be taken of the subject. But
there is also another and a different view. It may be said, that
it is true we know nothing of sensible objects, except the sen-
sations they excite in us ; that the fact of our receiving from
snow the particular sensation which is called a sensation of
white, is the ground on which we ascribe to that substance the
quality whiteness ; the sole proof of its possessing that quality.
But because one thing may be the sole evidence of the exis-
tence of another thing, it does not follow that the two are one
and the same. The attribute whiteness (it may be said) is not
the fact of receiving the sensation, but something in the
object itself ; a power inherent in it; something in virtue of
which the object produces the sensation. And when we affirn
that snow possesses the attribute whiteness, we do not merely
assert that the presence of snow produces in us that sensation,
but that it does so through, and by reason of, that power or
quality.

For the purposes of logic it is not of material importance
which of these opinions we adopt. The full discussion of the
subject belongs to the other department of scientific inquiry,
so often alluded to under the name of metaphysics ; but it may
be said here, that for the doctrine of the existence of a peculiar
species of entities called qualities, I can see no foundation
except in a tendency of the human mind which is the cause of
many delusions. I mean, the disposition, wherever we meet
with two names which are not precisely synonymous, to sup-
pose that they must be the names of two different things ;

THINGS DENOTED BY NAMES. 71

whereas in reality they may be names of the same thing viewed
in two different lights, or under different suppositions as to
surrounding circumstances. Because quality and sensation
cannot be put indiscriminately one for the other, it is supposed
that they cannot both signify the same thing, namely, the
impression or feeling with which we are affected through our
senses by the presence of an object; though there is at least
no absurdity in supposing that this identical impression or
feeling may be called a sensation when considered merely in
itself, and a quality when looked at in relation to any one of
the numerous objects, the presence of which to our organs
excites in our minds that among various other sensations or
feelings. And if this be admissible as a supposition, it rests
with those who contend for an entity per se called a quality,
to show that their opinion is preferable, or is anything in fact
but a lingering remnant of the old doctrine of occult causes ;
the very absurdity which Moliere so happily ridiculed when he
made one of his pedantic physicians account for the fact that
opium produces sleep by the maxim, Because it has a soporific
virtue.

It is evident that when the physician stated that opium
has a soporific virtue, he did not account for, but merely
asserted over again, the fact that it produces sleep. In like
manner, when we say that snow is white because it has the
quality of whiteness, we are only re-asserting in more technical
language the fact that it excites in us the sensation of white.
If it be said that the sensation must have some cause, I answer,
its cause is the presence of the assemblage of phenomena which
is termed the object. When we have asserted that as often as
the object is present, and our organs in their normal state, the
sensation takes place, we have stated all that we know about
the matter. There is no need, after assigning a certain and
intelligible cause, to suppose an occult cause besides, for the
purpose of enabling the real cause to produce its effect. If I
am asked, why does the presence of the object cause this sen-
sation in me, I cannot tell : I can only say that such is my
nature, and the nature of the object ; that the fact forms a
part of the constitution of things. And to this we must at last

72 NAMES AND PROPOSITIONS,

come, even after interpolating the imaginary entity. Whatever
number of links the chain of causes and effects may consist of,
how any one link produces the one which is next to it, remains
equally inexplicable to us. It is as easy to comprehend that
the object should produce the sensation directly and at once,
as that it should produce the same sensation by the aid of
something else called the power of producing it.

But, as the difficulties which may be felt in adopting this
view of the subject cannot be removed without discussions
transcending the bounds of our science, I content myself with
a passing indication, and shall, for the purposes of logic, adopt
a language compatible with either view of the nature of quali-
ties. I shall say, — what at least admits of no dispute, — that
the quality of whiteness ascribed to the object snow, is grounded
on its exciting in us the sensation of white ; and adopting the
language already used by the school logicians in the case of the
kind of attributes called Relations, I shall term the sensation
of white the foundation of the quality whiteness. For logical
purposes the sensation is the only essential part of what is
meant by the word ; the only part which we ever can be con-
cerned in proving. When that is proved, the quality is proved ;
if an object excites a sensation, it has, of course, the power of
exciting it.

IV. RELATIONS.

§ 10. The qualities of a body, we have said, are the
attributes grounded on the sensations which the presence of
that particular body to our organs excites in our minds. But
when we ascribe to any object the kind of attribute called a
Relation, the foundation of the attribute must be something
in which other objects are concerned besides itself and the
percipient.

As there may with propriety be said to be a relation
between any two things to which two correlative names are or
may be given, we may expect to discover what constitutes a
relation in general, if we enumerate the principal cases in which
mankind have imposed correlative names, and observe what
these cases have in common.

THINGS DENOTED BY NAMES. 73

What, then, is the character which is possessed in common
by states of circumstances so heterogeneous and discordant as
these: one thing like another; one thing unlike another; one
thing near another ; one thing far from another ; one thing
before, after, along with another ; one thing greater, equal,
less, than another ; one thing the cause of another, the effect
of another ; one person the master, servant, child, parent,
debtor, creditor, sovereign, subject, attorney, client, of another,
and so on ?

Omitting, for the present, the case of Eesemhlance, (a
relation which requires to be considered separately,) there seems
to be one thing common to all these cases, and only one ; that
in each of them there exists or occurs, or has existed or
occurred, or may be expected to exist or occur, some fact or
phenomenon, into which the two things which are said to be
related to each other, both enter as parties concerned. This
fact, or phenomenon, is what the Aristotelian logicians called
the fundamcntum relationis. Thus in the relation of greater
and less between two magnitudes, the fundamentum relationis
is the fact that one of the two magnitudes could, under certain
conditions, be included in, without entirely filling, the space
occupied by the other magnitude. In the relation of master
and servant, the fundamentum relationis is the fact that the
one has undertaken, or is compelled, to perform certain services
for the benefit and at the bidding of the other. Examples
might be indefinitely multiplied ; but it is already obvious
that whenever two tilings are said to be related, there is some
fact, or series of facts, into which they both enter ; and that
whenever any two things are involved in some one fact, or
series of facts, we may ascribe to those two things a mutual
relation grounded on the fact. Even if they have nothing in
common but what is common to all things, that they are
members of the universe, we call that a relation, and deno-
minate them fellow-creatures, fellow- beings, or fellow-denizens
of the universe. But in proportion as the fact into which the
two objects enter as parts is of a more special and peculiar, or
of a more complicated nature, so also is the relation grounded
upon it. And there are as many conceivable relations as there

74 NAMES AND PROPOSITIONS.

are conceivable kinds of fact in which two things can be jointly
concerned.

In the same manner, therefore, as a quality is an attribute
grounded on the fact that a certain sensation or sensations are
produced in us by the object, so an attribute grounded on some
fact into which the object enters jointly with another object,
is a relation between it and that other object. But the fact in
the latter case consists of the very same kind of elements as
the fact in the former : namely, states of consciousness. In
the case, for example, of any legal relation, as debtor and
creditor, principal and agent, guardian and ward, the funda-
mentum relationis consists entirely of thoughts, feelings, and
volitions (actual or contingent), either of the persons them-
selves or of other persons concerned in the same series of trans-
actions ; as, for instance, the intentions which would be formed
by a judge, in case a complaint were made to his tribunal of
the infringement of any of the legal obligations imposed by
the relation ; and the acts which the judge would perform in
consequence ; acts being (as we have already seen) another
word for intentions followed by an effect, and that effect being
but another word for sensations, or some other feelings, occa-
sioned either to the agent himself or to somebody else. There
is no part of what the names expressive of the relation imply,
that is not resolvable into states of consciousness ; outward
objects being, no doubt, supposed throughout as the causes by
which some of those states of consciousness are excited, and
minds as the subjects by which all of them are experienced,
but neither the external objects nor the minds making their
existence known otherwise than by the states of consciousness.

Cases of relation are not always so complicated as those to
which we last alluded. The simplest of all cases of relation
are those expressed by the words antecedent and consequent,
and by the word simultaneous. If we say, for instance, that
dawn preceded sunrise, the fact in which the two things, dawn
and sunrise, were jointly concerned, consisted only of the two
things themselves ; no third thing entered into the fact or
phenomenon at all. Unless, indeed, we choose to call the suc-
cession of the two objects a third thing; but their succession

THINGS DENOTED BY NAMES. 75

is not something added to the things themselves ; it is some-
thing involved in them. Dawn and sunrise announce them-
selves to our consciousness by two successive sensations. Our
consciousness of the succession of these sensations is not a
third sensation or feeling added to them ; we have not first the
two feelings, and then a feeling of their succession. To have
two feelings at all, implies having them either successively, or
else simultaneously. Sensations, or other feelings, being given,
succession and simultaneousness are the two conditions, to the
alternative of which they are subjected by the nature of our
faculties ; and no one has been able, or needs expect, to analyse
the matter any farther.

§ 11. In a somewhat similar position are two other sorts
of relations, Likeness and Unlikehess. I have two sensations;
we will suppose them to be simple ones ; two sensations of
white, or one sensation of white and another of black. I call
the first two sensations like ; the last two unlike. What is
the fact or phenomenon constituting the fundamentum of this
relation ? The two sensations first, and then what we call a
feeling of resemblance, or of want of resemblance. Let us
confine ourselves to the former case. Resemblance is evidently
a feeling ; a state of the consciousness of the observer. Whether
the feeling of the resemblance of the two colours be a third
state of consciousness, which I have after having the two sen-
sations of colour, or whether (like the feeling of their succes-
sion) it is involved in the sensations themselves, may be a
matter of discussion. But in either case, these feelings of
resemblance, and of its opposite dissimilarity, are parts of our
nature ; and parts so far from being capable of analysis, that
they are pre-supposed in every attempt to analyse any of our
other feelings. Likeness and unlikeness, therefore, as well
as antecedence, sequence, and simultaneousuess, must stand
apart among relations, as things sui generis. They are
attributes grounded on facts, that is, on states of conscious-
ness, but on states which are peculiar, unresolvable, and
inexplicable.

But, though likeness or unlikeness cannot be resolved into

76 NAMES AND PROPOSITIONS.

anything else, complex cases of likeness or unlikeness can be
resolved into simpler ones. When we say of two things which
consist of parts, that they are like one another, the likeness of
the wholes does admit of analysis ; it is compounded of like-
nesses between the various parts respectively, and of likeness
in their arrangement Of how vast a variety of resemblances
of parts must that resemblance be composed, which induces
us to say that a portrait, or a landscape, is like its original.
If one person mimics another with any success, of how many
simple likenesses must the general or complex likeness be
compounded : likeness in a succession of bodily postures ;
likeness in voice, or in the accents and intonations of the
voice ; likeness in the choice of words, and in the thoughts
or sentiments expressed, whether by word, countenance, or
gesture.

All likeness and unlikeness of which we have any cogni-
zance, resolve themselves into likeness and unlikeness between
states of our own, or some other, mind. When we say that
one body is like another, (since we know nothing of bodies
but the sensations which they excite,) we mean really that there
is a resemblance between the sensations excited by the two
bodies, or between some portions at least of those sensations.
If we say that two attributes are like one another, (since we
know nothing of attributes except the sensations or states of
feeling on which they are grounded,) we mean really that those
sensations, or states of feeling, resemble each other. We may
also say that two relations are alike. The fact of resemblance
between relations is sometimes called analogy, forming one of
the numerous meanings of that word. The relation in which
Priam stood to Hector, namely, that of father and son, resem-
bles the relation in which Philip stood to Alexander ; resem-
bles it so closely that they are called the same relation. The
relation in which Cromwell stood to England resembles the
relation in which Napoleon stood to France, though not so
closely as to be called the same relation. The meaning in both
these instances must be, that a resemblance existed between
the facts which constituted the fundamentum relationis.

This resemblance may exist in all conceivable gradations,

THINGS DENOTED BY NAMES. 77

from perfect undistinguisbableness to something extremely
slight. When we say, that a thought suggested to the mind
of a person of genius is like a seed cast into the ground,
because the former produces a multitude of other thoughts,
and the latter a multitude of other seeds, this is saying
that between the relation of an inventive mind to a thought
contained in it, and the relation of a fertile soil to a seed
contained in it, there exists a resemblance : the real resem-
blance being in the two fandamenta relationis, in each
of which there occurs a germ, producing by its develop-
ment a multitude of other things similar to itself. And
as, whenever two objects are jointly concerned in a pheno-
menon, this constitutes a relation between those objects,
so, if we suppose a second pair of objects concerned in a
second phenomenon, the slightest resemblance between the
two phenomena is sufficient to admit of its being said that
the two relations resemble ; provided, of course, the points of
resemblance are found in those portions of the two phenomena
respectively which are connoted by the relative names.

While speaking of resemblance, it is necessary to take
notice of an ambiguity of language, against which scarcely
any one is sufficiently on his guard. Resemblance, when it
exists in the highest degree of all, amounting to undis-
tinguishableness, is often called identity, and the two similar
things are said to be the same. I say often, not always ;
for we do not say that two visible objects, two persons for
instance, are the same, because they are so much alike that
one might be mistaken for the other : but we constantly use
this mode of expression when speaking of feelings; as when
I say that the sight of any object gives me the same sensation
or emotion to-day that it did yesterday, or the same which it
gives to some other person. This is evidently an incorrect
application of the word same ; for the feeling which I had
yesterday is gone, never to return ; what I have to-day is
another feeling, exactly like the former perhaps, but distinct
from it ; and it is evident that two different persons cannot
be experiencing the same feeling, in the sense in which we
say that they are both sitting at the same table. By a

78 NAMES AND PROPOSITIONS.

similar ambiguity \ve say, that two persons are ill of the
same disease ; that two persons hold the same office ; not in
the sense in which we say that they are engaged in the same
adventure, or sailing in the same ship, but in the sense that
they fill offices exactly similar, though, perhaps, in distant
places. Great confusion of ideas is often produced, and
many fallacies engendered, in otherwise enlightened under-
standings, by not being sufficiently alive to the fact (in itself
not always to be avoided), that they use the same name to
express ideas so different as those of identity and undis-
tinguishable resemblance. Among modern writers, Arch-
bishop Whately stands almost alone in having drawn atten-
tion to this distinction, and to the ambiguity connected
with it.

Several relations, generally called by other names, are really
cases of resemblance. As, for example, equality ; which is
but another word for the exact resemblance commonly called
identity, considered as subsisting between things in respect of
their quantity. And this example forms a suitable transition
to the third and last of the three heads under which, as already
remarked, Attributes are commonly arranged.

V. QUANTITY.

§ 12. Let us imagine two things, between which there
is no difference (that is, no dissimilarity), except in quantity
alone : for instance, a gallon of water, and more than a
gallon of water. A gallon of water, like any other external
object, makes its presence known to us by a set of sensations
which it excites. Ten gallons of water are also an external
object, making its presence known to us in a similar manner ;
and as we do not mistake ten gallons of water for a gallon
of water, it is plain that the set of sensations is more or less
different in the two cases. In like manner, a gallon of water,
and a gallon of wine, are two external objects, making their
presence known by two sets of sensations, which sensations
are different from each other. In the first case, however, we
say that the difference is in quantity ; in the last there is a

THINGS DENOTED BY NAMES. 79

difference in quality, while the quantity of the water and of
the wine is the same. What is the real distinction between
the two cases ? It is not within the province of Logic to ana-
lyse it ; nor to decide whether it is susceptible of analysis or
not. For us the following considerations are sufficient. It
is evident that the sensations I receive from the gallon of
water, and those I receive from the gallon of wine, are not
the same, that is, not precisely alike; neither are they alto-
gether unlike : they are partly similar, partly dissimilar ;
and that in which they resemble is precisely that in which
alone the gallon of water and the ten gallons do not resemble.
That in which the gallon of water and the gallon of wine are
like each other, and in which the gallon and the ten gallons
of water are unlike each other, is called their quantity. This
likeness and unlikeness I do not pretend to explain, no more
than any other kind of likeness or uulikeness. But my object
is to show, that when we say of two things that they differ
in quantity, just as when we say that they differ in quality,
the assertion is always grounded on a difference in the sensa-
tions which they excite. Nobody, I presume, will say, that
to see, or to lift, or to drink, ten gallons of water, does
not include in itself a different set of sensations from those
of seeing, lifting, or drinking one gallon ; or that to see or
handle a foot-rule, and to see or handle a yard-measure made
exactly like it, are the same sensations. I do not undertake
to say what the difference in the sensations is. Everybody
knows, and nobody can tell ; no more than any one could tell
what white is to a person who had never had the sensation.
But the difference, so far as cognizable by our faculties, lies in
the sensations. Whatever difference we say there is in the
things themselves, is, in this as in all other cases, grounded,
and grounded exclusively, on a difference in the sensations
excited by them.

VI. ATTRIBUTES CONCLUDED.

§ 13. Thus, then, all the attributes of bodies which are
classed under Quality or Quantity, are grounded on the sensa-

80 NAMES AND PROPOSITIONS.

tions which we receive from those bodies, and may be defined,
the powers which the bodies have of exciting those sensations.
And the same general explanation has been found to apply to
most of the attributes usually classed under the head of "Rela-
tion. They, too, are grounded on some fact or phenomenon
into which the related objects enter as parts ; that fact or phe-
nomenon having no meaning and no existence to us, except
the series of sensations or other states of consciousness by
which it makes itself known ; and the relation being simply
the power or capacity which the object possesses of taking
part along with the correlated object in the production of that
series of sensations or states of consciousness. We have been
obliged, indeed, to recoguise a somewhat different character in
certain peculiar relations, those of succession and simultaneity,
of likeness and unlikeness. These, not being grounded on
any fact or phenomenon distinct fiom the related objects
themselves, do not admit of the same kind of analysis. But
these relations, though not, like other relations, grounded on
states of consciousness, are themselves states of conscious-
ness : resemblance is nothing but our feeling of resemblance ;
succession is nothing but our feeling of succession. Or, if this
be disputed (and we cannot, without transgressing the bounds
of our science, discuss it here), at least our knowledge of these
relations, and even our possibility of knowledge, is confined to
those which subsist between sensations, or other states of con-
sciousness ; for, though we ascribe resemblance, or succession,
or simultaneity, to objects and to attributes, it is always in
virtue of resemblance or succession or simultaneity in the sen-
sations or states of consciousness which those objects excite,
and on which those attributes are grounded.

§ 14. In the preceding investigation we have, for the
sake of simplicity, considered bodies only, and omitted minds.
But what we have said, is applicable, mutatis mutandis, to the
latter. The attributes of minds, as well as those of bodies,
are grounded on states of feeling or consciousness. But in
the case of a mind, we have to consider its own states, as well
as those which it produces in other minds. Every attribute

THINGS DENOTED BY NAMES. 81

of a mind consists either in being itself affected in a certain
way, or affecting other minds in a certain way. Considered
in itself, we can predicate nothing of it but the series of its
own feelings. When we say of any mind, that it is devout,
or superstitious, or meditative, or cheerful, we mean that the
ideas, emotions, or volitions implied in those words, form a
frequently recurring part of the series of feelings, or states of
consciousness, which fill up the sentient existence of that mind.
In addition, however, to those attributes of a mind which
are grounded on its own states of feeling, attributes may also
be ascribed to it, in the same manner as to a body, grounded
on the feelings which it excites in other minds. A mind does
not, indeed, like a body, excite sensations, but it may excite
thoughts or emotions. The most important example of attri-
butes ascribed on this ground, is the employment of terms ex-
pressive of approbation or blame. When, for example, we say
of any character, or (in other words) of any mind, that it is
admirable, we mean that the contemplation of it excites the
sentiment of admiration ; and indeed somewhat more, for the
word implies that we not only feel admiration, but approve
that sentiment in ourselves. In some cases, under the sem-
blance of a single attribute, two are really predicated : one of
them, a state of the mind itself; the other, a state with which
other minds are affected by thinking of it. As when we say
of any one that he is generous. The word generosity expresses
a certain state of mind, but being a term of praise, it also ex-
presses that this state of mind excites in us another mental
state, called approbation. The assertion made, therefore, is
twofold, and of the following purport : Certain feelings form
habitually a part of this person's sentient existence ; and the
idea of those feelings of his, excites the sentiment of approba-
tion in ourselves or others.

As we thus ascribe attributes to minds on the ground of
ideas and emotions, so may we to bodies on similar grounds,
and not solely on the ground of sensations : as in speaking of
the beauty of a statue ; since this attribute is grounded on the
peculiar feeling of pleasure which the statue produces in our
minds ; which is not a sensation, but an emotion.
VOL. i. 6

82 NAMES AND PROPOSITIONS.

i

VII. GENERAL EESULTS.

§ 15. Our survey of the varieties of Things which have
been, or which are capable of being, named — which have been,
or are capable of being, either predicated of other Things,
or themselves made the subject of predications — is now con-
cluded.

Our enumeration commenced with Feelings. These we
scrupulously distinguished from the objects which excite them,
and from the organs by which they are, or may be supposed
to be, conveyed. Feelings are of four sorts : Sensations,
Thoughts, Emotions, and Volitions. What are called Per-
ceptions are merely a particular case of Belief, and belief is a
kind of thought. Actions are merely volitions followed by an
effect.

After Feelings we proceeded to Substances. These are
either Bodies or Minds. Without entering into the grounds
of the metaphysical doubts which have been raised concerning
the existence of Matter and Mind as objective realities, we
stated as sufficient for us the conclusion in which the best
thinkers are now for the most part agreed, that all we can
know of Matter is the sensations which it gives us, and the
order of occurrence of those sensations ; and that while the
substance Body is the unknown cause of our sensations, the
substance Mind is the unknown recipient.

The only remaining class of Nameable Things is Attributes ;
and these are of three kinds, Quality, Relation, and Quantity.
Qualities, like substances, are known to us no otbenvise than
by the sensations or other states of consciousness which they
excite : and while, in compliance with common usage, we have
continued to speak of them as a distinct class of Things, we
showed that in predicating them no one means to predicate
anything but those sensations or states of consciousness, on
which they may be said to be grounded, and by which alone
they can be defined or described. Relations, except the simple
cases of likeness and unlikeness, succession and simultaneity,
are similarly grounded on some fact or phenomenon, that is,
on some series of sensations or states of consciousness, more

THINGS DENOTED BY NAMES. 83

or less complicated. The third species of Attribute, Quantity,
is also manifestly grounded on something in our sensations
or states of feeling, since there is an indubitable difference in
the sensations excited by a larger and a smaller bulk, or by a
greater or a less degree of intensity, in any object of sense or of
consciousness. All attributes, therefore, are to us nothing but
either our sensations and other states of feeling, or something
inextricably involved therein ; and to this even the peculiar
and simple relations just adverted to are not exceptions.
Those peculiar relations, however, are so important, and, even
if they might in strictness be classed among states of con-
sciousness, are so fundamentally distinct from any other of
those states, that it would be a vain subtlety to bring them
under that common description, and it is necessary that they
should be classed apart.*

As the result, therefore, of our analysis, we obtain the fol-
lowing as an enumeration and classification of all Nameable
Things : —

1st. Feelings, or States of Consciousness.

2nd. The Minds which experience those feelings.

3rd. The Bodies, or external objects which excite certain
of those feelings, together with the powers or properties
whereby they excite them ; these latter (at least) being in-
cluded rather in compliance with common opinion, and because
their existence is taken for granted in the common language
from which I cannot prudently deviate, than because the
recognition of such powers or properties as real existences
appears to be warranted by a sound philosophy.

4th, and last. The Successions and Co-existences, the
Likenesses and Unlikenesses, between feelings or states of
consciousness. Those relations, when considered as subsist-

* Professor Bain (Loyic, i. 49) defines attributes as "points of commu-
nity among classes." This definition expresses well one point of view, but is
liable to the objection that it applies only to the attributes of classes ; though,
an object, unique in its kind, may be said to have attributes. Moreover, the
definition is not ultimate, since the points of community themselves admit
of, and require, further analysis ; and Mr. Bain does analyse them into resem-
blances in the sensations, or other states of consciousness excited by the object.

6—2

84 NAMES AND PROPOSITIONS.

ing between other things, exist in reality only between the
states of consciousness which those things, if bodies, excite,
if minds, either excite or experience.

This, until a better can be suggested, may serve as a sub-
stitute for the Categories of Aristotle considered as a Classifi-
cation of Existences. The practical application of it will
appear when we commence the inquiry into the Import of
Propositions; in other words, when we inquire what it is
which the mind actually believes, when it gives what is called
its assent to a proposition.

These four classes comprising, if the classification be cor-
rect, all Nameable Things, these or some of them must of
course compose the signification of all names ; and of these,
or some of them, is made up whatever we call a fact.

For distinction's sake, every fact which is solely composed
of feelings or states of consciousness considered as such, is
often called a Psychological or Subjective fact; while every
fact which is composed, either wholly or in part, of something
different from these, that is, of substances and attributes, is
called an Objective fact. We may say, then, that every ob-
jective fact is grounded on a corresponding subjective one;
and has no meaning to us, (apart from the subjective fact
which corresponds to it,) except as a name for the unknown
and inscrutable process by which that subjective or psycho-
logical fact is brought to pass.

CHAPTER IV.

OF PROPOSITIONS.

§ 1. IN treating of Propositions, as already in treating
of Names, some considerations of a comparatively elementary
nature respecting their form and varieties must be premised,
before entering upon that analysis of the import conveyed by
them, which is the real subject and purpose of this preliminary
book.

A proposition, we have before said, is a portion of discourse
in which a predicate is affirmed or denied of a subject. A
predicate and a subject are all that is necessarily required to
makeup a proposition : but as we cannot conclude from merely
seeing two names put together, that they are a predicate and
a subject, that is, that one of them is intended to be affirmed or
denied of the other, it is necessary that there should be some
mode or form of indicating that such is the intention ; some
sign to distinguish a predication from any other kind of dis-
course. This is sometimes done by a slight alteration of one
of the words, called an inflection; as when we say, Fire
burns ; the change of the second word from burn to burns
showing that we mean to affirm the predicate burn of the sub-
ject fire. But this function is more commonly fulfilled by the
word is, when an affirmation is intended, is not, when a
negation; or by some, other part of the verb to be. The word
which thus serves the purpose of a sign of predication is called,
as we formerly observed, the copula. It is important that
there should be no indistinctness in our conception of the
nature and office of the copula ; for confused notions respect-
ing it are among the causes which have spread mysticism
over the field of logic, and perverted its speculations into
logomachies.

It is apt to be supposed that the copula is something more

00 NAMES AND PROPOSITIONS.

than a mere sign of predication ; that it also signifies existence.
In the proposition, Socrates is just, it may seem to be implied
not only that the quality just can be affirmed of Socrates, but
moreover that Socrates is, that is to say, exists. This, how-
ever, only shows that there is an ambiguity in the word is ; a
word which not only performs the function of the copula in
affirmations, but has also a meaning of its own, in virtue of
which it may itself be made the predicate of a proposition.
That the employment of it as a copula does not necessarily
include the affirmation of existence, appears from such a pro-
position as this, A centaur is a fiction of the poets; where it
cannot possibly be implied that a centaur exists, since the
proposition itself expressly asserts that the thing has no real
existence.

Many volumes might be filled with the frivolous specula-
tions concerning the nature of Being, (TO ov, ovata, Ens, Enti-
tas, Essentia, and the like) which have arisen from overlook-
ing this double meaning of the word to be; from supposing
that when it signifies to exist, and when it signifies to be some
specified thing, as to be a man, to be Socrates, to be seen or
spoken of, to be a phantom, even to be a nonentity, it must
still, at bottom, answer to the same idea ; and that a meaning
must be found for it which shall suit all these cases. The fog
which rose from this narrow spot diffused itself at an early
period over the whole surface of metaphysics. Yet it becomes
us not to triumph over the great intellects of Plato and Ari-
stotle because we are now able to preserve ourselves from many
errors into which they, perhaps inevitably, fell. The fire-
teazer of a modern steam-engine produces by his exertions
far greater effects than Milo of Crotona could, but he is not
therefore a stronger man. The Greeks seldom knew any
language but their own. This rendered it far more difficult
for them than it is for us, to acquire a readiness in detecting
ambiguities. One of the advantages of having accurately
studied a plurality of languages, especially of those languages
which eminent thinkers have used as the vehicle of their
thoughts, is the practical lesson we learn respecting the ambi-
guities of words, by finding that the same word in one Ian-

PROPOSITIONS. 87

,guage corresponds, ou different occasions, to different words
in another. When not thus exercised, even the strongest
understandings find it difficult to believe that things which
have a common name, have not in some respect or other a
common nature ; and often expend much labour very unpro-
fitably (as was frequently done by the two philosophers just
mentioned) in vain attempts to discover in what this common
nature consists. But, the habit once formed, intellects much
inferior are capable of detecting even ambiguities which are
common to many languages : and it is surprising that the one
now under consideration, though it exists in the modern lan-
guages as well as in the ancient, should have been overlooked
by almost all authors. The quantity of futile speculation
which had been caused by a misapprehension of the nature
of the copula, was hinted at by Hobbes ; but Mr. James Mill*
was, I believe, the first who distinctly characterized the ambi-
guity, and pointed out how many errors in the received systems
of philosophy it has had to answer for. It has indeed misled
the moderns scarcely less than the ancients, though their
mistakes, because our understandings are not yet so com-
pletely emancipated from their influence, do not appear equally
irrational.

We shall now briefly review the principal distinctions
which exist among propositions, and the technical terms most
commonly in use to express those distinctions.

§ 2. A proposition being a portion of discourse in which
something is affirmed or denied of something, the first divi-
sion of propositions is into affirmative and negative. An
affirmative proposition is that in which the predicate is
affirmed of the subject; as, Csesar is dead. A negative pro-
position is that in which the predicate is denied of the subject ;
as, Ceesar is not dead. The copula, in this last species of
proposition, consists of the words is not, which are the sign of
negation ; is being the sign of affirmation.

Some logicians, among whom may be mentioned Hobbes,

Analysis of the Human Mind, i. 126 et seq.

NAMES AND PROPOSITIONS.

state this distinction differently ; they recognise only one form
of copnla, is, and attach the negative sign to the predicate.
" Csesar is dead," and " Csesar is not dead," according to these
writers, are propositions agreeing not in the subject and pre-
dicate, but in the subject only. They do not consider " dead,"
but " not dead," to be the predicate of the second proposi-
tion, and they accordingly define a negative proposition to be
one in which the predicate is a negative name. The point,
though not of much practical moment, deserves notice as an
example (not unfrequent in logic) where by means of an
apparent simplification, but which is merely verbal, matters
are made more complex than before. The notion of these
writers was, that they could get rid of the distinction between
affirming and denying, by treating every case of denying as
the affirming of a negative name. But what is meant by a
negative name ? A name expressive of the absence of an
attribute. So that when we affirm a negative name, what we
are really predicating is absence and not presence ; we are
asserting not that anything is, but that something is not ; to
express which operation no word seems so proper as the word
denying. The fundamental distinction is between a fact and
the non-existence of that fact; between seeing something and
not seeing it, between Csesar's being dead and his not being
dead; and if this were a merely verbal distinction, the gene-
ralization which brings both within the same form of assertion
would be a real simplification : the distinction, however, being
real, and in the facts, it is the generalization confounding the
distinction that is merely verbal ; and tends to obscure the
subject, by treating the difference between two kinds of truths
as if it were only a difference between two kinds of words.
To put things together, and to put them or keep them asunder,
will remain different operations, whatever tricks we may play
with language.

A remark of a similar nature may be applied to most of
those distinctions among propositions which are said to have
reference to their modality ; as, difference of tense or time ;
the sun did rise, the sun is rising, the sun will rise. These
differences, like that between affirmation and negation, might

PROPOSITIONS.

89

be glossed over by considering the incident of time as a mere
modification of the predicate : thus, The sun is an object
having risen, The sun is an object now rising, The sun is an
object to rise hereafter. But the simplification would be merely
verbal. Past, present, and future, do not constitute so many
different kinds of rising ; they are designations belonging to
the event asserted, to the sun's rising to-day. They affect,
not the predicate, but the applicability of the predicate to the
particular subject. That which we affirm to be past, present,
or future, is not what the subject signifies, nor what the pre-
dicate signifies, but specifically and expressly what the pre-
dication signifies ; what is expressed only by the proposition
as such, and not by either or both of the terms. Therefore
the circumstance of time is properly considered as attaching
to the copula, which is the sign of predication, and not to the
predicate. If the same cannot be said of such modifications
as these, Cssar may be dead ; Ceesar is perhaps dead ; it is
possible that Cassar is dead ; it is only because these fall alto-
gether under another head, being properly assertions not of
anything relating to the fact itself, but of the state of our own
mind in regard to it; namely, our absence of disbelief of it.
Thus " Caesar may be dead" means " I am not sure that Csesar
is alive."

§ 3. The next division of propositions is into Simple and
Complex ; more aptly (by Professor Bain*) termed Compound.
A simple proposition is that in which one predicate is affirmed
or denied of one subject. A compound proposition is that in
which there is more than one predicate, or more than one sub-
ject, or both.

At first sight this division has the air of an absurdity ; a
solemn distinction of things into one and more than one ; as
if we were to divide horses into single horses and teams of
horses. And it is true that what is called a complex (or com-
pound) proposition is often not a proposition at all, but several
propositions, held together by a conjunction. Such, for ex-

* Logic, i. 85.

VU NAMES AND PROPOSITIONS.

ample, is this: Ccesar is dead, and Brutus is alive: or even
this, Csesar is dead, but Brutus is alive. There are here two
distinct assertions; and we might as well call a street a com-
plex house, as these two propositions a complex proposition.
It is true that the syncategorematic words and arid but have a
meaning; but that meaning is so far from making the two
propositions one, that it adds a third proposition to them.
All particles are abbreviations, and generally abbreviations of
propositions ; a kind of short-hand, wherehy something which,
to be expressed fully, would have required a proposition or
a series of propositions, is suggested to the mind at once.
Thus the words, Caesar is dead and Brutus is alive, are
equivalent to these : Coesar is dead ; Brutus is alive ; it is
desired that the two preceding propositions should be thought
of together. If the words were, Csesar is dead, but Brutus is
alive, the sense would be equivalent to the same three pro-
positions together with a fourth ; " between the two preceding
propositions there exists a contrast :" viz. either between the
two facts themselves, or between the feelings with which it is
desired that they should be regarded.

In the instances cited the two propositions are kept visibly
distinct, each subject having its separate predicate, and each
predicate its separate subject. For brevity, however, and to
avoid repetition, the propositions are often blended together :
as in this, " Peter and James preached at Jerusalem and in
Galilee," which contains four propositions : Peter preached at
Jerusalem, Peter preached in Galilee, James preached at Jeru-
salem, James preached in Galilee.

We have seen that when the two or more propositions
comprised in what is called a complex proposition are stated
absolutely, and not under any condition or proviso, it is not
a proposition at all, but a plurality of propositions ; since
what it expresses is not a single assertion, but several asser-
tions, which, if true when joined, are true also when separated.
But there is a kind of proposition which, though it contains
a plurality of subjects and of predicates, and may be said in
one sense of the word to consist of several propositions, con-
tains but one assertion ;. and its truth does not at all imply

PROPOSITIONS. 91

that of the simple propositions which compose it. An
example of this is, when the simple propositions are con-
nected by the particle or ; as, either A is B or C is I) ; or by
the particle if; as, A is B if C is D. In the former case, the
proposition is called disjunctive, in the latter, conditional : the
name hypothetical was originally common to both. As has
been well remarked by Archbishop Whately and others, the
disjunctive form is resolvable into the conditional ; every dis-
junctive proposition being equivalent to two or more con-
ditional ones. " Either A is B or C is D," means, " if A is
not B, C is D ; and if C is not D, A is B." All hypothetical
propositions, therefore, though disjunctive in form, are con-
ditional in meaning ; and the words hypothetical and condi-
tional may be, as indeed they generally are, used synony-
mously. Propositions in which the assertion is not dependent
on a condition, are said, in the language of logicians, to be
categorical.

An hypothetical proposition is not, like the pretended
complex propositions which we previously considered, a mere
aggregation of simple propositions. The simple propositions
which form part of the words in which it is couched, form no
part of the assertion which it conveys. When we say, If the
Koran comes from God, Mahomet is the prophet of God, we
do not intend to affirm either that the Koran does come from
God, or that Mahomet is really his prophet. Neither of these
simple propositions may be true, and yet the truth of the
hypothetical proposition may be indisputable. What is
asserted is not the truth of either of the propositions, but the
inferribility of the one from the other. What, then, is the
subject, and what the predicate of the hypothetical proposi-
tion ? " The Koran" is not the subject of it, nor is '''Maho-
met:" for nothing is affirmed or denied either of the Koran
or of Mahomet. The real subject of the predication is the
entire proposition, " Mahomet is the prophet of God ;" and
the affirmation is, that this is a legitimate inference from the
proposition, " The Koran comes from God." The subject and
predicate, therefore, of an hypothetical proposition are names
of propositions. The subject is some one proposition. The

92 NAMES AND PROPOSITIONS.

predicate is a general relative name applicable to propositions ;
of this form — "an inference from so and so." A fresh instance
is here afforded of the remark, that particles are abbreviations ;
since " If A is B, C is D," is found to be an abbreviation of
the following : " The proposition C is D, is a legitimate infe-
rence from the proposition A is B."

The distinction, therefore, between hypothetical and cate-
gorical propositions, is not so great as it at first appears. In
the conditional, as well as in the categorical form, one predi-
cate is affirmed of one subject, and no more : but a conditional
proposition is a proposition concerning a proposition; the
subject of the assertion is itself an assertion. Nor is this a
property peculiar to hypothetical propositions. There are
other classes of assertions concerning propositions. Like other
things, a proposition has attributes which may be predicated
of it. The attribute predicated of it in an hypothetical pro-
position, is tbat of being an inference from a certain other
proposition. But this is only one of many attributes that
might be predicated. We may say, That the whole is greater
than its part, is an axiom in mathematics: That the Holy
Ghost proceeds from the Father alone, is a tenet of the Greek
Church : The doctrine of the divine right of kings was re-
nounced by Parliament at the Revolution : The infallibility
of the Pope has no countenance from Scripture. In all these
cases the subject of the predication is an entire proposition.
That which these different predicates are affirmed of, is the
proposition, " the whole is greater than its part ;" the propo-
sition, " the Holy Ghost proceeds from the Father alone ;"
the proposition, " kings have a divine right ;" the proposition,
" the Pope is infallible."

Seeing, then, that there is much less difference between
hypothetical propositions and any others, than one might be
led to imagine from their form, we should be at a loss to
account for the conspicuous position which they have been
selected to fill in treatises on logic, if we did not remember
that what they predicate of a proposition, namely, its being
an inference from something else, is precisely that one of

PROPOSITIONS. 93

its attributes with which most of all a logician is con
cerned.

§ 4. The next of the common divisions of Propositions is
into Universal, Particular, Indefinite, and Singular : a distinc-
tion founded on the degree of generality in which the name,
which is the subject of the proposition, is to be understood.
The following are examples :

All men are mortal — Universal.

Some men are mortal — Particular,

Man is mortal — Indefinite.

Julius Caesar is mortal — Singular.
The proposition is Singular, when the subject is an indi-
vidual name. The individual name needs not be a proper name.
" The Founder of Christianity was crucified," is as much a
singular proposition as " Christ was crucified."

When the name which is the subject of the proposition is
a general name, we may intend to affirm or deny the predicate,
either of all the things that the subject denotes, or only of
some. When the predicate is affirmed or denied of all and
each of the things denoted by the subject, the proposition is
universal ; when of some undefined portion of them only, it is
particular. Thus, All men are mortal ; Every man is mortal ;
are universal propositions. No man is immortal, is also an
universal proposition, since the predicate, immortal, is denied
of each and every individual denoted by the term man ; the
negative proposition being exactly equivalent to the following,
Every man is not-immortal. But " some men are wise,"
" some men are not wise," are particular propositions ; the
predicate wise being in the one case affirmed and in the other
denied not of each and every individual denoted by the term
man, but only of each and every one of some portion of those
individuals, without specifying what portion ; for if this were
specified, the proposition would be changed either into a sin-
gular proposition, or into an universal proposition with a dif-
ferent subject; as, for instance, "all properly instructed men
are wise." There are other forms of particular propositions ;

Vi NAMES AND PROPOSITIONS.

as, "Most men are imperfectly educated :" it being immaterial
how large a portion of the subject the predicate is asserted of,
as long as it is left uncertain how that portion is to be distin-
guished from the rest.*

When the form of the expression does not clearly show
whether the general name which is the subject of the proposi-
tion is meant to stand for all the individuals denoted by it, or
only for some of them, the proposition is, by some logicians,
called Indefinite ; but this, as Archbishop Whately observes,
is a solecism, of the same nature as that committed by some
grammarians when in their list of genders they enumerate tlie
doubtful gender. The speaker must mean to assert the propo-
sition either as an universal or as a particular proposition,
though he has failed to declare which: and it often happens
that though the words do not show which of the two he
intends, the context, or the custom of speech, supplies the
deficiency. Thus, when it is affirmed that " Man is mortal,"
nobody doubts that the assertion is intended of all human
beings ; and the word indicative of universality is commonly
omitted, only because the meaning is evident without it. In
the proposition, " Wine is good," it is understood with equal
readiness, though for somewhat different reasons, that the
assertion is not intended to be universal, but particular.f
As is observed by Professor Bain,j the chief examples

* Instead of Universal and Particular as applied to propositions, Professor
Bain proposes (Logic, i. 81) the terms Total and Partial; reserving the former
pair of terms for their inductive meaning, "the contrast between a general
proposition and the particulars or individuals that we derive it from." This
change in nomenclature would be attended with the further advantage, that
Singular propositions, which in the Syllogism follow the same rules as
Universal, would be included along with them in the same class, that of Total
predications. It is not the Subject's denoting many things or only one, that
is of importance in reasoning, it is that the assertion is made of the whole
or a part only of what the Subject denotes. The words Universal and Par-
ticular, however, are so familiar and so well understood in both the senses
mentioned by Mr. Eain, that the double meaning does not produce any material
inconvenience.

•f It may, however, be considered as equivalent to an universal proposition
with a different predicate, viz. "All wine is good qud wine," or "is good in
respect of the qualities which constitute it wine."
t Logic, i. 82.

PROPOSITIONS. 95

of Indefinite propositions occur " with names of material,
which are the subjects sometimes of universal, and at
other times of particular predication. 'Food is chemically
constituted by carbon, oxygen, &c.,' is a proposition of uni-
versal quantity ; the meaning is all food — all kinds of food.
' Food is necessary to animal life ' is a case of particular
quantity ; the meaning is some sort of food, not necessarily all
sorts. ' Metal is requisite in order to strength ' does not
mean all kinds of metal. ' Gold will make a way,' means a
portion of gold."

When a general name stands for each and every individual
which it is a name of, or in other words, which it denotes, it
is said by logicians to be distributed, or taken distributively.
Thus, in the proposition, All men are mortal, the subject, Man,
is distributed, because mortality is affirmed of each and every
man. The predicate, Mortal, is not distributed, because the
only mortals who are spoken of in the proposition are those
who happen to be men ; while the word may, for aught that
appears, and in fact does, comprehend within it an indefinite
number of objects besides men. In the proposition, Some men
are mortal, both the predicate and the subject are undistributed.
In the following, No men have wings, both the predicate and
the subject are distributed. Not only is the attribute of having
wings denied of the entire class Man, but that class is severed
and cast out from the whole of the class Winged, and not merely
from some part of that class.

This phraseology, which is of great service in stating arid
demonstrating the rules of the syllogism, enables us to express
very concisely the definitions of an universal and a particular
proposition. An universal proposition is that of which the
subject is distributed ; a particular proposition is that of which
the subject is undistributed.

There are many more distinctions among propositions than
those we have here stated, some of them of considerable im-
portance. But, for explaining and illustrating these, more
suitable opportunities will occur in the sequel.

CHAPTER V.

OF THE IMPORT OF PROPOSITIONS.

§ 1. AN inquiry into the nature of propositions must
have one of two objects : to analyse the state of mind called
Belief, or to analyse what is believed. All language recog-
nises a difference between a doctrine or opinion, and the fact
of entertaining the opinion ; between assent, and what is
assented to.

Logic, according to the conception here formed of it, has
no concern with the nature of the act of judging or believing;
the consideration of that act, as a phenomenon of the mind,
belongs to another science. Philosophers, however, from
Descartes downwards, and especially from the era of Leibnitz
and Locke, have by no means observed this distinction ; and
would have treated with great disrespect any attempt to analyse
the import of Propositions, unless founded on an analysis
of the act of Judgment. A proposition, they would have
said, is but the expression in words of a Judgment. The
thing expressed, not the mere verbal expression, is the im-
portant matter. When the mind assents to a proposition,
it judges. Let us find out what the mind does when it
judges, and we shall know what propositions mean, and not
otherwise.

Conformably to these views, almost all the writers on
Logic in the last two centuries, whether English, German, or
French, have made their theory of Propositions, from one end
to the other, a theory of Judgments. They considered a
Proposition, or a Judgment, for they used the two words indis-
criminately, to consist in affirming or denying one idea of
another. To judge, was to put two ideas together, or to bring
one idea under another, or to compare two ideas, or to
perceive the agreement or disagreement between two ideas :

IMPORT OF PROPOSITIONS. 97

and the whole doctrine of Propositions, together with the
theory of Reasoning, (always necessarily founded on the theory
of Propositions,) was stated as if Ideas, or Conceptions, or
whatever other term the writer preferred as a name for mental
representations generally, constituted essentially the subject
matter and substance of those operations.

It is, of course, true, that in any case of judgment, as for
instance when we judge that gold is yellow, a process takes
place in our minds, of which some one or other of these theories
is a partially correct account. We must have the idea of gold
and the idea of yellow, and these two ideas must be brought
together in our mind. But in the first place, it is evident that
this is only a part of what takes place ; for we may put two
ideas together without any act of belief; as when we merely
imagine something, such as a golden mountain ; or when we
actually disbelieve : for in order even to disbelieve that
Mahomet was an apostle of God, we must put the idea of
Mahomet and that of an apostle of God together. To determine
what it is that happens in the case of assent or dissent besides
putting two ideas together, is one of the most intricate of
metaphysical problems. But whatever the solution may be,
we may venture to assert that it can have nothing whatever
to do with the import of propositions ; for this reason, that
propositions (except sometimes when the mind itself is the
subject treated of) are not assertions respecting our ideas of
things, but assertions respecting the things themselves. In
order to believe that gold is yellow, I must, indeed, have the
idea of gold, and the idea of yellow, and something having re-
ference to those ideas must take place in my mind ; but my
belief has not reference to the ideas, it has reference to the
things. What I believe, is a fact relating to the outward
thing, gold, and to the impression made by that outward thing
upon the human organs ; not a fact relating to my conception
of gold, which would be a fact in my mental history, not a
fact of external nature. It is true, that in order to believe
this fact in external nature, another fact must take place in
my mind, a process must be performed upon my ideas ; but
so it must in everything else that I do. I cannot dig the

VOL. i. 7

98 NAMES AND PROPOSITIONS.

ground unless I have the idea of the ground, and of a spade,
and of all the other things I am operating upon, and unless I
put those ideas together.* But it would be a very ridiculous
description of digging the ground to say that it is putting
one idea into another. Digging is an operation which is
performed upon the things themselves, though it cannot he
performed unless I have in my mind the ideas of them. And
in like manner, believing is an act which has for its subject
the facts themselves, though a previous mental conception
of the facts is an indispensable condition. When I say that
fire causes heat, do I mean that my idea of fire causes my
idea of heat ? No : I mean that the natural phenomenon,
fire, causes the natural phenomenon, heat. When I mean
to assert anything respecting the ideas, I give them their
proper name, I call them ideas : as when I say, that a child's
idea of a battle is unlike the reality, or that the ideas enter-
tained of the Deity have a great effect on the characters of
mankind.

The notion that what is of primary importance to the
logician in a proposition, is the relation between the two ideas
corresponding to the subject and predicate, (instead of the
relation between the two phenomena which they respectively
express,) seems to me one of the most fatal errors ever intro-
duced into the philosophy of Logic; and the principal cause
why the theory of the science has made such inconsiderable
progress during the last two centuries. The treatises on Logic,
and on the branches of Mental Philosophy connected with
Logic, which have been produced since the intrusion of this
cardinal error, though sometimes written by men of extraor-
dinary abilities and attainments, almost always tacitly imply a
theory that the investigation of truth consists in contemplating

* Dr. Whewell (Philosophy of Discovery, p. 242) questions tins statement,
and asks, "Are we to say that a mole cannot dig the ground, except he has an
idea of the ground, and of the snout and paws with which he digs it ?" I do
not know what passes in a mole's mind, nor what amount of mental apprehen-
sion may or may not accompany his instinctive actions. But a human being
does not use a spade by instinct ; and he certainly could not use it unless he
had knowledge of a spade, and of the earth •which he uses it upon.

IMPORT OF PROPOSITIONS. 99

and handling our ideas, or conceptions of things, instead of
the things themselves: a doctrine tantamount to the assertion,
that the only mode of acquiring knowledge of nature is to
study it at second hand, as represented in our own minds.
Meanwhile, inquiries into every kind of natural phenomena
were incessantly establishing great and fruitful truths on most
important subjects, by processes upon which these views of the
nature of Judgment and Reasoning threw no light, and in
which they afforded no assistance whatever. No wonder that
those who knew by practical experience how truths are
arrived at, should deem a science futile, which consisted chiefly
of such speculations. What has been done for the advance-
ment of Logic since these doctrines came into vogue, has
been done not by professed logicians, but by discoverers in
the other sciences ; in whose methods of investigation many
principles of logic, not previously thought of, have suc-
cessively come forth into light, but who have generally com-
mitted the error of supposing that nothing whatever was known
of the art of philosophizing by the old logicians, because
their modern interpreters have written to so little purpose
respecting it.

We have to inquire, then, on the present occasion, not into
Judgment, but judgments; not into the act of believing, but
into the thing believed. What is the immediate object of
belief in a Proposition ? What is the matter of fact signified
by it ? What is it to which, when I assert the proposition, I
give my assent, and call upon others to give theirs ? What is
that which is expressed by the form of discourse called a Pro-
position, and the conformity of which to fact constitutes the
truth of the proposition ?

§ 2. One of the clearest and most consecutive thinkers
whom this country or the world has produced, I mean Hobbes,
has given the following answer to this question. In every
proposition (says he) what is signified is, the belief of the
speaker that the predicate is a name of the same thing of which
the subject is a name ; and if it really is so, the proposition is
true. Thus the proposition, All men are living beings (he

7—2

100

NAMES AND PROPOSITIONS.

would say) is true, because living being is a name of everything
of which man is a name. All men are six feet high, is not
true, because six feet high is not a name of everything (though
it is of some things) of which man is a name.

What is stated in this theory as the definition of a true
proposition, must be allowed to be a property which all true
propositions possess. The subject and predicate being both
of them names of things, if they were names of quite different
things the one name could not, consistently with its significa-
tion, be predicated of the other. If it be true that some men
are copper- coloured, it must be true — and the proposition does
really assert — that among the individuals denoted by the name
man, there are some who are also among those denoted by the
name copper-coloured. If it be true that all oxen ruminate, it
must be true that all the individuals denoted by the name ox
are also among those denoted by the name ruminating ; and
whoever asserts that all oxen ruminate, undoubtedly does
assert that this relation subsists between the two names.

The assertion, therefore, which, according to Hobbes, is
the only one made in any proposition, really is made in every
proposition : and his analysis has consequently one of the re-
quisites for being the true one. We may go a step farther ; it
is the only analysis that is rigorously true of all propositions
without exception. What he gives as the meaning of propo-
sitions, is part of the meaning of all propositions, and the
whole meaning of some. This, however, only shows what an
extremely minute fragment of meaning it is quite possible to
include within the logical formula of a proposition. It does
not show that no proposition means more. To warrant us in
putting together two words with a copula between them, it is
really enough that the thing or things denoted by one of the
names should be capable, without violation of usage, of being
called by the other name also. If, then, this be all the mean-
ing necessarily implied in the form of discourse called a Pro-
position, why do I object to it as the scientific definition of
what a proposition means ? Because, though the mere collo-
cation which makes the proposition a proposition, conveys no
more than this scanty amount of meaning, that same collo-

IMPORT OP PROPOSITIONS. 101

cation combined with other circumstances, that form combined
with other matter, does convey more, and the proposition in
those other circumstances does assert more, than merely that
relation between the two names.

The only propositions of which Hobbes' principle is a suffi-
cient account, are that limited and unimportant class in which
both the predicate and the subject are proper names. For, as
has already been remarked, proper names have strictly no
meaning; they are mere marks for individual objects: and
when a proper name is predicated of another proper name, all
the signification conveyed is, that both the names are marks
for the same object. But this is precisely what Hobbes pro-
duces as a theory of predication in general. His doctrine is
a full explanation of such predications as these : Hyde was
Clarendon, or, Tully is Cicero. It exhausts the meaning of
those propositions. But it is a sadly inadequate theory of
any others. That it should ever have been thought of as such,
can be accounted for only by the fact, that Hobbes, in common
with the other Nominalists, bestowed little or no attention
upon the connotation of words; and sought for their meaning
exclusively in what they denote : as if all names had been
(what none but proper names really are) marks put upon indi-
viduals ; and as if there were no difference between a proper
and a general name, except that the first denotes only one
individual, and the last a greater number.

It has been seen, however, that the meaning of all names,
except proper names and that portion of the class of abstract
names which are not connotative, resides in the connotation.
When, therefore, we are analysing the meaning of any pro-
position in which the predicate and the subject, or either
of them, are connotative names, it is to the connotation of
those terms that we must exclusively look, and not to what
they denote, or in the language of Hobbes (language so far
correct) are names of.

In asserting that the truth of a proposition depends on the
conformity of import between its terms, as, for instance, that
the proposition, Socrates is wise, is a true proposition, because
Socrates and wise are names applicable to, or, as he expresses

102 NAMES AND PROPOSITIONS.

it, names of, the same person ; it is very remarkable that so
powerful a thinker should not have asked himself the ques-
tion, But how came they to be names of the same person ?
Surely not because such was the intention of those who in-
vented the words. When mankind fixed the meaning of the
word wise, they were not thinking of Socrates, nor, when his
parents gave him the name of Socrates, were they thinking of
wisdom. The names happen to fit the same person because
of a certain fact, which fact was not known, nor in being,
when the names were invented. If we want to know what
the fact is, we shall find the clue to it in the connotation of
the names.

A bird or a stone, a man, or a wise man, means simply, an
object having such and such attributes. The real meaning of the
word man, is those attributes, and not Smith, Brown, and the
remainder of the individuals. The word mortal, in like manner
connotes a certain attribute or attributes ; and when we say,
All men are mortal, the meaning of the proposition is, that all
beings which possess the one set of attributes, possess also the
other. If, in our experience, the attributes connoted by man
are always accompanied by the attribute connoted by mortal, it
will follow as a consequence, that the class man will be wholly
included in the class mortal, and that mortal will be a name
of all things of which man is a name : but why ? Those
objects are brought under the name, by possessing the attri-
butes connoted by it : but their possession of the attributes is
the real condition on which the truth of the proposition
depends ; not ^their being called by the name. Connotative
names do not precede, but follow, the attributes which they
connote. If one attribute happens to be always found in con-
junction with another attribute, the concrete names which
answer to those attributes will of course be predicable of the
same subjects, and may be said, in Hobbes' language, (in the
propriety of which on this occasion I fully concur,) to be two
names for the same things. But the possibility of a concur-
rent application of the two names, is a mere consequence of
the conjunction between the two attributes, and was, in most
cases, never thought of when the names were introduced and

IMPORT OF PROPOSITIONS. 103

their signification fixed. That the diamond is combustible,
was a proposition certainly not dreamt of when the words
Diamond and Combustible first received their meaning ; and
could not have been discovered by the most ingenious and
refined analysis of the signification of those words. It was
found out by a very different process, namely, by exerting the
senses, and learning from them, that the attribute of com-
bustibility existed in the diamonds upon which the experi-
ment was tried ; the number or character of the experiments
being such, that what was true of those individuals might be
concluded to be true of all substances " called by the name,"
that is, of all substances possessing the attributes which the
name connotes. The assertion, therefore, when analysed, is,
that wherever we find certain attributes, there will be found a
certain other attribute : which is not a question of the signi-
fication of names, but of laws of nature ; the order existing
among phenomena.

§ 3. Although Hobbes' theory of Predication has not, in
the terms in which he stated it, met with a very favourable
reception from subsequent thinkers, a theory virtually iden-
tical with it, and not by any means so perspicuously expressed,
may almost be said to have taken the rank of an established
opinion. The most generally received notion of Predication
decidedly is that it consists in referring something to a class,
i.e., either placing an individual under a class, or placing one
class under another class. Thus, the proposition, Man is
mortal, asserts, according to this view of it, that the class
man is included in the class mortal. " Plato is a philosopher,"
asserts that the individual Plato is one of those who compose
the class philosopher. If the proposition is negative, then
instead of placing something in a class, it is said to exclude
something from a class. Thus, if the following be the propo-
sition, The elephant is not carnivorous; what is asserted
(according to this theory) is, that the elephant is excluded
from the class carnivorous, or is not numbered among the
things comprising that class. There is no real difference,
except in language, between this theory of Predication and

104 NAMES AND PROPOSITIONS.

the theory of Hobbes. For a class is absolutely nothing but
an indefinite number of individuals denoted by a general
name. The name given to them in common, is what makes
them a class. To refer anything to a class, therefore, is to
look upon it as one of the things which are to be called by
that common name. To exclude it from a class, is to say that
the common name is not applicable to it.

How widely these views of predication have prevailed, is
evident from this, that they are the basis of the celebrated
dictum de omni et nullo. When the syllogism is resolved, by
all who treat of it, into an inference that what is true of a
class is true of all things whatever that belong to the class;
and when this is laid down by almost all professed logicians
as the ultimate principle to which all reasoning owes its
validity; it is clear that in the general estimation of logi-
cians, the propositions of which reasonings are composed
can be the expression of nothing but the process of dividing
things into classes, and referring everything to its proper class.

This theory appears to me a signal example of a logical
error very often committed in logic, that of vaTtpov -n-portpov,
or explaining a thing by something which presupposes it.
When I say that snow is white, I may and ought to be think-
ing of snow as a class, because I am asserting a proposition
as true of all snow : but I am certainly not thinking of white
objects as a class; I am thinking of no white object whatever
except snow, but only of that, and of the sensation of white
which it gives me. When, indeed, I have judged, or assented
to the propositions, that snow is white, and that several other
things are also white, I gradually begin to think of white
objects as a class, including snow and those other things. But
this is a conception which followed, not preceded, those judg-
ments, and therefore cannot be given as an explanation of
them. Instead of explaining the effect by the cause, this
doctrine explains the cause by the effect, and is, I conceive,
founded on a latent misconception of the nature of classifi-
cation.

There is a sort of language very generally prevalent in these
discussions, which seems to suppose that classification is an

IMPORT OP PROPOSITIONS. 105

arrangement and grouping of definite and known individuals :
that when names were imposed, mankind took into considera-
tion all the individual objects in the universe, distributed them
into parcels or lists, and gave to the objects of each list a
common name, repeating this operation toties quoties until
they had invented all the general names of which language
consists; which having been once done, if a question subse-
quently arises whether a certain general name can be truly
predicated of a certain particular object, we have only (as it
were) to read the roll of the objects upon which that name was
conferred, and see whether the object about which the question
arises is to be found among them. The framers of language
(it would seem to be supposed) have predetermined all the
objects that are to compose each class, and we have only to
refer to the record of an antecedent decision.

So absurd a doctrine will be owned by nobody when thus
nakedly stated ; but if the commonly received explanations of
classification and naming do not imply this theory, it requires
to be shown how they admit of being reconciled with any other.

General names are not marks put upon definite objects;
classes are not made by drawing a line round a given number
of assignable individuals. The objects which compose any
given class are perpetually fluctuating. We may frame a class
without knowing the individuals, or even any of the indivi-
duals, of which it may be composed; we may do so while be-
lieving that no such individuals exist. If by the meaning of
a general name are to be understood the things which it is the
name of, no general name, except by accident, has a fixed
meaning at all, or ever long retains the same meaning. The
only mode in which any general name has a definite meaning,
is by being a name of an indefinite variety of things; namely,
of all things, known or unknown, past, present, or future,
which possess certain definite attributes. When, by studying
not the meaning of words, but the phenomena of nature, we
discover that these attributes are possessed by some object not
previously known to possess them, (as when chemists found
that the diamond was combustible), we include this new object
in the class ; but it did not already belong to the class. We

106

NAMES AND PROPOSITIONS,

place the individual in the class because the proposition is
true; the proposition is not true hecause the ohject is placed
in the class.*

It will appear hereafter, in treating of reasoning, how much
the theory of that intellectual process has heen vitiated by the
influence of these erroneous notions, and by the habit which
they exemplify of assimilating all the operations of the human
understanding which have truth for their object, to processes
of mere classification and naming. Unfortunately, the minds
which have been entangled in this net are precisely those which
have escaped the other cardinal error commented upon in the
beginning of the present chapter. Since the revolution which
dislodged Aristotle from the schools, logicians may almost be
divided into those who have looked upon reasoning as essen-
tially an affair of Ideas, and those who have looked upon it as
essentially an affair of Names.

Although, however, Hobbes' theory of Predication, accord-
ing to the well-known remark of Leibnitz, and the avowal of
Hobbes himself,f renders truth and falsity completely arbi-
trary, with no standard but the will of men, it must not be
concluded that either Hobbes, or any of the other thinkers
who have in the main agreed with him, did in fact consider

* Professor Bain remarks, in qualification of the statement in the text
(Logic, i. 50), that the word Class has two meanings; "the class definite, and
the class indefinite. The class definite is an enumeration of actual indivi-
duals, as the Peers of the Realm, the oceans of the globe, the known planets.
. . . The class indefinite is unenumerated. Such classes are stars, planets,
gold-bearing rocks, men, poets, virtuous. ... In this last acceptation of the
word, class name and general name are identical. The class name denotes an
indefinite number of individuals, and connotes the points of community or
likeness."

The theory controverted in the text, tacitly supposes all classes to be defi-
nite. I have assumed them to be indefinite ; because, for the purposes of
Logic, definite classes, as such, are almost useless ; though often serviceable as
moans of abridged expression. (Vide infra, book iii. ch. ii.)

f "From hence also this may be deduced, that the first truths were arbi-
trarily made by those that first of all imposed names upon things, or received
them from the imposition of others. For it is true (for example) that man is a
living creature, but it is for this reason, that it pleased men to impose both these
names on the same thing." — Computation or Logic, ch. iii. sect. 8.

IMPORT OF PROPOSITIONS. 107

the distinction between truth and error as less real, or attached
less importance to it, than other people. To suppose that they
did so would argue total unacquaintance with their o.ther spe-
culations. But this shows how little hold their doctrine pos-
sessed over their own minds. No person, at bottom, ever ima-
gined that there was nothing more in truth than propriety of
expression ; than using language in conformity to a previous
convention. When the inquiry was brought down from gene-
rals to a particular case, it has always been acknowledged that
there is a distinction between verbal and real questions ; that
some false propositions are uttered from ignorance of the
meaning of words, but that in others the source of the error is
a misapprehension of things ; that a person who has not the
use of language at all may form propositions mentally, and
that they may be untrue, that is, he may believe as matters of
fact what are not really so. This last admission cannot be
made in stronger terms than it is by Hobbes himself,* though
he will not allow such erroneous belief to be called falsity, but
only error. And he has himself laid down, in other places,
doctrines in which the true theory of predication is by implica-
tion contained. He distinctly says that general names are
given to things on account of their attributes, and that ab-
stract names are the names of those attributes. " Abstract is
that which in any subject denotes the cause of the concrete
name. . . . And these causes of names are the same with the
causes of our conceptions, namely, some power of action, or
affection, of the thing conceived, which some call the manner
by which anything works upon our senses, but by most men

* " Men are subject to err not only in affirming and denying, but also in
perception, and in silent cogitation. . . . Tacit errors, or the errors of sense
and cogitation, are made by passing from one imagination to the imagination of
another different thing ; or by feigning that to be past, or future, which never
was, nor ever shall be ; as when by seeing the image of the sun in water, we
imagine the sun itself to be there ; or by seeing swords, that there has been,
or shall be, fighting, because it uses to be so for the most part ; or when from
promises we feign the mind of the promiser to be such and such ; or, lastly,
when from any sign we vainly imagine something to be signified which is not.
And errors of this sort are common to all things that have sense." — Computa-
tion or Logic, ch. v. sect. 1.

108 NAMES AND PROPOSITIONS.

they are called accidents."* It is strange that having gone
so far. he should not have gone one step farther, and seen that
what he calls the cause of the concrete name, is in reality the
meaning of it; and that when we predicate of any subject a
name which is given because of an attribute (or, as he calls it,
an accident), our object is not to affirm the name, but, by
means of the name, to affirm the attribute.

§ 4. Let the predicate be, as we have said, a connotative
term ; and to take the simplest case first, let the subject be a
proper name : " The summit of Chimborazo is white." The
word white connotes an attribute which is possessed by the
individual object designated by the words " summit of Chim-
borazo ;" which attribute consists in the physical fact, of its
exciting in human beings the sensation which we call a sensa-
tion of white. It will be admitted that, by asserting the pro-
position, we wish to communicate information of that physical
fact, and are not thinking of the names, except as the neces-
sary means of making that communication. The meaning of
the proposition, therefore, is, that the individual thing denoted
by the subject, has the attributes connoted by the predicate.

If we now suppose the subject also to be a connotative
name, the meaning expressed by the proposition has advanced
a step farther in complication. Let us first suppose the pro-
position to be universal, as well as affirmative: "All men are
mortal." In this case, as in the last, what the proposition
asserts (or expresses a belief of) is, of course, that the objects
denoted by the subject (man) possess the attributes connoted
by the predicate (mortal). But the characteristic of this case
is, that the objects are no longer individually designated. They
are pointed out only by some of their attributes : they are the
objects called men, that is, possessing the attributes connoted
by the name man ; and the only thing known of them may be
those attributes : indeed, as the proposition is general, and the
objects denoted by the subject are therefore indefinite in
number, most of them are not known individually at all. The

* Ch. iii. sect. 3.

IMPORT OF PROPOSITIONS.

assertion, therefore, is not, as before, that the attributes which
the predicate connotes are possessed by any given individual,
or by any number of individuals previously known as John,
Thomas, &c., but that those attributes are possessed by each
and every individual possessing certain other attributes ; that
whatever has the attributes connoted by the subject, has also
those connoted by the predicate ; that the latter set of attri-
butes constantly accompany the former set. Whatever has the
attributes of man has the attribute of mortality ; mortality
constantly accompanies the attributes of man.*

If it be remembered that every attribute is grounded on
some fact or phenomenon, either of outward sense or of inward
consciousness, and that to possess an attribute is another
phrase for being the cause of, or forming part of, the fact or
phenomenon upon which the attribute is grounded ; we may
add one more step to complete the analysis. The proposition
which asserts that one attribute always accompanies another
attribute, really asserts thereby no other thing than this, that
one phenomenon always accompanies another phenomenon ;
insomuch that where we find the latter, we have assurance of
the existence of the former. Thus, in the proposition, All men
are mortal, the word man connotes the attributes which we
ascribe to a certain kind of living creatures, on the ground of
certain phenomena which they exhibit, and which are partly

* To the preceding statement it has been objected, that " we naturally
construe the subject of a proposition in its extension, and the predicate (which
therefore may be an adjective) in its intension, (connotation) : and that conse-
sequently coexistence of attributes does not, any more than the opposite theory
of equation of groups, correspond with the living processes of thought and
language." I acknowledge the distinction here drawn, which, indeed, I had
myself laid down and exemplified a few pages back (p. 104). But though it is
true that we naturally " construe the subject of a proposition in its extension,"
this extension, or in other words, the extent of the class denoted by the name,
is not apprehended or indicated directly. It is both apprehended and indi-
cated solely through the attributes. In the "living processes of thought and
language" the extension, though in this case really thought of (which in the
case of the predicate it is not), is thought of only through the medium of what
my acute and courteous critic terms the "intension."

For further illustrations of this subject, see Examination of Sir William
Hamilton's Philosophy, ch. xxii.

110 NAMES AND PROPOSITIONS.

physical phenomena, namely the impressions made on our
senses by their bodily form and structure, and partly mental
phenomena, namely the sentient and intellectual life which
they have of their own. All this is understood when we utter
the word man, by any one to whom the meaning of the word
is known. Now, when we say, Man is mortal, we mean that
wherever these various physical and mental phenomena are all
found, there we have assurance that the other physical and
mental, phenomenon, called death, will not fail to take place.
The proposition does not affirm ivhen ; for the connotation of
the word mortal goes no farther than to the occurrence of the
phenomenon at some time or other, leaving the particular time
undecided.

§ 5. We have already proceeded far enough, not only to
demonstrate the error of Hohbes, but to ascertain the real
import of by far the most numerous class of propositions.
The object of belief in a proposition, when it asserts anything
more than the meaning of words, is generally, as in the cases
which we have examined, either the co- existence or the se-
quence of two phenomena. At the very commencement of our
inquiry, we found that every act of belief implied two Things :
we have now ascertained what, in the most frequent case, these
two things are, namely two Phenomena, in other words, two
states of consciousness; and what it is which the proposition
affirms (or denies) to subsist between them, namely either suc-
cession or co-existence. And this case includes innumerable
instances which no one, previous to reflection, would think of
referring to it. Take the following example : A generous
person is worthy of honour. Who would expect to recognise
here a case of co-existence between phenomena ? But so it is.
The attribute which causes a person to be termed generous, is
ascribed to him on the ground of states of his mind, and par-
ticulars of his conduct : both are phenomena : the former are
facts of internal consciousness ; the latter, so far as distinct
from the former, are physical facts, or perceptions of the senses.
Worthy of honour admits of a similar analysis. Honour, as
here used, means a state of approving and admiring emotion,

IMPORT OF PROPOSITIONS. Ill

followed on occasion by corresponding outward acts. " Worthy
of honour" connotes all this, together with our approval of the
act of showing honour. All these are phenomena; states of
internal consciousness, accompanied or followed by physical
facts. When we say, A generous person is worthy of honour,
we affirm co-existence between the two complicated pheno-
mena connoted by the two terms respectively. We affirm,
that wherever and whenever the inward feelings and outward
facts implied in the word generosity have place, then and
there the existence and manifestation of an inward feeling,
honour, would be followed in our minds by another inward
feeling, approval.

After the analysis, in a former chapter, of the import of
names, many examples are not needed to illustrate the import
of propositions. When there is any obscurity, or difficulty,
it does not lie in the meaning of the proposition, but in the
meaning of the names which compose it; in the extremely
complicated connotation of many words ; the immense multi-
tude and prolonged series 'of facts which often constitute the
phenomenon connoted by a name. Bat where it is seen what
the phenomenon is, there is seldom any difficulty in seeing
that the assertion conveyed by the proposition is, the co-exis-
tence of one such phenomenon with another; or the succession
of one such phenomenon to another : so that where the one is
found, we may calculate on finding the other, though perhaps
not conversely.

This, however, though the most common, is not the only
meaning which propositions are ever intended to convey. In
the first place, sequences and co-existences are not only
asserted respecting Phenomena; we make propositions also
respecting those hidden causes of phenomena, which are
named substances and attributes. A substance, however,
being to us nothing but either that which causes, or that
which is conscious of, phenomena ; and the same being true,
mutatis mutandis, of attributes ; no assertion can be made, at
least with a meaning, concerning these unknown and un-
knowable entities, except in virtue of the Phenomena by
•which alone they manifest themselves to our faculties. When

112 NAMES AND PROPOSITIONS.

we say, Socrates was cotemporary with the Peloponnesian war,
the foundation of this assertion, as of all assertions concern-
ing substances, is an assertion concerning the phenomena
winch they exhibit, — namely, that the series of facts by which
Socrates manifested himself to mankind, and the series of
mental states which constituted his sentient existence, went
on simultaneously with the series of facts known by the name
of the Peloponnesian war. Still, the proposition as commonly
understood does not assert that alone ; it asserts that the
Thing in itself, the noumenon Socrates, was existing, and
doing or experiencing those various facts during the same
time. Co-existence and sequence, therefore, may be affirmed
or denied not only between phenomena, but between noumena,
or between a noumenon and phenomena. And both of nou-
mena and of phenomena we may affirm simple existence. But
what is a noumenon ? An unknown cause. In affirming,
therefore, the existence of a noumenon, we affirm causation.
Here, therefore, are two additional kinds of fact, capable of
being asserted in a proposition. Besides the propositions
which assert Sequence or Coexistence, there are some which
assert simple Existence ;* and others assert Causation, which,

* Professor Bain, in his Logic (i. 256), excludes Existence from the list,
considering it as a mere name. All propositions, he says, which predicate
mere existence "are more or less abbreviated, or elliptical: when fully ex-
pressed they fall under either coexistence or succession. When we say there
exists a conspiracy for a particular purpose, we mean that at the present time
a body of men have formed themselves into a society for a particular object ;
which is a complex affirmation, resolvable into propositions of coexistence and
succession (as causation). The assertion that the dodo does not exist, points to
the fact that this animal, once known in a certain place, has disappeared or
become extinct ; is no longer associated with the locality : all which may be
better stated without the use of the verb ' exist.' There is a debated ques-
tion— Does an ether exist? but the concrete form would be this — 'Are heat
and light and other radiant influences propagated by an ethereal medium dif-
fused in space ;' which is a proposition of causation. In like manner the ques-
tion of the Existence of a Deity cannot be discussed in that form. It is pro-
perly a question as to the First Cause of the Universe, and as to the continued
exertion of that Cause in providential superintendence." (i. 407.)

Mr. Bain thinks it "fictitious and unmeaning language" to carry up the
classification of Nature to one summum genus, Being, or that which Exists ;
since nothing can be perceived or apprehended but by way of contrast with

IMPORT OF PROPOSITIONS. 113

subject to the explanations which will follow in the Third
Book, must be considered provisionally as a distinct and
peculiar kind of assertion.

§ 6. To these four kinds of matter-of fact or assertion,
must be added a fifth, Resemblance. This was a species of
attribute which we found it impossible to analyse ; for which
nofimdamentum, distinct from the objects themselves, could
be assigned. Besides propositions which assert a sequence or
coexistence between two phenomena, there are therefore also
propositions which assert resemblance between them ; as, This
colour is like that colour ; — The heat of to-day is equal to the
heat of yesterday. It is true that such an assertion might
with some plausibility be brought within the description of

something else (of which important truth, under the name of Law of Rela-
tivity, he has been in our time the principal expounder and champion), and we
have no other class to oppose to Being, or fact to contrast with Existence.

I accept fully Mr. Bain's Law of Relativity, but I do not understand by it
that to enable us to apprehend or be conscious of any fact, it is necessary that
we should contrast it with some other positive fact. The antithesis necessary
to consciousness need not, I conceive, be an antithesis between two positives ;
it may be between one positive and its negative. Hobbes was undoubtedly
right when he said that a single sensation indefinitely prolonged would cease
to be felt at all ; but simple intermission, without other change, would restore
it to consciousness. In order to be conscious of heat, it is not necessary that we
should pass to it from cold ; it suffices that we should pass to it from a state of
no sensation, or from a sensation of some other kind. The relative opposite of
Being, considered as a summum genus, is Non-entity, or Nothing ; and we
have, now and then, occasion to consider and discuss things merely in contrast
with Non-entity.

I grant that the decision of questions of Existence usually if not always de-
pends on a previous question of either Causation or Coexistence. But Existence
is nevertheless a different thing from Causation or Coexistence, and can be
predicated apart from them. The meaning of the abstract name Existence,
and the connotation of the concrete name Being, consist, like the meaning of
all other names, in sensations or states of consciousness : their peculiarity is
that to exist, is to excite, or be capable of exciting, any sensations or states of
consciousness : uo matter what, but it is indispensable that there should be
some. It was from overlooking this that Hegel, finding that Being is an ab-
straction reached by thinking away all particular attributes, arrived at the self-
contradictory proposition on which he founded all his philosophy, that Being is
the same as Nothing. It is really the name of Something, taken in the most
comprehensive sense of the word.

VOL. I. 8

114

NAMES AND PROPOSITIONS.

an affirmation of sequence, by considering it as an assertion
that the simultaneous contemplation of the two colours is
followed by a specific feeling termed the feeling of resemblance.
But there would be nothing gained by encumbering ourselves,
especially in this place, with a generalization which may be
looked upon as strained. Logic does not undertake to analyse
mental facts into their ultimate elements. Resemblance be-
tween two phenomena is more intelligible in itself than any
explanation could make it, and under any classification must
remain specifically distinct from the ordinary cases of sequence
and co-existence.

It is sometimes said, that all propositions whatever, of
which the predicate is a general name, do, in point of fact,
affirm or deny resemblance. All such propositions affirm that
a thing belongs to a class ; but things being classed together
according to their resemblance, everything is of course classed
with the things which it is supposed to resemble most ; and
thence, it may be said, when we affirm that Gold is a metal, or
that Socrates is a man, the affirmation intended is, that gold
resembles other metals, and Socrates other men, more nearly
than they resemble the objects contained in any other of the
classes co-ordinate with these.

There is some slight degree of foundation for this remark,
but no more than a slight degree. The arrangement of things
into classes, such as the class metal, or the class man, is
grounded indeed on a resemblance among the things which
are placed in the same class, but not on a mere general resem-
blance: the resemblance it is grounded on consists in the
possession by all those things, of certain common peculiari-
ties ; and those peculiarities it is which the terms connote, and
which the propositions consequently assert; not the resem-
blance. For though when I say, Gold is a metal, 1 say by im-
plication that if there be any other metals it must resemble
them, yet if there were no other metals I might still assert the
proposition with the same meaning as at present, namely, that
gold has the various properties implied in the word metal ;
just as it might be said, Christians are men, even if there
were no men who were not Christians. Propositions, there-

IMPORT OF PROPOSITIONS. 115

fore, in which objects are referred to a class because they pos-
sess the attributes constituting the class, are so far from assert-
ing nothing but resemblance, that they do not, properly speak-
ing, assert resemblance at all.

But we remarked some time ago (and the reasons of the
remark will be more fully entered into in a subsequent Book*)
that there is sometimes a convenience in extending the
boundaries of a class so as to include things which possess
in a very inferior degree, if in any, some of the characteristic
properties of the class, — provided they resemble that class
more than any other, insomuch that the general propositions
which are true of the class, will be nearer to being true of
those things than any other equally general propositions.
For instance, there are substances called metals which have
very few of the properties by which metals are commonly
recognised ; and almost every great family of plants or animals
has a few anomalous genera or species on its borders, which
are admitted into it by a sort of courtesy, and concerning
which it has been matter of discussion to what family they
properly belonged. Now when the class-name is predicated
of any object of this description, we do, by so predicating it,
affirm resemblance and nothing more. And in order to be
scrupulously correct it ought to be said, that in every case in
which we predicate a general name, we affirm, not absolutely
that the object possesses the properties designated by the
name, but that it either possesses those properties, or if it does
not, at any rate resembles the things which do so, more than
it -resembles any other things. In most cases, however, it is
unnecessary to suppose any such alternative, the latter of the
two grounds being very seldom that on which the assertion is
made : and when it is, there is generally some slight diffe-
rence in the form of the expression, as, This species (or genus)
is considered, or may l>e ranked, as belonging to such and such
a family : we should hardly say positively that it does belong
to it, unless it possessed unequivocally the properties of which
the class-name is scientifically significant.

* Book iv. ch. vii.

8—2

116 NAMES AND PROPOSITIONS.

There is still another exceptional case, in which, though
the predicate is the name of a class, yet in predicating it we
affirm nothing but resemblance, the class being founded not
on resemblance in any given particular, but on general unan-
alysable resemblance. The classes in question are those into
•which our simple sensations, or other simple feelings, are
divided. Sensations of white, for instance, are classed toge-
ther, not because we can take them to pieces, and say they
are alike in this, and not alike in that, but because we feel
them to be alike altogether, though in different degrees.
When, therefore, I say, The colour I saw yesterday was a
white colour, or, The sensation I feel is one of tightness, in
both cases the attribute I affirm of the colour or of the other
sensation is mere resemblance — simple likeness to sensations
which I have had before, and which have had those names
bestowed upon them. The names of feelings, like other con-
crete general names, are connotative ; but they connote a
mere resemblance. When predicated of any individual feeling,
the information they convey is that of its likeness to the other
feelings which we have been accustomed to call by the same
name. Thus much may suffice in illustration of the kind of
propositions in which the matter-of-fact asserted (or denied) is
simple Resemblance.

Existence, Coexistence, Sequence, Causation, Resemblance:
one or other of these is asserted (or denied) in every proposi-
tion which is not merely verbal. This five-fold division is an
exhaustive classification of matters- of- fact; of all things that
can be believed, or tendered for belief; of all questions that
can be propounded, and all answers that can be returned to
them.

Professor Bain* distinguishes two kinds of Propositions of
Coexistence. " In the one kind, account is taken of Place ; they
may be described as propositions of Order in Place." In the
other kind, the coexistence which is predicated is termed by Mr.
Bain Co-inherence of Attributes. " This is a distinct variety
of Propositions of Coexistence. Instead of an arrangement

* Logic, i. 103-105.

IMPORT OF PROPOSITIONS. 117

in place with numerical intervals, we have the concurrence of
two or more attributes or powers in the same part or locality.
A mass of gold contains, in every atom, the concurring attri-
butes that mark the substance — weight, hardness, colour, lustre,
incorrosibility, &c. An animal, besides having parts situated
in place, has co-inhering functions in the same parts, exerted
by the very same masses and molecules of its substance. . . .
The Mind, which affords no Propositions of Order in Place,
has co-inhering functions. We affirm mind to contain Feeling,
Will, and Thought, not in local separation, but in commingling
exercise. The concurring properties of minerals, of plants, and
of the bodily and the mental structure of animals, are united
in affirmations of co-inherence."

The distinction is real and important But, as has been
seen, an Attribute, when it is anything but a simple unanalysable
Eesemblance between the subject and some other things, con-
sists in causing impressions of some sort on consciousness.
Consequently, the co-inherence of two attributes is but the co*
existence of the two states of consciousness implied in their
meaning: with the difference, however, that this coexistence
is sometimes potential only, the attribute being considered as
in existence though the fact on which it is grounded may not
be actually, but only potentially present. Snow, for instance,
is, with great convenience, said to be white even in a state of
total darkness, because, though we are not now conscious
of the colour, we shall be conscious of it as soon as morn-
ing breaks. Coinhereuce of attributes is therefore still a
case, though a complex one, of coexistence of states of con-
sciousness : a totally different thing, however, from Order in
Place. Being a part of simultaneity, it belongs not to Place
but to Time.

We may therefore (and we shall sometimes find it a con-
venience) instead of Coexistence and Sequence, say, for greater
particularity, Order in Place and Order in Time : Order in
Place being a specific mode of coexistence, not necessary to be
more particularly analysed here ; while the mere fact of co-
existence, whether between actual sensations, or between the
potentialities of causing them, known by the name of attri-

113 NAMES AND PROPOSITIONS.

butes, may be classed, together with Sequence, under the head
of Order in Time.

§ 7. In the foregoing inquiry into the import of Propo-
sitions, we have thought it necessary to analyse directly those
alone, in which the terms of the proposition (or the predicate
at least) are concrete terms. But, in doing so, we have indi-
rectly analysed those in which the terms are abstract. The
distinction between an abstract term and its corresponding
concrete, does not turn upon any difference in what they are
appointed to signify; for the real signification of a concrete
general name is, as we have so often said, its connotation ;
and what the concrete term connotes, forms the entire mean-
ing of the abstract name. Since there is nothing in the
import of an abstract name which is not in the import of the
corresponding concrete, it is natural to suppose that neither
can there be anything in the import of a proposition of which
the terms are abstract, but what there is in some proposition
which can be framed of concrete terms.

And this presumption a closer examination will confirm.
An abstract name is the name of an attribute, or combination
of attributes. The corresponding concrete is a name given to
things, because of, and in order to express, their possessing
that attribute, or that combination of attributes. When,
therefore, we predicate of anything a concrete name, the
attribute is what we in reality predicate of it. But it has
now been shown that in all propositions of which the predi-
cate is a concrete name, what is really predicated is one of
five things : Existence, Coexistence, Causation, Sequence, or
Resemblance. An attribute, therefore, is necessarily either
an existence, a coexistence, a causation, a sequence, or a
resemblance. When a proposition consists of a subject and
predicate which are abstract terms, it consists of terms which
must necessarily signify one or other of these things. When
we predicate of anything an abstract name, we affirm of the
thing that it is one or other of these five things ; that it is a
case of Existence, or of Coexistence, or of Causation, or of
Sequence, or of Resemblance.

IMPORT OF PROPOSITIONS. 119

It is impossible to imagine any proposition expressed in
abstract terms, which cannot be transformed into a precisely
equivalent proposition in which the terms are concrete ;
namely, either the concrete names which connote the attri-
butes themselves, or the names of the fundamenta of those
attributes ; the facts or phenomena on which they are
grounded. To illustrate the latter case, let us take this
proposition, of which the subject only is an abstract name,
"Thoughtlessness is dangerous." Thoughtlessness is an
attribute, grounded on the facts which we call thoughtless
actions ; and the proposition is equivalent to this, Thoughtless
actions are dangerous. In the next example the predicate as
well as the subject are abstract names : " Whiteness is a
colour;" or "The colour of snow is a whiteness." These
attributes being grounded on sensations, the equivalent pro-
positions in the concrete would be, The sensation of white is
one of the sensations called those of colour, — The sensation of
sight, caused by looking at snow, is one of the sensations
called sensations of white. In these propositions, as we
have before seen, the matter-of-fact asserted is a Resem-
blance. In the following examples, the concrete terms are
those which directly correspond to the abstract names ; con-
noting the attribute which these denote. " Prudence is a
virtue :" this may be rendered, " All prudent persons, in so
far as prudent, are virtuous :" " Courage is deserving of
honour," thus, " All courageous persons are deserving of
honour in so far as they are courageous :" which is equiva-
lent to this — "All courageous persons deserve an addition
to the honour, or a diminution of the disgrace, which would
attach to them on other grounds."

In order to throw still further light upon the import
of propositions of which the terms are abstract, we will sub-
ject one of the examples given above to a minuter analysis.
The proposition we shall select is the following : — " Prudence
is a virtue." Let us substitute for the word virtue an equiva-
lent but more definite expression, such as " a mental quality
beneficial to society," or " a mental quality pleasing to God,"
or whatever else we adopt as the definition of virtue. AYhat

120 NAMES AXD PROPOSITION'S.

the proposition asserts is a sequence, accompanied with causa-
tion ; namely, that benefit to society, or that the approval of
God, is consequent on, and caused by, prudence. Here is a
sequence ; but between what ? We understand the consequent
of the sequence, but we have yet to analyse the antecedent.
Prudence is an attribute ; and, in connexion with it, two
things besides itself are to be considered ; prudent persons,
who are the subjects of the attribute, and prudential conduct,
which may be called the foundation of it. Now is either of
these the antecedent ? and, first, is it meant, that the approval
of God, or benefit to society, is attendant upon all prudent per-
sons ? No ; except in so far as they are prudent ; for prudent
persons who are scoundrels can seldom on the whole be bene-
ficial to society, nor can they be acceptable to a good being. Is
it upon prudential conduct, then, that divine approbation and
benefit to mankind are supposed to be invariably consequent ?
Neither is this the assertion meant, when it is said that pru-
dence is a virtue ; except with the same reservation as before,
and for the same reason, namely, that prudential conduct,
' although in so far as it is prudential it is beneficial to society,
may yet, by reason of some other of its qualities, be productive
of an injury outweighing the benefit, and deserve a displeasure
exceeding the approbation which would be due to the pru-
dence. Neither the substance, therefore, (viz. the person,) nor
the phenomenon, (the conduct,) is an antecedent on which the
other term of the sequence is universally consequent. But the
proposition, " Prudence is a virtue," is an universal proposi
tion. What is it, then, upon which the proposition affirms the
effects in question to be universally consequent ? Upon that
in the person, and in the conduct, which causes them to be
called prudent, and which is equally in them when the action,
though prudent, is wicked; namely, a correct foresight of
consequences, a just estimation of their importance to the
object in view, and repression of any unreflecting impulse at
variance with the deliberate purpose. These, which are states
of the person's mind, are the real antecedent in the sequence,
the real cause in the causation, asserted by the proposition.
But these are also the real ground, or foundation, of the attri-

IMPORT OF PROPOSITIONS. 121

bute Prudence ; since wherever these states of mind exist we
may predicate prudence, even before we know whether any
conduct has followed. And in this manner every assertion
respecting an attribute, may be transformed into an assertion
exactly equivalent respecting the fact or phenomenon which
is the ground of the attribute. And no case can be assigned,
where that which is predicated of the fact or phenomenon, does
not belong to one or other of the five species formerly enume-
rated : it is either simple Existence, or it is some Sequence,
Coexistence, Causation, or Kesemblance.

And as these five are the only things which can be affirmed,
so are they the only things which can be denied. " No horses
are web-footed " denies that the attributes of a horse ever co-
exist with web-feet. It is scarcely necessary to apply the same
analysis to Particular affirmations and negations. " Some
birds are web-footed," affirms that, with the attributes con-
noted by bird, the phenomenon web-feet is sometimes co-exis-
tent : " Some birds are not web-footed," asserts that there are
other instances in which this co-existence does not have place.
Any further explanation of a thing which, if the previous ex-
position has been assented to, is so obvious, may here be
spared.

CHAPTER VI.

OF PROPOSITION'S MERELY VERBAL.

§ 1. As a preparation for the inquiry which is the proper
object of Logic, namely, in what manner propositions are to
be proved, we have found it necessary to inquire what they
contain .which requires, or is susceptible of, proof ; or (which
is the same thing) what they assert. In the course of this
preliminary investigation into the import of Propositions, we
examined the opinion of the Conceptualists, that a proposition
is the expression of a relation between two ideas ; and the doc-
trine of the extreme Nominalists, that it is the expression of
an agreement or disagreement between the meanings of two
names. We decided that, as general theories, both of these
are erroneous ; and that, though propositions may be made
both respecting names and respecting ideas, neither the one
nor the other are the subject-matter of Propositions considered
generally. We then examined the different kinds of Proposi-
tions, and found that, with the exception of those which are
merely verbal, they assert five different kinds of matters of fact,
namely, Existence, Order in Place, Order in Time, Causation,
and Resemblance ; that in every proposition one of these five
is either affirmed, or denied, of some fact or phenomenon, or of
some object the unknown source of a fact or phenomenon.

In distinguishing, however, the different kinds of matters
of fact asserted in propositions, we reserved one class of pro-
positions, which do not relate to any matter of fact, in the
proper sense of the term, at all, but to the meaning of names.
Since names and their signification are entirely arbitrary, such
propositions are not, strictly speaking, susceptible of truth
or falsity, but only of conformity or disconformity to usage or
convention ; and all the proof they are capable of, is proof of
usage ; proof that the words have been employed by others in

VERBAL AND REAL PROPOSITIONS. 123

the acceptation in which the speaker or writer desires to use
them. These propositions occupy, however, a conspicuous
place in philosophy ; and their nature and characteristics are
of as much importance in logic, as those of any of the other
classes of propositions previously adverted to.

If all propositions respecting the signification of words
were as simple and unimportant as those which served us
for examples when examining Hobbes' theory of predication,
viz. those of which the subject and predicate are proper names,
and which assert only that those names have, or that they
have not, been conventionally assigned to the same individual,
there would be little to attract to such propositions the atten-
tion of philosophers. But the class of merely verbal proposi-
tions embraces not only much more than these, but much more
than any propositions which at first sight present themselves
as verbal ; comprehending a kind of assertions which have
been regarded not only as relating to things, but as having
actually a more intimate relation with them than any other
propositions whatever. The student in philosophy will per-
ceive that I allude to the distinction on which so much stress
was laid by the schoolmen, and which has been retained either
under the same or under other names by most metaphysicians
to the present day, viz. between what were called essential,
and what were called accidental, propositions, and between
essential and accidental properties or attributes.

§ 2. Almost all metaphysicians prior to Locke, as well as
many since his time, have made a great mystery of Essential
Predication, and of predicates which are said to be of the
essence of the subject. The essence of a thing, they said, was
that without which the thing could neither be, nor be con-
ceived to be. Thus, rationality was of the essence of man,
because without rationality, man could not be conceived to
exist. The different attributes which made up the essence of
the thing were called its essential properties ; and a proposition
in which any of these were predicated of it was called an
Essential Proposition, and was considered to go deeper into the
nature of the thing, and to convey more important information

124

NAMES AND PROPOSITIONS.

respecting it, than any other proposition could do. All pro-
perties, not of the essence of the thing, were called its accidents ;
were supposed to have nothing at all, or nothing comparatively,
to do with its inmost nature ; and the propositions in which
any of these were predicated of it were called Accidental Pro-
positions. A connexion may he traced between this distinc-
tion, which originated with the schoolmen, and the well-known
dogmas of substantive secundce or general substances, and sub-
stantial forms, doctrines which under varieties of language per-
vaded alike the Aristotelian and the Platonic schools, and of
which more of the spirit has come down to modern times than
might be conjectured from the disuse of the phraseology.
The false views of the nature of classification and generaliza-
tion which prevailed among the schoolmen, and of which these
dogmas were the technical expression, afford the only explana-
tion which can be given of their having misunderstood the real
nature of those Essences which held so conspicuous a place in
their philosophy. They said, truly, that man cannot be con-
ceived without rationality. But though man cannot, a being
may be conceived exactly like a man in all points except that
one quality, and those others which are the conditions or con-
sequences of it. All therefore which is really true in the asser-
tion that man cannot be conceived without rationality, is only,
that if he had not rationality, he would not be reputed a man.
There is no impossibility in conceiving the thing, nor, for
aught we know, in its existing : the impossibility is in the con-
ventions of language, which will not allow the thing, even if
it exist, to be called by the name which is reserved for rational
beings. Rationality, in short, is involved in the meaning of
the word man : is one of the attributes connoted by the name.
The essence of man, simply means the whole of the attributes
connoted by the word ; and any one of those attributes taken
singly, is an essential property of man.

But these reflections, so easy to us, would have been difficult
to persons who thought, as most of the later Aristotelians did,
that objects were made what they were called, that gold (for
instance) was made gold, not by the possession of certain pro-
perties to which mankind have chosen to attach that name, but

VERBAL AND REAL PROPOSITIONS. 125

by participation in the nature of a certain general substance,
called gold in general, which substance, together with all the
properties that belonged to it, inhered in every individual piece
of gold.* As they did not consider these universal substances
to be attached to all general names, but only to some, they
thought that an object borrowed only a part of its properties
from an universal substance, and that the rest belonged to it
individually : the former they called its essence, and the latter
its accidents. The scholastic doctrine of essences long survived
the theory on which it rested, that of the existence of real
entities corresponding to general terms ; and it was reserved
for Locke at the end of the seventeenth century, to convince
philosophers that the supposed essences of classes were merely
the signification of their names ; nor, among the signal services
which his writings rendered to philosophy, was there one more
needful or more valuable.

Now, as the most familiar of the general names by which
an object is designated usually connotes not one only, but
several attributes of the object, each of which attributes sepa-
rately forms also the bond of union of some class, and the
meaning of some general name ; we may predicate of a name
which connotes a variety of attributes, another name which
connotes only one of these attributes, or some smaller number
of them than all. In such cases, the universal affirmative pro-
position will be true ; since whatever possesses the whole of
any set of attributes, must possess any part of that same set.
A proposition of this sort, however, conveys no information
to any one who previously understood the whole meaning of
the terms. The propositions, Every man is a corporeal being,
Every man is a living creature, Every man is rational, convey
no knowledge to any one who was already aware of the entire
meaning of the word man, for the meaning of the word

* The doctrines which prevented the real meaning of Essences from being
understood, had not assumed so settled a shape in the time of Aristotle and
his immediate followers, as was afterwards given to them by the Realists
of the middle ages. Aristotle himself (in his Treatise on the Categories) ex-
pressly denies that the Sivrtpai o'vtnai, or Substantise Secundae, inhere in a
subject. They are only, he says, predicated of it.

126 NAMES AND PROPOSITIONS.

includes all this : and that every man has the attributes con-
noted by all these predicates, is already asserted when he is
called a man. Now, of this nature are all the propositions
which have been called essential. They are, in fact, identical
propositions.

It is true that a proposition which predicates any attribute,
even though it be one implied in the name, is in most cases
understood to involve a tacit assertion that there exists a thing
corresponding to the name, and possessing the attributes con-
noted by it; and this implied assertion may convey informa-
tion, even to those who understood the meaning of the name.
But all information of this sort, conveyed by all the essential
propositions of which man can be made the subject, is included
in the assertion, Men exist. And this assumption of real ex-
istence is, after all, the result of an imperfection of language,
It arises from the ambiguity of the copula, which, in addition
to its proper office of a mark to show that an assertion is made,
is also, as formerly remarked, a concrete word connoting
existence. The actual existence of the subject of the propo-
sition is therefore only apparently, not really, implied in the
predication, if an essential one : we may say, A ghost is a dis-
embodied spirit, without believing in ghosts. But an accidental,
or non-essential, affirmation, does imply the real existence of
the subject, because in the case of a non-existent subject
there is nothing for the proposition to assert. Such a propo-
sition as, The ghost of a murdered person haunts the couch of
the murderer, can only have a meaning if understood as im-
plying a belief in ghosts ; for since the signification of the
word ghost implies nothing of the kind, the speaker either
means nothing, or means to assert a thing which he wishes to
be believed to have really taken place.

It will be hereafter seen that when any important conse-
quences seem to follow, as in mathematics, from an essential
proposition, or, in other words, from a proposition involved in
the meaning of a name, what they really flow from is the tacit
assumption of the real existence of the objects so named.
Apart from this assumption of real existence, the class of pro-
positions in which the predicate is of the essence of the subject

VERBAL AND REAL PROPOSITIONS. 127

(that is, in which the predicate connotes the whole or part of
what the subject connotes, but nothing besides) answer no
purpose but that of unfolding the whole or some part of the
meaning of the name, to those who did not previously know it^
Accordingly, the most useful, and in strictness the only useful
kind of essential propositions, are Definitions: which, to be
complete, should unfold the whole of what is involved in the
meaning of the word defined ; that is, (when it is a connotative
word,) the whole of what it connotes. In defining a name,
however, it is not usual to specify its entire connotation, but
so much only as is sufficient to mark out the objects usually
denoted by it from all other known objects. And sometimes
a merely accidental property, not involved in the meaning of
the name, answers this purpose equally well. The various
kinds of definition which these distinctions give rise to, and
the purposes to which they are respectively subservient, will be
minutely considered in the proper place.

§ 3. According to the above view of essential propositions,
no proposition can be reckoned such which relates to an indi-
vidual by name, that is, in which the subject is a proper name.
Individuals have no essence?. When the schoolmen talked of
the essence of an individual, they did not mean the properties
implied in its name, for the names of individuals imply no
properties. They regarded as of the essence of an individual,
whatever was of the essence of the species in which they were
accustomed to place that individual; i.e. of the class to which
it was most familiarly referred, and to which, therefore, they
conceived that it by nature belonged. Thus, because the pro-
position Man is a rational being, was an essential proposition,
they affirmed the same thing of the proposition, Julius Crosar
is a rational being. This followed very naturally if genera and
species were to be considered as entities, distinct from, but
inhering in, the individuals composing them. If man was a
substance inhering in each individual man, the essence of man
(whatever that might mean) was naturally supposed to accom-
pany it ; to inhere in John Thompson, and to form the common
essence of Thompson and Julius Cassar. It might then be

128 NAMES AND PROPOSITIONS.

fairly said, that rationality, being of the essence of Man, was
of the essence also of Thompson. But if Man altogether be
only the individual men and a name bestowed upon them in
consequence of certain common properties, what becomes of
John Thompson's essence ?

A fundamental error is seldom expelled from philosophy
by a single victory. It retreats slowly, defends every inch
of ground, and often, after it has been driven from the open
country, retains a footing in some remote fastness. The
essences of individuals were an unmeaning figment arising
from a misapprehension of the essences of classes, yet even
Locke, when he extirpated the parent error, could not shake
himself free from that which was its fruit. He distinguished
two sorts of essences, Real and Nominal. His nominal essences
were the essences of classes, explained nearly as we have now
explained them. Nor is anything wanting to render the third
book of Locke's Essay a nearly unexceptionable treatise on
the connotation of names, except to free its language from the
assumption of what are called Abstract Ideas, which unfor-
tunately is involved in the phraseology, though not necessarily
connected with the thoughts contained in that immortal Third
Book.* But besides nominal essences, he admitted real
essences, or essences of individual objects, which he supposed
to be the causes of the sensible properties of those objects.
We know not (said he) what these are ; (and this acknowledg-
ment rendered the fiction comparatively innocuous ;) but if we
did, we could, from them alone, demonstrate the sensible pro-
perties of the object, as tbe properties of the triangle are

* The always acute and often profound author of An Outline of Sematology
(Mr. B. H. Smart) justly says, "Locke will be much more intelligible, if, in
the majority of places, we substitute ' the knowledge of ' for what he calls ' the
Idea of " (p. 10). Among the many criticisms on Locke's use of the word
Idea, this is the one which, as it appears to me, most nearly hits the mark ;
and I quote it for the additional reason that it precisely expresses the point of
difference respecting the import of Propositions, between my view and what I
have spoken of as the Conceptualist view of them. Where a Conceptualist
says that a name or a proposition expresses our Idea of a thing, I should
generally say (instead of our Idea) our Knowledge, or Belief, concerning the
thing itself.

VERBAL AND REAL PROPOSITIONS. 129

demonstrated from the definition of the triangle. I shall have
occasion to revert to this theory in treating of Demonstration,
and of the conditions under which one property of a thing
admits of being demonstrated from another property. It is
enough here to remark that, according to this definition, the
real essence of an object has, in the progress of physics, come
to be conceived as nearly equivalent, in the case of bodies, to
their corpuscular structure : what it is now supposed to mean
in the case of any other entities, I would not take upon myself
to define.

§ 4. An essential proposition, then, is one which is purely
verbal ; which asserts of a thing under a particular name, only
what is asserted of it in the fact of calling it by that name ;
and which therefore either gives no information, or gives it
respecting the name, not the thing. Non-essential, or acci-
dental propositions, on the contrary, may be called Real Pro-
positions, in opposition to Verbal. They predicate of a thing
some fact not involved in the signification of the name by
which the proposition speaks of it ; some attribute not con-
noted by that name. Such are all propositions concerning
things individually designated, and all general or particular
propositions in which the predicate connotes any attribute not
connoted by the subject. All these, if true, add to our know-
ledge : they convey information, not already involved in the
names employed. When I am told that all, or even that some
objects, which have certain qualities, or which stand in certain
relations, have also certain other qualities, or stand in certain
other relations, I learn from this proposition a new fact ; a
fact not included in rny knowledge of the meaning of the
words, nor even of the existence of Things answering to the
signification of those words. It is this, class of propositions
only which are in themselves instructive, or from which any
instructive propositions can be inferred.*

* This distinction corresponds to that which is drawn by Kant and other
metaphysicians between what they term analytic, and synthetic, judgments ; the
former being those which can be evolved from the meaning of the terms used,

VOL. I. 9

130 NAMES AND PROPOSITIONS.

Nothing has probably contributed more to the opinion
so long prevalent of the futility of the school logic, than the
circumstance that almost all the examples used in the common
school books to illustrate the doctrine of predication and that
of the syllogism, consist of essential propositions. They were
usually taken either from the branches or from the main trunk
of the Predicamental Tree, which included nothing but what
was of the essence of the species : Omne corpus est substantia,
Omne animal est corpus, Omnis homo est corpus, Omnis homo
est animal, Omnis homo est rationalis, and so forth. It is
far from wonderful that the syllogistic art should have been
thought to be of no use in assisting correct reasoning, when
almost the only propositions which, in the hands of its pro-
fessed teachers, it was employed to prove, were such as every
one assented to without proof the moment he comprehended
the meaning of the words; and stood exactly on a level, in
point of evidence, with the premises from which they were
drawn. I have, therefore, throughout this work, avoided the
employment of essential propositions as examples, except
where the nature of the principle to be illustrated specifically
required them.

§ 5. With respect to propositions which do convey in-
formation — which assert something of a Thing, under a
name that does not already presuppose what is about to be
asserted ; there are two different aspects in which these, or
rather such of them as are general propositions, may be con-
sidered: we may either look at them as portions of speculative
truth, or as memoranda for practical use. According as we
consider propositions in one or the other of these lights, their
import may be conveniently expressed in one or in the other
of two formulas.

According to the formula which we have hitherto employed,
and which is best adapted to express the import of the pro-
position as a portion of our theoretical knowledge, All men
are mortal, means that the attributes of man are always
accompanied by the attribute mortality : No men are gods,
means that the attributes of man are never accompanied by

VERBAL, AND REAL PROPOSITIONS. 131

the attributes, or at least never by all the attributes, signified
by the word god. But when the proposition is considered as a
memorandum for practical use, we shall find a different
mode of expressing the same meaning better adapted to
indicate the office which the proposition performs. The prac-
tical use of a proposition is, to apprise or remind us what
we have to expect, in any individual case which comes within
the assertion contained in the proposition. In reference to
this purpose, the proposition, All men are mortal, means
that the attributes of man are evidence of, are a mark of,
mortality ; an indication by which the presence of that attri-
bute is made manifest. No men are gods, means that the
attributes of man are a mark or evidence that some or all
of the attributes understood to belong to a god are not there ;
that where the former are, we need not expect to find the
latter.

These two forms of expression are at bottom equivalent ;
but the one points the attention more directly to what a pro-
position means, the latter to the manner in which it is to be
used.

Now it is to be observed that Reasoning (the subject to
which we are next to proceed) is a process into which propo-
sitions enter not as ultimate results, but as means to the esta-
blishment of other propositions. We may expect, there-
fore, that the mode of exhibiting the import of a general
proposition which shows it in its application to practical use,
will best express the function which propositions perform in
Reasoning. And accordingly, in the theory of Reasoning,
the mode of viewing the subject which considers a Proposi-
tion as asserting that one fact or phenomenon is a mark or
evidence of another fact or phenomenon, will be found almost
indispensable. For the purposes of that Theory, the best
mode of defining the import of a proposition is not the mode
which shows most clearly what it is in itself, but that
which most distinctly suggests the manner in which it may
be made available for advancing from it to other proposi-
tions.

9—2

CHAPTER VII.

OF THE NATURE OF CLASSIFICATION, AND THE FIVE
PREDICABLES.

§ 1. IN examining into the nature of general proposi-
tions, we have adverted much less than is usual with logi-
cians to the ideas of a Class, and Classification ; ideas which,
since the Realist doctrine of General Substances went out of
vogue, have formed the hasis of almost every attempt at a
philosophical theory of general terms and general proposi-
tions. We have considered general names as having a mean-
ing, quite independently of their being the names of classes.
That circumstance is in truth accidental, it being wholly
immaterial to the signification of the name whether there are
many objects, or only one, to which it happens to be appli-
cable, or whether there be any at all. God is as much a
general term to the Christian or Jew as to the Polytheist ;
and dragon, hippogriff, chimera, mermaid, ghost, are as much
so as if real objects existed, corresponding to those names.
Every name the signification of which is constituted by attri-
butes, is potentially a name of an indefinite number of objects ;
but it needs not be actually the name of any ; and if of any,
it may be the name of only one. As soon as we employ a
name to connote attributes, the things, be they more or fewer,
which happen to possess those attributes, are constituted ipso
facto a class. But in predicating the name we predicate only
the attributes ; and the fact of belonging to a class does not,
in, many cases, come into view at all.

Although, however, Predication does not presuppose Clas-
sification, and though the theory of Names and of Propositions
is not cleared up, but only encumbered, by intruding the idea
of classification into it, there is nevertheless a close connexion
between Classification and the employment of General Names.

CLASSIFICATION AND THE PREDICABLES. 133

By every general name which we introduce, we create a class,
if there be any things, real or imaginary, to compose it ; that
is, any Things corresponding to the signification of the name.
Classes, therefore, mostly owe their existence to general lan-
guage. But general language, also, though that is not the
most common case, sometimes owes its existence to classes.
A general, which is as much as to say a significant, name, is
indeed mostly introduced because we have a signification to
express by it ; because we need a word by means of which to
predicate the attributes which it connotes. But it is also true
that a name is sometimes introduced because we have found it
convenient to create a class ; because we have thought it useful
for the regulation of our mental operations, that a certain
group of objects should be thought of together. A naturalist,
for purposes connected with his particular science, sees reason
to distribute the animal or vegetable creation into certain
groups rather than into any others, and he requires a name to
bind, as it were, each of his groups together. It must not how-
ever be supposed that such names, when introduced, differ in
any respect, as to their mode of signification, from other con-
notative names. The classes which they denote are, as much
as any other classes, constituted by certain common attributes,
and their names are significant of those attributes, and of
nothing else. The names of Cuvier's classes and orders,
Plantigrades, Digitigrades, &c., are as much the expression of
attributes as if those names had preceded, instead of grown
out of, his classification of animals. The only peculiarity of
the case is, that the convenience of classification was here the
primary motive for introducing the names ; while in other
cases the name is introduced as a means of predication, and
the formation of a class denoted by it is only an indirect con-
sequence.

The principles which ought to regulate Classification as a
logical process subservient to the investigation of truth, cannot
be discussed to any purpose until a much later stage of our
inquiry. But, of Classification as resulting from, and implied
in, the fact of employing general language, we cannot forbear
to treat here, without leaving the theory of general names'

134 NAMES AND PROPOSITIONS.

and of their employment in predication, mutilated and
formless.

§ 2. This portion of the theory of general language is
the subject of what is termed the doctrine of the Predicates ;
a set of distinctions handed down from Aristotle, and his fol-
lower Porphyry, many of which have taken a firm root in
scientific, and some of them even in popular, phraseology,
The predicables are a five-fold division of General Names, not
grounded as usual on a difference in their meaning, that is, in
the attribute which they connote, but on a difference in the
kind of class which they denote. We may predicate of a thing
five different varieties of class-name : — •

A yenus of the thing

A species (el£?oe).

A differentia (<>ia<popd).

A. proprium (ISiov).

An accidcns (crv/i/StjSjj/coc).

It is to be remarked of these distinctions, that they ex-
press, not what the predicate is in its own meaning, but what
relation it bears to the subject of which it happens on the par-
ticular occasion to be predicated. There are not some names
which are exclusively genera, and others which are exclusively
species, or differentiae ; but the same name is referred to one
or another predicable, according to the subject of which it is
predicated on the particular occasion. Animal, for instance,
is a genus with respect to man, or John ; a species with re-
spect to Substance, or Being. Rectangular is one of the
Differentia? of a geometrical square; it is merely one of the
Accidentia of the table at which I am writing. The words
genus, species, &c. are therefore relative terms ; they are
names applied to certain predicates, to express the relation
between them and some given subject: a relation grounded,
as we shall see, not on what the predicate connotes, but on
the class which it denotes, and on the place which, in some
given classification, that class occupies relatively to the parti-
cular subject.

§ 3. Of these five names, two, Genus and Species, are

CLASSIFICATION AND THE PREDICABLES. 135

•not only used by naturalists in a technical acceptation not
precisely agreeing with their philosophical meaning, but have
also acquired a popular acceptation, much more general than
either. In this popular sense any two classes, one of which
includes the whole of the other and more, may be called a
Genus and a Species. Such, for instance, are Animal and
Man ; Man and Mathematician. Animal is a Genus ; Man
and Brute are its two species; or we may divide it into a
greater number of species, as man, horse, dog, &c. Biped, or
two-footed animal, may also be considered a genus, of which
man and bird are two species. Taste is a genus, of which
sweet taste, sour taste, salt taste, &c. are species. Virtue is a
genus; justice, prudence, courage, fortitude, generosity, &c.
are its species.

The same class which is a genus with reference to the
sub-classes or species included in it, may be itself a species
with reference to a more comprehensive, or, as it is often
called, a superior genus. Man is a species with reference to
animal, but a genus with reference to the species Mathema-
tician. Animal is a genus, divided into two species, man and
brute ; but animal is also a species, which, with another species,,
vegetable, makes up the genus, organized being. Biped is a
genus with reference to man and bird, but a species with re-
spect to the superior genus, animal. Taste is a genus divided
into species, but also a species of the genus sensation. Virtue,
a genus with reference to justice, temperance, &c., is one of the
species of the genus, mental quality.

In this popular sense the words Genus and Species have
passed into common discourse. And it should be observed
that in ordinary parlance, not the name of the class, but the
class itself, is said to be the genus or species; not, of course,
the class in the sense of each individual of the class, but the
individuals collectively, considered as an aggregate whole ; the
name by which the class is designated being then called not
the genus or species, but the generic or specific name. And
this is an admissible form of expression ; nor is it of any im-
portance which of the two modes of speaking we adopt, pro-
vided the rest of our language is consistent with it ; but, if we

136 NAMES AND PROPOSITIONS.

call the class itself the genus, we must not talk of predicating
the genus. We predicate of man the name mortal; and by
predicating the name, we may he said, in an intelligible sense,
to predicate what the name expresses, the attribute mortality ;
but in no allowable sense of the word predication do we pre-
dicate of man the class mortal. We predicate of him the fact
of belonging to the class.

By the Aristotelian logicians, the terms genus and species
were used in a more restricted sense. They did not admit
every class which could he divided into other classes to be a
genus, or every class which could be included in a larger class
to be a species. Animal was by them considered a genus ; man
and brute co-ordinate species under that genus : biped, how-
ever, would not have been admitted to be a genus with re-
ference to man, but a proprium or accidens only. It was
requisite, according to their theory, that genus and species
should be of the essence of the subject. Animal was of the
essence of man ; biped was not. And in every classification
they considered some one class as the lowest or infima species.
Man, for instance, was a lowest species. Any further divisions
into which the class might be capable of being broken down,
as man into white, black, and red man, or into priest and lay-
man, they did not admit to be species.

It has been seen, however, in the preceding chapter, that
the distinction between the essence of a class, and the attri-
butes or properties which are not of its essence — a distinction
which has given occasion to so much abstruse speculation,
and to which so mysterious a character was formerly, and by
many writers is still, attached, — amounts to nothing more
than the difference between those attributes of the class which
are, and those which are not, involved in the signification of
the class-name. As applied to individuals, the word Essence,
we found, has no meaning, except in connexion with the ex-
ploded tenets of the Realists; and what the schoolmen chose
to call the essence of an individual, was simply the essence
of the class to which that individual was most familiarly
referred.

Is there no difference, then, save this merely verbal one,

CLASSIFICATION AND THE PREDICABLES. 137

between the classes which the schoolmen admitted to be genera
or species, and those to which they refused the title ? Is it
an error to regard some of the differences which exist among
objects as differences in kind (yenere or specie), and others only
as differences in the accidents ? Were the schoolmen right
or wrong in giving to some of the classes into which things
may be divided, the name of kinds, and considering others as
secondary divisions, grounded on differences of a compara-
tively superficial nature? Examination will show that the
Aristotelians did mean something by this distinction, and
something important; but which, being but indistinctly con-
ceived, was inadequately expressed by the phraseology of
essences, and the various other modes of speech to which they
had recourse.

§ 4. It is a fundamental principle in logic, that the power
of framing classes is unlimited, as long as there is any (even
the smallest) difference to found a distinction upon. Take
any attribute whatever, and if some things have it, and others
have not, we may ground on the attribute a division of all
things into two classes; and we actually do so, the moment
we create a name which connotes the attribute. The number
of possible classes, therefore, is boundless ; and there are as
many actual classes (either of real or of imaginary things) as
there are general names, positive and negative together.

But if we contemplate any one of the classes so formed,
such as the class animal or plant, or the class sulphur or phos-
phorus, or the class white or red, and consider in what parti-
culars the individuals included in the class differ from those
which do not come within it, we find a very remarkable diver-
sity in this respect between some classes and others. There
are some classes, the things contained in which differ from
other things only in certain particulars which may be num-
bered, while others differ in more than can be numbered, more
even than we need ever expect to know. Some classes have
little or nothing in common to characterize them by, except
precisely what is connoted by the name : white things, for ex-
ample, are not distinguished by any common properties except

138

NAMES AND PROPOSITIONS.

whiteness; or if they are, it is only by such as are in some
•way dependent on, or connected with, whiteness. But a hundred
generations have not exhausted the common properties of
animals or of plants, of sulphur or of phosphorus; nor do we
suppose them to be exhaustible, but proceed to new observa-
tions and experiments, in the full confidence of discovering
new properties which were by no means implied in those we
previously knew. While, if any one were to propose for in-
vestigation the common properties of all things which are of
the same colour, the same shape, or the same specific gravity,
the absurdity would be palpable. We have no ground to be-
lieve that any such common properties exist, except such as
may be shown to be involved in the supposition itself, or to be
derivable from it by some law of causation. It appears, there-
fore, that the properties, on which we ground our classes, some-
times exhaust all that the class has in common, or contain it
all by some mode of implication ; but in other instances we
make a selection of a few properties from among not only a
greater number, but a number inexhaustible by us, and to
which as we know no bounds, they may, so far as we are con-
cerned, be regarded as infinite.

There is no impropriety in saying that, of these two classi-
fications, the one answers to a much more radical distinction
in the things themselves, than the other does. And if any one
even chooses to say that the one classification is made by
nature, the other by us for our convenience, he will be right ;
provided he means no more than this : Where a certain
apparent difference between things (though perhaps in itself of
little moment) answers to we know not what number of other
differences, pervading not only their known properties, but
properties yet undiscovered, it is not optional but imperative
to recognise this difference as the foundation of a specific dis-
tinction ; while, on the contrary, differences that are merely
finite and determinate, like those designated by the words
white, black, or red, may be disregarded if the purpose for
which the classification is made does not require attention
to those particular properties. The differences, however, are
made by nature, in both cases; while the recognition of those

CLASSIFICATION AND THE PREDICABLES. 139

differences as grounds of classification and of naming, is,
equally in both cases, the act of man: only in the one case,
the ends of language and of classification would be subverted
if no notice were taken of the difference, while in the other
case, the necessity of taking notice of it depends on the im-
portance or unimportance of the particular qualities in which
the difference happens to consist.

Now, these classes, distinguished by unknown multitudes
of properties, and not solely by a few determinate ones — which
are parted off from one another by an unfathomable chasm,
instead of a mere ordinary ditch with a visible bottom — are
the only classes which, by the Aristotelian logicians, were
considered as genera or species. Differences which extended
only to a certain property or properties, and there terminated,
they considered as differences only in the accidents of things;
but where any class differed from other things by an infinite
series of differences, known and unknown, they considered the
distinction as one of kind, and spoke of it as being an essential
difference, which is also one of the current meanings of that
vague expression at the present day.

Conceiving the schoolmen to have been justified in drawing
a broad line of separation between these two kinds of classes
and of class-distinctions, I shall not only retain the division
itself, but continue to express it in their language. According
to that language, the proximate (or lowest) Kind to which
any individual is referable, is called its species. Conformably
to this, Isaac Newton would be said to be of the species man.
There are indeed numerous sub-classes included in the class
man, to which Newton also belongs; for example, Christian,
and Englishman, and Mathematician. But these, though
distinct classes, are not, in our sense of the term, distinct
Kinds of men. A Christian, for example, differs from other
human beings ; but he differs only in the attribute which
the word expresses, namely, belief in Christianity, and what-
ever else that implies, either as involved in the fact itself, or
connected with it through some law of cause and effect. We
should never think of inquiring what properties, unconnected
with Christianity, either as cause or effect, are common to

140 NAMES AND PROPOSITIONS.

all Christians and peculiar to them ; while in regard to all
Men, physiologists are perpetually carrying on such an
inquiry ; nor is the answer ever likely to be completed. Man,
therefore, we may call a species; Christian, or Mathematician,
we cannot.

Note here, that it is hy no means intended to imply that
there may not be different Kinds, or logical species, of man.
The various races and temperaments, the two sexes, and even
the various ages, may be differences of kind, within our mean-
ing of the term. I do not say that they are so. For in the
progress of physiology it may almost be said to be made out,
that the differences which really exist between different races,
sexes, &c., follow as consequences, under laws of nature, from
a small number of primary differences which can be pre-
cisely determiued, and which, as the phrase is, account for all
the rest. If this be so, these are not distinctions in kind ; no
more than Christian, Jew, Mussulman, and Pagan, a difference
which also carries many consequences along with it. And in
this way classes are often mistaken for real Kinds, which are
afterwards proved not to be so. But if it turned out that the
differences were not capable of being thus accounted for, then
Caucasian, Mongolian, Negro, &c. would be really different
Kinds of human beings, and entitled to be ranked as species
by the logician ; though not by the naturalist. For (as already
noticed) the word species is used in a different signification in
logic and in natural history. By the naturalist, organized
beings are not usually said to be of different species, if it is
supposed that they have descended from the same stock.
That, however, is a sense artificially given to the word, for
the technical purposes of a particular science. To the
logician, if a negro and a white man differ in the same manner
(however less in degree) as a horse and a camel do, that is, if
their differences are inexhaustible, and not referrible to any
common cause, they are different species, whether they are
descended from common ancestors or not. But if their dif-
ferences can all be traced to climate and habits, or to some
one or a few special differences in structure, they are not, in
the logician's view, specifically distinct.

CLASSIFICATION AND THE PREDICABLES.

When the infima species, or proximate Kind, to which an
individual helongs, has heen ascertained, the properties com-
mon to that Kind include necessarily the whole of the common
properties of every other real Kind to which the individual can
be referrible. Let the individual, for example, he Socrates, and
the proximate Kind, man. Animal, or living creature, is also
a real Kind, and includes Socrates ; hut, since it likewise in-
cludes man, or in other words, since all men are animals, the
properties common to animals form a portion of the common
properties of the sub-class, man. And if there be any class
which includes Socrates without including man, that class is
not a real Kind. Let the class, for example, be flat-nosed ;
that being a class which includes Socrates, without including
all men. To determine whether it is a real Kind, we must ask
ourselves this question : Have all flat-nosed animals, in addi-
tion to whatever is implied in their flat noses, any common
properties, other than those which are common to all animals
whatever? If they had; if a flat nose were a mark or index
to an indefinite number of other peculiarities, not deducible
from the former by an ascertainable law, then out of the
class man we might cut another class, flat-nosed man, which
according to our definition, would be a Kind. But if we could
do this, man would not be, as it was assumed to be, the
proximate Kind. Therefore, the properties of the proximate
Kind do comprehend those (whether known or unknown) of
all other Kinds to which the individual belongs ; which was
the point we undertook to prove. And hence, every other
Kind which is predicable of the individual, will be to the
proximate Kind in the relation of a genus, according to even
the popular acceptation of the terms genus and species ; that
is, it will be a larger class, including it and more.

We are now able to fix the logical meaning of these terms.
Every class which is a real Kind, that is, which is distin-
guished from all other classes by an indeterminate multitude
of properties not derivable from one another, is either a genus
or a species. A Kind which is not divisible into other Kinds,
cannot be a genus, because it has no species under it ; but it
is itself a species, both with reference to the individuals below

142 NAMES AND PROPOSITIONS.

and to the genera above (Species Prsedicabilis and Species
Subjicibilis.) But every Kind which admits of division into
real Kinds (as animal into mammal, bird, fish, &c., or bird
into various species of birds) is a genus to all below
it, a species to all genera in which it is itself included.
And here we may close this part of the discussion, and pass
to the three remaining predicables, Differentia, Proprium, and
Accidens.

§ 5. To begin with Differentia. This word is correlative
with the words genus and species, and as all admit, it signifies
the attribute which distinguishes a given species from every
other species of the same genus. This is so far clear : but Ave
may still ask, which of the distinguishing attributes it signi-
fies. For we have seen that every Kind (and a species must
be a Kind) is distinguished from other Kinds, not by any one
attribute, but by an indefinite number. Man, for instance, is
a species of the genus animal : Rational (or rationality, for it
is of no consequence here whether we use the concrete or the
abstract form) is generally assigned by logicians as the Diffe-
rentia; and doubtless this attribute serves the purpose of
distinction : but it has also been remarked of man, that he
is a cooking animal ; the only animal that dresses its food.
This, therefore, is another of the attributes by which the
species man is distinguished from other species of the same
genus : would this attribute serve equally well for a diffe-
rentia? The Aristotelians say No; having laid it down that
the differentia must, like the genus and species, be of the
essence of the subject.

And here we lose even that vestige of a meaning grounded
in the nature of the things themselves, which may be sup-
posed to be attached to the word essence when it is said that
genus and species must be of the essence of the thing. There
can be no doubt that when the schoolmen talked of the
essences of things as opposed to their accidents, they had
confusedly in view the distinction between differences of kind,
and the differences which are not of kind ; they meant to inti-
mate that genera and species must be Kinds. Their notion

CLASSIFICATION AXD THE PREDICABLES. 143

of the essence of a thing was a vague notion of a something
which makes it what it is, i. e. which makes it the Kind of
thing that it is — which causes it to have all that variety of
properties which distinguish its Kind. But when the matter
came to he looked at more closely, nobody could discover what
caused the thing to have all those properties, nor even that
there was anything which caused it to have them. Logicians,
however, not liking to admit this, and being unable to detect
what made the thing to be what it was, satisfied themselves
with what made it to be what it was called. Of the innu-
merable properties, known and unknown, that are common to
the class man, a portion only, and of course a very small
portion, are connoted by its name ; these few, however, will
naturally have been thus distinguished from the rest either for
their greater obviousness, or for greater supposed importance.
These properties, then, which were connoted by the name,
logicians seized upon, and called them the essence of the
species ; and not stopping there, they affirmed them, in the
case of the infima species, to be the essence of the individual
too ; for it was their maxim, that the species contained the
"whole essence" of the thing. Metaphysics, that fertile field
of delusion propagated by language, does not afford a more
signal instance of such delusion. On this account it was that
rationality, being connoted by the name man, was allowed to
be a differentia of the class ; but the peculiarity of cooking
their food, not being connoted, was relegated to the class of
accidental properties.

The distinction, therefore, between Differentia, Propriura,
and Accidens, is not grounded in the nature of things, but in
the connotation of names ; and we must seek it there, if we
wish to find what it is.

From the fact that the genus includes the species, in other
words denotes more than the species, or is predicable of a
greater number of individuals, it follows that the species must
connote more than the genus. It must connote all the attri-
butes which the genus connotes, or there would be nothing
to prevent it from denoting individuals not included in the
genus. And it must connote something besides, otherwise it

144 NAMES AND PROPOSITIONS.

would include the whole genus. Animal denotes all the indi-
viduals denoted by man, and many more. Man, therefore,
must connote all that animal connotes, otherwise there might
he men who are not animals ; and it must connote something
more than animal connotes, otherwise all animals would be
men. This surplus of connotation — this which the species
connotes over and above the connotation of the genus — is the
Differentia, or specific difference ; or, to state the same propo-
sition in other words, the Differentia is that which must be
added to the connotation of the genus, to complete the conno-
tation of the species.

The word man, for instance, exclusively of what it con-
notes in common with animal, also connotes rationality, and
at least some approximation to that external form which we
all know, but which as we have no name for it considered in
itself, we are content to call the human. The Differentia, or
specific difference, therefore, of man, as referred to the genus
animal, is that outward form and the possession of reason.
The Aristotelians said, the possession of reason, without the
outward form. But if they adhered to this, they would have,
been obliged to call the Houyhnhnms men. The question
never arose, and they were never called upon to decide how
such a case would have affected their notion of essentiality.
However this may be, they were satisfied with taking such a
portion of the differentia as sufficed to distinguish the species
from all other existing things, though by so doing they might
not exhaust the connotation of the name.

§ 6. And here, to prevent the notion of differentia from
being restricted within too narrow limits, it is necessary to
remark, that a species, even as referred to the same genus,
will not always have the same differentia, but a different one,
according to the principle and purpose which preside over the
particular classification. For example, a naturalist surveys
the various kinds of animals, and looks out for the classifica-
tion of them most in accordance with the order in which, for
zoological purposes, he considers it desirable that we should
think of them. With this view he finds it advisable that

CLASSIFICATION AND THE PREDICABLES. 145

one of his fundamental divisions should be into warm-blooded
and cold-blooded animals ; or into animals which breathe
with lungs and those which breathe with gills ; or into carni-
vorous, and frugivorous or graminivorous ; or into those
which walk on the flat part and those which walk on the
extremity of the foot, a distinction on which two of Cuvier's
families are .founded. In doing this, the naturalist creates as
many new classes ; which are by no means those to which the
individual animal is familiarly and spontaneously referred ;
nor should we ever think of assigning to them so prominent
a position in our arrangement of the animal kingdom, unless
for a preconceived purpose of scientific convenience. And to
the liberty of doing this there is no limit. In the examples
we have given, most of the classes are real Kinds, since each
of the peculiarities is an index to a multitude of properties
belonging to the class which it characterizes : but even if the
case were otherwise — if the other properties of those classes
could all be derived, by any process known to us, from the one
peculiarity on which the class is founded — even then, if these
derivative properties were of primary importance for the pur-
poses of the naturalist, he would be warranted in founding his
primary divisions on them.

If, however, practical convenience is a sufficient warrant
for making the main demarcations in our arrangement of
objects run in lines not coinciding with any distinction of
Kind, and so creating genera and species in the popular
sense which are not genera or species in the rigorous sense
at all ; d fortiori must we be warranted, when our genera
and species are real genera and species, in marking the dis-
tinction between them by those of their properties which con-
siderations of practical convenience most strongly recommend.
If we cut a species out of a given genus — the species man,
for instance, out of the genus animal — with an intention
on our part that the peculiarity by which we are to be
guided in the application of the name man should be
rationality, then rationality is the differentia of the species
man. Suppose, however, that being naturalists,' we, for the
purposes of our particular study, cut out of the genus animal
VOL. i. 10

146 NAMES AND PROPOSITIONS.

the same species man, but with an intention that the dis-
tinction hetween man and all other species of animal should
he, not rationality, hut the possession of "four incisors in
each jaw, tusks solitary, and erect posture." It is evident
that the word man, when used hy us as naturalists, no longer
connotes rationality, hut connotes the three other properties
specified ; for that which we have expressly in view when
we impose a name, assuredly forms part of the meaning of
that name. We may, therefore, lay it down as a maxim,
that wherever there is a Genus, and a Species marked out
from that genus hy an assignable differentia, the name of
the species must be connotative, and must connote the diffe-
rentia; but the connotation may he special — not involved in
the signification of the term as ordinarily used, hut given to-
it when employed as a term of art or science. The word Man
in common use, connotes rationality and a certain form, hut
does not connote the number or character of the teeth ; in the
Linnffian system it connotes the number of incisor and canine
teeth, but does not connote rationality nor any particular
form. The word man has, therefore, two different meanings ;
though not commonly considered as ambiguous, because it
happens in both cases io denote the same individual objects.
But a case is conceivable in which the ambiguity would
become evident : we have only to imagine that some new
kind of animal were discovered, having Linnseus's three cha-
racteristics of humanity, but not rational, or not of the human
form. In ordinary parlance, these animals would not be
called men ; but in natural history they must still be called
so hy those, if any there should be, who adhere to the Linusean
classification; and the question would arise, whether the word
should continue to be used in two senses, or the classification
be given up, and the technical sense of the term be abandoned
along with it.

Words not otherwise connotative may, in the mode just
adverted to, acquire a special or technical connotation. Thus
the word whiteness, as we have so often remarked, connotes
nothing ; it merely denotes the attribute corresponding to a
certain sensation : hut if we are making a classification of

CLASSIFICATION AND THE PREDICABLES. 147

colours, and desire to justify, or even merely to point out, the
particular place assigned to whiteness in our arrangement, we
may define it " the colour produced by the mixture of all the
simple rays ;" and this fact, though by no means implied in
the meaning of the word whiteness as ordinarily used, but
only known by subsequent scientific investigation, is part of
its meaning in the particular essay or treatise, and becomes
the differentia of the species.*

The differentia, therefore, of a species may be defined
to be, that part of the connotation of the specific name,
whether ordinary or special and technical, which distin-
guishes the species in question from all other species of the
genus to which on the particular occasion we are refer-
ring it.

§ 7. Having disposed of Genus, Species, and Differentia,
we shall not find much difficulty in attaining a clear concep-
tion of the distinction between the other two predicables, as
well as between them and the first three.

In the Aristotelian phraseology, Genus and Differentia
are of the essence of the subject; by which, as we have seen,
is really meant that the properties signified by the genus
and those signified by the differentia, form part of the con-
notation of the name denoting the species. Proprium and
Accidens, on the other hand, form no part of the essence, but
are predicated of the species only accidentally. Both are
Accidents, in the wider sense in which the accidents of a
thing are opposed to its essence ; though, in the doctrine of
the Predicables, Accidens is used for one sort of accident
only, Proprium being another sort. Proprium, continue the
schoolmen, is predicated accidentally, indeed, but necessarily ;
or, as they further explain it, signifies an attribute which is
not indeed part of the essence, but which flows from, or is a
consequence of, the essence, and is, therefore, inseparably

* If we allow a differentia to what is not really a species. For the distinc-
tion of Kinds, in the sense explained by us, not being in any way applicable to
attributes, it of course follows that although attributes may be put into classes,
those classes can be admitted to be genera or species only by courtesy.

10—2

148 NAMES AND PROPOSITIONS.

attached to the species ; e. g. the various properties of a
triangle, which, though no part of its definition, must neces-
sarily he possessed hy whatever comes under that definition.
Accidens, on the contrary, has no connexion whatever with
the essence, but may come and go, and the species still re-
main what it was before. If a species could exist without its
Propria, it must be capable of existing without that on which
its Propria are necessarily consequent, and therefore without
its essence, without that which constitutes it a species.
But an Accidens, whether separable or inseparable from the
species in actual experience, may be supposed separated,
without the necessity of supposing any other alteration ; or
at least, without supposing any of the essential properties of
the species to be altered, since with them an Accidens has no
connexion.

A Proprium, therefore, of the species, may be defined, any
attribute which belongs to all the individuals included in the
species, and which, though not connoted by the specific name,
(either ordinarily if the classification we are considering be for
ordinary purposes, or specially if it be for a special purpose,)
yet follows from some attribute which the name either ordi-
narily or specially connotes.

One attribute may follow from another in two ways ; and
there are consequently two kinds of Proprium. It may
follow as a conclusion follows premises, or it may follow as
an effect follows a cause. Thus, the attribute of having the
opposite sides equal, which is not one of those connoted by
the word Parallelogram, nevertheless follows from those con-
noted by it, namely, from having the opposite sides straight
lines and parallel, and the number of sides four. The attri-
bute, therefore, of having the opposite sides equal, is a Pro-
prium of the class parallelogram ; and a Proprium of the
first kind, which follows from the connoted attributes by way
of demonstration. The attribute of being capable of under-
standing language, is a Proprium of the species man, since
without being connoted by the word, it follows from an attri-
bute which the word does connote, viz., from the attribute
of rationality. But this is a Proprium of the second kind,

CLASSIFICATION AND THE PREDICABLES. 149

which follows by way of causation. How it is that one pro-
perty of a thing follows, or can be inferred, from another;
under what conditions this is possible, and what is the exact
meaning of the phrase ; are among the questions which will
occupy us in the two succeeding Books. At present it needs
only be said, that whether a Proprium follows by demonstra-
tion or by causation, it follows necessarily ; that is to say, its
not following would be inconsistent with some law which we
regard as a part of the constitution either of our thinking
faculty or of the universe.

§ 8. Under the remaining predicable, Accidens, are in-
cluded all attributes of a thing which are neither involved in
the signification of the name (whether ordinarily or as a term
of art), nor have, so far as we know, any necessary connexion
with attributes which are so involved. They are commonly
divided into Separable and Inseparable Accidents. Inseparable
accidents are those which — although we know of no connexion
between them and the attributes constitutive of the species,
and although, therefore, so far as we are aware, they might be
absent without making the name inapplicable and the species
a different species — are yet never in fact known to be absent.
A concise mode of expressing the same meaning is, that in-
separable accidents are properties which are universal to the
species, but not necessary to it. Thus, blackness is an attri-
bute of a crow, and, as far as we know, an universal one. But
if we were to discover a race of white birds, in other respects
resembling crows, we should not say, These are not crows ; we
should say, These are white crows. Crow, therefore, does not
connote blackness ; nor, from any of the attributes which it
does connote, whether as a word in popular use or as a term
of art, could blackness be inferred. Not only, therefore, can
we conceive a white crow, but we know of no reason why such
an animal should not exist. Since, however, none but black
crows are known to exist, blackness, in the present state of our
knowledge, ranks as an accident, but an inseparable accident,
of the species crow.

Separable Accidents are those which are found, in point of

150 NAMES AND PROPOSITIONS.

fact, to be sometimes absent from tbe species ; which are not
only not necessary, but not even universal. They are such as
do not belong to every individual of the species, but only to
some individuals ; or if to all, not at all times. Thus the
colour of an European is one of the separable accidents of
the species man, because it is not an attribute of all human
creatures. Being born, is also (speaking in the logical sense)
a separable accident of the species man, because, though an
attribute of all human beings, it is so only at one particular
time. A fortiori those attributes which are not constant even
in the same individual, as, to be in one or in another place, to
be hot or cold, sitting or walking, must be ranked as separable
accidents.

CHAPTEE VIII.

OF DEFINITION".

§ 1. ONE necessary part of the theory of Names and of
Propositions remains to be treated of in this place : the theory
of Definitions. As being the most important of the class of
propositions which we have characterized as purely verbal,
they have already received some notice in the chapter pre-
ceding the last. But their fuller treatment was at that time
postponed, because definition is so closely connected with clas-
sification, that, until the nature of the latter process is in some
measure understood, the former cannot be discussed to much
purpose.

The simplest and most correct notion of a Definition is, a
proposition declaratory of the meaning of a word ; namely,
either the meaning which it bears in common acceptation, or
that which the speaker or writer, for the particular purposes of
his discourse, intends to annex to it.

The definition of a word being the proposition which
enunciates its meaning, words which have no meaning are
unsusceptible of definition. Proper names, therefore, cannot
be defined. A proper name being a mere mark put upon an
individual, and of which it is the characteristic property to be
destitute of meaning, its meaning cannot of course be de-
clared ; though we may indicate by language, as we might
indicate still more conveniently by pointing with the finger,
upon what individual that particular mark has been, or is
intended to be, put. It is no definition of " John Thomson"
to say he is " the son of General Thomson ;" for the name
John Thomson does not express this. Neither is it any
definition of "John Thomson" to say he is "the man now
crossing the street." These propositions may serve to make
known who is the particular man to whom the name belongs,
but that may be done still more unambiguously by pointing to

152 NAMES AND PROPOSITIONS. .

him, which, however, has not been esteemed one of the modes
of definition.

In the case of connotative names, the meaning, as has been
so often observed, is the connotation ; and the definition of a
connotative name, is the proposition which declares its conno-
tation. This might be done either directly or indirectly. The
direct mode would be by a proposition in this form : " Man"
(or whatsoever the word may be) " is a name connoting such
and such attributes," or " is a name which, when predicated of
anything, signifies the possession of such and such attributes
by that thing." Or thus : Man is everything which possesses
such and such attributes : Man is everything which possesses
corporeity, organization, life, rationality, and certain pecu-
liarities of external form.

This form of definition is the most precise and least equi-
vocal of any ; but it is not brief enough, and is besides too
technical for common discourse. The more usual mode of
declaring the connotation of a name, is to predicate of it
another name or names of known signification, which connote
the same aggregation of attributes. This may be done either
by predicating of the name intended to be defined, another
counotative name exactly synonymous, as, " Man is a human
being," which is not commonly accounted a definition at all ;
or by predicating two or more connotative names, which make
up among them the whole connotation of the name to be
defined. In this last case, again, we may either compose
our definition of as many connotative names as there are
attributes, each attribute being connoted by one, as, Man is
a corporeal, organized, animated, rational being, shaped so
and so ; or we may employ names which connote several of
the attributes at once, as, Man is a rational animal, shaped so
and so.

The definition of a name, according to this view of it, is
the sum total of all the essential propositions which can be
framed with that name for their subject. All propositions the
truth of which is implied in the name, all those which we are
made aware of by merely hearing the name, are included in
the definition, if complete, and may be evolved from it without

DEFINITIOX. 153

the aid of any other premises ; whether the definition expresses
them in two or three words, or in a larger number. It is,
therefore, not without reason that Condillac and other writers
have affirmed a definition to be an analysis. To resolve any
rvinplex whole into the elements of which it is compounded,
is the meaning of analysis : and this we do when we replace
ono word which connotes a set of attributes collectively, by
two or more which connote the same attributes singly, or in
smaller Croups.

§ 2. From this, however, the question naturally arises, in
what manner aro we to define a name which connotes only a
single attribute : lor instance, " white," which connotes nothing
but whiteness ; " rational," which connotes nothing but the
possession of reason. It might seem that the meaning of such
names could only be declared in two ways ; by a synonymous
term, if any such can be found ; or in the direct way already
alluded to : " White is a name connoting the attribute white-
ness." Let us see, however, whether tho analysis of the mean-
ing of the name, that is, the breaking down of that meaning
into several parts, admits of being carried farther. Without
at present deciding this question as to the word white, it is
obvious that in the case of rational some further explanation
may be given of its meaning than is contained in the propo-
sition, " Kational is that which possesses the attribute of
reason;" since the attribute reason itself admits of being de-
fined. And here we must turn our attention to the definitions
of attributes, or rather of the names of attributes, that is, of
abstract names.

In regard to such names of attributes as are connotative,
and express attributes of those attributes, there is no diffi-
culty : like other connotative names they are defined by de-
claring their connotation. Thus the word fault may be defined,
" a quality productive of evil or inconvenience." Sometimes,
again, the attribute to be defined is not one attribute, but an
union of several : we have only, therefore, to put together the
names of all the attributes taken separately, and we obtain
the definition of the name which belongs to them all taken

154 NAMES AND PROPOSITIONS.

together; n definition which will correspond exactly to that
of the corresponding concrete name. For, as we define a con-
crete name by enumerating the attributes which it connotes,
and as the attributes connoted by a concrete name form the
entire signification of the corresponding abstract name, the
same enumeration will serve for the definition of both. Thus,
if the definition of a human being be this, " a being, corporeal,
animated, rational, shaped so and so," the definition of humanity
will be corporeity and animal life, combined with rationality,
and with such and such a shape.

When, on the other hand, the abstract name does not
express a complication of attributes, but a single attribute, we
must remember that every attribute is grounded on some fact
or phenomenon, from which, and which alone, it derives its
meaning. To that fact or phenomenon, called in a former
chapter the foundation of the attribute, we must, therefore,
have recourse for its definition. Now, the foundation of the
attribute may be a phenomenon of any degree of complexity,
consisting of many different parts, either coexistent or in suc-
cession. To obtain a definition of the attribute, we must
analyse the phenomenon into these parts. Eloquence, for
example, is the name of one attribute only ; but this attribute
is grounded on external effects of a complicated nature, flowing
from acts of the person to whom we ascribe the attribute ; and
by resolving this phenomenon of causation into its two parts,
the cause and the effect, we obtain a definition of eloquence,
viz. the power of influencing the feelings by speech or writing.

A name, therefore, whether concrete or abstract, admits of
definition, provided we are able to analyse, that is, to distin-
guish into parts, the attribute or set of attributes which con-
stitute the meaning both of the concrete name and of the
corresponding abstract: if a set of attributes, by enumerating
them ; if a single attribute, by dissecting the fact or pheno-
menon (whether of perception or of internal consciousness)
which is the foundation of the attribute. But, further, even
when the fact is one of our simple feelings or states of con-
sciousness, and therefore unsusceptible of analysis, the names
both of the object and of the attribute still admit of definition :

DEFINITION. 155

or rather, would do so if all our simple feelings had names.
Whiteness may be defined, the property or power of exciting
the sensation of white. A white object may be defined, an
object which excites the sensation of white. The only names
which are unsusceptible of definition, because their meaning
is unsusceptible of analysis, are the names of the simple feel-
ings themselves. These are in the same condition as proper
names. They are not indeed, like proper names, unmeaning ;
for the words sensation of white signify, that the sensation
which I so denominate resembles other sensations which I re-
member to have had before, and to have called by that name.
But as we have no words by which to recal those former sen-
sations, except the very word which we seek to define, or some
other which, being exactly synonymous with it, requires defi-
nition as much, words cannot unfold the signification of this
class of names ; and we are obliged to make a direct appeal to
the personal experience of the individual whom we address.

§ 3. Having stated what seems to be the true idea of a
Definition, I proceed to examine some opinions of philo-
sophers, and some popular conceptions on the subject, which
conflict more or less with that idea.

The only adequate definition of a name is, as already re-
mai'ked, one which declares the facts, and the whole of the facts,
which the name involves in its signification. But with most
persons the object of a definition does not embrace so much ;
they look for nothing more, in a definition, than a guide to
the correct use of the term — a protection against applying it
in a manner inconsistent with custom and convention. Any-
thing, therefore, is to them a sufficient definition of a term,
which will serve as a correct index to what the term denotes ;
though not embracing the whole, and sometimes, perhaps, not
even any part, of what it connotes. This gives rise to two
sorts of imperfect, or unscientific definition; Essential but in-
complete Definitions, and Accidental Definitions, or Descrip-
tions. In the former, a connotative name is defined by a part
only of its connotation ; in the latter, by something which
forms no part of the connotation at all.

156 NAMES AND PROPOSITIONS.

An example of the first kind of imperfect definitions is the
following : — Man is a rational animal. It is impossible to
consider this as a complete definition of the word Man, since
(as before remarked) if we adhered to it we should be obliged
to call the Houyhnhnms men ; but as there happen to be no
Houyhnhnms, this imperfect definition is sufficient to mark
out and distinguish from all other things, the objects at present
denoted by " man ;" all the beings actually known to exist, of
whom the name is predicable. Though the word is defined by
some only among the attributes which it connotes, not by all,
it happens that all known objects which possess the enume-
rated attributes, possess also those which are omitted ; so that
the field of predication which the word covers, and the employ-
ment of it which is conformable to usage, are as well indicated
by the inadequate definition as by an adequate one. Such
definitions, however, are always liable to be overthrown by the
discovery of new objects in nature.

Definitions of this kind are what logicians have had in
view, when they laid down the rule, that the definition of a
species should be per genus et differ entiam. Differentia being
seldom taken to mean the whole of the peculiarities constitu-
tive of the species, but some one of those peculiarities only,
a complete definition would be per genus et differentias, rather
than differentiam. It would include, with the name of the
superior genus, not merely some attribute which distinguishes
the species intended to be defined from all other species of the
same genus, but all the attributes implied in the name of the
species, which the name of the superior genus has not already
implied. The assertion, however, that a definition must of
necessity consist of a genus and differentias, is not tenable. It
was early remarked by logicians, that the summum genus in
any classification, having no genus superior to itself, could not
be defined in this manner. Yet we have seen that all names,
except those of our elementary feelings, are susceptible of
definition in the strictest sense ; by setting forth in words the
constituent parts of the fact or phenomenon, of which the
connotation of every word is ultimately composed.

DEFINITION. 157

§ 4. Although the first kind of imperfect definition,
(which defines a connotative term by a part only of what it
connotes, hut a part sufficient to mark out correctly the
boundaries of its denotation,) has been considered by the
ancients, and by logicians in general, as a complete definition ;
it has always been deemed necessary that the attributes em-
ployed should really form part of the connotation ; for the
rule was that the definition must be drawn from the essence
of the class ; and this would not have been the case if it had
been in any degree made up of attributes not connoted by the
name. The second kind of imperfect definition, therefore, in
which the name of a class is defined by any of its accidents, —
that is, by attributes which are not included in its connota-
tion,— has been rejected from the rank of genuine Definition
by all logicians, and has been termed Description.

This kind of imperfect definition, however, takes its rise
from the same cause as the other, namely, the willingness to
accept as a definition anything which, whether it expounds
the meaning of the name or not, enables us to discriminate the
things denoted by the name from all other things, and conse-
quently to employ the term in predication without deviating
from established usage. This purpose is duly answered by
stating any (no matter what) of the attributes which are
common to the whole of the class, and peculiar to it; or any
combination of attributes which happens to be peculiar to it,
though separately each of those attributes may be common to
it with some other things. It is only necessary that the defi-
nition (or description) thus formed, should be convertible with
the name which it professes to define ; that is, should be
exactly co-extensive with it, being predicable of everything of
which it is predicable, and of nothing of which it is not pre-
dicable ; though the attributes specified may have no con-
nexion with those which mankind had in view when they
formed or recognised the class, and gave it a name. The fol-
lowing are correct definitions of Man, according to this test :
Man is a mammiferous animal, having (by nature) two hands
(for the human species answers to this description, and no

158 NAMES AND PROPOSITIONS.

other animal does) : Man is an animal who cooks his food :
Man is a featherless biped.

What would otherwise be a mere description, may be
raised to the rank of a real definition by the peculiar purpose
which the speaker or writer has in view. As was seen in the
preceding chapter, it may, for the ends of a particular art or
science, or for the more convenient statement of an author's
particular doctrines, be advisable to give to some general name,
without altering its denotation, a special connotation, different
from its ordinary one. When this is done, a definition of the
name by means of the attributes which make up the special
connotation, though in general a mere accidental definition or
description, becomes on the particular occasion and for the
particular purpose a complete and genuine definition. This
actually occurs with respect to one of the preceding examples,
"Man is a mammiferous animal having two hands," which is
the scientific definition of man, considered as one of the species
in Cuvier's distribution of the animal kingdom.

In cases of this sort, though the definition is still a decla-
ration of the meaning which in the particular instance the
name is appointed to convey, it cannot be said that to state
the meaning of the word is the purpose of the definition. The
purpose is not to expound a name, but a classification. The
special meaning which Cuvier assigned to the word Man,
(quite foreign to its ordinary meaning, though involving no
change in the denotation of the word,) was incidental to a
plan of arranging animals into classes on a certain principle,
that is, according to a certain set of distinctions. And since
the definition of Man according to the ordinary connotation of
the word, though it would have answered every other purpose
of a definition, would not have pointed out the place which
the species ought to occupy in that particular classification ;
he gave the word a special connotation, that he might be able
to define it by the kind of attributes on which, for reasons of
scientific convenience, he had resolved to found his division of
animated nature.

Scientific definitions, whether they are definitions of scien-
tific terms, or of common terms used in a scientific sense, are

DEFINITION. 159

almost always of the kind last spoken of: their main purpose
is to serve as the landmarks of scientific classification. And
since the classifications in any science are continually modified
as scientific knowledge advances, the definitions in the sciences
are also constantly varying. A striking instance is afforded
hy the words Acid and Alkali, especially the former. As-
experimental discovery advanced, the substances classed with
acids have been constantly multiplying, and by a natural con-
sequence the attributes connoted by the word have receded and
become fewer. At first it connoted the attributes, of combin-
ing with an alkali to form a neutral substance (called a salt) ;
being compounded of a base and oxygen ; causticity to the
taste and touch ; fluidity, &c. The true analysis of muriatic
acid, into chlorine and hydrogen, caused the second property,
composition from a base and oxygen, to be excluded from
the connotation. The same discovery fixed the attention of
chemists upon hydrogen as an important element in acids ;
and more recent discoveries having led to the recognition of
its presence in sulphuric, nitric, and many other acids, where
its existence was not previously suspected, there is now a ten-
dency to include the presence of this element in the conno-
tation of the word. But carbonic acid, silica, sulphurous acid,
have no hydrogen in their composition ; that property cannot
therefore be connoted by the term, unless those substances
are no longer to be considered acids. Causticity and fluidity
have long since been excluded from the characteristics of the
class, by the inclusion of silica and many other substances in
it; and the formation of neutral bodies by combination with
alkalis, together with such electro-chemical peculiarities as
this is supposed to imply, are now the only differentia; which
form the fixed connotation of the word Acid, as a term of
chemical science.

What is true of the definition of any term of science, is of
course true of the 'definition of a science itself; and accord-
ingly, (as observed in the Introductory Chapter of this work,}
the definition of a science must necessarily be progressive and
provisional. Any extension of knowledge or alteration in the
current opinions respecting the subject matter, may lead to a

160 NAMES AND PROPOSITIONS.

change more or less extensive in the particulars included in
the science ; and its composition being thus altered, it may
easily happen that a different set of characteristics will be
found better adapted as differentise for defining its name.

In the same manner in which a special or technical defini-
tion has for its object to expound the artificial classification
out of which it grows ; the Aristotelian logicians seem to
have imagined that it was also the business of ordinary defini-
tion to expound the ordinary, and what they deemed the
natural, classification of things, namely, the division of them
into Kinds ; and to show the place which each Kind occupies,
as superior, collateral, or subordinate, among other Kinds.
This notion would account for the rule that all definition
must necessarily be per genus et differentiam, and would also
explain why a single differentia was deemed sufficient But
to expound, or express in words, a distinction of Kind, has
already been shown to be an impossibility : the very meaning
of a Kind is, that the properties which distinguish it do not
grow out of one another, and cannot therefore be set forth in
words, even by implication, otherwise than by enumerating
them all : and all are not known, nor are ever likely to be so. It
is idle, therefore, to look to this as one of the purposes of a
definition : while, if it be only required that the definition of a
Kind should indicate what kinds include it or are included by
it, any definitions which expound the connotation of the names
will do this : for the name of each class must necessarily con-
note enough of its properties to fix the boundaries of the
class. If the definition, therefore, be a full statement of the
connotation, it is all that a definition can be required to be.*

* Professor Bain, in his Logic, takes a peculiar view of Definition. He holds
(i. 71) with the present work, that " the definition in its full import, is the sum
of all the properties connoted by the name ; it exhausts the meaning of a word."
But he regards the meaning of a general name as including, not indeed all the
common properties of the class named, but all of them that are ultimate pro-
perties, not resolvable into one another. " The enumeration of the attributes
of oxygen, of gold, of man, should be an enumeration of the final (so far as can
be made out,) the underivable, powers or functions of each," and nothing less
than this is a -complete Definition (i. 75). An independent property, not
derivable from other properties, even if previously unknown, yet as soon as dis-

DEFINITION. 161

§ 5. Of the two incomplete and popular modes of defini-
tion, and in what they differ from the complete or philoso-
phical mode, enough has now been said. We shall next ex-
amine an ancient doctrine, once generally prevalent and still
by no means exploded, which I regard as the source of a great
part of the obscurity hanging over some of the most important
processes of the understanding in the pursuit of truth. Ac-
cording to this, the definitions of which we have now treated

covered becomes, according to him, part of the meaning of the term, and
should be included in the definition. " When we are told that diamond, which
we know to be a transparent, glittering, hard, and high-priced substance, is
composed of carbon, and is combustible, we must put these additional proper-
ties on the same level as the rest ; to us they are henceforth connoted by the
name" (i. 73). Consequently the propositions that diamond is composed of
carbon, and that it is combustible, are regarded by Me. Bain as merely verbal
propositions. He carries this doctrine so far as to say that unless mortality
can be shown to be a consequence of the ultimate laws of animal organization,
mortality is connoted by man, and " Man is Mortal " is a merely verbal propo-
sition. And one of the peculiarities (I think a disadvantageous peculiarity) of
his able and valuable treatise, is the large number of propositions requiring
proof, and learnt by experience, which, in conformity withjihis doctrine, he con-
siders as not real, but verbal, propositions.

The objection I have to this language is that it confounds, or at least con-
fuses, a much more important distinction than that which it diaws. The only
reason for dividing Propositions into real and verbal, is in Older to discriminate
propositions which convey information about facts, from those which do not. A
proposition which affirms that an object has a given attribute, while designating
the object by a name which already signifies the attribute, adds no information to
that which was already possessed by all who understood the name. Biit when this
issaid, it is implied that, by the signification of a name, is meant the signification
attached to it in the common usage of life. I cannot think we ought to say
that the meaning of a word includes matters of fact which are unknown to every
person who uses the word unless he has learnt them by special study of a par-
ticular department of Nature ; or that because a few persons are aware of these
matters of fact, the affirmation of them is a proposition conveying no informa-
tion. I hold that (special scientific connotation apart) a name means, or con-
notes, only the properties which it is a mark of in the general mind ; and that
in the case of any additional properties, however uniformly found to accompany
these, it remains possible that a thing which did not possess the properties might
still be thought entitled to the name. Ruminant, according to Mr. Bain's use
of langUHge, connotes cloven hoofed, since the two properties are always found
together, and no connexion has ever been discovered between them : but rumi-
nant does not mean cloven-hoofed ; and were an animal to be discovered which
chews the cud, but has its feet undivided, I venture to say that it would still be
called ruminant.

VOL. I. J 1

162 NAMES AND PROPOSITIONS.

are only one of two sorts into which definitions may be
divided, viz. definitions of names, and definitions of things.
The former are intended to explain the meaning of a term ;
the latter, the nature of a thing ; the last being incompa-
rably the most important.

This opinion was held by the ancient philosophers, and by
their followers, with the exception of the Nominalists ; but as
the spirit of modern metaphysics, until a recent period, has
been on the whole a Nominalist spirit, the notion of defini-
tions of things has been to a certain extent in abeyance, still
continuing, however, to breed confusion in logic, by its conse-
quences indeed rather than by itself. Yet the doctrine in its
own proper form now and then breaks out, and has appeared
(among other places) where it was scarcely to be expected, in
a justly admired work, Archbishop Whately's Logic.* In a
review of that work published by me in the Westminster

* In the fuller discussion which Archbishop Whately has given to this
subject in his later editions, he almost ceases to regard the definitions of names
and those of things as, in any important sense, distinct. He seems (9th ed.
p. 145) to limit the notion of a Real Definition to one which "explains any-
thing more of the nature of the thing than is implied in the name ;" (including
under the word "implied," not only what the name connotes, but everything
which can be deduced by reasoning from the attributes connoted). Even this,
as he adds, is usually called, not a Definition, but a Description ; and (as it
seems to me) rightly so called. A Description, I conceive, can only be ranked
among Definitions, when taken (as in the case of the zoological definition of
man) to fulfil the true office of a Definition, by declaring the connotation given
to a word in some special use, as a term of science or art : which special con-
notation of course would not be expressed by the proper definition of the word
in its ordinary employment.

Mr. De Morgan, exactly reversing the doctrine of Archbishop "VVhately, un-
derstands by a Real Definition one which contains less than the Nominal Defi -
nition, provided only that what it contains is sufficient for distinction. " By
real definition I mean such an explanation of the word, be it the whole of the
meaning or only part, as will be sufficient to separate the things contained
under that word from all others. Thus the following, I believe, is a complete
definition of an elephant : An animal which naturally drinks by drawing the
water into its nose, and then spurting it into its mouth." — Formal Logic, p. 36.
Mr. De Morgan's general proposition and his example are at variance ; for the
peculiar mode of drinking of the elephant certainly forms no part of the mean-
ing of the word elephant. It could not be said, because a person happened to
be ignorant of this property, that he did not know what an elephant means.

DEFINITION. 163

Review for January 1828, and containing some opinions which
I no longer entertain, I find the following observations on the
question now before us ; observations with which my present
view of that question is still sufficiently in accordance.

"The distinction between nominal and real definitions,
between definitions of words and what are called definitions
of things, though conformable to the ideas of most of the
Aristotelian logicians, cannot, as it appears to us, be main-
tained. We apprehend that no definition is ever intended to
' explain and unfold the nature of a thing.' It is some confir-
mation of our opinion, that none of those writers who have
thought that there were definitions of things, have ever suc-
ceeded in discovering any criterion by which the definition of
a thing can be distinguished from any other proposition
relating to the thing. The definition, they say, unfolds the
nature of the thing : but no definition can unfold its whole
nature ; and every proposition in which any quality whatever
is predicated of the thing, unfolds some part of its nature.
The true state of the case we take to be this. All definitions
are of names, and of names only ; but, in some definitions, it
is clearly apparent, that nothing is intended except to explain
the meaning of the word ; while in others, besides explaining
the meaning of the word, it is intended to be implied that
there exists a thing, corresponding to the word. Whether
this be or be not implied in any given case, cannot be collected
from the mere form of the expression. ' A centaur is an
animal with the upper parts of a man and the lower parts of a
horse,' and ' A triangle is a rectilineal figure with three sides,'
are, in form, expressions precisely similar ; although in the
former it is not implied that any thing, conformable to the
term, really exists, while in the latter it is ; as may be seen by
substituting, in both definitions, the word means for is. In
the first expression, ' A centaur means an animal,' &c., the
sense would remain unchanged : in the second, ' A triangle
means,' &c., the meaning would be altered, since it would be
obviously impossible to deduce any of the truths of geometry
from a proposition expressive only of the manner in which we
intend to employ a particular sign.

11—2

164 NAMES AND PROPOSITIONS.

" There are, therefore, expressions, commonly passing for
definitions, which include in themselves more than the mere
explanation of the meaning of a term. But it is not correct
to call an expression of this sort a peculiar kind of definition.
Its difference from the other kind consists in this, that it is
not a definition, but a definition and something more. The
definition above given of a triangle, obviously comprises not
one, but two propositions, perfectly distinguishable. The one
is, ' There may exist a figure, bounded by three straight lines;'
the other, ' And this figure may be termed a triangle.' The
former of these propositions is not a definition at all : the
latter is a mere nominal definition, or explanation of the use
and application of a term. The first is susceptible of truth or
falsehood, and may therefore be made the foundation of a
train of reasoning. The latter can neither be true nor false ;
the only character it is susceptible of is that of conformity or
disconformity to the ordinary usage of language."

There is a real distinction, then, between definitions of
names, and what are erroneously called definitions of things ;
but it is, that the latter, along with the meaning of a name,
covertly asserts a matter of fact. This covert assertion is not
a definition, but a postulate. The definition is a mere iden-
tical proposition, which gives information only about the use
of language, and from which no conclusions affecting matters
of fact can possibly be drawn. The accompanying postulate
on the other hand, affirms a fact, which may lead to conse-
quences of every degree of importance. *It affirms the actual
or possible existence of Things possessing the combination of
attributes set forth in the definition ; and this, if true, may be
foundation sufficient on which to build a whole fabric of
scientific truth.

We have already made, and shall often have to repeat, the
remark, that the philosophers who overthrew Realism by no
means got rid of the consequences of Realism, but retained
long afterwards, in their own philosophy, numerous proposi-
tions which could only have a rational meaning as part of
a Realistic system. It had been handed down from Aristotle,
and probably from earlier times, as an obvious truth, that the

DEFINITION. 165

science of Geometry is deduced from definitions. This, so
long as a definition was considered to be a proposition " un*
folding the nature of the thing," did well enough. But
Hobbes followed, and rejected utterly the notion that a defi-
nition declares the nature of the thing, or does anything but
state the meaning of a name ; yet he continued to affirm as
broadly as any of his predecessors, that the ap\ai, principia,
or original premises of mathematics, and even of all science,
are definitions ; producing the singular paradox, that systems
of scientific truth, nay, all truths whatever at which we arrive
by reasoning, are deduced from the arbitrary conventions of
mankind concerning the signification of words.

To save the credit of the doctrine that definitions are the
premises of scientific knowledge, the proviso is sometimes
added, that they are so only under a certain condition, namely,
that they be framed conformably to the phenomena of nature ;
that is, that they ascribe such meanings to terms as shall
suit objects actually existing. But this is only an instance of
the attempt so often made, to escape from the necessity of
abandoning old language after the ideas which it expresses
have been exchanged for contrary ones. From the meaning
of a name (we are told) it is possible to infer physical facts,
provided the name has corresponding to it an existing thing.
But if this proviso be necessary, from which of the two is
the inference really drawn ? From the existence of a thing
having the properties, or from the existence of a name mean-
ing them ?

Take, for instance, any of the definitions laid down as
premises in Euclid's Elements ; the definition, let us say, of a
circle. This, being analysed, consists of two propositions ;
the one an assumption with respect to a matter of fact, the
other a genuine definition. " A figure may exist, having all
the points in the line which bounds it equally distant from a
single point within it :" " Any figure possessing this property
is called a circle." Let us look at one of the demonstrations
which are said to depend on this definition, and observe to
which of the two propositions contained in it the demonstra-
tion really appeals. " About the centre A, describe the circle

NAMES AND PROPOSITIONS.

B 0 D." Here is an assumption that a figure, such as the
definition expresses, may be described ; which is no other than
the postulate, or covert assumption, involved in the so-called
definition. But whether that figure be called a circle or not
is quite immateiial. The purpose would be as well answered,
in all respects except brevity, were we to say, " Through the
point B, draw a line returning into itself, of which every point
shall be at an equal distance from the point A." By this the
definition of a circle would be got rid of, and rendered need-
less; but not the postulate implied in it; without that the
demonstration could not stand. The circle being now described,
let us proceed to the consequence. " Since B C D is a circle,
the radius B A is equal to the radius C A." B A is equal to
C A, not because B C D is a circle, but because B C D is a
figure with the radii equal. Our warrant for assuming that
such a figure about the centre A, with the radius B A, may be
made to exist, is the postulate. Whether the admissibility of
these postulates rests on intuition, or on proof, may be a
matter of dispute ; but in either case they are the premises on
which the theorems depend ; and while these are retained it
would make no difference in the certainty of geometrical
truths, though every definition in Euclid, and every technical
term therein defined, were laid aside.

It is, perhaps, superfluous to dwell at so much length on
what is so nearly self-evident; but when a distinction, obvious
as it may appear, has been confounded, and by powerful intel-
lects, it is better to say too much than too little for the pur-
pose of rendering such mistakes impossible in future. I will,
therefore, detain the reader while I point out one of the absurd
consequences flowing from the supposition that definitions, as
such, are the premises in any of our reasonings, except such
as relate to words only. If this supposition were true, we
might argue correctly from true premises, and arrive at a false
conclusion. We should only have to assume as a premise the
definition of a nonentity; or rather of a name which has
no entity corresponding to it. Let this, for instance, be our
definition :

A dragon is a serpent breathing flame.

DEFINITION.

This proposition, considered only as a definition, is indis-
putably correct. A dragon is a serpent breathing flame : the
word means that. The tacit assumption, indeed, (if there were
any sucb understood assertion), of the existence of an object
with properties corresponding to the definition, would, in the
present instance, be false. Out of this definition we may carve
the premises of the following syllogism :

A dragon is a thing which breathes flame:
A dragon is a serpent :
From which the conclusion is,

Therefore some serpent or serpents breathe flame : —
an unexceptionable syllogism in the first mode of the third
figure, in which both premises are true and yet the conclusion
false ; which every logician knows to be an absurdity. The
conclusion being false and the syllogism correct, the premises
cannot be true. But the premises, considered as parts of a
definition, are true. Therefore, the premises considered as
parts of a definition cannot be the real ones. The real pre-
mises must be —

A dragon is a really existing thing which breathes flame :

A dragon is a really existing serpent :

which implied premises being false, the falsity of the conclu-
sion presents no absurdity.

If we would determine what conclusion follows from the
same ostensible premises when the tacit assumption of real
existence is left out, let us, according to the recommendation
in a previous page, substitute means for is. We then have —

Dragon is a word meaning a thing which breathes flame :

Dragon is a word meaning a serpent :
From which the conclusion is,

Some word or words which mean a serpent, also mean a

thing which breathes flame :

where the conclusion (as well as the premises) is true, and
is the only kind of conclusion which can ever follow from a
definition, namely, a proposition relating to the meaning of
words.

There is still another shape into which we may transform
this syllogism. We may suppose the middle term to be the

168 NAMES AXD PROPOSITION'S.

designation neither of a thing nor of a name, but of an idea.
We then have —

The idea of a dragon is an idea of a thing which breathes
flame :

The idea of a dragon is an idea of a serpent :

Therefore, there is an idea of& serpent, which is an idea of
a thing breathing flame.

Here the conclusion is true, and also the premises ; but the
premises are not definitions. They are propositions affirming
that an idea existing in the mind, includes certain ideal ele-
ments. The truth of the conclusion follows from the existence
of the psychological phenomenon called the idea of a dragon ;
and therefore still from the tacit assumption of a matter of
fact.*

When, as in this last syllogism, the conclusion is a propo-

* In tbe only attempt which, so far as I know, has been made to refute
the preceding argumentation, it is maintained that in the first form of the
syllogism,

A dragon is a thing which breathes flame,

A dragon is a serpent,

Therefore some serpent or serpents breathe flame,

"there is just as much truth in the conclusion as there is in the premir.es, or
rather, no more in the latter than in the former. If the general name serpent
includes both real and imaginary serpents, there is no falsity in the conclusion ;
if not, there is falsity in the minor premise."

Let us, then, try to set out the syllogism on the hypothesis that the name
serpent includes imaginary serpents. We shall find that it is now necessary to
alter the predicates ; for it cannot be asserted that an imaginary creature
breathes flame ; in predicating of it such a fact, we assert by the most positive
implication that it is real and not imaginary. The conclusion must run thus,
" Some serpent or serpents either do or are imagined to breathe flame." And
to prove this conclusion by the instance of dragons, the premises must be, A
dragon is imagined as breathing flame. A dragon is a (real or imaginary) ser-
pent : from which it undoubtedly follows, that there are serpents which are
imagined to breathe flame ; but the major premise is not a definition, nor part
of a definition ; which is all that I am concerned to prove.

Let us now examine the other assertion — that if the word serpent stands for
none but real serpents, the minor premise (a dragon is a serpent) is false. This
is exactly what I have myself said of the premise, considered as a statement of
fact : but it is not false as part of the definition of a dragon ; and since the
premises, or one of them, must be false, (the conclusion being so,) the real
premise cannot be the definition, which is true, but the statement of fact,
which is false.

DEFINITION.

169

sition respecting an idea, the assumption on which it depends
may be merely that of the existence of an idea. But when
the conclusion is a proposition concerning a Thing, the postu-
late involved in the definition which stands as the apparent
premise, is the existence of a thing conformable to the defini-
tion, and not merely of an idea conformable to it. This as-
sumption of real existence we always convey the impression
that we intend to make, when we profess to define any name
which is already known to be a name of really existing objects.
On this account it is, that the assumption was not necessarily
implied in the definition of a dragon, while there was no doubt
of its being included in the definition of a circle.

§ 6. One of the circumstances which have contributed to
keep up the notion, that demonstrative truths follow from
definitions rather than from the postulates implied in those
definitions, is, that the postulates, even in those sciences
which are considered to surpass all others in demonstrative
certainty, are not always exactly true. It is not true that a
circle exists, or can be described, which has all its radii exactly
equal. Such accuracy is ideal only ; it is not found in nature,
still less can it be realized by art. People had a difficulty,
therefore, in conceiving that the most certain of all con-
clusions could rest on premises which, instead of being cer-
tainly true, are certainly not true to the full extent asserted.
This apparent paradox will be examined when we come to
treat of Demonstration ; where we shall be able to show that
as much of the postulate is true, as is required to support as
much as is true of the conclusion. Philosophers, however, to
whom this view had not occurred, or whom it did not satisfy,
have thought it indispensable that there should be found in
definitions something more certain, or at least more accu-
rately true, than the implied postulate of the real existence of
a corresponding object. And this something they flattered
themselves they had found, when they laid it down that a
definition is a statement and analysis not of the mere mean-
ing of a word, nor yet of the nature of a thing, but of an idea.
Thus, the proposition, "A circle is a plane figure bounded

170 NAMES AND PROPOSITIONS.

by a line all the points of which are at an equal distance from
a given point within it," was considered by them, not as an
assertion that any real circle has that property, (which would
not be exactly true,) but that we conceive a circle as having it ;
that our abstract idea of a circle is an idea of a figure with
its radii exactly equal.

Conformably to this it is said, that the subject-matter of
mathematics, and of every other demonstrative science, is not
things as they really exist, but abstractions of the mind. A
geometrical line is a line without breadth ; but no such line
exists in nature ; it is a notion merely suggested to the mind
by its experience of nature. The definition (it is said) is a
definition of this mental line, not of any actual line : and it is
only of the mental line, not of any line existing in nature, that
the theorems of geometry are accurately true.

Allowing this doctrine respecting the nature of demonstra-
tive truth to be correct (which, in a subsequent place, I
shall endeavour to prove that it is not ;) even on that suppo-
sition, the conclusions which seem to follow from a definition,
do not follow from the definition as such, but from an implied
postulate. Even if it be true that there is no object in
nature answering to the definition of a line, and that the
geometrical properties of lines are not true of any lines in
nature, but only of the idea of a line; the definition, at all
events, postulates the real existence of such an idea : it
assumes that the mind can frame, or rather has framed, the
notion of length without breadth, and without any other sen-
sible property whatever. To me, indeed, it appears that the
mind cannot form any such notion ; it cannot conceive length
without breadth; it can only, in contemplating objects, attend
to their length, exclusively of their other sensible qualities,
and so determine what properties may be predicated of them
in virtue of their length alone. If this be true, the postulate
involved in the geometrical definition of a line, is the real
existence, not of length without breadth, but merely of length,
that is, of long objects. This is quite enough to support all
the truths of geometry, since every property of a geometrical
line is really a property of all physical objects in so far as

DEFINITION. 171

possessing length. But even what I hold to be the false doc-
trine on the subject, leaves the conclusion that our reasonings
are grounded on the matters of fact postulated in definitions,
and not on the definitions themselves, entirely unaffected ;
and accordingly this conclusion is one which I have in
common with Dr. Whewell, in his Philosophy of the Inductive
Sciences : though, on the nature of demonstrative truth, Dr.
Whewell's opinions are greatly at variance with mine. And
here, as in many other instances, I gladly acknowledge that
his writings are eminently serviceable in clearing from con-
fusion the initial steps in the analysis of the mental processes,
even where his views respecting the ultimate analysis are such
as (though with unfeigned respect) I cannot but regard as
fundamentally erroneous.

§ 7. Although, according to the opinion here presented,
Definitions are properly of names only, and not of things, it
does not follow from this that definitions are arbitrary. How
to define a name, may not only be an inquiry of considerable
difficulty and intricacy, but may involve considerations going
deep into the nature of the things which are denoted by the
name. Such, for instance, are the inquiries which form the
subjects of the most important of Plato's Dialogues ; as,
" What is rhetoric ?" the topic of the Gorgias, or " What is
justice ?" that of the Kepublic. Such, also, is the question
scornfully asked by Pilate, " What is truth ?" and the funda-
mental question with speculative moralists in all ages, " What
is virtue ?"

It would be a mistake to represent these difficult and
noble inquiries as having nothing in view beyond ascertaining
the conventional meaning of a name. They are inquiries not
so much to determine what is, as what should be, the meaning
of a name ; which, like other practical questions of terminology,
requires for its solution that we should enter, and sometimes
enter very deeply, into the properties not merely of names but
of the things named.

Although the meaning of every concrete general name
resides in the attributes which it connotes, the objects were

172

NAMES AND PROPOSITIONS.

named before the attributes ; as appears from the fact that in
all languages, abstract names are mostly compounds or other
derivatives of the concrete names which correspond to them.
Connotative names, therefore, were, after proper names, the
first which were used : and in the simpler cases, no doubt, a
distinct connotation was present to the minds of those who
first used the name, and was distinctly intended by them to be
conveyed by it. The first person who used the word white, as
applied to snow or to any other object, knew, no doubt, very
well what quality he intended to predicate, and had a perfectly
distinct conception in his mind of the attribute signified by
the name.

But where the resemblances and differences on which our
classifications are founded are not of this palpable and easily
determinable kind ; especially where they consist not in any
one quality but in a number of qualities, the effects of which,
being blended together, are not very easily discriminated, and
referred each to its true source ; it often happens that names
are applied to nameable objects, with no distinct connotation
present to the minds of those who apply them. They are only
influenced by a general resemblance between the new object
and all or some of the old familiar objects which they have
been accustomed to call by that name. This, as we have
seen, is the law which even the mind of the philosopher
must follow, in giving names to the simple elementary feel-
ings of our nature : but, where the things to be named are
complex wholes, a philosopher is not content with noticing
a general resemblance ; he examines what the resemblance
consists in : and he only gives the same name to things which
resemble one another in the same definite particulars. The
philosopher, therefore, habitually employs his general names
with a definite connotation. But language was not made,
and can only in some small degree be mended, by philoso-
phers. In the minds of the real arbiters of language, general
names, especially where the classes they denote cannot be
brought before the tribunal of the outward senses to be iden-
tified and discriminated, connote little more than a vague
gross resemblance to the things which they were earliest, or

DEFINITION. 173

have been most, accustomed to call by those names. When,
for instance, ordinary persons predicate the words just or un-
just of any action, noble or mean of any sentiment, expression,
or demeanour, statesman or charlatan of any personage figur-
ing in politics, do they mean to affirm of those various sub-
jects any determinate attributes, of whatever kind ? No : they
merely recognise, as they think, some likeness, more or less
vague and loose, between these and some other things which
they have been accustomed to denominate or to hear denomi-
nated by those appellations.

Language, as Sir James Mackintosh used to say of govern-
ments, " is not made, but grows." A name is not imposed at
once and by previous purpose upon a class of objects, but is
first applied to one thing, and then extended by a series of
transitions to another and another. By this process (as has
been remarked by several writers, and illustrated with great
force and clearness by Dugald Stewart in his Philosophical
Essays) a name not unfrequently passes by successive links of
resemblance from one object to another, until it becomes ap-
plied to things having nothing in common with the first things
to which the name was given ; which, however, do not, for
that reason, drop the name ; so that it at last denotes a con-
fused huddle of objects, having nothing whatever in common ;
and connotes nothing, not even a vague and general resem-
blance. When a name has fallen into this state, in which by
predicating it of any object we assert literally nothing about
the object, it has become unfit for the purposes either of
thought or of the communication of thought ; and can only
be made serviceable by stripping it of some part of its multi-
farious denotation, and confining it to objects possessed of
some attributes in common, which it may be made to connote.
Such are the inconveniences of a language which "is not made,
but grows." Like the governments which are in a similar
case, it may be compared to a road which is not made but has
made itself: it requires continual mending in order to be
passable.

From this it is already evident, why the question respect-
ing the definition of an abstract name is often one of so much

174 NAMES AND PROPOSITIONS.

.difficulty. The question, What is justice? is, in other words,
What is the attribute which mankind mean to predicate when
they call an action just ? To which the first answer is, that
having come to no precise agreement on the point, they do
not mean to predicate distinctly any attribute at all. Never-
theless, all believe that there is some common attribute Be-
longing to all the actions which they are in the habit of calling
just. The question then must he, whether there is any such
common attribute ? and. in the first place, whether mankind
agree sufficiently with one another as to the particular actions
which they do or do not call just, to render the inquiry, what
quality those actions have in common, a possible one : if so,
whether the actions really have any quality in common ; and
if they have, what it is. Of these three, the first alone is an
inquiry into usage and convention ; the other two are inquiries
into matters of fact. And if the second question (whether the
actions form a class at all) has been answered negatively, there
remains a fourth, often more arduous than all the rest, namely,
how best to form a class artificially, which the name may
denote.

And here it is fitting to remark, that the study of the
spontaneous growth of languages is of the utmost importance
to those who would logically remodel them. The classifica-
tions rudely made by established language, when retouched, as
they almost all require to be, by the hands of the logician, are
often in themselves excellently suited to his purposes. As
compared with the classifications of a philosopher, they are
like the customary law of a country, which has grown up as
it were spontaneously, compared with laws methodized and
digested into a code : the former are a far less perfect instru-
ment than the latter ; but being the result of a long, though
unscientific, course of experience, they contain a mass of mate-
rials which may be made very usefully available in the forma-
tion of the systematic body of written law. In like manner,
the established grouping of objects under a common name,
even when founded only on a gross and general resemblance,
is evidence, in the first place, that the resemblance is obvious,
and therefore considerable ; and, in the next place, that it is

DEFINITION. 175

a resemblance which has struck great numbers of persons
during a series of years and ages. Even when a name, by
successive extensions, has come to be applied to things among
which there does not exist this gross resemblance common to
them all, still at every step in its progress we shall find such
a resemblance. And these transitions of the meaning of words
are often an index to real connexions between the things de-
noted by them, which might otherwise escape the notice of
thinkers; of those at least who, from using a different lan-
guage, or from any difference in their habitual associations,
have fixed their attention in preference on some other aspect
of the things. The history of philosophy abounds in examples
of such oversights, committed for want of perceiving the hidden
link that connected together the seemingly disparate meanings
of some ambiguous word.*

Whenever the inquiry into the definition of the name of
any real object consists of anything else than a mere comparison
of authorities, we tacitly assume that a meaning must be found
for the name, compatible with its continuing to denote, if pos-
sible all, but at any rate the greater or the more important
part, of the things of which it is commonly predicated. The
inquiry, therefore, into the definition, is an inquiry into the
resemblances and differences among those things : whether
there be any resemblance running through them all ; if not,
through what portion of them such a general resemblance can
be traced : and finally, what are the common attributes, the

* " Few people" (I have said in another place) "have reflected how great
a knowledge of Things is required to enable a man to affirm that any given
argument turns wholly upon words. There is, perhaps, not one of the leading
terms of philosophy which is not used in almost innumerable shades of meaning,
to express ideas more or less widely different from one another. Between two
of these ideas a sagacious and penetrating mind will discern, as it were intui-
tively, an unobvious link of connexion, upon which, though perhaps unable to
give a logical account of it, he will found a perfectly valid argument, which his
critic, not having so keen an insight into the Things, will mistake for a fallacy
turning on the double meaning of a term. And the greater the genius of him
who thus safely leaps over the chasm, the greater will probably be the crowing
and vain glory of the mere logician, who, hobbling after him, evinces his own
superior wisdom by pausing on its brink, and giving up as desperate his proper
business of bridging it over."

176 NAMES AND PROPOSITIONS.

possession of which gives to them all, or to that portion of
them, the character of resemblance which has led to their being
classed together. When these common attributes have been
ascertained and specified, the name which belongs in common
to the resembling objects acquires a distinct instead of a vague
connotation ; and by possessing this distinct connotation, be-
comes susceptible of definition.

In giving a distinct connotation to the general name, the
philosopher will endeavour to fix upon such attributes as,
while they are common to all the things usually denoted by
the name, are also of greatest importance in themselves ; either
directly, or from the number, the conspicuousness, or the
interesting character, of the consequences to which they lead.
He will select, as far as possible, such differentiae as lead to the
greatest number of interesting propria. For these, rather than
the more obscure and recondite qualities on which they often
depend, give that general character and aspect to a set of
objects, which determine the groups into which they naturally
fall. But to penetrate to the more hidden agreement on which
these obvious and superficial agreements depend, is often one
of the most difficult of scientific problems. As it is among the
most difficult, so it seldom fails to be among the most im-
portant. And since upon the result of this inquiry respecting
the causes of the properties of a class of things, there inci-
dentally depends the question what shall be the meaning of a
word ; some of the most profound and most valuable investi-
gations which philosophy presents to us, have been introduced
by, and have offered themselves under the guise of, inquiries
into the definition of a name.

BOOK II.

OF REASONING.

VOL 1. 12

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CHAPTER I.

OF INFERENCE, OR REASONING, IN GENERAL.

§ 1 . IN the preceding Book, we have been occupied not
with the nature of Proof, but with the nature of Assertion:
the import conveyed by a Proposition, whether that Proposi-
tion be true or false; not the means by which to discriminate
true from false Propositions. The proper subject, however, of
Logic is Proof. Before we could understand what Proof is, it
was necessary to understand what that is to which proof is
applicable; what that is which can be a subject of belief or
disbelief, of affirmation or denial ; what, in short, the different
kinds of Propositions assert.

This preliminary inquiry we have prosecuted to a definite
result. Assertion, in the first place, relates either to the
meaning of words, or to some property of the things which
words signify. Assertions respecting the meaning of words,
among which definitions are the most important, hold a place,
and an indispensable one, in philosophy ; but as the meaning
of words is essentially arbitrary, this class of assertions are
not susceptible of truth or falsity, nor therefore of proof or
disproof. Assertions respecting Things, or what may be called
Pieal Propositions, in contradistinction to verbal ones, are of
various sorts. We have analysed the import of each sort, and
have ascertained the nature of the things they relate to, and
the nature of what they severally assert respecting those
things. We found that whatever be the form of the propo-
sition, and whatever its nominal subject or predicate, the real
subject of every proposition is some one or more facts or phe-
nomena of consciousness, or some one or more of the hidden
causes or powers to which we ascribe those facts; and that
what is predicated or asserted, either in the affirmative or

12—2

180 REASONING.

negative, of those phenomena or those powers, is always
either Existence, Order in Place, Order in Time, Causation,
or Resemblance. This, then, is the theory of the Import of
Propositions, reduced to its ultimate elements : but there is
another and a less abstruse expression for it, which, though
stopping short in an earlier stage of the analysis, is suffi-
ciently scientific for many of the purposes for which such a
general expression is required. This expression recognises
the commonly received distinction between Subject and Attri-
bute, and gives the following as the analysis of the meaning
of propositions : — Every Proposition asserts, that some given
subject does or does not possess some attribute ; or that some
attribute is or is not (either in all or in some portion of the
subjects in which it is met with) conjoined with some other
attribute.

We shall now for the present take our leave of this portion
of our inquiry, and proceed to the peculiar problem of the
Science of Logic, namely, how the assertions, of which we
have analysed the import, are proved or disproved ; such of
them, at least, as, not being amenable to direct consciousness
or intuition, are appropriate subjects of proof.

We say of a fact or statement, that it is proved, when we
believe its truth by reason of some other fact or statement
from which it is said to follow. Most of the propositions,
whether affirmative or negative, universal, particular, or
singular, which we believe, are not believed on their own
evidence, but on the ground of something previously assented
to, from which they are said to be inferred. To infer a
proposition from a previous proposition or propositions; to
give credence to it, or claim credence for it, as a conclusion
from something else; is to reason, in the most extensive sense
of the term. There is a narrower sense, in which the name
reasoning is confined to the form of inference which is termed
ratiocination, and of which the syllogism is the general type.
The reasons for not conforming to this restricted use of the
term were stated in an earlier stage of our inquiry, and addi-
tional motives will be suggested by the considerations on
which we are now about to enter.

INFERENCE IN GENERAL. 181

§ 2. In proceeding to take into consideration the cases
in which inferences can legitimately be drawn, we shall first
mention some cases in which the inference is apparent, not
real ; and which require notice chiefly that they may not he
confounded with cases of inference properly so called. This
occurs when the proposition ostensibly inferred from another,
appears on analysis to be merely a repetition of the same, or
part of the same, assertion, which was contained in the first.
All the cases mentioned in books of Logic as examples of
sequipollency or equivalence of propositions, are of this nature.
Thus, if we were to argue, No man is incapable of reason,
for every man is rational ; or, All men are mortal, for no
man is exempt from death ; it would be plain that we were
not proving the proposition, but only appealing to another
mode of wording it, which may or may not be more readily
comprehensible by the hearer, or better adapted to suggest
the real proof, but which contains in itself no shadow of
proof.

Another case is where, from an universal proposition, we
affect to infer another which differs from it only in being par-
ticular : as All A is B, therefore Some A is B : No A is B,
therefore Some A is not B. This, too, is not to conclude one
proposition from another, but to repeat a second time some-
thing which had been asserted at first ; with the difference,
that we do not here repeat the whole of the previous assertion,
but only an indefinite part of it.

A third case is where, the antecedent having affirmed a
predicate of a given subject, the consequent affirms of the
same subject something already connoted by the former pre-
dicate : as, Socrates is a man, therefore Socrates is a living
creature; where all that is connoted by living creature was
affirmed of Socrates when he was asserted to be a man.
If the propositions are negative, we must invert their order,
thus : Socrates is not a 'living creature, therefore he is not a
man ; for if we deny the less, the greater, which includes it,
is already denied by implication. These, therefore, are not
really cases of inference; and yet the trivial examples by
which, in manuals of Logic, the rules of the syllogism are

182 REASONING.

illustrated, are often of this ill-chosen kind ; formal demon-
strations of conclusions to which whoever understands the
terms used in the statement of the data, has already, and
consciously, assented.*

The most complex case of this sort of apparent inference
is what is called the Conversion of propositions ; which
consists in turning the predicate into a suhject, and the
subject into a predicate, and framing out of the same terms
thus reversed, another proposition* which must be true if the
former is true. Thus, from the particular affirmative proposi-
tion, Some A is B, we may infer that Some B is A. From
the universal negative, No A is B, we may conclude that
No B is A. From the universal affirmative proposition, All
A is B, it cannot be inferred that all B is A ; though
all water is liquid, it is not implied that all liquid is water;
but it is implied that some liquid is so ; and hence the pro-
position, All A is B, is legitimately convertible into Some
B is A. This process, which converts an universal propo-
sition into a particular, is termed conversion per accidcns.
From the proposition, Some A is not B, we cannot even infer
that some B is not A ; though some men are not Englishmen,
it does not follow that some Englishmen are not men. The
only mode usually recognised of converting a particular nega-
tive proposition, is in the form, Some A is not B, therefore,
something which is not B is A ; and this is termed conver-
sion by contraposition. In this case, however, the predicate
and subject are not merely reversed, but one of them is
changed. Instead of [A] and [B], the terms of the new
proposition are [a thing which is not B], and [A]. The
original proposition, Some A is not B, is first changed into
a proposition sequipollent with it, Some A is " a thing which
is not B ;" and the proposition, being now no longer a
particular negative, but a particular affirmative, admits of

* The different cases of ^Equipollency, or " Equivalent Prepositional
Forms, " are set forth with some fulness in Professor Bain's Logic. One of the
commonest of these changes of expression, that from affirming a proposition to
denying its negative, or vice versd, Mr. Bain designates, very happily, by the
name Obversion.

INFERENCE IN GENERAL. 183

conversion in the first mode, or as it is called, simple con-
version.*

In all these cases there is not really any inference ; there is
in the conclusion no new truth, nothing but what was already
asserted in the premises, and obvious to whoever apprehends
them. The fact asserted in the conclusion is either the very
same fact, or part of the fact, asserted in the original proposi-
tion. This follows from our previous analysis of the Import
of Propositions. When we say, for example, that some lawful
sovereigns are tyrants, what is the meaning of the assertion ?
That the attributes connoted by the term " lawful sovereign,"
and the attributes connoted by the term "tyrant," sometimes
coexist in the same individual. Now this is also precisely
what we mean, when we say that some tyrants are lawful
sovereigns ; which, therefore, is not a second proposition
inferred from the first, any more than the English translation
of Euclid's Elements is a collection of theorems different from,
and consequences of, those contained in the Greek original.
Again, if we assert that no great general is a rash man.
we mean that the attributes connoted by " great general,"
and those connoted by " rash," never coexist in the same SUD-
ject ; which is also the exact meaning which would be ex-
pressed by saying, that no rash man is a great general. When
we say that all quadrupeds are warm-blooded, we assert, not
only that the attributes connoted by " quadruped " and those
connoted by " warm-blooded " sometimes coexist, but that the
former never exist without the latter : now the proposition,
Some warm-blooded creatures are quadrupeds, expresses the
first half of this meaning, dropping the latter half ; and
therefore has been already affirmed in the antecedent proposi-
tion, All quadrupeds are warm-blooded. But that all warm-
blooded creatures are quadrupeds, or, in other words, that the
attributes connoted by " warm-blooded " never exist without
those connoted by " quadruped," has not been asserted, and

* As Sir William Hamilton has pointed out, " Some A is not B " may also
be converted in the following form : " No B is some A." Some men are not
negroes ; therefore, No negroes are some men (e. g. Europeans).

184 REASONING.

cannot be inferred. In order to reassert, in an inverted form,
the whole of what was affirmed in the proposition, All quad-
rupeds are warm-blooded, we must convert it by contra-
position, thus, Nothing which is not warm-blooded is a quad-
ruped. This proposition, and the one from which it is derived,
are exactly equivalent, and either of them may be substituted
for the other; for, to say that when the attributes of a quad-
ruped are present, those of a warm-blooded creature are present,
is to say that when the latter are absent the former are absent.
In a manual for young students, it would be proper to
dwell at greater length on the conversion and sequipollency of
propositions. For though that cannot be called reasoning
or inference which is a mere reassertion in different words
of what had been asserted before, there is no more important
intellectual habit, nor any the cultivation of which falls more
strictly within the province of the art of logic, than that
of discerning rapidly and surely the identity of an assertion
when disguised under diversity of language. That important
chapter in logical treatises which relates to the Opposition
of Propositions, and the excellent technical language which
logic provides for distinguishing the different kinds or modes
of opposition, are of use chiefly for this purpose. Such con-
siderations as these, that contrary propositions may both be
false, but cannot both be true ; that subcontrary propositions
may both be true, but cannot both be false ; that of two con-
tradictory propositions one must be true and the other false ;
that of two subalternate propositions the truth of the uni-
versal proves the truth of the particular, and the falsity of the
particular proves the falsity of the universal, but not vice
versa ;* are apt to appear, at first sight, very technical and

* All A is B j

I contraries.
No A is B i

Some A is B j aubcontrarieg.
Some A is not B )

i contradictories.
Some A is not B )

[ also contradictories.
Some A is B J

All A is B ) , No AisB )

\ and I respectively subalternate.

Some A is B ) borne A is not B )

INFERENCE IN GENERAL. 185

mysterious, but when explained, seem almost too obvious
to require so formal a statement, since tbe same amount
of explanation which is necessary to make the principles in-
telligible, would enable the truths which they convey to be
apprehended in any particular case which can occur. In this
respect, however, these axioms of logic are on a level with
those of mathematics. That things which are equal to the
same thing are equal to one another, is as obvious in any par-
ticular case as it is in the general statement : and if no such
general maxim had ever been laid down, the demonstrations in
Euclid would never have halted for any difficulty in stepping
across the gap which this axiom at present serves to bridge
over. Yet no one has ever censured writers on geometry, for
placing a list of these elementary generalizations at the head
of their treatises, as a first exercise to the learner of the faculty
which will be required in him at every step, that of appre-
hending a general truth. And the student of logic, in the dis-
cussion even of such truths as we have cited above, acquires
habits of circumspect interpretation of words, and of exactly
measuring the length and breadth of his assertions, which are
among the most indispensable conditions of any considerable
mental attainment, and which it is one of the primary objects
of logical discipline to cultivate.

§ 3. Having noticed, in order to exclude from the pro-
vince of Reasoning or Inference properly so called, the cases
in which the progression from one truth to another is only
apparent, the logical consequent being a mere repetition of the
logical antecedent ; we now pass to those which are cases of
inference in the proper acceptation of the term, those in which
we set out from known truths, to arrive at others really dis-
tinct from them.

Reasoning, in the extended sense in which I use the term,
and in which it is synonymous with Inference, is popularly
said to be of two kinds : reasoning from particulars to gene-
rals, and reasoning from generals to particulars ; the former
being called Induction, the latter Ratiocination or Syllogism.
It will presently be shown that there is a third species of

REASONING.

reasoning, which falls under neither of these descriptions, and
Avhich, nevertheless, is not only valid, but is the foundation of
both the others.

It is necessary to observe, that the expressions, reasoning
from particulars to generals, and reasoning from generals to
particulars, are recommended by brevity rather than by pre-
cision, and do not adequately mark, without the aid of a
commentary, the distinction between Induction (in the sense
now adverted to) and Ratiocination. The meaning intended
by these expressions is, that Induction is inferring a propo-
sition from propositions less general than itself, and Ratioci-
nation is inferring a proposition from propositions equally
or more general. When, from the observation of a number
of individual instances, we ascend to a general proposition, or
when, by combining a number of general propositions, we
conclude from them another proposition still more general,
the process, which is substantially the same in both instances,
is called Induction. When from a general proposition, not
alone (for from a single proposition nothing can be concluded
which is not involved in the terms), but by combining it with
other propositions, we infer a proposition of the same degree
of generality with itself, or a less general proposition, or a
proposition merely individual, the process is Ratiocination.
When, in short, the conclusion is more general than the
largest of the premises, the argument is commonly called
Induction ; when less general, or equally general, it is Ratio-
cination.

As all experience begins with individual cases, and pro-
ceeds from them to generals, it might seem most conformable
to the natural order of thought that Induction should be
treated of before we touch upon Ratiocination. It will, how-
ever, be advantageous, in a science which aims at tracing our
acquired knowledge to its sources, that the inquirer should
commence with the latter rather than with the earlier stages of
the process of constructing our knowledge ; and should trace
derivative truths backward to the truths from which they are
deduced, and on which they depend for their evidence, before
attempting to point out the original spring from which both

INFERENCE IN GENERAL. 187

ultimately take their rise. The advantages of this order of
proceeding in the present instance will manifest themselves as
we advance, in a manner superseding the necessity of any
further justification or explanation.

Of Induction, therefore, we shall say no more at present,
than that it at least is, without doubt, a process of real infe-
rence. The conclusion in an induction embraces more than is
contained in the premises. The principle or law collected
from particular instances, the general proposition in which we
embody the result of our experience, covers a much larger
extent of ground than the individual experiments which form
its basis. A principle ascertained by experience, is more than
a mere summing up of what has been specifically observed in
the individual cases which have been examined ; it is a gene-
ralization grounded on those cases, and expressive of our
belief, that what we there found true is true in an indefinite
number of cases which we have not examined, and are never
likely to examine. The nature and grounds of this inference,
and the conditions necessary to make it legitimate, will be the
subject of discussion in the Third Book : but that such infe-
rence really takes place is not susceptible of question. In
every induction we proceed from truths which we knew, to
truths which we did not know • from facts certified by obser-
vation, to facts which we have not observed, and even to facts
not capable of being now observed ; future facts, for example ;
but which we do not hesitate to believe on the sole evidence
of the induction itself.

Induction, then, is a real process of Reasoning or Inference.
Whether, and in what sense, as much can be said of the Syl-
logism, remains to be determined by the examination into
which we are about to enter.

CHAPTER II.

OF RATIOCINATION, OR SYLLOGISM.

§ 1. THE analysis of the Syllogism has been so accurately
and fully performed in the common manuals of Logic, that in
the present work, which is not designed as a manual, it is
sufficient to recapitulate, memorice causa, the leading results
of that analysis, as a foundation for the remarks to he after-
wards made on the functions of the Syllogism, and the place
which it holds in science.

To a legitimate syllogism it is essential that there should
be three, and no more than three, propositions, namely, the
conclusion, or proposition to be proved, and two other pro-
positions which together prove it, and which are called the pre-
mises. It is essential that there should be three, and no more than
three, terms, namely, the subject and predicate of the conclu-
sion, and another called the middleterm, which must be found
in both premises, since it is by means of it that the other two
terms are to be connected together. The predicate of the con-
clusion is called the major term of the syllogism ; the subject of
the conclusion is called the minor term. As there can be but
three terms, the major and minor terms must each be found in
one, and only one, of the premises, together with the middleterm
which is in them both. The premise which contains the
middleterm and the major term is called the major premise ;
that which contains the middleterm and the minor term is
called the minor premise.

Syllogisms are divided by some logicians into three figures,
by others into four, according to the position of the middle-
term, which may either be the subject in both premises, the
predicate in both, or the subject in one and the predicate in
the other. The most common case is that in which the middle-
term is the subject of the major premise and the predicate of

RATIOCINATION, OR SYLLOGISM.

189

the minor. This is reckoned as the first figure. When the
middleterm is the predicate in both premises, the syllogism
belongs to the second figure ; when it is the subject in both, to
the third. In the fourth figure the middleterm is the subject
of the minor premise and the predicate of the major. Those
writers who reckon no more than three figures, include this
case in the first.

Each figure is divided into moods, according to what are
called the quantity and quality of the propositions, that is, ac-
cording as they are universal or particular, affirmative or nega-
tive. The following are examples of all the legitimate moods,
that is, all those in which the conclusion correctly follows from
the premises. A is the minor term, C the major, B the middle-
term.

FIRST FIGURE.

All B is C No B is C All B is C

All A is B All A is B Some A is B

therefore therefore therefore

All A is C No A is 0 Some A is C

SECOND FIGURE.

No C is B All C is B No C is B
All A is B No A is B Some A is B
therefore therefore therefore
No A is C No A is 0 Some A is not C Some A is notC

THIRD FIGURE.

All B is C No B is C Some B is C All B is C Some B is not C No B is C

All B is A All B is A All B is A Some B is A All B is A Some B is A

therefore therefore therefore therefore therefore therefore

Some A is C Some A is not C Some A is C Some A is C Some A is not C Some A is not C

FOURTH FIGURE.

All C is B All C is B Some C is B No 0 is B No C is B
All B is A No B is A All B is A All B is A Some B is A

therefore therefore therefore therefore therefore
Some A is C Some A is not C Some A is C Some A is not C Some A is not C

In these exemplars, or blank forms for making syllogisms,
no place is assigned to singular propositions ; not, of course,
because such propositions are not used in ratiocination, but
because, their predicate being affirmed or denied of the
whole of the subject, they are ranked, for the purposes of the
syllogism, with universal propositions. Thus, these two syllo-
gisms—

No B is C
Some A is B

therefore
Some A is not C

All C is B
Some A is not B
therefore

190 REASONING.

All men are mortal, All men are mortal,

All kings are men, Socrates is a man,

therefore therefore

All kings are mortal, Socrates is mortal,

are arguments precisely similar, and are both ranked in the

first mood of the first figure.*

* Professor Bain denies the claim of Singular Propositions to be classed, for
the purposes of ratiocination, with Universal ; though they come within the
designation which he himself proposes as an equivalent for Universal, that of
Total. He would even, to use his own expression, banish them entirely from
the syllogism. He takes as an example,

Socrates is wise,
Socrates is poor, therefore
Some poor men are wise,

or more properly (as he observes) "one poor man is wise." " Now, if wise, poor,
and a man, are attributes belonging to the meaning of the word Socrates,
there is then no march of reasoning at all. We have given in Socrates, inter
alia, the facts wise, poor, and a man, and we merely repeat the concurrence
which is selected from the whole aggregate of properties making up the whole,
Socrates. The case is one under the head ' Greater and Less Connotation' in
Equivalent Propositional Forms, or Immediate Inference.

" But the example in this form does not do justice to the syllogism of singu-
lars. We must suppose both propositions to be real, the predicates being in no
way involved in the subject. Thus

Socrates was the master of Plato,

Socrates fought at Delium,

The master of Plato fought at Delium.

': It may fairly be doubted whether the transitions, in this instance, are any-
thing more than equivalent forms. For the proposition ' Socrates was the master
of Plato and fought at Delium,' compounded out of the two premises, is obviously
nothing more than a grammatical abbreviation. No one can say that there is
here any change of meaning, or anything beyond a verbal modification of the
original form. The next step is, 'The master of Plato fought at Delium,'
which is the previous statement cut down by the omission of Socrates. It
contents itself with reproducing a part of the meaning, or saying less than had
been previously said. The full equivalent of the affirmation is, ' The master
of Plato fought at Delium, and the master of Plato was Socrates :' the new
form omits the last piece of information, and gives only the first. Now, we
never consider that we have made a real inference, a step in advance, when we
repeat less than we are entitled to say, or drop from a complex statement some
portion not desired at the moment. Such an operation keeps strictly within
the domain of equivalence, or Immediate Inference. In no way, therefore,
can a syllogism with two singular premises be viewed as a genuine syllogistic
or deductive inference." (Logic, i. 159.)

The first argument, as will have been seen, rests upon the supposition that
the name Socrates has a meaning ; that man, wise, and poor, are parts of this

RATIOCINATION, OR SYLLOGISM. 191

The reasons why syllogisms in any of the above forms are
legitimate, that is, why, if the premises are true, the conclu-
sion must inevitably be so, and why this is not the case in
any other possible mood, (that is, in any other combination of
universal and particular, affirmative and negative propositions,)
any person taking interest in these inquiries may be presumed
to have either learned from the common school books of the
syllogistic logic, or to be capable of discovering for himself.
The reader may, however, be referred, for every needful expla-
nation, to Archbishop Whately's Elements of Logic, where he
will find stated with philosophical precision, and explained with
remarkable perspicuity, the whole of the common doctrine of
the syllogism.

All valid ratiocination ; all reasoning by which, from gene-
ral propositions previously admitted, other propositions equally
or less general are inferred; may be exhibited in some of the
above forms. The whole of Euclid, for example, might be

meaning ; and that by predicating them of Socrates we convey no informa-
tion ; a view of the signification of names which, for reasons already given,*
I cannot admit, and which, as applied to the class of names which Socrates
belongs to, is at war with Mr. Bain's own definition of a Proper Name (i. 148)
" a single meaningless mark or designation appropriated to the thing." Such
names, Mr. Bain proceeded to say, do not necessarily indicate even human beings :
much less then does the name Socrates include the meaning of wise or poor.
Otherwise it would follow that if Socrates had grown rich, or had lost his
mental faculties by illness, he would no longer have been called Socrates.

The second part of Mr. Bain's argument, in which he contends that even
when the premises convey real information, the conclusion is merely the premises
with a part left out, is applicable, if at all, as much to universal propositions as
to singular. In every syllogism the conclusion contains less than is asserted in
the two premises taken together. Suppose the syllogism to be

All bees are intelligent,

All bees are insects, therefore

Some insects are intelligent :

one might use the same liberty taken by Mr. Bain, of joining together the two
premises as if they were one — "All bees are insects and intelligent" — and
might say that in omitting the middle term tees we make no real inference, but
merely reproduce part of what had been previously said. Mr. Bain's is really
an objection to the syllogism itself, or at all events to the third figure : it has
no special applicability to singular propositions.

* Note to § 4 of the chapter on Definition, supra, p. 160.

192 REASONING.

thrown without difficulty into a series of syllogisms, regular in
mood and figure.

Though a syllogism framed according to any of these for-
mulae is a valid argument, all correct ratiocination admits of
being stated in syllogisms of the first figure alone. The rules
for throwing an argument in any of the other figures into the
first figure, are called rules for the reduction of syllogisms.
It is done by the conversion of one or other, or both, of the
premises. Thus an argument in the first mood of the second

figure, as —

No 0 is B

All A is B
therefore

No A is 0,

may be reduced as follows. The proposition, No C is B,
being an universal negative, admits of simple conversion, and
may be changed into No B is C, which, as we sh'owed, is the
very same assertion in other words — the same fact differently
expressed. This transformation having been effected, the
argument assumes the following form : —

No B is C

All A is B
therefore

No A is C,

which is a good syllogism in the second mood of the first
figure. Again, an argument in the first mood of the third
figure must resemble the following : —

All B is C

All Bis A
therefore

Some A is C,

where the minor premise, All B is A, conformably to what
was laid down in the last chapter respecting universal affirma-
tives, does not admit of simple conversion, but may be
converted per accidens, thus, Some A is B ; which, though it
does not express the whole of what is asserted in the propo-
sition All B is A, expresses, as was formerly shown, part
of it, and must therefore be true if the whole is true. We

RATIOCINATION, OR SYLLOGISM. 193

have, then, as the result of the reduction, the following syllo-
gism in the third mood of the first figure : —

All B is C
Some A is B,

from which it obviously follows, that

Some A is C.

In the same manner, or in a manner on which after these
examples it is not necessary to enlarge, every mood of the
second, third, and fourth figures may be reduced to some one
of the four moods of the first. In other words, every conclu-
sion which can be proved in any of the last three figures,
may be proved in the first figure from the same premises,
with a slight alteration in the mere manner of expressing
them. Every valid ratiocination, therefore, may be stated in
the first figure, that is, in one of the following forms : —

Every B is C No B is C

AHA ) • T, All A )

isB, isB,

Some A ) Some A j

therefore therefore

All A ) is c No A is

Some A j Some A is not

Or if more" significant symbols are preferred : —

To prove an affirmative, the argument must admit of being
stated in this form : —

All animals are mortal ;

All men \

Some men I are animals ;

Socrates j

therefore
All men

Some men
Socrates

are mortal.

To prove a negative, the argument must be capable of being
expressed in this form : —

No one who is capable of self-control is necessarily

vicious ;
VOL. i. 13

194 REASONING.

All negroes \

Some negroes L are capable of self-control;

Mr. A's negro )

therefore

No negroes are ]

Some negroes are not r necessarily vicious.
Mr. A's negro is not '

Though all ratiocination admits of being thrown into one
or the other of these forms, and sometimes gains consider-
ably by the transformation, both in clearness and in the
obviousness of its consequence ; there are, no doubt, cases
in which the argument falls more naturally into one of the
other three figures, and in which its conclusiveness is more
apparent at the first glance in those figures, than when reduced
to the first. Thus, if the proposition were that pagans may be
virtuous, and the evidence to prove it were the example of
Aristides ; a syllogism in the third figure,

Aristides was virtuous,

Aristides was a pagan,
therefore

Some pagan was virtuous,

would be a more natural mode of stating the argument, and
would carry conviction more instantly home, than the same
ratiocination strained into the first figure, thus —

Aristides was virtuous,

Some pagan was Aristides,
therefore

Some pagan was virtuous.

A German philosopher, Lambert, whose Neues Organon
(published in the year 1704) contains among other things one
of the most elaborate and complete expositions which had ever
been made of the syllogistic doctrine, has expressly examined
what sort of arguments fall most naturally and suitably into
each of the four figures ; and his investigation is characterized
by great ingenuity and clearness of thought* The argument,

* His conclusions are, ' ' The first figure is suited to the discovery or proof
of the propeities of a thing ; the second to the discovery or proof of the dis-

RATIOCINATION, OR SYLLOGISM. 195

however, is one and the same, in whichever figure it is
expressed ; since, as we have already seen, the premises of a
syllogism in the second, third, or fourth figure, and those of the
syllogism in the first figure to which it may be reduced, are the
same premises in everything except language, or, at least, as
much of them as contributes to the proof of the conclusion is
the same. We are therefore at liberty, in conformity with the
general opinion of logicians, to consider the two elementary
forms of the first figure as the universal types of all correct ratio-
cination ; the one, when the conclusion to be proved is affirma-
tive, the other, when it is negative ; even though certain argu-
ments may have a tendency to clothe themselves in the forms of
the second, third, and fourth figures ; which, however, cannot
possibly happen with the only class of arguments which are of
first-rate scientific importance, those in which the conclusion
is an universal affirmative, such conclusions being susceptible
of proof in the first figure alone.*

tinctions between things ; the third to the discovery or proof of instances and
exceptions ; the fourth to the discovery, or exclusion, of the different species of
a genus." The reference of syllogisms in the last three figures to the dictum
de omni et nullo is, in Lambert's opinion, strained and unnatural : to each of
the three belongs, according to him, a separate axiom, co-ordinate and of equal
authority with that dictum, and to which he gives the names of dictum de
diverso for the second figure, dictum de exemplo for the third, and dictum de
reciproco for the fourth. See part i. or Dianoiologie, chap. iv. § 229 et scqq.
Mr. Bailey, (Theory of Reasoning, 2nd ed. pp. 70-74) takes a similar view of the
subject.

* Since this chapter was written, two treatises havo appeared (or rather a
treatise and a fragment of a treatise), which aim at a further improvement in
the theory of the forms of ratiocination : Mr. De Morgan's " Formal Logic ;
or, the Calculus of Inference, Necessary and Probable ;" and the " New
Analytic of Logical Forms," attached as an Appendix to Sir William Hamil-
ton's Discussions on Philosophy, and at greater length, to his posthumous Lec-
tures on Logic.

In Mr. De Morgan's volume — abounding, in its more popular parts, with
valuable observations felicitously expressed— the principal feature of originality
is an attempt to bring within strict technical rules the cases in which a conclu-
sion can be drawn from premises of a form usually classed as particular. Mr. De
Morgan observes, very justly, that from the premises Most Bs are Cs, most
Bs are As, it may be concluded with certainty that some As are Cs, since two
portions of the class B, each of them comprising more than half, must neces-
sarily in part consist of the same individuals. Following out this line of

13—2

196 REASONING.

§ 2. On examining, then, these two general formulae, we
find that in both of them, one premise, the major, is an uni-
versal proposition ; and according as this is affirmative or
negative, the conclusion is so too. All ratiocination, there-
fore, starts from a general proposition, principle, or assump-
tion : a proposition in which a predicate is affirmed or denied
of an entire class ; that is, in which some attribute, or the
negation of some attribute, is asserted of an indefinite number
of objects distinguished by a common characteristic, and de-
signated in consequence, by a common name.

thought, it is equally evident that if we knew exactly what proportion the
" most" in each of the premises bear to the entire class B, we could increase in
a corresponding degree the definiteness of the conclusion. Thus if 60 per cent
of B are included in C, and 70 per cent in A, 30 per cent at least must be
common to both ; in other words, the number of As which are Cs, and of Cs
which are As, must be at least equal to 30 per cent of the class B. Proceeding
on this conception of " numerically definite propositions," and extending it to
such forms as these: — "45 Xs (or more) are each of them one of 70 Ys," or
" 45 Xs (or more) are no one of them to be found among 70 Ys," and examin-
ing what inferences admit of being drawn from the various combinations which
may be made of premises of this description, Mr. De Morgan establishes uni-
versal formulae for such inferences ; creating for that purpose not only a new
technical language, but a formidable array of symbols analogous to those of
algebra.

Since it is undeniable that inferences, in the cases examined by Mr. De
Morgan, can legitimately be drawn, and that the ordinary theory takes no
account of them, I will not say that it was not worth while to show in detail
how these also could be reduced to formulae as rigorous as those of Aristotle.
What Mr. De Morgan has done was worth doing once (perhaps more than once,
as a school exercise) ; but I question if its results are worth studying and
mastering for any practical purpose. The practical use of technical forms of
reasoning is to bar out fallacies : but the fallacies which require to be guarded
against in ratiocination properly so called, arise from the incautious use of the
common forms of language ; and the logician must track the fallacy into that
territory, instead of waiting for it on a territory of his own. While he remains
among propositions which have acquired the numerical precision of the Calculus
of Probabilities, the enemy is left in possession of the only ground on which he
can be formidable. And since the propositions (short of universal) on which
a thinker has to depend, either for purposes of speculation or of practice, do
not, except in a few peculiar cases, admit of any numerical precision ; common
reasoning cannot be translated into Mr. De Morgan's forms, which therefore
cannot serve any purpose as a test of it.

Sir William Hamilton's theory of the " quantification of the predicate " may
be described as follows : —

RATIOCINATION, OB SYLLOGISM. 197

The other premise is always affirmative, and asserts that
something (which may be either an individual, a class, or part
of a class) belongs to, or is included in, the class respecting
which something was affirmed or denied in the major premise.
It follows that the attribute affirmed or denied of the entire
class may (if that affirmation or denial was correct) be affirmed
or denied of the object or objects alleged to be included in
the class: and this is precisely the assertion made in the con-
clusion. ,

Whether or not the foregoing is an adequate account of

"Logically" (I quote his words) "we ought io take into account the
quantity, always understood in thought, but usually, for manifest reasons,
elided in its expression, not only of the subject, but also of the predicate of a
judgment." All A is B, is equivalent to all A is some B. No A is B, to No
A is any B. Some A is B, is tantamount to some A is some B. Some A is
not B, to Some A is not any B. As in these forms of assertion the predicate
is exactly coextensive with the subject, they all admit of simple conversion ;
and by this we obtain two additional forms — Some B is all A, and No B is
some A. We may also make the assertion All A is all B, which will be true
if the classes A and B are exactly coextensive. The last three forms, though
conveying real assertions, have no place in the ordinary classification of Pro-
positions. All propositions, then, being supposed to be translated into this
language, and written each in that one of the preceding forms which answers
to its signification, there emerges a new set of syllogistic rules, materially dif-
ferent from the common ones. A general view of the points of difference may
be given in the words of Sir W. Hamilton (Discussions, 2nd ed. p. 651) : —

" The revocation of the two terms of a Proposition to their true relation ; a
proposition being always an equation of its subject and its predicate.

" The consequent reduction of the Conversion of Propositions from three
species to one — that of Simple Conversion.

' ' The reduction of all the General Laws of Categorical Syllogisms to a single
Canon.

" The evolution from that one canon of all the Species and varieties of
Syllogisms.

" The abrogation of all the Special Laics of Syllogism.

" A demonstration of the exclusive possibility of Three Syllogistic Figures ;
and (on new grounds) the scientific and final abolition of the Fourth.

" A manifestation that Figure is an unessential variation in syllogistic form ;
and the consequent absurdity of Reducing the syllogisms of the other figures
to the first.

" An enouncement of one Organic Principle for each Figure.

"A determination of the true number of the Legitimate Moods ; with

"Their amplification in number (thirty -six) ;

"Their numerical equality under all the figures ; and

198 REASONING.

the constituent parts of the syllogism, will be presently con-
sidered ; but as far as it goes it is a true account. It has ac-
cordingly been generalized, and erected into a logical maxim,
on which all ratiocination is said to be founded, insomuch that
to reason, and to apply the maxim, are supposed to be one and
the same thing. The maxim is, That whatever can be affirmed
(or denied) of a class, may be affirmed (or denied) of every-
thing included in the class. This axiom, supposed to be the
basis of the syllogistic theory, is termed by logicians the dictum
de omni et nullo.

" Their relative equivalence, or virtual identity, throughout every schematic
difference.

"That, m the second and third figures, the extremes holding both the same
relation to the middle term, there is not, as in the first, an opposition and sub-
ordination between a term major and a term minor, mutually containing and
contained, in the counter wholes of Extension and Comprehension.

"Consequently, in the second and third figures, there is no determinate
major and minor premise, and there are two indifferent conclusions : whereas
in the first the premises are determinate, and there is a single proximate con-
clusion."

This doctrine, like that of Mr. De Morgan previously noticed, is a real
addition to the syllogistic theory ; aud has moreover this advantage over Mr.
De Morgan's "numerically definite Syllogism," that the forms it supplies are
really available as a test of the correctness of ratiocination ; since propositions
in the common form may always have their predicates quantified, and so be
made amenable to Sir W. Hamilton's rules. Considered however as a con-
tribution to the Science of Logic, that is, to the analysis of the mental pro-
cesses concerned in reasoning, the new doctrine appears to me, I confess, not
merely superfluous, but erroneous ; since the form in which it clothes proposi-
tions does not, like the ordinary form, express what is in the mind of the
speaker when he enunciates the proposition. I cannot think Sir William
Hamilton right in maintaining that the quantity of the predicate is "always
understood in thought.'' It is implied, but is not present to the mind of the
person who asserts the proposition. The quantification of the predicate, instead
of being a means of bringing out more clearly the meaning of the proposition,
actually leads the mind out of the proposition, into another order of ideas. For
when we say, All men are mortal, we simply mean to affirm the attribute mor-
tality of all men ; without thinking at all of the class mortal in the concrete, or
troubling ourselves about whether it contains any other beings or not. It is
only for some artificial purpose that we ever look at the proposition in the aspect
in which the predicate also is thought of as a class-name, either including the
subject only, or the subject and something more. (See above, p. 104.)

For a fuller discussion of this subject, see the twenty- second chapter of a
work already referred to, "An Examination of Sir William Hamilton's Philo-
sophy."

RATIOCINATION, OB SYLLOGISM. 199

This maxim, however, when considered as a principle of
reasoning, appears suited to a system of metaphysics once
indeed generally received, but which for the last two centuries
has been considered as finally abandoned, though there have
not been wanting in our own day attempts at its revival. So
long as what are termed Universals were regarded as a peculiar
kind of substances, having an objective existence distinct from
the individual objects classed under them, the dictum de omni
conveyed an important meaning; because it expressed the
intercommunity of nature, which it was necessary on that
theory that we should suppose to exist between those general
substances and the particular substances which were subordi-
nated to them. That everything predicable of the universal
was predicable of the various individuals contained under it,
was then no identical proposition, but a statement of what was
conceived as a fundamental law of the universe. The assertion
that the entire nature and properties of the substantia secunda
formed part of the nature and properties of each of the indi-
vidual substances called by the same name ; that the properties
of Man, for example, were properties of all men ; was a pro-
position of real significance when man did not mean all men,
but something inherent in men, and vastly superior to them
in dignity. Now, however, when it is known that a class, an
universal, a genus or species, is not an entity per se, but neither
more nor less than the individual substances themselves which
are placed in the class, and that there is nothing real in the
matter except those objects, a common name given to them,
and common attributes indicated by the name ; what, I should
be glad to know, do we learn by being told, that whatever can
be affirmed of a class, may be affirmed of every object con-
tained in the class ? The class is nothing but the objects
contained in it : and the dictum de omni merely amounts to
the identical proposition, that whatever is true of certain ob-
jects, is true of each of those objects. If all ratiocination
were no more than the application of this maxim to particular
cases, the syllogism would indeed be, what it has so often been
declared to be, solemn trifling. The dictum de omni is on a
par with another truth, which in its time was also reckoned of

200 REASONING.

great importance, " Whatever is, is/' To give any real mean-
ing to the dictum de omni, we must consider it not as an axiom,
hut as a definition ; we must look upon it as intended to ex-
plain, in a circuitous and paraphrastic manner, the meaning
of the word class.

An error which seemed finally refuted and dislodged from
thought, often needs only put on a new suit of phrases, to he
welcomed back to its old quarters, and allowed to repose
unquestioned for another cycle of ages. Modern philosophers
have not heen sparing in their contempt for the scholastic
dogma that genera and species are a peculiar kind of sub-
stances, which general substances being the only permanent
things, while the individual substances comprehended under
them are in a perpetual flux, knowledge, which necessarily
imports stability, can only have relation to those general sub-
stances or universals, and not to the facts or particulars
included under them. Yet, though nominally rejected, this
very doctrine, whether disguised under the Abstract Ideas of
Locke (whose speculations, however, it has less vitiated than
those of perhaps any other writer who has been infected with
it), under the ultra-nominalism of Hobbes and Condillac, or
the ontology of the later German schools, has never ceased to
poison philosophy. Once accustomed to consider scientific
investigation as essentially consisting in the study of uni-
versals, men did not drop this habit of thought when they
ceased to regard universals as possessing an independent ex-
istence : and even those who went the length of considering
them as mere names, could not free themselves from the notion
that the investigation of truth consisted entirely or partly in
some kind of conjuration or juggle with those names. When
a philosopher adopted fully the Nominalist view of the signi-
fication of general language, retaining along with it the dictum
de omni as the foundation of all reasoning, two such premises
fairly put together were likely, if he was a consistent thinker,
to land him in rather startling conclusions. Accordingly it has
been seriously held, by writers of deserved celebrity, that the
process of arriving at new truths by reasoning consists in the
mere substitution of one set of arbitrary signs for another;

RATIOCINATION, OR SYLLOGISM. 201

a doctrine which they suppose to derive irresistible confirma-
tion from the example of algebra. If there were any process
in sorcery or necromancy more preternatural than this, I
should be much surprised. The culminating point of this
philosophy is the noted aphorism of Condillac, that a science
is nothing, or scarcely anything, but une langue bien faite ;
in other words that the one sufficient rule for discovering the
nature and properties of objects is to name them properly : as
if the reverse were not the truth, that it is impossible to name
them properly except in proportion as we are already acquainted
with their nature and properties. Can it be necessary to say,
that none, not even the most trivial knowledge with respect
to Things, ever was or could be originally got at by any con-
ceivable manipulation of mere names, as such ; and that what
can be learned from names, is only what somebody who used
the names knew before ? Philosophical analysis confirms the
indication of common sense, that the function of names is but
that of enabling us to remember and to communicate our
thoughts. That they also strengthen, even to an incalculable
extent, the power of thought itself, is most true : but they do
this by no intrinsic and peculiar virtue ; they do it by the
power inherent in an artificial memory, an instrument of which
few have adequately considered the immense potency. As an
artificial memory, language truly is, what it has so often been
called, an instrument of thought ; but it is one thing to be the
instrument, and another to be the exclusive subject upon which
the instrument is exercised. We think, indeed, to a consider-
able extent, by means of names, but what we think of, are the
things called by those names; and there cannot be a greater
error than to imagine that thought can be carried on with
nothing in our mind but names, or that we can make the
names think for us.

§ 3. Those who considered the dictum de omni as the
foundation of the syllogism, looked upon arguments in a
manner corresponding to the erroneous view which Hobbes
took of propositions. Because there are some propositions
which are merely verbal, Hobbes, in order apparently that his

202 REASONING.

definition might be rigorously universal, defined a proposition
as if no propositions declared anything except the meaning of
words. If Hobbes was right ; if no further account than this
could be given of the import of propositions ; no theory could
be given but the commonly received one, of the combination of
propositions in a syllogism. If the minor premise asserted
nothing more than that something belongs to a class, and if
the major premise asserted nothing of that class except that
it is included in another class, the conclusion would only be
that what was included in the lower class is included in the
higher, and the result, therefore, nothing except that the
classification is consistent with itself. But we have seen that
it is no sufficient account of the meaning of a proposition, to
say that it refers something to, or excludes something from, a
class. Every proposition which conveys real information
asserts a matter of fact, dependent on the laws of nature, and
not on classification. It asserts that a given object does or
does not possess a given attribute ; or it asserts that two attri-
butes, or sets of attributes, do or do not (constantly or
occasionally) coexist. Since such is the purport of all pro-
positions which convey any real knowledge, and since ra-
tiocination is a mode of acquiring real knowledge, any
theory of ratiocination which does not recognise this import
of propositions, cannot, we may be sure, be the true one.

Applying this view of propositions to the two premises of
a syllogism, we obtain the following results. The major pre-
mise, which, as already remarked, is always universal, asserts,
that all things which have a certain attribute (or attributes)
have or have not along with it, a certain other attribute
(or attributes). The minor premise asserts that the thing or
set of things which are the subject of that premise, have the
first-mentioned attribute ; and the conclusion is, that they
have (or that they have not), the second. Thus in our former
example,

All men are mortal,

Socrates is a man,
therefore

Socrates is mortal,

RATIOCINATION, OR SYLLOGISM. 203

the subject and predicate of the major premise are connotative
terms, denoting objects and connoting attributes. The asser-
tion in the major premise is, that along with one of the two
sets of attributes, we always find the other : that the attri-
butes connoted by "man" never exist unless conjoined with
the attribute called mortality. The assertion in the minor
premise is that the individual named Socrates possesses the
former attributes ; and it is concluded that he possesses also
the attribute mortality. Or if both the premises are general
propositions, as

All men are mortal,

All kings are men,
therefore

All kings are mortal,

the minor premise asserts that the attributes denoted by king-
ship only exist in conjunction with those signified by the word
man. The major asserts as before, that the last-mentioned
attributes are never found without the attribute of mortality.
The conclusion is, that wherever the attributes of kingship are
found, that of mortality is found also.

If the major premise were negative, as, No men are omni-
potent, it would assert, not that the attributes connoted by
"man" never exist without, but that they never exist with,
those connoted by " omnipotent :" from which, together with
the minor premise, it is concluded, that the same incompa-
tibility exists between the attribute omnipotence and those
constituting a king. In a similar manner we might analyse
any other example of the syllogism.

If we generalize this process, and look out for the prin-
ciple or law involved in every such inference, and presupposed
in every syllogism, the propositions of which are anything
more than merely verbal ; we find, not the unmeaning dictum
de omni et nullo, but a fundamental principle, or rather two
principles, strikingly resembling the axioms of mathematics.
The first, which is the principle of affirmative syllogisms, is,
that things which coexist with the same thing, coexist with
one another: or (still more precisely) a thing which coexists
with another thing, which other coexists with a third thing,

204 REASONING.

also coexists with that third thing. The second is the prin-
ciple of negative syllogisms, and is to this effect : that a thing
which coexists with another thing, with which other a third
thing does not coexist, is not coexistent with that third thing.
These axioms manifestly relate to facts, and not to conven-
tions ; and one or other of them is the ground of the legiti-
macy of every argument in which facts and not conventions
are the matter treated of.*

§ 4. It remains to translate this exposition of the syllo-
gism from the one into the other of the two languages in

* Mr. Herbert Spencer (Principles of Psychology, pp. 125-7) though his
theory of the syllogism coincides with all that is essential of mine, thinks it a
logical fallacy to present the two axioms in the text, as the regulating principles
of syllogism. He charges me with falling into the error pointed out by Arch-
bishop Whately and myself, of confounding exact likeness with literal identity ;
and maintains, that we ought not to say that Socrates possesses the same attri-
butes which are connoted by the word Man, but only that he possesses attri-
butes exactly like them : according to which phraseology, Socrates, and the
attribute mortality, are not two things coexisting with the same thing, as the
axiom asserts, but two things coexisting with two different things.

The question between Mr. Spencer and me is merely one of language ; for
neither of us (if I understand Mr. Spencer's opinions rightly) believes an attri-
bute to be a real thing, possessed of objective existence ; we believe it to be a
particular mode of naming our sensations, or our expectations of sensation,
when looked at in their relation to an external object which excites them. The
question raised by Mr. Spencer does not, therefore, concern the properties of
any really existing thing, but the comparative appropriateness, for philosophical
purposes, of two different modes of using a name. Considered in this point of
view, the phraseology I have employed, which is that commonly used by philo-
sophers, seems to me to be the best. Mr. Spencer is of opinion that because
Socrates and Alcibiades are not the same man, the attribute which constitutes
them men should not be called the same attribute ; that because the humanity
of one man and that of another express themselves to our senses not by the
same individual sensations but by sensations exactly alike, humanity ought to
be regarded as a different attribute in every different man. But on this
showing, the humanity even of any one man should be considered as different
attributes now and half-an-hour hence ; for the sensations by which it will then
manifest itself to my organs will not be a continuation of my present sensations,
but a repetition of them ; fresh sensations, not identical with, but only exactly
like the present. If every general conception, instead of being " the One in the
Many," were considered to be as many different conceptions as there are things
to which it is applicable, there would be no such thing as general language.
A name would have no general meaning if man connoted one thing when pre-

RATIOCINATION, OR SYLLOGISM. 205

which we formerly remarked* that all propositions, and of
course therefore all combinations of propositions, might be
expressed. We observed that a proposition might be con-
sidered in two different lights ; as a portion of our knowledge
of nature, or as a memorandum for our guidance. Under the
former, or speculative aspect, an affirmative general proposi-
tion is an assertion of a speculative truth, viz. that whatever
has a certain attribute has a certain other attribute. Under
the other aspect, it is to be regarded not as a part of our
knowledge, but as an aid for our practical exigencies, by
enabling us, when we see or learn that an object possesses

dicated of John, and another, though closely resembling, thing when predicated
of William. Accordingly a recent pamphlet asserts the impossibility of general
knowledge on this precise ground.

The meaning of any general name is some outward or inward phenomenon,
consisting, in the last resort, of feelings ; and these feelings, if their continuity
is for an instant broken, are no longer the same feelings, in the sense of indi-
vidual identity. What, then, is the common something which gives a meaning
to the general name ? Mr. Spencer can only say, it is the similarity of the
feelings ; and I rejoin, the attribute is precisely that similarity. The names of
attributes are in their ultimate analysis names for the resemblances of our sen-
sations (or other feelings). Every general name, whether abstract or concrete,
denotes or connotes one or more of those resemblances. It will not, probably,
be denied, that if a hundred sensations are undistinguishably alike, their resem-
blance ought to be spoken of as one resemblance, and not a hundred resem-
blances which merely resemble one another. The things compared are many,
but the something common to all of them must be conceived as one, just as the
name is conceived as one, though corresponding to numerically different sensa-
tions of sound each time it is pronounced. The general term man does not
connote the sensations derived once from one man, which, once gone, can no
more occur again than the same flash of lightning. It connotes the general type
of the sensations derived always from all men, and the power (always thought
of as one) of producing sensations of that type. And the axiom might be thus
worded : Two types of sensation each of which coexists with a third type,
coexist with another ; or Two powers each of which coexists with a third power
coexist with one another.

Mr. Spencer has misunderstood me in another particular. He supposes that
the coexistence spoken of in the axiom, of two things with the same third
thing, means simultaneousness in time. The coexistence meant is that of being
jointly attributes of the same subject. The attribute of being born without
teeth, and the attribute of having thirty-two teeth in mature age, are in this
sense coexistent, both being attributes of man, though ex vi termini never of
the same man at the same time.

* Supra, p. 130.

206 REASONING.

one of the two attributes, to infer that it possesses the other ;
thus employing the first attribute as a mark or evidence of the
second. Thus regarded, every syllogism comes within the
following general formula : —

Attribute A is a mark of attribute B,
The given object has the mark A,

therefore

The given object has the attribute B.

Referred to this type, the arguments which we have lately
cited as specimens of the syllogism, will express themselves
in the following manner : —

The attributes of man are a mark of the attribute mortality,
Socrates has the attributes of man,

therefore

Socrates has the attribute mortality.
And again,

The attributes of man are a mark of the attribute mortality,
The attributes of a king are a mark of the attributes of man,

therefore
The attributes of a king are a mark of the attribute mortality.

And, lastly,
The attributes of man are a mark of the absence of the

attribute omnipotence,
The attributes of a king are a mark of the attributes of man,

therefore
The attributes of a king are a mark of the absence of the

attribute signified by the word omnipotent
(or, are evidence of the absence of that attribute).
To correspond with this alteration in the form of the
syllogisms, the axioms on which the syllogistic process is
founded must undergo "a corresponding transformation. In
this altered phraseology, both those axioms may be brought
under one general expression ; namely, that whatever has any
mark, has that which it is a mark of. Or, when the minor
premise as well as the major is universal, we may state it
thus : Whatever is a mark of any mark, is a mark of that
which this last is a mark of. To trace the identity of these
.axioms with those previously laid down, may be left to the

RATIOCINATION, OR SYLLOGISM.

intelligent reader. We shall find, as we proceed, the great
convenience of the phraseology into which we have last thrown
them, and which is better adapted than any I am acquainted
with, to express with precision and force what is aimed at, and
actually accomplished, in every case of the ascertainment of
a truth by ratiocination.*

* Professor Bain (Logic, i. 157) considers the axiom (or rather axioms) here
proposed as a substitute for the dictum de omni, to possess certain advantages,
but to be " unworkable as a basis of the syllogism. The fatal defect consists
in this, that it is ill-adapted to bring out the difference between total and
partial coincidence of terms, the observation of which is the essential pre-
caution in syllogizing correctly. Tf all the terms were coextensive, the axiom
would flow on admirably ; A carries B, all B and none but B ; B carries C in
the same manner ; at once A carries C, without limitation or reserve. But in
point of fact, we know that while A carries B, other things carry B also ;
whence a process of limitation is required, in transferring A to C through B.
A (in common with other things) carries B ; B (in common with other things)
carries C ; whence A (in common with other things) carries C. The axiom
provides no means of making this limitation ; if we were to follow A literally,
we should be led to suppose A and C coextensive : for such is the only obvious
meaning of ' the attribute A coincides with the attribute C. ' ':

It ie certainly possible that a careless learner here and there may suppose
that if A carries B, it follows that B carries A. But if any one is so incautious
as to commit this mistake, the very earliest lesson in the logic of inference, the
Conversion of propositions, will correct it. The first of the two forms in
which T have stated the axiom, is in some degree open to Mr. Bain's criticism :
when B is said to coexist with A, (it must be by a lapsus calami that Mr. Bain
uses the word coincide) it is possible, in the absence of warning, to suppose the
meaning to be that the two things are only found together. But this mis-
interpretation is excluded by the other, or practical, form of the maxim ; Nota
notce est nota rei ipsius. No. one would be in any danger of inferring that
because a is a mark of b, b can never exist without a ; that because being in a
confirmed consumption is a mark of being about to die, no one dies who is not
in a consumption ; that because being coal is a mark of having come out of the
earth, nothing can come out of the earth except coal. Ordinary knowledge of
English seems a sufficient protection against these mistakes, since in speaking
of a mark of anything we are never understood as implying reciprocity.

A more fundamental objection is stated by Mr. Bain in a subsequent pas-
sage (p. 158). "The axiom does not accommodate itself to the type of Deduc-
tive Reasoning as contrasted with Induction — the application of a general
principle to a special case. Anything that fails to make prominent this cir-
cumstance is not adapted as a foundation for the syllogism." But though it
may be proper to limit the term Deduction to the application of a general
principle to a special case, it has never been held that Ratiocination or Syllo-
gism is subject to the same limitation ; and the adoption of it would exclude a

208 REASONING.

great amount of valid and conclusive syllogistic reasoning. Moreover if the
dictum de omni makes prominent the fact of the application of a general prin-
ciple to a particular case, the axiom I propose makes prominent the condition
which alone makes that application a real inference.

I conclude, therefore, that both forms have their value, and their place in
Logic. The dictum de omni should be retained as the fundamental axiom of
the logic of mere consistency, often called Formal Logic ; nor have I ever
quarrelled with the use of it in that character, nor proposed to banish it from
treatises on Formal Logic. But the other is the proper axiom for the logic of
the pursuit of truth by way of Deduction ; and the recognition of it can alone
show how it is possible that deductive reasoning can be a road to truth.

CHAPTER III.

OF THE FUNCTIONS AND LOGICAL VALUE OF THE
SYLLOGISM.

§ I. WE have shown -what is the real nature of the truths
with which the Syllogism is conversant, in contradistinction
to the more superficial manner in which their import is con-
ceived in the common theory ; and what are the fundamental
axioms on which its probative force or conclusiveness depends.
We have now to inquire, whether the syllogistic process, that
of reasoning from generals to particulars, is, or is not, a pro-
cess of inference ; a progress from the known to the unknown :
a means of coming to a knowledge of something which we did
not know before.

Logicians have been remarkably unanimous in their mode
of answering this question. It is universally allowed that a
syllogism is vicious if there be anything more in the conclu-
sion than was assumed in the premises. But this is, in fact,
to say, that nothing ever was, or can be, proved by syllogism,
which was not known, or assumed to be known, before. Is
ratiocination, then, not a process of inference ? And is the
syllogism, to which the word reasoning has so often been
represented to be exclusively appropriate, not really entitled
to be called reasoning at all ? This seems an inevitable con-
sequence of the doctrine, admitted by all writers on the
subject, that a syllogism can prove no more than is involved
in the premises. Yet the acknowledgment so explicitly made,
has not prevented one set of writers from continuing to repre-
sent the syllogism as the correct analysis of what the mind
actually performs in discovering and proving the larger half
of the truths, whether of science or of daily life, which we
believe ; while those who have avoided this inconsistency, and
followed out the general theorem respecting the logical value
VOL. i. 14

210 REASONING.

of the syllogism to its legitimate corollary, have been led to
impute uselessness and frivolity to the syllogistic theory itself,
on the ground of the petitio principii which they allege to be
inherent in every syllogism. As I believe both these opinions
to be fundamentally erroneous, I must request the attention
of the reader to certain considerations, without which any just
appreciation of the true character of the syllogism, and the
functions it performs in philosophy, appears to me impossible ;
but which seem to have been either overlooked, or insuffi-
ciently adverted to, both by the defenders of the syllogistic
theory and by its assailants.

§ 2. It must be granted that in every syllogism, consi-
dered as an argument to prove the conclusion, there is a
petitio principii. When we say,

All men are mortal,

Socrates is a man,
therefore

Socrates is mortal ;

it is unanswerably urged by the adversaries of the syllogistic
theory, that the proposition, Socrates is mortal, is presupposed
in the more general assumption, All men are mortal : that we
cannot be assured of the mortality of all men, unless we are
already certain of the mortality of every individual man: that
if it be still doubtful whether Socrates, or any other individual
we choose to name, be mortal or not, the same degree of un-
certainty must hang over the assertion, All men are mortal :
that the general principle, instead of being given as evidence
of the particular case, cannot itself be taken for true without
exception, until every shadow of doubt which could affect any
case comprised with it, is dispelled by evidence aliunde ; and
then what remains for the syllogism to prove ? That, in short,
no reasoning from generals to particulars can, as such, prove
anything: since from a general principle we cannot infer
any particulars, but those which the principle itself assumes as
known.

This doctrine appears to me irrefragable ; and if logicians,
though unable to dispute it, have usually exhibited a strong

FUNCTIONS AND VALUE OF THE SYLLOGISM. 211

disposition to explain it away, tins was not because they could
discover any flaw in the argument itself, but because the con-
trary opinion seemed to rest on arguments equally indis-
putable. In the syllogism last referred to, for example, or in
any of those which we previously constructed, is it not evi-
dent that the conclusion may, to the person to whom the
syllogism is presented, be actually and bond fide a new truth?
Is it not matter of daily experience that truths previously
unthought of, facts which have not been, and cannot be,
directly observed, are arrived at by way of general reasoning?
We believe that the Duke of Wellington is mortal. We do
not know this by direct observation, so long as he is not yet
dead. If we were asked how, this being the case, we know
the duke to be mortal, we should probably answer, Because all
men are so. Here, therefore, we arrive at the knowledge of a
truth not (as yet) susceptible of observation, by a reasoning
which admits of being exhibited in the following syllogism : —
All men are mortal,

The Duke of Wellington is a man,
therefore

The Duke of Wellington is mortal.

And since a large portion of our knowledge is thus acquired,
logicians have persisted in representing the syllogism as a
process of inference or proof; though none of them has cleared
up the difficulty which arises from the inconsistency between
that assertion, and the principle, that if there be anything in
the conclusion which was not already asserted in the pre-
mises, the argument is vicious. For it is impossible to attach
any serious scientific value to such a mere salvo, as the dis-
tinction drawn between being involved by implication in the
premises, and being directly asserted in them. When Arch-
bishop Whately says* that the object of reasoning is " merely
to expand and unfold the assertions wrapt up, as it were, and
implied in those with which we set out, and to bring a person
to perceive and acknowledge the full force of that which he
has admitted," he does not, I think, meet the real difficulty re-

* Logic, p. 239 (9th ed.).

14—2

212 REASONING.

quiring to be explained, namely, how it happens that a science,
like geometry, can be all " wrapt up" in a few definitions and
axioms. Nor does this defence of the syllogism differ much
from what its assailants urge against it as an accusation,
when they charge it with being of no use except to those who
seek to press the consequences of an admission into which a
person has been entrapped without having considered and
understood its full force. When you admitted the major
premise, you asserted the conclusion ; but, says Archbishop
Whately, you asserted it by implication merely: this, how-
ever, can here only mean that you asserted it unconsciously ;
that you did not know you were asserting it ; but, if so, the
difficulty revives in this shape — Ought you not to have
known ? Were you warranted in asserting the general pro-
position without having satisfied yourself of the truth of
everything which it fairly includes ? And if not, is not the
syllogistic art primd facie what its assailants affirm it to be,
a contrivance for catching you in a trap, and holding you fast
in it ?*

§ 3. From this difficulty there appears to be but one
issue. The proposition that the Duke of Wellington is
mortal, is evidently an inference ; it is got at as a conclusion
from something else ; but do we, in reality, conclude it from
the proposition, All men are mortal ? I answer, no.

* It is hardly necessary to say, that I am not contending for any such
absurdity as that we actually " ought to have known " and considered the case
of every individual man, past, present, and future, before affirming that all men
are mortal : although this interpretation has been, strangely enough, put upon
the preceding observations. There is no difference between me and Archbishop
Whately. or any other defender of the syl'ogism, on the practical part of the
matter ; I am only pointing out an inconsistency in the logical theory of it, as
conceived by almost all writers. I do not say that a person who affirmed,
before the Duke of Wellington was born, that all men are mortal, Icnew that the
Duke of Wellington was mortal ; but I do say that he asserted it ; and I ask
for an explanation of the apparent logical fallacy, of adducing in proof of the
Duke of Wellington's mortaliiy, a general statement which presupposes it.
Finding no sufficient resolution of this difficulty in any of the writers on Logic,
I have attempted tr. supply one.

FUNCTIONS AND VALUE OP THE SYLLOGISM, 213

The error committed is, I conceive, that of overlooking
the distinction between two parts of the process of philoso-
phizing, the inferring part, and the registering part; and
ascribing to the latter the functions of the former. The mistake
is that of referring a person to his own notes for the origin of
his knowledge. If a person is asked a question, and is at the
moment unable to answer it, he may refresh his memory by
turning to a memorandum which he carries about with him.
But if he were asked, how the fact came to his knowledge, he
would scarcely answer, because it was set down in his note-
book: unless the book was written, like the -Koran, with a
quill from the wing of the angel Gabriel.

Assuming that the proposition, The Duke of Wellington
is mortal, is immediately an inference from the proposition,
All men are mortal ; whence do we derive our knowledge of
that general truth ? Of course from observation. Now, all
which man can observe are individual cases. From these all
general truths must be drawn, and into these they may be
again resolved ; for a general truth is but an aggregate of par-
ticular truths ; a comprehensive expression, by which an inde-
finite number of individual facts are affirmed or denied at once.
But a general proposition is not merely a compendious, form
for recording and preserving in the memory a nutftber of par-
ticular facts, all of which have been observed. Generalization
is not a process of mere naming, it is also a process of in-
ference. From instances which we have observed, we feel
warranted in concluding, that what we found true in those
instances, holds in all similar ones, past, present, and future,
however numerous they may be. We then, by that valuable
contrivance of language which enables us to speak of many as
if they were one. record all that we have observed, together
with all that we infer from our observations, in one concise
expression ; and have thus only one proposition, instead of an
endless number, to remember or to communicate. The results
of many observations and inferences, and instructions for
making innumerable inferences in unforeseen cases, are com-
pressed into one short sentence.

When, therefore, we conclude from the death of John and

214 REASONING.

Thomas, and every other person we ever heard of in whose
case the experiment had been fairly tried, that the Duke of
Wellington is mortal like the rest; we may, indeed, pass
through the generalization, All men are mortal, as an inter-
mediate stage ; hut it is not in the latter half of the process,
the descent from all men to the Duke of Wellington, that
the inference resides. The inference is finished when we
have asserted that all men are mortal. What remains to
be performed afterwards is merely deciphering our own
notes.

Archbishop Wbately has contended that syllogizing, or
reasoning from generals to particulars, is not, agreeably to
the vulgar idea, a peculiar mode of reasoning, but the philo-
sophical analysis of the mode in which all men reason, and
must do so if they reason at all. With the deference due
to so high an authority, I cannot help thinking that the
vulgar notion is, in this case, the more correct. If, from our
experience of John, Thomas, &c., who once were living, but
are now dead, we are entitled to conclude that all human
beings are mortal, we might surely without any logical incon-
sequence have concluded at once from those instances, that
the Duke of Wellington is mortal. The mortality of John,
Thomas, and others is, after all, the whole evidence we
have for the mortality of the Duke of Wellington. Not one
iota is added to the proof by interpolating a general pro-
position. Since the individual cases are all the evidence we
can possess, evidence which no logical form into which we
choose to throw it can make greater than it is; and since
that evidence is either sufficient in itself, or, if insufficient
for the one purpose, cannot be sufficient for the other; I am
unable to see why we should be forbidden to take the shortest
cut from these sufficient premises to the conclusion, and con-
strained to travel the " high priori road," by the arbitrary
fiat of logicians. I cannot perceive why it should be impos-
sible to journey from one place to another unless we "march
up a hill, and then march down again." It may be the safest
road, and there may be a resting-place at the top of the hill,
affording a commanding view of the surrounding country ;

FUNCTIONS AND VALUE OP THE SYLLOGISM. 215

but for the mere purpose of arriving at our journey's end, our
taking that road is perfectly optional ; it is a question of time,
trouble, and danger.

Not only may we reason from particulars to particulars
without passing through generals, but we perpetually do so
reason. All our earliest inferences are of this nature. From
the first dawn of intelligence we draw inferences, but years
elapse before we learn the use of general language. The
child, who, having burnt his fingers, avoids to thrust them
again into the fire, has reasoned or inferred, though he has
never thought of the general maxim, Fire burns. He knows
from memory that he has been burnt, and on this evidence
believes, when he sees a candle, that if he puts his finger into
the flame of it, he will be burnt again. He believes this in
every case which happens to arise; but without looking, in
each instance, beyond the present case. He is not generalis-
ing ; he is inferring a particular from particulars. In the same
way, also, brutes reason. There is no gi'ound for attributing
to any of the lower animals the use of signs, of such a nature
as to render general propositions possible. But those animals
profit by experience, and avoid what they have found to cause
them pain, in the same manner, though not always with the
same skill, as a human creature. Not only the burnt child,
but the burnt dog, dreads the fire.

I believe that, in point of fact, when drawing inferences
from our personal experience, and not from maxims handed
down to us by books or tradition, we much oftener conclude
from particulars to particulars directly, than through the
intermediate agency of any general proposition. We are
constantly reasoning from ourselves to other people, or from
one person to another, without giving ourselves the trouble
to erect our observations into general maxims of human or
external nature. When we conclude that some person will,
on some given occasion, feel or act so and so, we sometimes
judge from an enlarged consideration of the manner in which
human beings in general, or persons of some particular cha-
racter, are accustomed to feel and act ; but much oftener from
merely recollecting the feelings and conduct of the same

216 REASONING.

person in some previous instance, or from considering how we
should feel or act ourselves. It is not only the village
matron, who. when called to a consultation upon the case of
a neighbour's child, pronounces on the evil and its remedy
simply on the recollection and authority of what she accounts
the similar case of her Lucy. We all, where we have no
definite maxims to steer by, guide ourselves in the same
way : and if we have an extensive experience, and retain its
impressions strongly, we may acquire in this manner a very
considerable power of accurate judgment, which we may be
utterly incapable of justifying or of communicating to others.
Among the higher order of practical intellects there have
been many of whom it was remarked how admirably they
suited their means to their ends, without being able to give
any sufficient reasons for what they did ; and applied, or
seemed to apply, recondite principles which they were
wholly unable to state. This is a natural consequence of
having a mind stored with appropriate particulars, and
having been long accustomed to reason at once from these
to fresh particulars, without practising the habit of stating to
oneself or to others the corresponding general propositions.
An old warrior, on a rapid glance at the outlines of the
ground, is able at once to give the necessary orders for a
skilful arrangement of his troops ; though if he has received
little theoretical instruction, and has seldom been called
upon to answer to other people for his conduct, he may
never have had in his mind a single general theorem
respecting the relation between ground and array. But his
experience of encampments, in circumstances more or less
similar, has left a number of vivid, unexpressed, ungenera-
lized analogies in his mind, the most appropriate of which,
instantly suggesting itself, determines him to a judicious
arrangement.

The skill of an uneducated person in the use of weapons,
or of tools, is of a precisely similar nature. The savage who
executes unerringly the exact throw which brings down his
game, or his enemy, in the manner most suited to his purpose,
under the operation of all the conditions necessarily involved,

FUNCTIONS AND VALUE OF THE SYLLOGISM. 217

the weight and form of the weapon, the direction and distance
of the object, the action of the wind, &c., owes this power
to a long series of previous experiments, the results of which
he certainly never framed into any verbal theorems or rules.
The same thing may generally be said of any other extraordi-
nary manual dexterity. Not long ago a Scotch manufacturer
procured from England, at a high rate of wages, a working
dyer, famous for producing very fine colours, with the view
of teaching to his other workmen the same skill. The work-
man came; but his mode of proportioning the ingredients,
in which lay the secret of the effects he produced, was by
taking them up in handfuls, while the common method was to
weigh them. The manufacturer sought to make him turn his
handling system into an equivalent weighing system, that the
general principle of his peculiar mode of proceeding might
be ascertained. This, however, the man found himself quite
unable to do, and therefore could impart his skill to nobody.
He had, from the individual cases of his own experience,
established a connexion in his mind between fine effects of
colour, and tactual perceptions in handling his dyeing
materials ; and from these perceptions he could, in any par-
ticular case, infer the means to be employed, and the effects
which would be produced, but could not put others in pos-
session of the grounds on which he proceeded, from having
never generalized them in bis own mind, or expressed them
in language.

Almost every one knows Lord Mansfield's advice to a
man of practical good sense, who, being appointed governor
of a colony, had to preside in its court of justice, without
previous judicial practice or legal education. The advice
was to give his decision boldly, for it would probably be
right; but never to venture on assigning reasons, for they
would almost infallibly be wrong. In cases like this, which
are of no uncommon occurrence, it would be absurd to sup-
pose that the bad reason was the source of the good decision.
Lord Mansfield knew that if any reason were assigned it
would be necessarily an afterthought, the judge being in fact
guided by impressions from past experience, without the

218 REASONING.

circuitous process of framing general principles from them,
and that if he attempted to frame any such he would
assuredly fail. Lord Mansfield, however, would not have
doubted that a man of equal experience who had also a
mind stored with general propositions derived by legitimate
induction from that experience, would have been greatly pre-
ferable as a judge, to one, however sagacious, who could not
be trusted with the explanation and justification of his own
judgments. The cases of men of talent performing wonderful
things they know not bow, are examples of the rudest and
most spontaneous form of the operations of superior minds.
It is a defect in them, and often a source of errors, not to
have generalized as they went on ; but generalization, though
a help, the most important indeed of all helps, is not an
essential.

Even the scientifically instructed, who possess, in the form
of general propositions, a systematic record of the results of the
experience of mankind, need not always revert to those general
propositions in order to apply that experience to a new case.
It is justly remarked by Dugald Stewart, that though the
reasonings in mathematics depend entirely on the axioms, it is
by no means necessary to our seeing the conclusiveness of the
proof, that the axioms should be expressly adverted to. When
it is inferred that AB is equal to CD because each of them is
equal to E F, the most uncultivated understanding, as soon as
the propositions were understood, would assent to the in-
ference, without having ever heard of the general truth that
"things which are equal to the same thing are equal to one
another." This remark of Stewart, consistently followed out,
goes to the root, as I conceive, of the philosophy of ratiocina-
tion ; and it is to be regretted that he himself stopt short
at a much more limited application of it. He saw that the
general propositions on which a reasoning is said to depend,
may, in certain cases, be altogether omitted, without impairing
its probative force. But he imagined this to be a peculiarity
belonging to axioms ; and argued from it, that axioms are not
the foundations or first principles of geometry, from which all
the other truths of the science are synthetically deduced (as

FUNCTIONS AND VALUE OF THE SYLLOGISM. 219

the laws of motion and of the composition of forces in dyna-
mics, the equal mobility of fluids in hydrostatics, the laws of
reflection and refraction in optics, are the first principles of
those sciences) ; but are merely necessary assumptions, self-
evident indeed, and the denial of which would annihilate all
demonstration, but from which, as premises, nothing can be
demonstrated. In the present, as in many other instances,
this thoughtful and elegant writer has perceived an important
truth, but only by halves. Finding, in the case of geometrical
axioms, that general names have not any talismanic virtue for
conjuring new truths out of the well where they lie hid, and not
seeing that this is equally true in every other case of generali-
zation, he contended that axioms are in their nature barren of
consequences, and that the really fruitful truths, the real first
principles of geometry, are the definitions ; that the definition,
for example, of the circle is to the properties of the circle, what
the laws of equilibrium and of the pressure of the atmosphere
are to the rise of the mercury in the Torricellian tube. Yet
all that he had asserted respecting the function to which the
axioms are confined in the demonstrations of geometry, holds
equally true of the definitions. Every demonstration in Euclid
might be carried on without them. This is apparent from the
ordinary process of proving a proposition of geometry by means
of a diagram. What assumption, in fact, do we set out from,
to demonstrate by a diagram any of the properties of the
circle ? Not that in all circles the radii are equal, but only
that they are so in the circle ABC. As our warrant for
assuming this, we appeal, it is true, to the definition of a
circle in general ; but it is only necessary that the assumption
be granted in the case of the particular circle supposed. From
this, which is not a general but a singular proposition, com-
bined with other propositions of a similar kind, some of which
irhen generalised are called definitions, and others axioms, we
prove that a certain conclusion is true, not of all circles, but
of the particular circle ABC ; or at least would be so, if the
facts precisely accorded with our assumptions. The enuncia-
tion, as it is called, that is, the general theorem which stands
at the head of the demonstration, is not the proposition

220 REASONING.

actually demonstrated. One instance only is demonstrated :
but the process by which this is done, is a process which,
when we consider its nature, we perceive might be exactly
copied in an indefinite number of other instances; in every
instance which conforms to certain conditions. The con-
trivance of general language furnishing us with terms which
connote these conditions, we are able to assert this indefinite
multitude of truths in a single expression, and this expression
is the general theorem. By dropping the use of diagrams, and
substituting, in the demonstrations, general phrases for the
letters of the alphabet, we might prove the general theorem
directly, that is, we might demonstrate all the cases at once ;
and to do this we must, of course, employ as our premises, the
axioms and definitions in their general form. But this only
means, that if we can prove an individual conclusion by assum-
ing an individual fact, then in whatever case we are warranted
in making an exactly similar assumption, we may draw an
exactly similar conclusion. The definition is a sort of notice
to ourselves and others, what assumptions we think ourselves
entitled to make. And so in all cases, the general propositions,
whether called definitions, axioms, or laws of nature, which we
lay down at the beginning of our reasonings, are merely
abridged statements, in a kind of short-hand, of the parti-
cular facts, which, as occasion arises, we either think we may
proceed on as proved, or intend to assume. In any one de-
monstration it is enough if we assume for a particular case
suitably selected, what by the statement of the definition or
principle we announce that we intend to assume in all cases
which may arise. The definition of the circle, therefore, is to
one of Euclid's demonstrations, exactly what, according to
Stewart, the axioms are; that is, the demonstration does not
depend on it, but yet if we deny it the demonstration fails. The
proof does not rest on the general assumption, but on a similar
assumption confined to the particular case : that case, however,
being chosen as a specimen or paradigm of the whole class of
cases included in the theorem, there can be no ground for
making the assumption in that case which does not exist
in every other ; and to deny the assumption as a general

FUNCTIONS AND VALUE OF THE SYLLOGISM. 221

truth, is to deny the right of making it in the particular
instance.

There are, undoubtedly, the most ample reasons for stating
both the principles and the theorems in their general form,
and these will be explained presently, so far as explanation is
requisite. But, that unpractised learners, even in making use
of one theorem to demonstrate another, reason rather from
particular to particular than from the general proposition, is
manifest from the difficulty they find in applying a theorem
to a case in which the configuration of the diagram is
extremely unlike that of the diagram by which the original
theorem was demonstrated. A difficulty which, except in
cases of unusual mental power, long practice can alone
remove, and removes chiefly by rendering us familiar with
all the configurations consistent with the general conditions
of the theorem.

§ 4. From the considerations now adduced, the following
conclusions seem to be established. All inference is from
particulars to particulars : General propositions are merely
registers of such inferences already made, and short formulae
for making more: The major premise of a syllogism, conse-
quently, is a formula of this description : and the conclusion
is not an inference drawn from the formula, but an inference
drawn according to the formula : the real logical antecedent,
or premise, being the particular facts from which the general
proposition was collected by induction. Those facts, and the
individual instances which supplied them, may have been for-
gotten : but a record remains, not indeed descriptive of the
facts themselves, but showing how those cases may be distin-
guished, respecting which, the facts, when known, were consi-
dered to warrant a given inference. According to the indica-
tions of this record we draw our conclusion : which is, to all
intents and purposes, a conclusion from the forgotten facts.
For this it is essential that we should read the record correctly:
and the rules of the syllogism are a set of precautions to ensure
our doing so.

This view of the functions of the syllogism is confirmed

222 REASONING.

by the consideration of precisely those cases which might he
expected to he least favourable to it, namely, those in which
ratiocination is independent of any previous induction. We
have already observed that the syllogism, in the ordinary
course of our reasoning, is only the latter half of the process
of travelling from premises to a conclusion. There are, how-
ever, some peculiar cases in which it is the whole process.
Particulars alone are capable of being subjected to observation ;
and all knowledge which is derived from observation, begins,
therefore, of necessity, in particulars ; but our knowledge may,
in cases of certain descriptions, be conceived as coming to us
from other sources than observation. It may present itself as
coming from testimony, which, on the occasion and for the
purpose in hand, is accepted as of an authoritative character :
and the information thus communicated, may be conceived to
comprise not only particular facts but general propositions, as
when a scientific doctrine is accepted without examination on
the authority of writers, or a theological doctrine on that of
Scripture. Or the generalization may not be, in the ordinary
sense, an assertion at all, but a command; a law, not in the
philosophical, but in the moral and political sense of the term :
an expression of the desire of a superior, that we, or any
number of other persons, shall conform our conduct to certain
general instructions. So far as this asserts a fact, namely, a
volition of the legislator, that fact is an individual fact, and the
proposition, therefore, is not a general proposition. But the
description therein contained of the conduct which it is the
will of the legislator that his subjects should observe, is general.
The proposition asserts, not that all men are anything, but
that all men shall do something.

In both these cases the generalities are the original data,
and the particulars are elicited from them by a process which
correctly resolves itself into a series of syllogisms. The real
nature, however, of the supposed deductive process, is evident
enough. The only point to be determined is, whether the
authority which declared the general proposition, intended to
include this case in it; and whether the legislator intended his
.command to apply to the present case among others, or not.

FUNCTIONS AND VALUE OF THE SYLLOGISM. 223

This is ascertained by examining whether the case possesses
the marks by which, as those authorities have signified, the
cases -which they meant to certify or to influence may be
known. The object of the inquiry is to make out the witness's
or the legislator's intention, through the indication given by
their words. This is a question, as the Germans express it,
of hermeneutics. The operation is not a process of inference,
but a process of interpretation.

In this last phrase we have obtained an expression which
appears to me to characterize, more aptly than any other, the
functions of the syllogism in all cases. When the premises
are given by authority, the function of Reasoning is to ascer-
tain the testimony of a witness, or the will of a legislator, by
interpreting the signs in which the one has intimated his
assertion and the other his command. In like manner, when
the premises are derived from observation, the function of
Reasoning is to ascertain what we (or our predecessors)
formerly thought might be inferred from the observed facts,
and to do this by interpreting a memorandum of ours, or of
theirs. The memorandum reminds us, that from evidence,
more or less carefully weighed, it formerly appeared that a
certain attribute might be inferred wherever we perceive a
certain mark. The proposition, All men are mortal (for
instance) shows that we have had experience from which we
thought it followed that the attributes connoted by the term
man, are a mark of mortality. But when we conclude that
the Duke of Wellington is mortal, we do not infer this from
the memorandum, but from the former experience. All that
we infer from the memorandum is our own previous belief,
(or that of those who transmitted to us the proposition), con-
cerning the inferences which that former experience would
warrant.

This view of the nature of the syllogism renders con-
sistent and intelligible what otherwise remains obscure and
confused in the theory of Archbishop Whately and other
enlightened defenders of the syllogistic doctrine, respecting
the limits to which its functions are confined. They affirm in
as explicit terms as can be used, that the sole office of general

REASONING.

reasoning is to prevent inconsistency in our opinions ; to pre-
vent us from assenting to anything, the truth of which would
contradict something to which we had previously on good
grounds given our assent And they tell us, that the sole
ground which a syllogism affords for assenting to the conclu-
sion, is that the supposition of its being false, combined with
the supposition that the premises are true, would lead to a
contradiction in terms. Now this would be but a lame
account of the real grounds which we have for believing the
facts which we learn from reasoning, in contradistinction to
observation. The true reason why we believe that the Duke
of Wellington will die, is that his fathers, and our fathers,
and all other persons who were cotemporary with them, have
died. Those facts are the real premises of the reasoning. But
we are not led to infer the conclusion from those premises,
by the necessity of avoiding any verbal inconsistency. There
is no contradiction in supposing that all those persons have
died, and that the Duke of Wellington may, notwithstand-
ing, live for ever. But there would be a contradiction if we
first, on the ground of those same premises, made a general
assertion including and covering the case of the Dnke of
Wellington, and then refused to stand to it in the individual
case. There is an inconsistency to be avoided between the
memorandum we make of the inferences which may be justly
drawn in future cases, and the inferences we actually draw in
those cases when they arise. With this view we interpret our
own formula, precisely as a judge interprets a law : in order
that we may avoid drawing any inferences not conformable to
our former intention, as a judge avoids giving any decision
not conformable to the legislator's intention. The rules for
this interpretation are the rules of the syllogism : and its
sole purpose is to maintain consistency between the conclu-
sions we draw in every particular case, and the previous
general directions for drawing them ; whether those general
directions were framed by ourselves as the result of induction,
or were received by us from an authority competent to give
them.

FUNCTION'S AND VALUE OF THE SYLLOGISM. 225

§ 5. In the above observations it has, I think, been
shown, that, though there is always a process of reasoning or
inference where a syllogism is used, the syllogism is not a cor-
rect analysis of that process of reasoning or inference; which
is, on the contrary, (when not a mere inference from testi-
mony) an inference from particulars to particulars; authorized
by a previous inference from particulars to generals, and sub-
stantially the same with it ; of the nature, therefore, of Induc-
tion. But while these conclusions appear to me undeniable,
I must yet enter a protest, as strong as that of Archbishop
Whately himself, against the doctrine that the syllogistic art
is useless for the purposes of reasoning. The reasoning lies in
the act of generalization, not in interpreting the record of that
act ; but the syllogistic form is an indispensable collateral
security for the correctness of the generalization itself.

It has already been seen, that if we have a collection of
particulars sufficient for grounding an induction, we need not
frame a general proposition ; we may reason at once from those
particulars to other particulars. But it is to be remarked
withal, that whenever, from a set of particular cases, we can
legitimately draw any inference, we may legitimately make
our inference a general one. If, from observation and expe-
riment, we can conclude to one new case, so may we to an
indefinite number. If that which has held true in our past
experience will therefore hold in time to come, it will hold not
merely in some individual case, but in all cases of some given
description. Every induction, therefore, which suffices to
prove one fact, proves an indefinite multitude of facts : the
experience which justifies a single prediction must be such as
will suffice to bear out a general theorem. This theorem it is
extremely important to ascertain and declare, in its broadest
form of generality ; and thus to place before our minds, in its
full extent, the whole of what our evidence must prove if it
proves anything.

This throwing of the whole body of possible inferences

from a given set of particulars, into one general expression,

operates as a security for their being just inferences, in more

ways than one. First, the general principle presents a larger

VOL. i. 15

226 REASONING.

object to the imagination than any of the singular propositions
which it contains. A process of thought which leads to a com-
prehensive generality, is felt as of greater importance than one
which terminates in an insulated fact ; and. the mind is, even
unconsciously, led to bestow greater attention upon the pro-
cess, and to weigh more carefully the sufficiency of the expe-
rience appealed to, for supporting the inference grounded upon
it. There is another, and a more important, advantage. In
reasoning from a course of individual observations to some
new and unobserved case, which we are but imperfectly ac-
quainted with (or we should not be inquiring into it), and in
which, since we are inquiring into it, we probably feel a pecu-
liar interest ; there is very little to prevent us from giving way
to negligence, or to any bias which may affect our wishes or
our imagination, and, under that influence, accepting insuffi-
cient evidence as sufficient. But if, instead of concluding
straight to the particular case, we place before ourselves an
entire class of facts — the whole contents of a general proposi-
tion, every tittle of which is legitimately inferrible from our
premises, if that one particular conclusion is so ; there is then
a considerable likelihood that if the premises are insufficient,
and the general inference, therefore, groundless, it will com-
prise within it some fact or facts the reverse of which we already
know to be true ; and we shall thus discover the error in our
generalization by a reductio ad impossibile.

Thus if, during the reign of Marcus Aurelius, a subject of
the Roman empire, under the bias naturally given to the ima-
gination and expectations by the lives and characters of the
Antonines, had been disposed to expect that Commodus would
be a just ruler; supposing him to stop there, he might only
have been undeceived by sad experience. But if he reflected
that this expectation could not be justifiable unless from the
same evidence he was warranted in concluding some general
proposition, as, for instance, that all Roman emperors are just
rulers; he would immediately have thought of Nero, Domi-
tian, and other instances, which, showing the falsity of the
general conclusion, and therefore the insufficiency of the pre-
mises, would have warned him that those premises could not

FUNCTIONS AND VALUE OF THE SYLLOGISM. 227

prove in the instance of Commodus, what they were inade-
quate to prove in any collection of cases in which his was
included.

The advantage, in judging whether any controverted in-
ference is legitimate, of referring to a parallel case, is univer-
sally acknowledged. But by ascending to the general propo-
sition, we bring under our view not one parallel case only, but
all possible parallel cases at once ; all cases to which the same
set of evidentiary considerations are applicable.

When, therefore, we argue from a number of known cases
to another case supposed to be analogous, it is always possible,
and generally advantageous, to divert our argument into the
circuitous channel of an induction from those known cases to
a general proposition, and a subsequent application of that
general proposition to the unknown case. This second part
of the operation, which, as before observed, is essentially a pro-
cess of interpretation, will be resolvable into a syllogism or a
series of syllogisms, the majors of which will be general pro-
positions embracing whole classes of cases ; every one of which
propositions must be true in all its extent, if the argument is
maintainable. If, therefore, any fact fairly coming within the
range of one of these general propositions, and consequently
asserted by it, is known or suspected to be other than the
proposition asserts it to be, this mode of stating the argument
causes us to know or to suspect that the original observations,
which are the real grounds of our conclusion, are not sufficient
to support it. And in proportion to the greater chance of our
detecting the inconclusiveness of our evidence, will be the in-
creased reliance we are entitled to place in it if no such evidence
of defect shall appear.

The value, therefore, of the syllogistic form, and of the
rules for using it correctly, does not consist in their being the
form and the rules according to which our reasonings are neces-
sarily, or even usually, made; but in their furnishing us with
a mode in which those reasonings may always be represented,
and which is admirably calculated, if they are inconclusive,
to bring their inconclusiveness to light. An induction from
particulars to generals, followed by a syllogistic process from

15—2

228 REASONING.

those generals to other particulars, is a form in which we may
always state our reasonings if we please. It is not a form in
which we must reason, but it is a form in which we may reason,
and into which it is indispensable to throw our reasoning,
when there is any doubt of its validity : though when the case
is familiar and little complicated, and there is no suspicion of
error, we may, and do, reason at once from the known parti-
cular cases to unknown ones.*

These are the uses of syllogism, as a mode of verifying
any given argument. Its ulterior uses, as respects the general
course of our intellectual operations, hardly require illustra-
tion, being in fact the acknowledged uses of general language.
They amount substantially to this, that the inductions may
be made once for all : a single careful interrogation of expe-
rience may suffice, and the result may be registered in the
form of a general proposition, which is committed to memory
or to writing, and from which afterwards we have only to
syllogize. The particulars of our experiments may then be
dismissed from the memory, in which it would be impossible
to retain so great a multitude of details; while the knowledge
which those details afforded for future use, and which would
otherwise be lost as soon as the observations were forgotten,
or as their record became too bulky for reference, is retained
in a commodious and immediately available shape by means
of general language.

Against this advantage is to be set the countervailing
inconvenience, that inferences originally made on insufficient
evidence, become consecrated, and, as it were, hardened into
general maxims ; and the mind cleaves to them from habit,
after it has outgrown any liability to be misled- by similar

* The language of ratiocination would, I think, be brought into closer agree-
ment with the real nature of the process, if the general propositions employed
in reasoning, instead of being in the form All men are mortal, or Every man is
mortal, were expressed in the form Any man is mortal. This mode of expression,
exhibiting as the type of all reasoning from experience "The men A, B, C, &c.
are so and so, therefore any man is so and so," would much better manifest the
true idea — that inductive reasoning is always, at bottom, inference from par-
ticulars to particulars, and that the whole function of general propositions in
reasoning, is to vouch for the legitimacy of such inferences.

FUNCTIONS AND VALUE OP THE SYLLOGISM. 229

fallacious appearances if they were now for the first time pre-
sented ; but having forgotten the particulars, it does not
think of revising its own former decision. An inevitable
drawback, which, however considerable in itself, forms evi-
dently but a small set-off against the immense benefits of
general language.

The use of the syllogism is in truth no other than the use
of general propositions in reasoning. We can reason with-
out them ; in simple and obvious cases we habitually do so ;
minds of great sagacity can do it in cases not simple and
obvious, provided their experience supplies them with in-
stances essentially similar to every combination of circum-
stances likely to arise. But other minds, and the same minds
where they have not the same pre-eminent advantages of per-
sonal experience, are quite helpless without the aid of general
propositions, wherever the case presents the smallest complica-
tion ; and if we mado no general propositions, few persons
would get much beyond those simple inferences which are
drawn by the more intelligent of the brutes. Though not
necessary to reasoning, general propositions are necessary to
any considerable progress in reasoning. It is, therefore,
natural and indispensable to separate the process of investiga-
tion into two parts ; and obtain general formulae for determin-
ing what inferences may be drawn, before the occasion arises
for drawing the inferences. The work of drawing them is
then that of applying the formula ; and the rules of syllo-
gism are a system of securities for the correctness of the
application.

§ 6. To complete the series of considerations connected
with the philosophical character of the syllogism, it is requi-
site to consider, since the syllogism is not the universal type
of the reasoning process, what is the real type. This resolves
itself into the question, what is the nature of the minor pre-
mise, and in what manner it contributes to establish the con-
clusion : for as to the major, we now fully understand, that
the place which it nominally occupies in our reasonings,
properly belongs to the individual facts or observations of

230 REASONING.

which it expresses the general result ; the major itself being
no real part of the argument, hut an intermediate halting-
place for the mind, interposed by an artifice of language
between the real premises and the conclusion, by way of a
security, which it is in a most material degree, for the cor-
rectness of the process. The minor, however, being an indis-
pensable part of the syllogistic expression of an argument,
without doubt either is, or corresponds to, an equally indis-
pensable part of the argument itself, and we have only to
inquire what part.

It is perhaps worth while to notice here a speculation
of a philosopher to whom mental science is much indebted,
but who, though a very penetrating, was a very hasty thinker,
and whose want of due circumspection rendered him fully as
remarkable for what he did not see, as for what he saw. I
allude to Dr. Thomas Brown, whose theory of ratiocination
is peculiar. He saw the petitio principii which is inherent
in every syllogism, if we consider the major to be itself
the evidence by which the conclusion is proved, instead of
being, what in fact it is, an assertion of the existence of
evidence sufficient to prove any conclusion of a given descrip-
tion. Seeing this, Dr. Brown not only failed to see the
immense advantage, in point of security for correctness, which
is gained by interposing this step between the real evidence
and the conclusion ; but he thought it incumbent on him to
strike out the major altogether from the reasoning process,
without substituting anything else, and maintained that our
reasonings consist only of the minor premise and the conclu-
sion, Socrates is a man, therefore Socrates is mortal : thus
actually suppressing, as an unnecessary step in the argument,
the appeal to former experience. The absurdity of this was
disguised from him by the opinion he adopted, that reasoning
is merely analysing our own general notions, or abstract ideas ;
and that the proposition, Socrates is mortal, is evolved from
the proposition, Socrates is a man, simply by recognising the
notion of mortality as already contained in the notion we form
of a man.

After the explanations so fully entered into on the subject

FUNCTIONS AND VALUE OF THE SYLLOGISM. 231

of propositions, much further discussion cannot be necessary
to make the radical error of this view of ratiocination appa-
rent. If the word man connoted mortality ; if the meaning of
"mortal" were involved in the meaning of "man;" we might,
undoubtedly, evolve the conclusion from the minor alone,
because the minor would have already asserted it. But if, as
is in fact the case, the word man does not connote mortality,
how does it appear that in the mind of every person who
admits Socrates to be a man, the idea of man must include
the idea of mortality ? Dr. Brown could not help seeing this
difficulty, and in order to avoid it, was led, contrary to his
intention, to re-establish, under another name, that step in
the argument which corresponds to the major, by affirming
the necessity of previously perceiving the relation between the
idea of man and the idea of mortal. If the reasoner has
not previously perceived this relation, he will not, says Dr.
Brown, infer because Socrates is a man, that Socrates is
mortal. But even this admission, though amounting to a
surrender of the doctrine that an argument consists of the
minor and the conclusion alone, will not save the remainder of
Dr. Brown's theory. The failure of assent to the argument
does not take place merely because the reasoner, for want of
due analysis, does not perceive that his idea of man includes
the idea of mortality ; it takes place, much more commonly,
because in his mind that relation between the two ideas has
never existed. And in truth it never does exist, except as the
result of experience. Consenting, for the sake of the argu-
ment, to discuss the question on a supposition of which we
have recognised the radical incorrectness, namely, that the
meaning of a proposition relates to the ideas of the things
spoken of, and not to the things themselves ; I must yet ob-
serve, that the idea of man, as an universal idea, the common
property of all rational creatures, cannot involve anything but
what is strictly implied in the name. If any one includes in
his own private idea of man, as no doubt is always the case,
some other attributes, such for instance as mortality, he does
so only as the consequence of experience, after having satis-
fied himself that all men possess that attribute : so that what-

REASONING.

ever the idea contains, in any person's mind, beyond what
is included in the conventional signification of the word, has
been added to it as the result of assent to a proposition;
while Dr. Brown's theory requires us to suppose, on the con-
trary, that assent to the proposition is produced by evolving,
through an analytic process, this very element out of the
idea. This theory, therefore, may be considered as sufficiently
refuted ; and the minor premise must be regarded as totally
insufficient to prove the conclusion, except with the assistance
of the major, or of that which the major represents, namely,
the various singular propositions expressive of the series of
observations, of which the generalization called the major
premise is the result.

In the argument, then, which proves that Socrates is
mortal, one indispensable part of the premises will be as
follows : " My father, and my father's father, A, B, C, and
an indefinite number of other persons, were mortal ;" which
is only an expression in different words of the observed fact
that they have died. This is the major premise divested of
the petitio principii, and cut down to as much as is really
known by direct evidence.

In order to connect this proposition with the conclusion
Socrates is mortal, the additional link necessary is such a pro-
position as the following : " Socrates resembles my father, and
my father's father, and the other individuals specified." This
proposition we assert when we say that Socrates is a man.
By saying so we likewise assert in what respect he resembles
them, namely, in the attributes connoted by the word man.
And we conclude that he further resembles them in the attri-
bute mortality.

§ 7. We have thus obtained what we were seeking, an
universal type of the reasoning process. We find it resolv-
able in all cases into the following elements : Certain indi-
viduals have a given attribute ; an individual or individuals
resemble the former in certain other attributes ; therefore
they resemble them also in the given attribute. This type of
ratiocination does not claim, like the syllogism, to be con-

FUNCTIONS AND VALUE OF THE SYLLOGISM. 233

elusive from the mere form of the expression ; nor can it
possibly be so. That one proposition does or does not
assert the very fact which was already asserted in another,
may appear from the form of the expression, that is, from a
comparison of the language ; but when the two propositions
assert facts which are bond fide different, whether the one
fact proves the other or not can never appear from the lan-
guage, but must depend on other considerations. Whether,
from the attributes in which Socrates resembles those men
who have heretofore died, it is allowable to infer that he re-
sembles them also in being mortal, is a question of Induction ;
and is to be decided by the principles or canons which we
shall hereafter recognise as tests of the correct performance of
that great mental operation.

Meanwhile, however, it is certain, as before remarked,
that if this inference can be drawn as to Socrates, it can be
drawn as to all others who resemble the observed individuals
in the same attributes in which he resembles them ; that is
(to express the thing concisely) of all mankind. If, therefore,
the argument be admissible in the case of Socrates, we are at
liberty, once for all, to treat the possession of the attributes
of man as a mark, or satisfactory evidence, of the attribute of
mortality. This we do by laying down the universal pro-
position, All men are mortal, and interpreting this, as occasion
arises, in its application to Socrates and others. By this
means we establish a very convenient division of the entire
logical operation into two steps ; first, that of ascertaining
what attributes are marks of mortality; and, secondly, whether
any given individuals possess those marks. And it will
generally be advisable, in our speculations on the reasoning
process, to consider this double operation as in fact taking
place, and all reasoning as carried on in the form into which
it must necessarily be thrown to enable us to apply to it any
test of its correct performance.

Although, therefore, all processes of thought in which the
ultimate premises are particulars, whether we conclude from
particulars to a general formula, or from particulars to other
particulars according to that formula, are equally Induction ;

234 REASONING.

we shall yet, conformably to usage, consider the name Induc-
tion as more peculiarly belonging to the process of establish-
ing the general proposition, and the remaining operation,
which is substantially that of interpreting the general propo-
sition, we shall call by its usual name, Deduction. And we
shall consider every process by which anything is inferred
respecting an unobserved case, as consisting of an Induction
followed by a Deduction ; because, although the process needs
not necessarily be carried on in this form, it is always suscep-
tible of the form, and must be thrown into it when assurance
of scientific accuracy is needed and desired.

§ 8. The theory of the syllogism laid down in the pre-
ceding pages, has obtained, among other important adhesions,
three of peculiar value; those of Sir John Herschel,* Dr.
Whewell,f and Mr. Bailey ;J Sir John Herschel considering
the doctrine, though not strictly " a discovery," having been
anticipated by Berkeley, § to be " one of the greatest steps
which have yet been made in the philosophy of Logic."
" When we consider" (to quote the further words of the same
authority) "the inveteracy of the habits and prejudices which
it has cast to the winds," there is no cause for misgiving in
the fact that other thinkers, no less entitled to consideration,
have formed a very different estimate of it. Their principal
objection cannot be better or more succinctly stated than by
borrowing a sentence from Archbishop Whately.|| "In every
case where an inference is drawn from Induction (unless that

* Review of Quetelet on Probabilities, Essays, p. 367.

•f* Philosophy of Discovery, p. 289.

* Theory of Reasoning, ch. iv. to which I may refer for an able statement
and enforcement of the grounds of the doctrine.

§ On a recent careful reperusal of Berkeley's whole works, I have been
unable to find this doctrine in them. Sir John Herschel probably meant that
it is implied in Berkeley's argument against abstract ideas. But I cannot find
that Berkeley saw the implication, or had ever asked himself what bearing his
argument had on the theory of the syllogism. Still less can I admit that the
doctrine is (as has been affirmed by one of my ablest and most candid critics)
" among the standing marks of what is called the empirical philosophy."
I) Logic, book iv. ch. i. sect. 1.

FUNCTIONS AND VALUE OF THE SYLLOGISM.

name is to be given to a mere random guess without any
grounds at all) we must form a judgment that the instance or
instances adduced are sufficient to authorize the conclusion ;
that it is allowable to take these instances as a sample war-
ranting an inference respecting the whole class ;" and the
expression of this judgment in words (it has been said by
several of my critics) is the major premise.

I quite admit that the major is an affirmation of the suffi-
ciency of the evidence on which the conclusion rests. That it
is so, is the very essence of my own theory. And whoever
admits that the major premise is only this, adopts the theory
in its essentials.

But I cannot concede that this recognition of the suffi-
ciency of the evidence — that is, of the correctness of the induc-
tion— is a part of the induction itself; unless we ought to say
that it is a part of everything we do, to satisfy ourselves that
it has been done rightly. We conclude from known instances
to unknown by the impulse of the generalizing propensity ;
and (until after a considerable amount of practice and mental
discipline) the question of the sufficiency of the evidence is
only raised by a retrospective act, turning back upon our own
footsteps, and examining whether we were warranted in doing
what we have provisionally done. To speak of this reflex opera-
tion as part of the original one, requiring to be expressed in
words in order that the verbal formula may correctly represent
the psychological process, appears to me false psychology.*
We review our syllogistic as well as our inductive pro-
cesses, and recognise that they have been correctly per-
formed ; but logicians do not add a third premise to the
syllogism, to express this act of recognition. A careful copyist
verifies his transcript by collating it with the original ; and
if no error appears, he recognises that the transcript has been
correctly made. But we do not call the examination of the
copy a part of the act of copying.

The conclusion in an induction is inferred from the evi-

* See the important chapter on Belief, in Professor Bain's great treatise,
The Emotions and the Will, pp. 581 4.

236

REASONING.

deuce itself, and not from a recognition of the sufficiency of
the evidence ; as I infer that my friend is walking towards me
because I see him, and not because I recognise that my eyes
are open, and that eyesight is a means of knowledge. In all
operations which require care, it is good to assure ourselves
that the process has been performed accurately ; but the test-
ing of the process is not the process itself; and, besides, may
have been omitted altogether, and yet the process be correct.
It is precisely because that operation is omitted in ordinary
unscientific reasoning, that there is anything gained in cer-
tainty by throwing reasoning into the syllogistic form. To
make sure, as far as possible, that it shall not be omitted, we
make the testing operation a part of the reasoning process
itself. We insist that the inference from particulars to par-
ticulars shall pass through a general proposition. But this is
a security for good reasoning, not a condition of all reasoning ;
and in some cases not even a security. Our most familiar in-
ferences are all made before we learn the use of general pro-
positions; and a person of untutored sagacity will skilfully
apply his acquired experience to adjacent cases, though he
would bungle grievously in fixing the limits of the appropriate
general theorem. But though he may conclude rightly, he
never, properly speaking, knows whether he has done so or
not ; he has not tested his reasoning. Now, this is precisely
what forms of reasoning do for us. We do not need them to
enable us to reason, but to enable us to know whether we
reason correctly.

In still further answer to the objection, it may be added
that — even when the test has been applied, and the sufficiency
of the evidence recognised — if it is sufficient to support the
general proposition, it is sufficient also to support an inference
from particulars to particulars without passing through the
general proposition. The inquirer who has logically satisfied
himself that the conditions of legitimate induction were realized
in the cases A, B, C, would be as much justified in concluding
directly to the Duke of Wellington as in concluding to all
men. The general conclusion is never legitimate, unless the
particular one would be so too ; and in no sense, intelligible

FUNCTIONS AND VALUE OF THE SYLLOGISM. 237

to me, can the particular conclusion be said to be drawn from
the general one. Whenever there is ground for drawing any
conclusion at all from particular instances, there is ground for
a general conclusion ; but that this general conclusion should
be actually drawn, however useful, cannot be an indispensable
condition of the validity of the inference in the particular case.
A man gives away sixpence by the same power by which he
disposes of his whole fortune ; but it is not necessary to the
legality of the smaller act, that he should make a formal asser-
tion of his right to the greater one.

Some additional remarks, in reply to minor objections, are
appended.*

* A writer in the "British Quarterly Keview " (August, 1846), in a review
of this treatise, endeavours to show that there is no petitio pnncipii in the
syllogism, by denying that the proposition, All men are mortal, asserts or
assumes that Socrates is mortal. In support of this denial, he argues that we
may, and in fact do, admit the general proposition that all men are mortal, with-
out having particularly examined the case of Socrates, and even without knowing
whether the individual so named is a man or something else. But this of course
was never denied. That we can and do draw conclusions concerning cases
specifically unknown to us, is the datum from which all who discuss this subject
must set out. The question is, in what terms the evidence, or ground, on which
we draw these conclusions, may best be designated — whether it is most correct
to say, that the unknown case is proved by known cases, or that it is proved by
a general proposition including both sets of cases, the unknown and the known ?
I contend for the former mode of expression. I hold it an abuse of language to
say, that the proof that Socrates is mortal, is that all men are mortal. Turn it
in what way we will, this seems to me to be asserting that a thing is the proof
of itself. Whoever pronounces the words, All men are mortal, has affirmed
that Socrates is mortal, though he may never have heard of Socrates ; for since
Socrates, whether known to be so or not, really is a man, he is included in the
words, All men, and in every assertion of which they are the subject. If the
reviewer does not see that there is a difficulty here, I can only advise him to
reconsider the subject until he does : after which he will be a better judge of
the success or failure of an attempt to remove the difficulty. That he had re-
flected very little on the point when he wrote his remarks, is shown by his over-
sight respecting the dictum de omni et nullo. He acknowledges that this maxim
as commonly expressed, — " Whatever is true of a class, is true of everything in-
cluded in the class," is a mere identical proposition, since the class is nothing
but the things included in it. But he thinks this defect would be cured by
wording the maxim thus, — " Whatever is true of a class, is true of everything
•which can be shown to be a member of the class :" as if a thing could " be
shown " to be a member of the class without being one. If a class means the

238 REASONING.

§ 9. The preceding considerations enable us to under-
stand the true nature of what is termed, by recent writers,
Formal Logic, and the relation between it and Logic in the
widest sense. Logic, as I conceive it, is the entire theory
of the ascertainment of reasoned or inferred truth. Formal

sum of all the things included in the class, the things which can " be shown "
to be included iu it are part of the sum, and the dictum is as much an identical
proposition with respect to them as to the rest. One would almost imagine that,
in the reviewer's opinion, things are not members of a class until they are called
up publicly to take their place in it — that so long, in fact, as Socrates is not
known to be a man, he is not a man, and any assertion which can be made con-
cerning men does not at all regard him, nor is affected as to its truth or falsity
by anything in which he is concerned.

The difference between the reviewer's theory and mine may be thus stated.
Both admit that when we say, All men are mortal, we make an assertion reach-
ing beyond the sphere of our knowledge of individual cases ; and that when a
new individual, Socrates, is brought within the field of our knowledge by
means of the minor premise, we learn that we have already made an assertion
respecting Socrates without knowing it : our own general formula being, to that
extent, for the first time interpreted to us. But according to the reviewer's
theory, the smaller assertion is proved by the larger : while I contend, that both
assertions are proved together, by the same evidence, namely, the grounds of
experience on which the general assertion was made, and by which it must be
justified.

The reviewer says, that if the major premise included the conclusion, " we
should be able to affirm the conclusion without the intervention of the minor
premise ; but every one sees that that is impossible." A similar argument is
urged by Mr. De Morgan (Formal Logic, p. 259) : " The whole objection
tacitly assumes the superfluity of the minor ; that is, tacitly assumes we know
Socrates* to be a man as soon as we know him to be Socrates." The objection
would be well grounded if the assertion that the major premise includes the
conclusion, meant that it individually specifies all it includes. As however the
only indication it gives is a description by marks, we have still to compare any
new individual with the marks ; and to show that this comparison has been
made, is the office of the minor. But since, by supposition, the new individual
has the marks, whether we have ascertained him to have them or not ; if we
have affirmed the major premise, we have asserted him to be mortal. Now my
position is that this assertion cannot be a necessary part of the argument. It
cannot be a necessary condition of reasoning that we should begin by making
an assertion, which is afterwards to be employed in proving a part of itself.
I can conceive only one way out of this difficulty, viz. that what really forms
the proof is the other part of the assertion ; the portion of it, the truth of which
has been ascertained previously : and that the unproved part is bound up in

* Mr. De Morgan says "Plato," but to prevent confusion I have kept to my
own exemplum.

FUNCTIONS AND VALUE OF THE SYLLOGISM. 239

Logic, therefore, which Sir William Hamilton from his own
point of view, and Archbishop Whately from his, have repre-
sented as the whole of Logic properly so called, is really a
very subordinate part of it, not being directly concerned with
the process of Reasoning or Inference in the sense in which
that process is a part of the Investigation of Truth. What,
then, is Formal Logic ? The name seems to be properly
applied to all that portion of doctrine which relates to the
equivalence of different modes of expression ; the rules for
determining when assertions in a given form imply or suppose
the truth or falsity of other assertions. This includes the
theory of the Import of Propositions, and of their Conver-
sion, ^Equipollence, and Opposition ; of those falsely called
Inductions (to be hereafter spoken of*), in which the apparent

one formula with the proved part in mere anticipation, and as a memorandum
of the nature of the conclusions which we are prepared to prove.

With respect to the minor premise in its formal shape, the minor as it
stands in the syllogism, predicating of Socrates a definite class name, I readily
admit that it is no more a necessary part of reasoning than the major. When
there is a major, doing its work by means of a class name, minors are needed
to interpret it : but reasoning can be carried on without either the one or the
other. They are not the conditions of reasoning, but a precaution against
erroneous reasoning. The only minor premise necessary to reasoning in the
example under consideration, is, Socrates is HJcc A, B, C, and the other indi-
viduals who are known to have died. And this is the only universal type of
that step in the reasoning process which is represented by the minor. Expe-
rience, however, of the uncertainty of this loose mode of inference, teaches the
expediency of determining beforehand what kind of likeness to the cases
observed, is necessary to bring an unobserved case within the same predicate ;
and the answer to this question is the major. The minor then identifies
the precise kind of likeness possessed by Socrates, as being the kind
required by the formula. Thus the syllogistic major and the syllogistic
minor start into existence together, and are called forth by the same
exigency. When we conclude from personal experience without referring to
any record — to any general theorems, either written, or traditional, or mentally
registered by ourselves as conclusions of our own drawing — we do not use, in
our thoughts, either a major or a minor, such as the syllogism puts into words.
When, however, we revise this rough inference from particulars to particulars,
and substitute a carefal one, the revision consists in selecting two syllogistic
premises. But this neither alters nor adds to the evidence we had before ;
it only puts us in a better position for judging whether our inference from
particulars to particulars is well grounded.

* Infra, book iii. ch. ii.

24:0 REASONING.

generalization is a mere abridged statement of cases known
individually ; and finally, of the syllogism : while the theory
of Naming, and of (what is inseparably connected with it)
Definition, though belonging still more to the other and larger
kind of logic than to this, is a necessary preliminary to this.
The end aimed at by Formal Logic, and attained by the ob-
servance of its precepts, is not truth, but consistency. It has
been seen that this is the only direct purpose of the rules of
the syllogism ; the intention and effect of which is simply to
keep our inferences or conclusions in complete consistency
with our general formulae or directions for drawing them. The
Logic of Consistency is a necessary auxiliary to the logic of
truth, not only because what is inconsistent with itself or with
other truths cannot be true, but also because truth can only
be successfully pursued by drawing inferences from experience,
which, if warrantable at all, admit of being generalized, and,
to test their warrantableness, require to be exhibited in a gene-
ralized form ; after which the correctness of their application
to particular cases is a question which specially concerns the
Logic of Consistency. This Logic, not requiring any pre-
liminary knowledge of the processes or conclusions of the
various sciences, may be studied with benefit in a much earlier
stage of education than the Logic of Truth : and the practice
which has empirically obtained of teaching it apart, through
elementary treatises which do not attempt to include anything
else, though the reasons assigned for the practice are in
general very far from philosophical, admits of philosophical
justification.

CHAPTER IV.

OF TRAINS OF REASONING, AND DEDUCTIVE SCIENCES.

§ 1. IN our analysis of the syllogism, it appeared that
the minor premise always affirms a resemblance between a new
case and some cases previously known ; while the major
premise asserts something which, having been found true of
those known cases, we consider ourselves warranted in holding
true of any other case resembling the former in certain given
particulars.

If all ratiocinations resembled, as to the minor premise,
the examples which were exclusively employed in the preced-
ing chapter ; if the resemblance, which that premise asserts,
•were obvious to the senses, as in the proposition " Socrates is
a man," or were at once ascertainable by direct observation ;
there would be no necessity for trains of reasoning, and De-
ductive or Batiocinative Sciences would not exist. Trains of
reasoning exist only for the sake of extending an induction
founded, as all inductions must be, on observed cases, to other
cases in which we not only cannot directly observe the fact
which is to be proved, but cannot directly observe even the
mark which is to prove it.

§ 2. Suppose the syllogism to be, All cows ruminate,
the animal which is before me is a cow, therefore it ruminates.
The minor, if true at all, is obviously so : the only premise
the establishment of which requires any anterior process of
inquiry, is the major; and provided the induction of which
that premise is the expression was correctly performed, the
conclusion respecting the animal now present will be in-
stantly drawn ; because, as soon as she is compared with the
formula, she will be identified as being included in it. But
suppose the syllogism to be the following : — All arsenic is
VOL. i. 16

242

REASONING.

poisonous, the substance which is before me is arsenic, there-
fore it is poisonous. The truth of the minor may not here be
obvious at first sight ; it may not be intuitively evident, but
may itself be known only by inference. It may be the con-
clusion of another argument, which, thrown into the syllogistic
form, would stand thus: — Whatever when lighted produces
a dark spot on a piece of white porcelain held in the flame,
which spot is soluble in hypochloride of calcium, is arsenic;
the substance before me conforms to this condition ; therefore
it is arsenic. To establish, therefore, the ultimate conclusion,
The substance before me is poisonous, requires a process,
which, in order to be syllogistically expressed, stands in need
of two syllogisms ; and we have a Train of Reasoning.

When, however, we thus add syllogism to syllogism, we-
are really adding induction to induction. Two separate induc-
tions must have taken place to render this chain of inference
possible ; inductions founded, probably, on different sets of
individual instances, but which converge in their results, so
that the instance which is the subject of inquiry comes within
the range of them both. The record of these inductions is-
contained in the majors of the two syllogisms. First, we, or
others for us, have examined various objects which yielded
under the given circumstances a dark spot with the given pro-
perty, and found that they possessed the properties connoted
by the word arsenic ; they were metallic, volatile, their vapour
had a smell of garlic, and so forth. Next, we, or others for
us, have examined various specimens which possessed this
metallic and volatile character, whose vapour had this smell,
&c., and have invariably found that they were poisonous.
The first observation we judge that we may extend to all sub-
stances whatever which yield that particular kind of dark spot ;
the second, to all metallic and volatile substances resembling
those we examined ; and consequently, not to those only which
are seen to be such, but to those which are concluded to be
such by the prior induction. The substance before us is only
seen to come within one of these inductions ; but by means of
this one, it is brought within the other. We are still, as be-
fore, concluding from particulars to particulars ; but we are

TRAINS OF REASONING. 243

now concluding from particulars observed, to other particulars
which are not, as in the simple case, seen to resemble them in
material points, but inferred to do so, because resembling
them in something else, which we have been led by quite a
different set of instances to consider as a mark of the former
resemblance.

This first example of a train of reasoning is still extremely
simple, the series consisting of only two syllogisms. The fol-
lowing is somewhat more complicated : — No government,
which earnestly seeks the good of its subjects, is likely to be
overthrown; some particular government earnestly seeks the
good of its subjects, therefore it is not likely to be overthrown.
The major premise in this argument we shall suppose not to
be derived from considerations a priori, but to be a generaliza-
tion from history, which, whether correct or erroneous, must
have been founded on observation of governments concerning
•whose desire of the good of their subjects there was no doubt.
It has been found, or thought to be found, that these were not
easily overthrown, and it has been deemed that those instances
warranted an extension of the same predicate to any and every
government which resembles them in the attribute of desiring
earnestly the good of its subjects. But does the government
in question thus resemble them ? This may be debated pro
and con by many arguments, and must, in any case, be proved
by another induction ; for we cannet directly observe the sen-
timents and desires of the persons who carry on the govern-
ment. To prove the minor, therefore, we require an argument
in this form : Every government which acts in a certain
manner, desires the good of its subjects; the supposed govern-
ment acts in that particular manner, therefore it desires the
good of its subjects. But is it true that the government acts in
the manner supposed ? This minor also may require proof ;
still another induction, as thus : — What is asserted by intelli-
gent and disinterested witnesses, may be believed to be true ;
that the government acts in this manner, is asserted by such
witnesses, therefore it may be believed to be true. The argu-
ment hence consists of three steps. Having the evidence of
our senses that the case of the government under considera-

16—2

244 REASONING.

tion resembles a number of former cases, in the circumstance
of having something asserted respecting it by intelligent and
disinterested witnesses, we infer, first, that, as in those former
instances, so in this instance, the assertion is true. Secondly,
what was asserted of the government being that it acts in a
particular manner, and other governments or persons having
been observed to act in the same manner, the government in
question is brought into known resemblance with those other
governments or persons ; and since they were known to desire
the good of the people, it is thereupon, by a second induction,
inferred that the particular government spoken of, desires the
• good of the people. This brings that government into known
resemblance with the other governments which were thought
likely to escape revolution, and thence, by a third induction,
it is concluded that this particular government is also likely
to escape. This is still reasoning from particulars to par-
ticulars, but we now reason to the new instance from three
distinct sets of former instances : to one only of those sets of
instances do we directly perceive the new one to be similar;
but from that similarity we inductively infer that it has the
attribute by which it is assimilated to the next set, and brought
within the corresponding induction ; after which by a repeti-
tion of the same operation we infer it to be similar to the third
set, and hence a third induction conducts us to the ultimate
conclusion.

§ 3. Notwithstanding the superior complication of these
examples, compared with those by which in the preceding
chapter we illustrated the general theory of reasoning, every
doctrine which we then laid down holds equally true in these
more intricate cases. The successive general propositions are
not steps in the reasoning, are not intermediate links in the
chain of inference, between the particulars observed and those
which we apply the observation. If we had sufficiently
Capacious memories, and a sufficient power of maintaining
order among a huge mass of details, the reasoning could go
on without any general propositions ; they are mere formulee
for inferring particulars from particulars. The principle of

TRAINS OF REASONING. 245

general reasoning is (as before explained), that if, from obser-
vation of certain known particulars, what was seen to be true
of them can be inferred to be true of any others, it may be
inferred of all others which are of a certain description. And
in order that we may never fail to draw this conclusion in a
new case when it can be drawn correctly, and may avoid
drawing it when it cannot, we determine once for all what are
the distinguishing marks by which such cases may be recog-
nised. The subsequent process is merely that of identifying
an object, and ascertaining it to have those marks; whether
we identify it by the very marks themselves, or by others
which we have ascertained (through another and a similar
process) to be marks of those marks. The real inference is
always from particulars to particulars, from the observed in-
stances to an unobserved one : but in drawing this inference,
we conform to a formula which we have adopted for our
guidance in such operations, and which is a record of the
criteria by which we thought we had ascertained that we might
distinguish when the inference could, and when it could not,
be drawn. The real premises are the individual observations,
even though they may have been forgotten, or, being the ob-
servations of others and not of ourselves, may, to us, never
have been known : but we have before us proof that we or
others once thought them sufficient for an induction, and we
have marks to show whether any new case is one of those to
which, if then known, the induction would have been deemed
to extend. These marks we either recognise at once, or by
the aid of other marks, which by another previous induction
we collected to be marks of the first. Even these marks of
marks may only be recognised through a third set of marks ;
and we may have a train of reasoning, of any length, to bring
a new case within the scope of an induction grounded on
particulars its similarity to which is only ascertained in this
indirect manner.

Thus, in the preceding example, the ultimate inductive in-
ference was, that a certain government was not likely to be
overthrown ; this inference was drawn according to a formula
in which desire of the public good was set down as a mark of

246 REASONING.

not being likely to be overthrown ; a mark of this mark was,
acting in a particular manner ; and a mark of acting in that
manner was, being asserted to do so by intelligent and disin-
terested witnesses : this mark, the government under discus-
sion was recognised by the senses as possessing. Hence that
government fell within the last induction, and by it was brought
within all the others. The perceived resemblance of the case
to one set of observed particular cases, brought it into known
resemblance with another set, and that with a third.

In the more complex branches of knowledge, the deduc-
tions seldom consist, as in the examples hitherto exhibited, of
a single chain, a a mark of b, b of c, c of d, therefore a a mark
of d. They consist (to carry on the same metaphor) of several
chains united at the extremity, as thus : a a mark of d, b of e,
c of /, d e f of n, therefore a b c a mark of n. Suppose, for
example, the following combination of circumstances ; 1 st,
rays of light impinging on a reflecting surface ; 2nd, that sur-
face parabolic ; 3rd, those rays parallel to each other and to the
axis of the surface. It is to be proved that the concourse of
these three circumstances is a mark that the reflected rays will
pass through the focus of the parabolic surface. Now, each of
the three circumstances is singly a mark of something material
to the case. Eays of light impinging on a reflecting surface
are a mark that those rays will be reflected at an angle equal
to the angle of incidence. The parabolic form of the surface,
is a mark that, from any point of it, a line drawn to the focus
and a line parallel to the axis will make equal angles with the
surface. And finally, the parallelism of the rays to the axis is
a mark that their angle of incidence coincides with one of these
equal angles. The three marks taken together are therefore a
mark of all these three things united. But the three united
are evidently a mark that the angle of reflection must coincide
•with the other of the two equal angles, that formed by a line
drawn to the focus; and this again, by the fundamental
axiom concerning straight lines, is a mark that the reflected
rays pass through the focus. Most chains of physical deduc-
tion are of this more complicated type ; and even in mathema-
tics such are abundant, as in all propositions where the

TRAINS OF REASONING. 247

hypothesis includes numerous conditions: "If a circle be taken,
=and if within that circle a point be taken, not tbe centre, and
?/ straight lines be drawn from that point to the circumference,
then," &c.

§ 4. The considerations now stated remove a serious diffi-
culty from the view we have taken of reasoning ; which view
might otherwise have seemed not easily reconcilable with the
fact that tbere are Deductive or Eatiocinative Sciences. It
might seem to follow, if all reasoning be induction, that the
difficulties of philosophical investigation must lie in the induc-
tions exclusively, and that when these were easy, and suscep-
tible of no doubt or hesitation, there could be no science, or, at
least, no difficulties in science. The existence, for example, of
an extensive Science of Mathematics, requiring the highest
scientific genius in those who contributed to its creation, and
calling for a most continued and vigorous exertion of intellect
in order to appropriate it when created, may seem hard to be
accounted for on the foregoing theory. But the considera-
tions more recently adduced remove the mystery, by showing,
that even when the inductions themselves are obvious, there
may be much difficulty in finding whether the particular case
which is the subject of inquiry comes within them ; and ample
room for scientific ingenuity in so combining various inductions,
as, by means of one within which the case evidently falls, to
bring it witbin others in which it cannot be directly seen to be
included.

When the more obvious of the inductions which can be
made in any science from direct observations, have been made,
and general formulas have been framed, determining the limits
within which these inductions are applicable ; as often as a new
case can be at once seen to come within one of the formulas,
the induction is applied to the new case, and the business is
ended. But new cases are continually arising, which do not
obviously come within any formula whereby the question we
want solved in respect of them could be answered. Let us take
an instance from geometry : and as it is taken only for illus-
tration, let the reader concede to us for the present, what we

REASONING.

shall endeavour to prove in the next chapter, that the first
principles of geometry are results of induction. Our example
shall be the fifth proposition of the first book of Euclid. The
inquiry is, Are the angles at the base of an isosceles triangle
equal or unequal ? The first thing to be considered is, what
inductions we have, from which we can infer equality or in-
equality. For inferring equality we have the following for-
mula : — Things which being applied to each other coincide,
are equals. Things which are equal to the same thing are
equals. A whole and the sum of its parts are equals. The
sums of equal things are equals. The differences of equal
things are equals. There are no other original formula) to
prove equality. For inferring inequality we have the following:
A whole and its parts are unequals. The sums of equal
things and unequal things are unequals. The differences of
equal things and unequal things are unequals. In all, eight
formula. The angles at the base of an isosceles triangle do
not obviously come within any of these. The formulae specify
certain marks of equality and of inequality, but the angles
cannot be perceived intuitively to have any of those marks.
On examination it appears that they have ; and we ultimately
succeed in bringing them within the formula, " The differences
of equal things are equal." Whence comes the difficulty of re-
cognising these angles as the differences of equal things ?
Because each of them is the difference not of one pair only,
but of innumerable pairs of angles ; and out of these we had
to imagine and select two, which could either be intuitively
perceived to be equals, or possessed some of the marks of
equality set down in the various formulas. By an exercise of
ingenuity, which, on the part of the first inventor, deserves to
be regarded as considerable, two pairs of angles were hit upon,
which united these requisites. First, it could be perceived in-
tuitively that their differences were the angles at the base ; and,
secondly, they possessed one of the marks of equality, namely,
coincidence when applied to one another. This coincidence,
however, was not perceived intuitively, but inferred, in con-
formity to another formula.

For greater clearness, I subjoin an analysis of the demon-

TRAINS OF REASONING. 249

stration. Euclid, it will be remembered, demonstrates his fifth
proposition by means of the fourth. This it is not allowable
for us to do, because we are undertaking to trace deductive
truths not to prior deductions, but to their original inductive
foundation. We must therefore use the premises of the fourth
proposition instead of its conclu-
sion, and prove the fifth directly
from first principles. To do so
requires six formulas. (We must
begin, as in Euclid, by prolonging
the equal sides AB, AC, to equal
distances, and joining the extre-
mities BE, DC.)

FIRST FORMULA. The sums of equals are equal.

AD and AE are sums of equals by the supposition. Hav-
ing that mark of equality, they are concluded by this formula
to be equal.

SECOND FORMULA. Equal straight lines or angles, being

applied to one another, coincide.

AC, AB, are within this formula by supposition ; AD, AE,
have been brought within it by the preceding step. The
angle at A considered as an angle of the triangle ABE, and the
same angle considered as an angle of the triangle ACD, are of
course within the formula. All these pairs therefore possess
the property which, according to the second formula, is a mark
that when applied to one another they will coincide. Conceive
them, then, applied to one another, by turning over the triangle
ABE, and laying it on the triangle ACD in such a manner
that AB of the one shall lie upon AC of the other. Then, by
the equality of the angles, AE will lie on AD. But AB and
AC, AE and AD are equals ; therefore they will coincide alto-
gether, and of course at their extremities, D, E, and B, C.

THIRD FORMULA. Straight lines, having their extremities
coincident, coincide.

B E and C D have been brought within this formula by
the preceding induction ; they will, therefore, coincide.

250 REASONING.

FOURTH FORMULA. — Angles, having their sides coincident,

coincide.

The third induction having shown that BE and CD coin-
cide, and the second that AB, AC, coincide, the angles ABE
and ACD are thereby brought within the fourth formula, and
accordingly coincide.

FIFTH FORMULA. — Things which coincide are equal.

The angles ABE and ACD are brought within this formula
by the induction immediately preceding. This train of rea-
soning being also applicable, mutatis mutandis, to the angles
EEC, DCB, these also are brought within the fifth formula.
And, finally,

SIXTH FORMULA. — The differences of equals are equal.

The angle ABC being the difference of ABE, CBE, and
the angle ACB being the difference of ACD, DCB ; which
have been proved to be equals ; ABC and ACB are brought
•within the last formula by the whole of the previous process.
The difficulty here encountered is chiefly that of figuring
to ourselves the two angles at the base of the triangle ABC
as remainders made by cutting one pair of angles out of
another, while each pair shall be corresponding angles of tri-
angles which have two sides and the intervening angle equal.
It is by this happy contrivance that so many different induc-
tions are brought to bear upon the same particular case. And
this not being at all an obvious thought, it may be seen from
an example so near the threshold of mathematics, how much
scope there may well be for scientific dexterity in the higher
branches of that and other sciences, in order so to combine a
few simple inductions, as to bring within each of them innu-
merable cases which are not obviously included in it ; and how
long, and numerous, and complicated may be the processes
necessary for bringing the inductions together, even when each
induction may itself be very easy and simple. All the induc-
tions involved in all geometry are comprised in those simple
ones, the formulae of which are the Axioms, and a few of the

TRAINS OP REASONING. 251

so-called Definitions. The remainder of the science is made
up of the processes employed for bringing unforeseen cases
within these inductions ; or (in syllogistic language) for prov-
ing the minors necessary to complete the syllogisms ; the
majors being the definitions and axioms. In those definitions
and axioms are laid down the whole of the marks, by an artful
combination of which it has been found possible to discover
and prove all that is proved in geometry. The marks being so
few, and the inductions which furnish them being so obvious
and familiar; the connecting of several of them together,
which constitutes Deductions, or Trains of Reasoning, forms
the whole difficulty of the science, and with a trifling exception,
its whole bulk ; and hence Geometry is a Deductive Science.

§ 5. It will be seen hereafter* that there are weighty
scientific reasons for giving to every science as much of the
character of a Deductive Science as possible; for endeavouring
to construct the science from the fewest and the simplest pos-
sible inductions, and to make these, by any combinations
however complicated, suffice for proving even such truths,
relating to complex cases, as could be proved, if we chose, by
inductions from specific experience. Every branch of natural
philosophy was originally experimental ; each generalization
rested on a special induction, and was derived from its own
distinct set of observations and experiments. From being
sciences of pure experiment, as the phrase is, or, to speak
more correctly, sciences in which the reasonings mostly consist
of no more than one step, and are expressed by single syllo-
gisms, all these sciences have become to some extent, and
some of them in nearly the whole of their extent, sciences of
pure reasoning ; whereby multitudes of truths, already known
by induction from as many different sets of experiments, have
come to be exhibited as deductions or corollaries from induc-
tive propositions of a simpler and more universal character.
Thus mechanics, hydrostatics, optics, acoustics, thermology,
have successively been rendered mathematical ; and astronomy

* Infra, book iii. cL. iv. § 3, and elsewhere.

252 REASONING.

was brought by Newton within the laws of general mechanics.
Why it is that the substitution of this circuitous mode of pro-
ceeding for a process apparently much easier and more natural,
is held, and justly, to be the greatest triumph of the investi-
gation of nature, we are not, in this stage of our inquiry, pre-
pared to examine. But it is necessary to remark, that although,
by this progressive transformation, all sciences tend to become
more and more Deductive, they are not, therefore, the less
Inductive ; every step in the Deduction is still an Induction.
The opposition is not between the terms Deductive and Induc-
tive, but between Deductive and Experimental. A science is
experimental, in proportion as every new case, which presents
any peculiar features, stands in need of a new set of observa-
tions and experiments — a fresh induction. It is deductive, in
proportion as it can draw conclusions, respecting cases of a
new kind, by processes which bring those cases under old
inductions ; by ascertaining that cases which cannot be
observed to have the requisite marks, have, however, marks
of those marks.

We can now, therefore, perceive what is the generic dis-
tinction between sciences which can be made Deductive, and
those which must as yet remain Experimental. The difference
consists in our having been able, or not yet able, to discover
marks of marks. If by our various inductions we have been
able to proceed no further than to such propositions as these,
a a mark of b, or a and b marks of one another, c a mark of
d, or c and d marks of one another, without anything to con-
nect a or & with c or d ; we have a science of detached and
mutually independent generalizations, such as these, that acids-
redden vegetable blues, and that alkalies colour them green ;
from neither of which propositions could we, directly or indi-
rectly, infer the other : and a science, so far as it is composed
of such propositions, is purely experimental. Chemistry, in
the present state of our knowledge, has not yet thrown off
this character. There are other sciences, however, of which
the propositions are of this kind : a a mark of b} b a mark of
c, c of d, d of e, &c. In these sciences we can mount the
ladder from a to e by a process of ratiocination ; we can con-

TRAINS OF REASONING. 253

elude that a is a mark of e, and that every object which has
the mark a has the property e, although, perhaps, we never
were able to observe a and e together, and although even d,
our only direct mark of e, may not be perceptible in those
objects, but only inferrible. Or, varying the first metaphor,
we may be said to get from a to e underground : the marks b,

c, d, which indicate the route, must all be possessed somewhere
by the objects concerning which we are inquiring; but they
are below the surface : a is the only mark that is visible, and
by it we are able to trace in succession all the rest.

§ 6. We can now understand how an experimental may
transform itself into a deductive science by the mere progress
of experiment. In an experimental science, the inductions,
as we have said, lie detached, as, a a mark of b, c a mark of

d, e a mark of/, and so on : now, a new set of instances, and
a consequent new induction, may at any time bridge over the
interval between two of these unconnected arches ; b, for
example, may be ascertained to be a mark of c, which enables us
thenceforth to prove deductively that a is a mark of c. Or, as
sometimes happens, some comprehensive induction may raise an
arch high in the air, which bridges over hosts of them at once :
b, d,f, and all the rest, turning out to be marks of some one
thing, or of things between which a connexion has already
been traced. As when Newton discovered that the motions, whe-
ther regular or apparently anomalous, of all the bodies of the
solar system, (each of which motions had been inferred by a
separate logical operation, from separate marks,) were all marks
of moving round a common centre, with a centripetal force
varying directly as the mass, and inversely as the square of the
distance from that centre. This is the greatest example which
has yet occurred of the transformation, at one stroke, of a
science which was still to a great degree merely experimental,
into a deductive science.

Transformations of the same nature, but on a smaller scale,
continually take place in the less advanced branches of physical
knowledge, without enabling them to throw off the character of
experimental sciences. Thus with regard to the two uncon-

254 REASONING.

nected propositions before cited, namely, Acids redden vegetable
blues, Alkalies make them green ; it is remarked by Liebig,
that all blue colouring matters which are reddened by acids
(as well as, reciprocally, all red colouring matters \vhich are
rendered blue by alkalies) contain nitrogen : and it is quite
possible that this circumstance may one day furnish a bond of
connexion between the two propositions in question, by show-
ing that the antagonistic action of acids and alkalies in pro-
ducing or destroying the colour blue, is the result of some
one, more general, law. Although this connecting of detached
generalizations is so much gain, it tends but little to give a
deductive character to any science as a whole; because the new
courses of observation and experiment, which thus enable us
to connect together a few general truths, usually make known
to us a still greater number of unconnected new ones. Hence
chemistry, though similar extensions and simplifications of its
generalizations are continually taking place, is still in the main
an experimental science ; and is likely so to continue unless
some comprehensive induction should be hereafter arrived at,
which, like Newton's, shall connect a vast number of the
smaller known inductions together, and change the whole
method of the science at once. Chemistry has already one
great generalization, which, though relating to one of the sub-
ordinate aspects of chemical phenomena, possesses within its
limited sphere this comprehensive character; the principle of
Dalton, called the atomic theory, or the doctrine of chemical
equivalents : which by enabling us to a certain extent to fore-
see the proportions in which two substances will combine,
before the experiment has been tried, constitutes undoubtedly
a source of new chemical truths obtainable by deduction, as
well as a connecting principle for all truths of the same de-
scription previously obtained by experiment.

§ 7. The discoveries which change the method of a
science from experimental to deductive, mostly consist in
establishing, either by deduction or by direct experiment, that
the varieties of a particular phenomenon uniformly accompany
the varieties of some other phenomenon better known. Thus

TRAINS OF REASONING. 255

the science of sound, which previously stood in the lowest
rank of merely experimental science, became deductive when
it was proved by experiment that every variety of sound was
consequent on, and therefore a mark of, a distinct and de-
finable variety of oscillatory motion among the particles of the
transmitting medium. When this was ascertained, it followed
that every relation of succession or coexistence which ob-
tained between phenomena of the more known class, obtained
also between the phenomena which correspond to them
in the other class. Every sound, being a mark of a parti-
cular oscillatory motion, became a mark of everything which,
by the laws of dynamics, was known to be inferrible from
that motion ; and everything which by those same laws was
a mark of any oscillatory motion among the particles of an
elastic medium, became a mark of the corresponding sound.
And thus many truths, not before suspected, concerning
sound, become deducible from the known laws of the propa-
gation of motion through an elastic medium ; while facts
already empirically known respecting sound, become an indi-
cation of corresponding properties of vibrating bodies, pre-
viously undiscovered.

But the grand agent for transforming experimental into de-
ductive sciences, is the science of number. The properties of
number, alone among all known phenomena, are, in the most
rigorous sense, properties of all things whatever. All things
are not coloured, or ponderable, or even extended ; but all
things are numerable. And if we consider this science in its
whole extent, from common arithmetic up to the calculus of
variations, the truths already ascertained seem all but infinite,
and admit of indefinite extension.

These truths, though affirmable of all things whatever, of
course apply to them only in respect of their quantity. But
if it comes to be discovered that variations of quality in any
class of phenomena, correspond regularly to variations of
quantity either in those same or in some other phenomena;
every formula of mathematics applicable to quantities which
vary in that particular manner, becomes a mark of a corre-
sponding general truth respecting the variations in quality

256 REASONING.

which accompany them : and the science of quantity heing (as
far as any science can he) altogether deductive, the theory of
that particular kind of qualities becomes, to this extent, de-
ductive likewise.

The most striking instance in point which history affords
(though not an example of an experimental science rendered
deductive, hut of an unparalleled extension given to the de-
ductive process in a science which was deductive already), is
the revolution in geometry which originated with Descartes,
and was completed hy Clairaui These great mathematicians
pointed out the importance of the fact, that to every variety
of position in points, direction in lines, or form in curves or
surfaces (all of which are Qualities), there corresponds a pecu-
liar relation of quantity between either two or three rectilineal
co-ordinates ; insomuch that if the law were known according
to which those co-ordinates vary relatively to one another,
every other geometrical property of the line or surface in
question, whether relating to quantity or quality, would he
capable of being inferred. Hence it followed that every
geometrical question could be solved, if the corresponding
algebraical one could ; and geometry received an accession
(actual or potential) of new truths, corresponding to every
property of numbers which the progress of the calculus had
brought, or might in future bring, to light. In the same
general manner, mechanics, astronomy, and in a less degree,
every branch of natural philosophy commonly so called, have
been made algebraical. The varieties of physical phenomena
with which those sciences are conversant, have been found to
answer to determinable varieties in the quantity of some
circumstance or other; or at least to varieties of form or
position, for which corresponding equations of quantity had
already been, or were suceptible of being, discovered by
geometers.

In these various transformations, the propositions of the
science of number do but fulfil the function proper to all pro-
positions forming a train of reasoning, viz. that of enabling
us to arrive in an indirect method, by marks of marks, at such
of the properties of objects as we cannot directly ascertain (or

TRAINS OF REASONING. 257

not so conveniently) by experiment. We travel from a given
visible or tangible fact, through the truths of numbers, to the
facts sought. The given fact is a mark that a certain relation
subsists between the quantities of some of the elements con-
cerned ; while the fact sought presupposes a certain relation
between the quantities of some other elements : now, if these
last quantities are dependent in some known manner upon the
former, or vice versa, we can argue from the numerical relation
between the one set of quantities, to determine that which
subsists between the other set ; the theorems of the calculus
affording the intermediate links. And thus one gf the two
physical facts becomes a mark of the other, by being a mark
of a mark of a mark of it.

VOL. I.

17

CHAPTER V.

OF DEMONSTRATION, AND NECESSARY TRUTHS.

§ 1. IF, as laid down in the two preceding chapters, the
foundation of all sciences, even deductive or demonstrative
sciences, is Induction ; if every step in the ratiocinations even
of geometry is an act of induction ; and if a train of reasoning
is but bringing many inductions to bear upon the same subject
of inquiry, and drawing a case within one induction by means
of another ; wherein lies the peculiar certainty always ascribed
to the sciences which are entirely, or almost entirely, deduc-
tive ? Why are they called the Exact Sciences ? Why are
mathematical certainty, and the evidence of demonstration,
common phrases to express the very highest degree of assu-
rance attainable by reason ? Why are mathematics by almost
all philosophers, and (by some) even those branches of natural
philosophy which, through the medium of mathematics, have
been converted into deductive sciences, considered to be inde-
pendent of the evidence of experience and observation, and
characterized as systems of Necessary Truth ?

The answer I conceive to be, that this character of neces-
sity, ascribed to the truths of mathematics, and even (with
some reservations to be hereafter made) the peculiar certainty
attributed to them, is an illusion ; in order to sustain which,
it is necessary to suppose that those truths relate to, and ex-
press the properties of, purely imaginary objects. It is
acknowledged that the conclusions of geometry are deduced,
partly at least, from the so-called Definitions, and that those
definitions are assumed to be correct representations, as far as
they go, of the objects with which geometry is conversant.
Now we have pointed out that, from a definition as such, no

DEMONSTRATION, AND NECESSARY TRUTHS. 259

proposition, unless it be one concerning the meaning of a
word, can ever follow; and that what apparently follows from a
definition, follows in reality from an implied assumption that
there exists a real thing conformable thereto. This assumption,
in the case of the definitions of geometry, is not strictly true :
there exist no real things exactly conformable to the definitions.
There exist no points without magnitude; no lines without
breadth, nor perfectly straight ; no circles with all their radii
exactly equal, nor squares with all their angles perfectly right.
It will perhaps be said that the assumption does not extend to
the actual, but only to the possible, existence of such things. I
answer that, according to any test we have of possibility, they
are not even possible. Their existence, so far as we can form
any judgment, would seem to be inconsistent with the physical
constitution of our planet at least, if not of the universe.
To get rid of this difficulty, and at the same time to save the
credit of the supposed system of necessary truth, it is
customary to say that the points, lines, circles, and squares
which are the subject of geometry, exist in our conceptions
merely, and are part of our minds ; which minds, by working on
their own materials, construct an a priori science, the evidence
of which is purely mental, and has nothing whatever to do
with outward experience. By howsoever high authorities this
doctrine may have been sanctioned, it appears to me psycho-
logically incorrect. The points, lines, circles, and squares
which any one has in his mind, are (I apprehend) simply
copies of the points, lines, circles, and squares which he has
known in his experience. Our idea of a point, I apprehend
to be simply our idea of the minimum visiblle, the smallest
portion of surface which we can see. A line, as defined by
geometers, is wholly inconceivable. We can reason about a
line as if it had no breadth ; because we have a power, which
is the foundation of all the control we can exercise over the
operations of our minds ; the power, when a perception is
present to our senses, or a conception to our intellects, of
attending to a part only of that perception or conception,
instead of the whole. But we cannot conceive a line without,
breadth ; we can form no mental picture of such a line : all

17—2

260 REASONING.

the lines which we have in our minds are lines possessing
hreadth. If any one doubts this, we may refer him to his
own experience. I much question if any one who fancies that
he can conceive what is called a mathematical line, thinks so
from the evidence of his consciousness : I suspect it is rather
because he supposes that unless such a conception were
possible, mathematics could not exist as a science : a supposi-
tion which there will be no difficulty in showing to be entirely
groundless.

Since, then, neither in nature, nor in the human mind, do
there exist any objects exactly corresponding to the definitions
of geometry, while yet that science cannot be supposed to be
conversant about non-entities ; nothing remains but to consider
geometry as conversant with such lines, angles, and figures, as
really exist; and the definitions, as they are called, must be
regarded as some of our first and most obvious generalizations
concerning those natural objects. The correctness of those
generalizations, as generalizations, is without a flaw : the
equality of all the radii of a circle is true of all circles, so far
as it is true of any one : but it is not exactly true of any
circle ; it is only nearly true ; so nearly that no error of any
importance in practice will be incurred by feigning it to be
exactly true. When we have occasion to extend these induc-
tions, or their consequences, to cases in which the error would
be appreciable — to lines of perceptible breadth or thickness,
parallels which deviate sensibly from equidistance, and the like
— we correct our conclusions, by combining with them a fresh
set of propositions relating to the aberration ; just as we also
take in propositions relating to the physical or chemical pro-
perties of the material, if those properties happen to introduce
any modification into the result ; which they easily may, even
with respect to figure and magnitude, as in the case, for
instance, of expansion by heat So long, however, as there
exists no practical necessity for attending to any of the
properties of the object except its geometrical properties, or to
any of the natural irregularities in those, it is convenient to
neglect the consideration of the other properties and of the
irregularities, and to reason as if these did not exist : accord-

DEMONSTRATION, AND NECESSARY TRUTHS. 261

ingly, we formally announce in the definitions, that we intend
to proceed on this plan. But it is an error to suppose,
because we resolve to confine our attention to a certain number
of the properties of an object, that we therefore conceive, or
have an idea of, the object, denuded of its other properties.
We are thinking, all the time, of precisely such objects as we
have seen and touched, and with all the properties which
naturally belong to them ; but, for scientific convenience, we
feign them to be divested of all properties, except those which
are material to our purpose, and in regard to which we design
to consider them.

The peculiar accuracy, supposed to be characteristic of the
first principles of geometry, thus appears to be fictitious. The
assertions on which the reasonings of the science are founded,
do not, any more than in. other sciences, exactly correspond
with the fact ; but we suppose that they do so, for the sake of
tracing the consequences which follow from the supposition.
The opinion of Dugald Stewart respecting the foundations of
geometry, is, I conceive, substantially correct ; that it is
built on hypotheses ; that it owes to this alone the peculiar
certainty supposed to distinguish it ; and that in any science
whatever, by reasoning from a set of hypotheses, we may
obtain a body of conclusions as certain as those of geometry,
that is, as strictly in accordance with the hypotheses, and as
irresistibly compelling assent, on condition that those hypo-
theses are true.*

* It is justly remarked by Professor Bain (Logic, ii. 134) that the word
Hypothesis is here used in a somewhat peculiar sense. An hypothesis, in
science, usually means a supposition not proved to be true, but surmised to be
so, because if true it would account for certain known facts ; and the final
result of the speculation may be to prove its truth. The hypotheses spoken
of in the text are of a different character ; they are known not to be literally
true, while as much of them as is true is not hypothetical, but certain. The
two cases, however, resemble in the circumstance that in both we reason, not
from a truth, but from an assumption, and the truth therefore of the con-
clusions is conditional, not categorical. This suffices to justify, in point of
logical propriety, Stewart's use of the term. It is of course needful to bear
in mind that the hypothetical element in the definitions of geometry is the
assumption that what is very nearly true is exactly so. This unreal exactitude
might be called a fiction, as properly as an hypothesis ; but that appellation,

262 REASONING.

When, therefore, it is affirmed that the conclusions of
geometry are necessary truths, the necessity consists in reality
only in this, that they correctly follow from the suppositions
from which they are deduced. Those suppositions are so far
from being necessary, that they are not even true ; they pur-
posely depart, more or less widely, from the truth. The only
sense in which necessity can be ascribed to the conclusions of
any scientific investigation, is that of legitimately following
from some assumption, which, by the conditions of the inquiry,
is not to be questioned. In this relation, of course, the deri-
vative truths of every deductive science must stand to the
inductions, or assumptions, on which the science is founded,
and which, whether true or untrue, certain or doubtful in
themselves, are always supposed certain for the purposes of the
particular science. And therefore the conclusions of all
deductive sciences were said by the ancients to be necessary
propositions. We have observed already that to be predicated
necessarily was characteristic of the predicable Proprium, and
that a proprium was any property of a thing which could be
deduced from its essence, that is, from the properties included
in its definition.

§ 2. The important doctrine of Dugald Stewart, which
I have endeavoured to enforce, has been contested by Dr.
Whewell, both in the dissertation appended to his excellent
Mechanical Euclid, and in his elaborate work on the Philo-
sophy of the Inductive Sciences ; in which last he also replies
to au article in the Edinburgh Review, (ascribed to a writer
of great scientific eminence), in which Stewart's opinion was
defended against his former strictures. The supposed refuta-
tion of Stewart consists in proving against him (as has also
been done in this work) that the premises of geometry are
not definitions, but assumptions of the real existence of things
corresponding to those definitions. This, however, is doing
little for Dr. Whewell's purpose ; for it is these very assump-

utill more than the other, would fail to point out the close relation which exists
between the fictitious point or line and the points and lines of which we have
experience.

DEMONSTRATION', AND NECESSARY TRUTHS. 263

tions which are asserted to be hypotheses, and which he, if he
denies that geometry is founded on hypotheses, must show to
be absolute truths. All he does, however, is to observe, that
they at any rate, are not arbitrary hypotheses ; that we should
not be at liberty to substitute other hypotheses for them ; that
not only " a definition, to be admissible, must necessarily refer
to and agree with some conception which we can distinctly
frame in our thoughts," but that the straight lines, for instance,
which we define, must be " those by which angles are contained
those by which triangles are bounded, those of which parallel-
ism may be predicated, and the like."* And this is true ; but
this has never been contradicted. Those who say that the
premises of geometry are hypotheses, are not bound to main-
tain them to be hypotheses which have no relation whatever
to fact. Since an hypothesis framed for the purpose of scien-
tific inquiry must relate to something which has real existence,
(for there can be no science respecting non-entities,) it follows
that any hypothesis we make respecting an object, to facilitate
our study of it, must not involve anything which is distinctly
false, and repugnant to its real nature : we must not ascribe
to the thing any property which it has not ; our liberty extends
only to slightly exaggerating some of those which it has, (by
assuming it to be completely what it really is very nearly,)
and suppressing others, under the indispensable obligation of
restoring them whenever, and in as far as, their presence or
absence would make any material difference in the truth of
our conclusions. Of this nature, accordingly, are the first
principles involved in the definitions of geometry. That the
hypotheses should be of this particular character, is however
no further necessary, than inasmuch as no others could enable
us to deduce conclusions which, with due corrections, would
be true of real objects : and in fact, when our aim is only to
illustrate truths, and not to investigate them, we are not under
any such restriction. We might suppose an imaginary animal,
and work out by deduction, from the known laws of physiology,
its natural history ; or an imaginary commonwealth, and from

* Mechanical Euclid, pp. 149 et seqq.

264 REASONING.

the elements composing it, might argue what -would be its
fate. And the conclusions which we might thus draw from
purely arbitrary hypotheses, might form a highly useful in-
tellectual exercise : but as they could only teach us what
would be the properties of objects which do not really exist,
they would not constitute any addition to our knowledge of
nature: while on the contrary, if the hypothesis merely divests
a real object of some portion of its properties, without cloth-
ing it in false ones, the conclusions will always express, under
known liability to correction, actual truth.

§ 3. But though Dr. Whewell has not shaken Stewart's
doctrine as to the hypothetical character of that portion of
the first principles of geometry which are involved in the so-
called definitions, he has, I conceive, greatly the advantage of
Stewart on another important point in the theory of geome-
trical reasoning ; the necessity of admitting, among those first
principles, axioms as well as definitions. Some of the axioms
of Euclid might, no doubt, be exhibited in the form of defini-
tions, or might be deduced, by reasoning, from propositions
similar to what are so called. Thus, if instead of the axiom,
Magnitudes which can be made to coincide are equal, we in-
troduce a definition, " Equal magnitudes are those which may
be so applied to one another as to coincide ;" the three axioms
which follow (Magnitudes which are equal to the same are
equal to one another — If equals are added to equals the sums
are equal — If equals are taken from equals the remainders
ure equal,) may be proved by an imaginary superposition, re-
sembling that by which the fourth proposition of the first
book of Euclid is demonstrated. But though these and
several others may be struck out of the list of first principles,
because, though not requiring demonstration, they are suscep-
tible of it; there will be found in the list of axioms two or
three fundamental truths, not capable of being demonstrated :
among which must be reckoned the proposition that two
straight lines cannot inclose a space, (or its equivalent, Straight
lines which coincide in two points coincide altogether,) and
some property of parallel lines, other than that which con-

DEMONSTRATION, AND NECESSARY TRUTHS. 265

stitutes their definition : one of the most suitable for the pur-
pose being that selected by Professor Playfair: "Two straight
lines which intersect each other cannot both of them be parallel
to a third straight line."*

The axioms, as well those which are indemonstrable as those
which admit of being demonstrated, differ from that other
class of fundamental principles which are involved in the
definitions, in this, that they are true without any mixture of
hypothesis. That things which are equal to the same thing
are equal to one another, is as true of the lines and figures in
nature, as it would be of the imaginary ones assumed in the
definitions. In this respect, however, mathematics are only
on a par with most other sciences. In almost all sciences
there are some general propositions which are exactly true,
while the greater part are only more or less distant approxi-
mations to the truth. Thus in mechanics, the first law of
motion (the continuance of a movement once impressed, until
stopped or slackened by some resisting force) is true without
qualification or error. The rotation of the earth in twenty-
four hours, of the same length as in our time, has gone on since
the first accurate observations, without the increase or diminu-
tion of one second in all that period. These are inductions
which require no fiction to make them be received as accurately
true : but along with them there are others, as for instance the
propositions respecting the figure of the earth, which are but
approximations to the truth ; and in order to use them for the
further advancement of our knowledge, we must feign that they
are exactly true, though they really want something of being so.

* We might, it is true, insert this property into the definition of parallel
lines, framing the definition so as to require, both that when produced indefi-
nitely they shall never meet, and also that any straight line which intersects one
of them shall, if prolonged, meet the other. But by doing this we by no
means get rid of the assumption ; we are still obliged to take for granted the
geometrical truth, that all straight lines in the same plane, which have the
former of these properties, have also the latter. For if it were possible that
they should not, that is, if any straight lines in the same plane, other than
those which are parallel according to the definition, had the property of never
meeting although indefinitely produced, the demonstrations of the subsequent
portions of the theory of parallels could not be maintained.

266 REASONING.

§ 4. It remains to inquire, what is the ground of our
belief in axioms — what is the evidence on which they rest ? I
answer, they are experimental truths ; generalizations from ob-
servation. The proposition, Two straight lines cannot inclose
a space — or in other words, Two straight lines which have
once met, do not meet again, but continue to diverge — is an
induction from the evidence of our senses.

This opinion runs counter to a scientific prejudice of long
standing and great strength, and there is probably no pro-
position enunciated in this work for which a more unfavourable
reception is to be expected. It is, however, no new opinion ;
and even if it were so, would be entitled to be judged, not by
its novelty, but by the strength of the arguments by which it
can be supported. I consider it very fortunate that so emi-
nent a champion of the contrary opinion as Dr. Whewell, has
found occasion for a most elaborate treatment of the whole
theory of axioms, in attempting to construct the philosophy
of the mathematical and physical sciences on the basis of the
doctrine against which I now contend. Whoever is anxious
that a discussion should go to the bottom of the subject, must
rejoice to see the opposite side of the question worthily repre-
sented. If what is said by Dr. Whewell, in support of an
opinion which he has made the foundation of a systematic
•work, can be shown not to be conclusive, enough will have
been done, without going elsewhere in quest of stronger argu-
ments and a more powerful adversary.

It is not necessary to show that the truths which we call
axioms are originally suggested by observation, and that we
should never have known that two straight lines cannot inclose
a space if we had never seen a straight line : thus much being
admitted by Dr. Whewell, and by all, in recent times, who
have taken his view of the subject. But they Contend, that it
is not experience which proves the axiom ; but that its truth
is perceived a priori, by the constitution of the mind itself,
from the first moment when the meaning of. the proposition is
apprehended ; and without any necessity for verifying it by
repeated trials, as is requisite in the case of truths really ascer-
tained by observation.

DEMONSTRATION, AND NECESSARY TRUTHS. 267

They cannot, however, but allow that the truth of the
axiom, Two straight lines cannot inclose a space, even if
evident independently of experience, is also evident from ex-
perience. Whether the axiom needs confirmation or not, it
receives confirmation in almost every instant of our lives;
since we cannot look at any two straight lines which intersect
one another, without seeing that from that point they continue
to diverge more and move. Experimental proof crowds in
upon us in such endless profusion, and without one instance
in which there can be even a suspicion of an exception to the
rule, that we should soon have stronger ground for believing
the axiom, even as an experimental truth, than we have for
almost any of the general truths which we confessedly learn
from the evidence of our senses. Independently of d, priori
evidence, we should certainly believe it with an intensity of
conviction far greater than we accord to any ordinary physical
truth : and this too at a time of life much earlier than that
from which we date almost any part of our acquired know-
ledge, and much too early to admit of our retaining any
recollection of the history of our intellectual operations at
that period. Where then is the necessity for assuming that
our recognition of these truths has a different origin from the
rest of our knowledge, when its existence is perfectly accounted
for by supposing its origin to be the same ? when the causes
which produce belief in all other instances, exist in this
instance, and in a degree of strength as much superior to
what exists in other cases, as the intensity of the belief itself
is superior ? The burden of proof lies on the advocates of
the contrary opinion : it is for them to point out some fact,
inconsistent with the supposition that this part of our know-
ledge of nature is derived from the same sources as every other
part.*

* Some persons find themselves prevented from believing that the axiom,
Two straight lines cannot inclose a space, could ever become known to us
through experience, by a difficulty which may be stated as follows. If the
straight lines spoken of are those contemplated in the definition — lines abso-
lutely without breadth and absolutely straight ; — that such are incapable of
inclosing a space is not proved by exj eriente, for lines such as these do not pre-

268

REASONING.

This, for instance, they would be able to do, if they could
prove chronologically that we had the conviction (at least
practically) so early in infancy as to be anterior to those im-
pressions on the senses, upon which, on the other theory, the
conviction is founded. This, however, cannot be proved : the
point being too far back to be within the reach of memory, and
too obscure for external observation. The advocates of the
a priori theory are obliged to have recourse to other arguments.
These are reducible to two, which I shall endeavour to state as
clearly and as forcibly as possible.

§ 5. In the first place it is said, that if our assent to the
proposition that two straight lines cannot inclose a space,
were derived from the senses, we could only be convinced of
its truth by actual trial, that is, by seeing or feeling the
straight lines ; whereas in fact it is seen to be true by merely
thinking of them. That a stone thrown into water goes to the
bottom, may be perceived by our senses, but mere thinking
of a stone thrown into the water would never have led us to
that conclusion : not so, however, with the axioms relating to
straight lines: if I could be made to conceive what a straight

sent themselves in our experience. If, on the other hand, the lines meant are
such straight lines as we do meet with in experience, lines straight enough for
practical purposes, but in reality slightly zigzag, and with some, however
trifling, breadth ; as applied to these lines the axiom is not true, for two of
them may, and sometimes do, inclose a small portion of space. In neither case,
therefore, does experience prove the axiom.

Those who employ this argument to show that geometrical axioms cannot
be proved by induction, show themselves unfamiliar with a common and per-
fectly valid mode of inductive proof; proof by approximation. Though
experience furnishes us with no lines so unimpeachably straight that two of
them are incapable of inclosing the smallest space, it presents us with grada-
tions of lines possessing less and less either of breadth or of flexure, of which
series the straight line of the definition is the ideal limit. And observation
shows that just as much, and as nearly, as the straight lines of experience
approximate to having no breadth or flexure, so much and so nearly does the
space-inclosing power of any two of them approach to zero. The inference
that if they had no breadth or flexure at all, they would inclose no space at all,
is a correct inductive inference from these facts, conformable to one of the
four Inductive Methods hereinafter characterized, the Method of Concomitant
Variations ; of which the mathematical Doctrine of Limits presents the
extreme case.

DEMONSTRATION, AND NECESSARY TRUTHS. 269

line is, without having seen one, I should at once recognise
that two such lines cannot inclose a space. Intuition is " ima-
ginary looking;"* but experience must be real looking: if we
see a property of straight lines to be true by merely fancying
ourselves to be looking at them, the ground of our belief can-
not be the senses, or experience ; it must be something mental.

To this argument it might be added in the case of this
particular axiom, (for the assertion would not be true of all
axioms,) that the evidence of it from actual ocular inspection
is not only unnecessary, but unattainable. What says the
axiom ? That two straight lines cannot inclose a space ; that
after having once intersected, if they are prolonged to infinity
they do not meet, but continue to diverge from one another.
How can this, in any single case, be proved by actual obser-
vation ? We may follow the lines to any distance we please ;
but we cannot follow them to infinity : for aught our senses
can testify, they may, immediately beyond the farthest point
to which we have traced them, begin to approach, and at last
meet. Unless, therefore, we had some other proof of the im-
possibility than observation affords us, we should have no
ground for believing the axiom at all.

To these arguments, which I trust I cannot be accused of
understating, a satisfactory answer will, I conceive, be found,
if we advert to one of the characteristic properties of geome-
trical forms — their capacity of being painted in the imagination
with a distinctness equal to reality : in other words, the
exact resemblance of our ideas of form to the sensations which
suggest them. This, in the first place, enables us to make
(at least with a little practice) mental pictures of all possible
combinations of lines and angles, which resemble the realities
quite as well as any which we could make on paper ; and in.
the next place, make those pictures just as fit subjects of
geometrical experimentation as the realities themselves ; inas-
much as pictures, if sufficiently accurate, exhibit of course all
the properties which would be manifested by the realities at
one given instant, and on simple inspection : and in geometry

* Whewell's History of Scientific Ideas, i. 140.

270 REASONING.

we are concerned only with such properties, and not with that
which pictures could not exhibit, the mutual action of bodies
one upon another. The foundations of geometry would there-
fore be laid in direct experience, even if the experiments (which
in this case consist merely in attentive contemplation) were
practised solely upon what we call our ideas, that is, upon the
diagrams in our minds, and not upon outward objects. For
in all systems of experimentation we take some objects to
serve as representatives of all which resemble them ; and in
the present case the conditions which qualify a real object to
be the representative of its class, are completely fulfilled by an
object existing only in our fancy. Without denying, therefore,
the possibility of satisfying ourselves that two straight lines
cannot inclose a space, by merely thinking of straight lines
without actually looking at them ; I contend, that we do not
believe this truth on the ground of the imaginary intuition
simply, but because we know that the imaginary lines exactly
resemble real ones, and that we may conclude from them to
real ones with quite as much certainty as we could conclude
from one real line to another. The conclusion, therefore, is
still an induction from observation. And we should not be
authorized to substitute observation of the image in our mind,
for observation of the reality, if we had not learnt by long-
continued experience that the properties of the reality are faith-
fully represented in the image ; just as we should be scienti-
fically warranted in describing an animal which we have never
seen, from a picture made of it with a daguerreotype ; but not
until we had learnt by ample experience, that observation of
such a picture is precisely equivalent to observation of the
original.

These considerations also remove the objection arising from
the impossibility of ocularly'following the lines in their pro-
longation to infinity. For though, in order actually to see
that two given lines never meet, it would be necessary to
follow them to infinity ; yet without doing so we may know
that if .they ever do meet, or if, after diverging from one
another, they begin again to approach, this must take place
not at an infinite, but at a finite distance. Supposing, there-

DEMONSTRATION, AND NECESSARY TRUTHS. 271

fore, such to be the case, \ve can transport ourselves thither in
imagination, and can frame a mental image of the appearance
which one or both of the lines must present at that point,
which we may rely on as being precisely similar to the reality.
Now, whether we fix our contemplation upon this imaginary
picture, or call to mind the generalizations we have had occa-
sion to make from former ocular observation, we learn by the
evidence of experience, that a line which, after diverging from
another straight line, begins to approach to it, produces
the impression on our senses which we describe by the ex-
pression, " a bent line," not by the expression, " a straight
line."*

* Dr. Whewell (Philosophy of Discovery, p. 289) thinks it unreasonable to
contend that we know by experience, that our idea of a line exactly resembles
a real line. " It does not appear, " he says, " how we can compare our ideas
with the realises, since we know the realities only by our ideas." We know
the realities by our sensations. Dr. Whewell surely does not hold the "doc-
trine of perception by means of ideas," which Reid gave himself so much
trouble to refute.

If Dr. Whewell doubts whether we compare our ideas with the corresponding
sensations, and assume that they resemble, let me ask on what evidence do we
judge that a portrait of a person not present is like the original. Surely because
it is like our idea, or mental image of the person, and because our idea is like
the man himself.

Dr. Whewell also says, that it does not appear why this resemblance of ideas
to the sensations of which they are copies, should be spoken of as if it were a
peculiarity of one class of ideas, those of space. My reply is, that I do not so
speak of it. The peculiarity I contend for is only one of degree. All our
ideas of sensation of course resemble the corresponding sensations, but they do
so with very different degrees of exactness and of reliability. No one, I pre-
sume, can recall in imagination a colour or an odour with the same distinctness
and accuracy with which almost every one can mentally reproduce an image of
a straight line or a triangle. To the extent, however, of their capabilities of
accuracy, our recollections of colours or of odours may serve as subjects of
experimentation, as well as those of lines and spaces, and may yield conclusions
which will be true of their external prototypes. A person in whom, either
from natural gift or from cultivation, the impressions of colour were peculiarly
vivid and distinct, if asked which of two blue flowers was of the darkest tinge,
though he might never have compared the two, or even looked at them together,
might be able to give a confident answer on the faith of his distinct recollection
of the colours ; that is, he might examine his mental pictures, and find there a
property of the outward objects. But in hardly any case except that of simple
geometrical forms, could this be done by mankind generally, with a degree of

272 REASONING.

The preceding, argument, which is, to my mind unanswer-
able, merges, however, in a still more comprehensive one,
which is stated most clearly and conclusively hy Professor
Bain. The psychological reason why axioms, and indeed many
propositions not ordinarily classed as such, may be learnt from
the idea only without referring to the fact, is that in the process
of acquiring the idea we have learnt the fact. The proposition
is assented to as soon as the terms are understood, because in
learning to understand the terms we have acquired the experience
which proves the proposition to be true. "We required,"
savs Mr. Bain,* " concrete experience in the first instance, to
attain to the notion of whole and part ; but the notion, once
arrived at, implies that the whole is greater. In fact, we could
not have the notion without an experience tantamount to this

conclusion When we have mastered the notion of

straightness, we have also mastered that aspect of it expressed
by the affirmation that two straight lines cannot inclose a
space. No intuitive or innate powers or perceptions are needed

in such cases We cannot have the full meaning of

Straightness, without going through a comparison of straight
objects among themselves, and with their opposites, bent or
crooked objects. The result of this comparison is, inter alia,
that straightness in two lines is seen to be incompatible with
inclosing a space ; the inclosure of space involves crookedness
in at least one of the lines." And similarly, in the case of
every first principle,f " the same knowledge that makes it
understood, suffices to verify it." The more this observation

assurance equal to that which is given by a contemplation of the objects them-
selves. Persons differ most widely in the precision of their recollection, even
of forms : one person, when he has looked any one in the face for half a minute,
can draw an accurate likeness of him from memory ; another may have seen
him every day for six months, and hardly know whether his nose is long or
short. But everybody has & perfectly distinct mental image of a straight line,
a circle, or a rectangle. And every one concludes confidently from these mental
images to the corresponding outward things. The truth is, that we may, and
continually do, study nature in our recollections, when the objects themselves
are absent ; and in the case of geometrical forms we can perfectly, but in most
other cases only imperfectly, trust our recollections.

* Logic, i. 222. t Ibid. 226.

DEMONSTRATION', AND NECESSARY TRUTHS. 273

is considered the more (I am convinced) it will be felt to go
to the very root of the controversy.

§ 6. The first of the two arguments in support of the
theory that axioms are ct priori truths, having, I think, been
sufficiently answered ; I proceed to the second, which is usually
the most relied on. Axioms (it is asserted) are conceived by
us not only as true, but as universally and necessarily true.
Now, experience cannot possibly give to any proposition this
character. I may have seen snow a hundred times, and may
have seen that it was white, but this cannot give me entire
assurance even that all snow is white ; much less that snow
must be white. " However many instances we may have ob-
served of the truth of a proposition, there is nothing to assure
us that the nex^ case shall not be an exception to the rule.
If it be strictly true that every ruminant animal yet known
has cloven hoofs, we still cannot be sure that some creature
will not hereafter be discovered which has the first of these
attributes, without having the other. . . . Experience must
always consist of a limited number of observations; and, how-
ever numerous these may be, they can show nothing with re-
gard to the infinite number of cases in which the experiment
has not been made." Besides, Axioms are not only universal,
they are also necessary. Now " experience cannot offer the
smallest ground for the necessity of a proposition. She can
observe and record what has happened ; but she cannot find,
in any case, or in any accumulation of cases, any reason for
what must happen. She may see objects side by side ; but she
cannot see a reason why they must ever be side by side. She
finds certain events to occur in succession ; but the succession
supplies, in its occurrence, no reason for its recurrence. She
contemplates external objects ; but she cannot detect any in-
ternal bond, which iudissolubly connects the future with the
past, the possible with the real. To learn a proposition by
experience, and to see it to be necessarily true, are two alto-
gether different processes of thought."* And Dr. Whewell

* History of Scientific Ideas, i. 65-67.
VOL. I. 18

274 REASONING.

adds, " If any one does not clearly comprehend this distinction
of necessary and contingent truths, he will not be able to go
along with us in our researches into the foundations of human
knowledge ; nor, indeed, to pursue with success any specula-
tion on the subject."*

In the following passage, we are told what the distinction
is, the non-recognition of which incurs this denunciation.
" Necessary truths are those in which we not only learn that
the proposition is true, but see that it must be true ; in which
the negation of the truth is not only false, but impossible ; in
which we cannot, even by an effort of imagination, or in a sup-
position, conceive the reverse of that which is asserted. That
there are such truths cannot be doubted. We may take, for
example, all relations of number. Three and Two added to-
gether make Five. We cannot conceive it to be otherwise.
We cannot, by any freak of thought, imagine Three and Two
to make Seven. "t

Although Dr.Whewell has naturally and properly employed
a variety of phrases to bring his meaning more forcibly home,
he would, I presume, allow that they are all equivalent ; and
that what he means by a necessary truth, would be sufficiently
defined, a proposition the negation of which is not only false
but inconceivable. I am unable to find in any of his expres-
sions, turn them what way you will, a meaning beyond this,
and I do not believe he would contend that they mean any-
thing more.

This, therefore, is the principle asserted : that propositions,
the negation of which is inconceivable, or in other words, which
we cannot figure to ourselves as being false, must rest on evi-
dence of a higher and more cogent description than any which
experience can afford.

Now I cannot but wonder that so much stress should be
laid on the circumstance of inconceivableness, when there is
such ample experience to show, that our capacity or incapacity
of conceiving a thing has very little to do with the possibility
of the thing in itself; but is in truth very much an affair

J* History of Scientific Ideas, i. 60. f Ibid. 58, 59.

DEMONSTRATION, AND NECESSARY TRUTHS. 275

of accident, and depends on the past history and hahits of our
own minds. There is no more generally acknowledged fact
in human nature, than the extreme difficulty at first felt in
conceiving anything as possible, which is in contradiction to
long established and familiar experience ; or even to old
familiar habits of thought. And this difficulty is a necessary
result of the fundamental laws of the human mind. When
•we have often seen and thought of two things together, and
have never in any one instance either seen or thought of them
separately, there is by the primary law of association an in-
creasing difficulty, which may in the end become insuperable,
of conceiving the two things apart. This is most of all con-
spicuous in uneducated persons, who are in general utterly
unable to separate any two ideas which have once become
firmly associated in their minds ; and if persons of cultivated
intellect have any advantage on the point, it is only because,
having seen and heard and read more, and being more accus-
tomed to exercise their imagination, they have experienced
their sensations and thoughts in more varied combinations, and
have been prevented from forming many of these inseparable
associations. But this advantage has necessarily its limits.
The most practised intellect is not exempt from the universal
laws of our conceptive faculty. If daily habit presents to any
one for a long period two facts in combination, and if he is not
led during that period either by accident or by his voluntary
mental operations to think of them apart, he will probably in
time become incapable of doing so even by the strongest effort;
and the supposition that the two facts can be separated in
nature, will at last present itself to his mind with all the
characters of an inconceivable phenomenon.* There are re-
markable instances of this in the history of science : instances
in which the most instructed men rejected as impossible,

* " If all mankind had spoken one language, we cannot doubt that there
would have been a powerful, perhaps a universal, school of philosophers, who
would have believed in the inherent connexion between names and things, who
would have taken the sound man to be the mode of agitatiug the air which is
essentially communicative of the ideas of reason, cookery, bipedality, &c." — De
Morgan, Formal Logic, p. 246.

18-— 2

276 REASONING.

because inconceivable, things which their posterity, by earlier
practice and longer perseverance in the attempt, found it
quite easy to conceive, and -which everybody now knows to be
true. There was a time when men of the most cultivated in-
tellects, and the most emancipated from the dominion of early
prejudice, could not credit the existence of antipodes ; were
unable to conceive, in opposition to old association, the force
of gravity acting upwards instead of downwards. The
Cartesians long rejected the Newtonian doctrine of the gravi-
tation of all bodies towards one another, on the faith of a
general proposition, the reverse of which seemed to them to be
inconceivable — the proposition that a body cannot act where it
is not. All the cumbrous machinery of imaginary vortices,
assumed without the smallest particle of evidence, appeared to
these philosophers a more rational mode of explaining the
heavenly motions, than one which involved what seemed to
them so great an absurdity.* And they no doubt found it as
impossible to conceive that a body should act upon the earth
from the distance of the sun or moon, as we find it to conceive
an end to space or time, or two straight lines inclosing a space.
Newton himself had not been able to realize the conception,
or we should not have had his hypothesis of a subtle ether, the
occult cause of gravitation ; and his writings prove, that
though he deemed the particular nature of the intermediate
agency a matter of conjecture, the necessity of some such
agency appeared to him indubitable.

* It would be difficult to name a man more remarkable at once for the
greatness and the wide range of his mental accomplishments, than Leibnitz.
Yet this eminent man gave as a reason for rejecting Newton's scheme of the
solar system, that God could not make a body revolve round a distant centre,
unless either by some impelling mechanism, or by miracle: — "Tout ce qui
n'est pas explicable" says he in a letter to the Abbe* Conti, " par la nature des
creatures, est miraculeux. II ne suffit pas de dire : Dieu a fait une telle loi de
nature ; done la chose est naturelle. II faut que la loi soit executable par les
natures des creatures. Si Dieu donnait cette loi, par exemple, a un corps libre,
de tourner a 1'entour d'un certain centre, il faudrait ou qu'il y joignit d'autres
corps qui par leur impulsion I' obliged ssent de rester toujours dans son orbite
circulaire, ou quil mtt un ange a ses trousses, ou enfin il faudrait qu"il y
concourut extraordinairement ; car naturellement il s'e"cartera par la tangente."
— Works of Leibnitz, ed. Dutens, iii. 446.

DEMONSTRATION, AND NECESSARY TRUTHS. 277

If, then, it be so natural to the human mind, even in a
high state of culture, to be incapable of conceiving, and on
that ground to believe impossible, what is afterwards not only
found to be conceivable but proved to be true ; what wonder
if in cases where the association is still older, more confirmed,
and more familiar, and in which nothing ever occurs to shake
our conviction, or even suggest to us any conception at vari-
ance with the association, the acquired incapacity should con-
tinue, and be mistaken for a natural incapacity ? It is true,
our experience of the varieties in nature enables us, within
certain limits, to conceive other varieties analogous to them.
We can conceive the sun or moon falling ; for though we
never saw them fall, nor ever perhaps imagined them falling,
we have seen so many other things fall, that we have innumer-
able familiar analogies to assist the conception ; which, after
all, we should probably have some difficulty in framing, were
we not well accustomed to see the sun and moon move (or ap-
pear to move,) so that we are only called upon to conceive a
slight change in the direction of motion, a circumstance
familiar to our experience. But when experience affords no
model on which to shape the new conception, how is it possible
for us to form it ? How, for example, can we imagine an end
to space or time ? We never saw any object without some-
thing beyond it, nor experienced any feeling without something
following it. When, therefore, we attempt to conceive the
last point of space, we have the idea irresistibly raised of
other points beyond it. When we try to imagine the last in-
stant of time, we cannot help conceiving another instant after
it. Nor is there any necessity to assume, as is done by a
modern school of metaphysicians, a peculiar fundamental law
of the mind to account for the feeling of infinity inherent in
our conceptions of space and time ; that apparent infinity is
sufficiently accounted for by simpler and universally acknow-
ledged laws.

Now, in the case of a geometrical axiom, such, for example,
as that two straight lines cannot inclose a space, — a truth
which is testified to us by our very earliest impressions of the
external world, — how is it possible (whether those external

278 REASONING.

impressions be or be not the ground of our belief) that the re-
verse of the proposition could be otherwise than inconceivable
to us ? What analogy have we, what similar orde* of facts in
any other branch of our experience, to facilitate to us the con-
ception of two straight lines inclosing a space ? Nor is even
this all. I have already called attention to the peculiar pro-
perty of our impressions of form, that the ideas or mental images
exactly resemble their prototypes, and adequately represent
them for the purposes of scientific observation. From this,
and from the intuitive character of the observation, which in
this case reduces itself to simple inspection, we cannot so much
as call up in our imagination two straight lines, in order to at-
tempt to conceive them inclosing a space, without by that very
act repeating the scientific experiment which establishes the
contrary. Will it really be contended that the inconceivable-
ness of the thing, in such circumstances, proves anything
against the experimental origin of the conviction '? Is it not
clear that in whichever mode our belief in the proposition may
have originated, the impossibility of our conceiving the nega-
tive of it must, on either hypothesis, be the same ? As, then,
Dr. Whewell exhorts those who have any difficulty in recognis-
ing the distinction held by him between necessary and con-
tingent truths, to study geometry, — a condition which I can
assure him I have conscientiously fulfilled, — I, in return, with
equal confidence, exhort those who agree with him, to study
the general laws of association ; being convinced that nothing
more is requisite than a moderate familiarity with those laws,
to dispel the illusion which ascribes a peculiar necessity to our
earliest inductions from experience, and measures the possi-
bility of things in themselves, by the human capacity of
conceiving them.

I hope to be pardoned for adding, that Dr. Whewell him-
self has both confirmed by his testimony the effect of habitual
association in giving to an experimental truth the appearance
of a necessary one, and afforded a striking instance of that
remarkable law in his own person. In his Philosophy of the
Inductive Sciences he continually asserts, that propositions
which not only are not self-evident, but which we know to

DEMONSTRATION, AND NECESSARY TRUTHS. 279

have been discovered gradually, and by great efforts of genius
and patience, have, when once established, appeared so self-
evident that, but for historical proof, it would have been impos-
sible to conceive that they had not been recognised from the
first by all persons in a sound state of their faculties. " We
now despise those who, in the Copernican controversy, could
not conceive the apparent motion of the sun on the heliocentric
hypothesis; or those who, in opposition to Galileo, thought
that a uniform force might be that which generated a velocity
proportional to the space ; or those who held there was some-
thing absurd in Newton's doctrine of the different refrangibility
of differently coloured rays; or those who imagined that when
elements combine, their sensible qualities must be manifest in
the compound ; or those who were reluctant to give up the
distinction of vegetables into herbs, shrubs, and trees. We
cannot help thinking that men must have been singularly dull
of comprehension, to find a difficulty in admitting what is to
us so plain and simple. We have a latent persuasion that we
in their place should have been wiser and more clear-sighted ;
that we should have taken the right side, and given our assent
at once to the truth. Yet in reality such a persuasion is a
mere delusion. The persons who, in such instances as the
above, were on the losing side, were very far, in most cases,
from being persons more prejudiced, or stupid, or narrow-
minded, than the greater part of mankind now are; and the
cause for which they fought was far from being a manifestly
bad one, till it had been so decided by the result of the war.

. . So complete has been the victory of truth in most of
these instances, that at present we can hardly imagine the
struggle to have been necessary. The very essence of these
triumphs is, that they lead us to regard the views we reject as
not only false but inconceivable."*

This last proposition is precisely what I contend for; and
I ask no more, in order to overthrow the whole theory of its
author on the nature of the evidence of axioms. For what is
that theory ? That the truth of axioms cannot have been

* Novum Oryanum. Renovatum, pp. 32, 33.

280 REASONING.

learnt from experience, because their falsity is inconceivable.
But Dr. Whewell himself says, that we are continually led, by
the natural progress of thought, to regard as inconceivable what
our forefathers not only conceived but believed, nay even (he
might have added) were unable to conceive the reverse of.
He cannot intend to justify this mode of thoii'ght : he cannot
mean to say, that we can be right in regarding as inconceivable
what others have conceived, and as self-evident what to others
did not appear evident at all. After so complete an admission
that inconceivableness is an accidental thing, not inherent in
the phenomenon itself, but dependent on the mental history of
the person who tries to conceive it, how can he ever call upon
us to reject a proposition as impossible on no other ground
than its iuconceivableness ? Yet he not only does so, but has
unintentionally afforded some of the most remarkable examples
which can be cited of the very illusion which he has himself
so clearly pointed out. I select as specimens, his remarks on the
evidence of the three laws of motion, and of the atomic theory.
With respect to the laws of motion, Dr. Whewell says :
" No one can doubt that, in historical fact, these laws were
collected from experience. That such is the case, is no
matter of conjecture. We know the time, the persons, the
circumstances, belonging to each step of each discovery."*
After this testimony, to adduce evidence of the fact would be
superfluous. And not only were these laws by no means
intuitively evident, but some of them were originally para-
doxes. The first law was especially so. That a body, once
in motion, would continue for ever to move in the same direc-
tion with undiminished velocity unless acted upon by some
new force, was a proposition which mankind found for a long
time the greatest difficulty in crediting. It stood opposed to
apparent experience of the most familiar kind, which taught
that it was the nature of motion to abate gradually, and at last
terminate of itself. Yet when once the contrary doctrine was
firmly established, mathematicians, as Dr. Whewell observes,
speedily began to believe that laws, thus contradictory to first

* History of Scientific Ideas, i. 264.

DEMONSTRATION, AND NECESSARY TRUTHS. 281

appearances, and which, even after full proof had been ob-
tained, it had required generations to render familiar to the
minds of the scientific world, were under "a demonstrable
necessity, compelling them to be such as they are and no
other;" and he himself, though not venturing ""absolutely
to pronounce" that all these laws " can be rigorously traced to
an absolute necessity in the nature of things,"* does actually
so think of the law just mentioned; of which he says:
" Though the discovery of the first law of motion was made,
historically speaking, by means of experiment, we have now
attained a point of view in which we see that it might have
been certainly known to be true, independently of experi-
ence.'^ Can there be a more striking exemplification than is
here afforded, of the effect of association which we have
described ? Philosophers, for generations, have the most ex-
traordinary difficulty in putting certain ideas together; they
at last succeed in doing so ; and after a sufficient repetition of
the process, they first fancy a natural bond between the ideas,
then experience a growing difficulty, which at last, by the con-
tinuation of the same progress, becomes an impossibility, of
severing them from one another. If such be the progress of
an experimental conviction of which the date is of yesterday,
and which is in opposition to first appearances, how must it
fare with those which are conformable to appearances familiar
from the first dawn of intelligence, and of the conclusiveness
of which, from the earliest records of human thought, no sceptic
has suggested even a momentary doubt?

The other instance which I shall quote is a truly astonish-
ing one, and may be called the reductio ad absurdum of the
theory of inconceivableness. Speaking of the laws of chemical
composition, Dr. Whewell says :£ " That they could never have
been clearly understood, and therefore never firmly established,
without laborious and exact experiments, is certain ; but yet
we may venture to say, that being once known, they possess
an evidence beyond that of mere experiment. For how in

* Hist. Sc. Id., i. 263. f Ibid. 240.

J Ibid. ii. 25, 26.

282 REASONING.

fact can we conceive combinations, otherwise than as definite
in kind and quality ? If we were to suppose each element
ready to combine with any other indifferently, and indifferently
in any quantity, we should have a world in which all would
be confusion and indefiuiteness. There would be no fixed
kinds of bodies. Salts, and stones, and ores, would ap-
proach to and graduate into each other by insensible de-
grees. Instead of this, we know that the world consists of
bodies distinguishable from each other by definite differences,
capable of being classified and named, and of having general
propositions asserted concerning them. And as we cannot
conceive a world in tvhich this should not be the case, it would
appear that we cannot conceive a state of things in which the
laws of the combination of elements should not be of that de-
finite and measured kind which we have above asserted."

That a philosopher of Dr. Whewell's eminence should
gravely assert that we cannot conceive a world in which the
simple elements should combine in other than definite pro-
portions ; that by dint of meditating on a scientific truth, the
original discoverer of which was still living, he should have
rendered the association in his own mind between the idea
of combination and that of constant proportions so familiar
and intimate as to be unable to conceive the one fact without
the other; is so signal an instance of the mental law for which
I am contending, that one word more in illustration must be
superfluous.

In the latest and most complete elaboration of his meta-
physical system (the Philosophy of Discovery), as well as in
the earlier discourse on the Fundamental Antithesis of Philo-
sophy, reprinted as an appendix to that work, Dr. Whewell,
while very candidly admitting that his language was open to
misconception, disclaims having intended to say that mankind
in general can now perceive the law of definite proportions in
chemical combination to be a necessary truth. All he meant
was that philosophical chemists in a future generation may
possibly see this. " Some truths may be seen by intuition,
but yet the intuition of them may be a rare and a difficult at-

DEMONSTRATION, AND NECESSARY TRUTHS. 283

tainment."* And he explains that the inconceivableness which,
accordingly to his theory, is the test of axioms, " depends
entirely upon the clearness of the Ideas which the axioms
involve. So long as those ideas are vague and indistinct, the
contrary of an axiom may he assented to, though it cannot be
distinctly conceived. It may be assented to, not because it is
possible, but because we do not see clearly what is possible.
To a person who is only beginning to think geometrically,
there may appear nothing absurd in the assertion, that two
straight lines may inclose a space. And in the same manner,
to a person who is only beginning to think of mechanical
truths, it may not appear to be absurd, that in mechanical
processes, Reaction should be greater or less than Action ; and
so, again, to a person who has not thought steadily about Sub-
stance, it may not appear inconceivable, that by chemical
operations, we should generate new matter, or destroy matter
which already exists."f Necessary truths, therefore, are not
those of which we cannot conceive, but " those of which we
cannot distinctly conceive, the contrary."! So long as our
ideas are indistinct altogether, we do not know what is or is
not capable of being distinctly conceived ; but, by the ever
increasing distinctness with which scientific men apprehend the
general conceptions of science, they in time come to perceive
that there are certain laws of nature, which, though historically
and as a matter of fact they were learnt from experience, we
cannot, now that we know them, distinctly conceive to be other
than they are.

The account which I should give of this progress of the
scientific mind is somewhat different. After a general law of
nature has been ascertained, men's minds do not at first acquire
a complete facility of familiarly representing to themselves the
phenomena of nature in the character which that law assigns
to them. The habit which constitutes the scientific cast of
mind, that of conceiving facts of all descriptions conformably
to the laws which regulate them — phenomena of all descrip-

* Phil of Disc., p. 339. f Ibid. p. 338. J Ibid. p. 463.

284

REASONING.

tions according to the relations which have heen ascertained
really to exist between them ; this habit, in the case of newly
discovered relations, comes only by degrees. So long as it is
not thoroughly formed, no necessary character is ascribed to
the new truth. But in time, the philosopher attains a state of
mind in which his mental picture of nature spontaneously
represents to him all the phenomena with which the new theory
is concerned, in the exact light in which the theory regards
them : all images or conceptions derived from any other theory,
or from the confused view of the facts which is anterior to any
theory, having entirely disappeared from his mind. The mode
of representing facts which results from the theory, has now
become, to his faculties, the only natural mode of conceiving
them. It is a known truth, that a prolonged habit of arrang-
ing phenomena in certain groups, and explaining them by
means of certain principles, makes any other arrangement or
explanation of these facts be felt as unnatural : and it may at
last become as difficult to him to represent the facts to himself
in any other mode, as it often was, originally, to represent
them in that mode.

But, further, (if the theory is true, as we are supposing it to
be,) any other mode in which he tries, or in which he was for-
merly accustomed, to represent the phenomena, will be seen
by him to be inconsistent with the facts that suggested the new
theory — facts which now form a part of his mental picture of
nature. And since a contradiction is always inconceivable, his
imagination rejects these false theories, and declares itself in-
capable of conceiving them. Their inconceivableness to him
does not, however, result from anything in the theories them-
selves, intrinsically and a priori repugnant to the human
faculties ; it results from the repugnance between them and a
portion of the facts ; which facts as long as he did not know,
or did not distinctly realize in his mental representations, the
false theory did not appear other than conceivable ; it becomes
inconceivable, merely from the fact that contradictory elements
cannot be combined in the same conception. Although, then,
his real reason for rejecting theories at variance with the true
one, is no other than that they clash with his experience, he

DEMONSTRATION, AND NECESSARY TRUTHS. 285

easily falls into the belief, that he rejects them because they
are inconceivable, and that he adopts the true theory because
it is self-evident, and does not need the evidence of experience
at all.

This I take to be the real and sufficient explanation of the
paradoxical truth, on which so much stress is laid by Dr.
Whewell, that a scientifically cultivated mind is actually, in
virtue of that cultivation, unable to conceive suppositions
which a common man conceives without the smallest difficulty.
For there is nothing inconceivable in the suppositions them-
selves ; the impossibility is in combining them with facts
inconsistent with them, as part of the same mental picture ; an
obstacle of course only felt by those who know the facts, and
are able to perceive the inconsistency. As far as the suppo-
sitions themselves are concerned, in the case of many of Dr.
Whewell's necessary truths the negative of the axiom is, and
probably will be as long as the human race lasts, as easily
conceivable as the affirmative. There is no axiom (for example)
to which Dr. Whewell ascribes a more thorough character of
necessity and self-evidence, than that of the indestructibility
of matter. That this is a true law of nature I fully admit ;
but I imagine there is no human being to whom the opposite
supposition is inconceivable — who has any difficulty in
imagining a portion of matter annihilated : inasmuch as its
apparent annihilation, in no respect distinguishable from real
by our unassisted senses, takes place every time that water
dries up, or fuel is consumed. Again, the law that bodies
combine chemically in definite proportions is undeniably true;
but few besides Dr. Whewell have reached the point which he
seems personally to have arrived at, (though he only dares
prophesy similar success to the multitude after the lapse of
generations,) that of being unable to conceive a world in which
the elements are ready to combine with one another " indiffe-
rently in any quantity ; " nor is it likely that we shall ever rise
to this sublime height of inability, so long as all the mechani-
cal mixtures in our planet, whether solid, liquid, or aeriform,
exhibit to our daily observation the very phenomenon declared
to be inconceivable.

286 REASONING.

According to Dr. Whewell, these and similar laws of nature
cannot be drawn from experience, inasmuch as they are, on
the contrary, assumed in the interpretation of experience. Our
inability to " add to or diminish the quantity of matter in the
world," is a truth which " neither is nor can be derived from
experience ; for the experiments which we make to verify it
presuppose its truth. . . . When men began to use the
balance in chemical analysis, they did not prove by trial, but
took for granted, as self-evident, that the weight of the whole
must be found in the aggregate weight of the elements."*
True, it is assumed ; but, I apprehend, no otherwise than as
all experimental inquiry assumes provisionally some theory or
hypothesis, which is to be finally held true or not, according as
the experiments decide. The hypothesis chosen for this pur-
pose will naturally be one which groups together some consi-
derable number of facts already known. The proposition that
the material of the world, as estimated by weight, is neither
increased nor diminished by any of the processes of nature or
art, had many appearances in its favour to begin with. It
expressed truly a great number of familiar facts. There were
other facts which it had the appearance of conflicting with,
and which made its truth, as an universal law of nature, at first
doubtful. Because it was doubtful, experiments were devised
to verify it. Men assumed its truth hypothetical!}7, and pro-
ceeded to try whether, on more careful examination, the pheno-
mena which apparently pointed to a different conclusion, would
not be found to be consistent with it. This turned out to be
the case ; and from that time the doctrine took its place as an
universal truth, but as one proved to be such by experience.
That the theory itself preceded the proof of its truth — that it
had to be conceived before it could be proved, and in order
that it might be proved — does not imply that it was self-evi-
dent, and did not need proof. Otherwise all the true theories
in the sciences are necessary and self-evident ; for no one
knows better than Dr. Whewell that they all began by being
assumed, for the purpose of connecting them by deductions

* Phil, of Disc., pp. 472, 473.

DEMONSTRATION, AND NECESSARY TRUTHS. 287

with those facts of experience on which, as evidence, they now
confessedly rest.*

* The Quarterly Review for June 1841, contained an article of great ability
on Dr. Whewell's two great works (since acknowledged and reprinted in Sir
John Herschel's Essays) which maintains, on the subject of axioms, the doc-
trine advanced in the text, that they are generalizations from experience, and
supports that opinion by a line of argument strikingly coinciding with mine.
When I state that the whole of the present chapter (except the last four pages,
added in the fifth edition) was written before I had seen the article, (the greater
part, indeed, before it was published,) it is not my object to occupy the reader's
attention with a matter so unimportant as the degree of originality which may
or may not belong to any portion of my own speculations, but to obtain for an
opinion which is opposed to reigning doctrines, the recommendation derived
from a striking concurrence of sentiment between two inquirers entirely inde-
pendent of one another. I embrace the opportunity of citing from a writer of
the extensive acquirements in physical and metaphysical knowledge and the
capacity of systematic thought which the article evinces, passages so remark-
ably in unison with my own views as the following : —

'•' The truths of geometry are summed up and embodied in its definitions
and axioms. . . . Let us turn to the axioms, and what do we find ? A string
of propositions concerning magnitude in the abstract, which are equally true of
space, time, force, number, and every other magnitude susceptible of aggrega-
tion and subdivision. Such propositions, where they are not mere definitions,
as some of them are, carry their inductive origin on the face of their enuncia-
tion. . . . Those which declare that two straight lines cannot inclose a space,
and that two straight lines which cut one another cannot both be parallel to a
third, are in reality the only ones which express characteristic properties of space,
and these it will be worth while to consider more nearly. Now the only clear
notion we can form of straightness is uniformity of direction, for space in its
ultimate analysis is nothing but an assemblage of distances and directions. And
(not to dwell on the notion of continued contemplation, i.e., mental experience,
as included in the very idea of uniformity ; nor on that of transfer of the con-
templating being from point- to point, and of experience, during such transfer,
of the homogeneity of the interval passed over) we cannot even propose the
proposition in an intelligible form to any one whose experience ever since he was
born has not assured him of the fact. The unity of direction, or that we can-
not march from a given point by more than one path direct to the same object,
is matter of practical experience long before it can by possibility become matter
of abstract thought. We cannot attempt mentally to exemplify the conditions of
the assertion in an imaginary case opposed to it, without violating our habitual
recollection of this experience, and defacing our mental picture of space as grounded
on it. What but experience, we may ask, can possibly assure us of the homo-
geneity of the parts of distance, time, force, and measurable aggregates in
general, on which the truth of the other axioms depends ? As regards the latter
axiom, after what has been said it must be clear that the very same course of
remarks equally applies to its case, and that its truth is quite as much forced on

288 REASONING.

the mind as that of the former by daily and hourly experience, . . . including
always, be it observed, in our notion of experience, that which is gained by con-
templation of the inward picture which the mind forms to itself in any proposed
case, or which it arbitrarily selects as an example — such picture, in virtue of the
extreme simplicity of these primary relations, being called up by the imagination
with as much vividness and clearness as could be done by any external impres-
sion, which is the only meaning we can attach to the word intuition, as applied to
such relations."

And again, of the axioms ot mechanics : — "As we admit no such proposi-
tions, other than as truths inductively collected from observation, even in
geometry itself, it can hardly be expected that, in a science of obviously con-
tingent relations, we should acquiesce in a contrary view. Let us take one of
these axioms and examine its evidence: for instance, that equal forces perpen-
dicularly applied at the opposite ends of equal arms of a straight lever will
balance each other. What but experience, we may ask, in the first place, can
possibly inform us that a force so applied will have any tendency to turn the
lever on its centre at all ? or that force can be so transmitted along a rigid line
perpendicular to its direction, as to act elsewhere in space than along its own
line of action ? Surely this is so far from being self-evident that it has even a
paradoxical appearance, which is only to be removed by giving our lever thick-
ness, material composition, and molecular powers. Again, we conclude, that
the two forces, being equal and applied under precisely similar circumstances,
must, if they exert any effort at all to turn the lever, exert equal and
opposite efforts : but what a priori reasoning can possibly assure us that they
do act under precisely similar circumstances ? that points which differ in place
are similarly circumstanced as regards the exertion of force ? that universal
space may not have relations to universal force — or, at all events, that the orga-
nization of the material universe may not be such as to place that portion of
space occupied by it in such relations to the forces exerted in it, as may invali-
date the absolute similarity of circumstances assumed ? Or we may argue,
what have we to do with the notion of angular movement in the lever at all ?
The case is one of rest, and of quiescent destruction of force by force. Now
how is this destruction effected ? Assuredly by the counter-pressure which sup-
ports the fulcrum. But would not this destruction equally arise, and by the same
amount of counter-acting force, if each force simply pressed its own half of the lever
against the fulcrum ? And what can assure us that it is not so, except removal of
one or other force, and consequent tilting of the lever ? The other fundamenta
axiom of statics, that the pressure on the point of support is the sum of the
weights ... is merely a scientific transformation and more refined mode of
Stating a coarse and obvious result of universal experience, viz. that the weight
of a rigid body is the same, handle it or suspend it in what position or by what
point we will, and that whatever sustains it sustains its total weight. Assuredly,
as Mr. Whewell justly remarks, ' No one probably ever made a trial for the
purpose of showing that the pressure on the support is equal to the sum of the
weights.' . . . But it is precisely because in every action of his life from earliest
infancy he has been continually making the trial, and seeing it made by every
other living being about him, that he never dreams of staking its result on one
additional attempt made with scientific accuracy. This would be as if a man

DEMONSTRATION, AND NECESSARY TRUTHS. 289

should resolve to decide by experiment whether his eyes were useful for the pur-
pose of seeing, by hermetically sealing himself up for half an hour in a metal case."

On the " paradox of universal propositions obtained by experience," the same
writer says : " If there be necessary and universal truths expressible in proposi-
tions of axiomatic simplicity and obviousness, and having for their subject-
matter the elements of all our experience and all our knowledge, surely these
are the truths which, if experience suggest to us any truths at all, it ought to
suggest most readily, clearly, and unceasingly. If it were a truth, universal
and necessary, that a net is spread over the whole surface of every planetary
globe, we should not travel far on our own without getting entangled in its
meshes, and making the necessity of some means of extrication an axiom of
locomotion. . . . There is, therefore, nothing paradoxical, but the reverse, in
our being led by observation to a recognition of such truths, as general propo-
sitions, coextensive at least with all human experience. That they pervade all
the objects of experience, must ensure their continual suggestion by experience ;
that they are true, must ensure that consistency of suggestion, that iteration
of uncontradicted assertion, which commands implicit assent, and removes all
occasion of exception ; that they are simple, and admit of no misunderstanding,
must secure their admission by every mind."

" A truth, necessary and universal, relative to any object of our knowledge,
must verify itself in every instance where that object is before our contempla-
tion, and if at the same time it be simple and intelligible, its verification must
be obvious. The sentiment of such a truth cannot, therefore, but be present to our
minds whenever that object is contemplated, and must therefore make a part of the
mental picture or idea of that object which we may on any occasion summon
before our imagination. . . . All propositions, therefore, become not only
untrue but inconceivable, if ... axioms be violated in their enunciation."

Another eminent mathematician had previously sanctioned by his authority
the doctrine of the origin of geometrical axipms in experience. " Geometry
is thus founded likewise on observation ; but of a kind so familiar and obvious,
that the primary notions which it furnishes might seem intuitive."— Sir John
Leslie, quoted by Sir William Hamilton, Discourses, &c. p, 272.

VOL. I.

19

CHAPTER VI.

THE SAME SUBJECT CONTINUED.

§ 1. IN the examination which formed the subject of
the last chapter, into the nature of the evidence of those
deductive sciences which are commonly represented to be
systems of necessary truth, we have been led to the following
conclusions. The results of those sciences are indeed neces-
sary, in the sense of necessarily following from certain first
principles, commonly called axioms and definitions; that is,
of being certainly true if those axioms and definitions are so ;
for the word necessity, even in this acceptation of it, means
no more than certainty. But their claim to the character of
necessity in any sense beyond this, as implying an evidence
independent of and superior to observation and experience,
must depend on the previous establishment of such a claim in
favour of the definitions and axioms themselves. With regard
to axioms, we found that, considered as experimental truths,
they rest on superabundant and obvious evidence. We in-
quired, whether, since this is the case, it be imperative to
suppose any other evidence of those truths than experimental
evidence, any other origin for our belief of them than an expe-
rimental origin. We decided, that the burden of proof lies
with those who maintain the affirmative, and we examined, at
considerable length, such arguments as they have produced.
The examination having led to the rejection of those argu-
ments, we have thought ourselves warranted in concluding
that axioms are but a class, the most universal class, of in-
ductions from experience ; the simplest and easiest cases of
generalization from the facts furnished to us by our senses or
by our internal consciousness.

While the axioms of demonstrative sciences thus ap-
peared to be experimental truths, the definitions, as they are

DEMONSTRATION, AND NECESSARY TRUTHS. 291

incorrectly called, in those sciences, were found by us to be
generalizations from experience which are not even, accurately
speaking, truths ; being propositions in which, while we assert
of some kind of object, some property or properties which
observation shows to belong to it, we at the same time deny
that it possesses any other properties, though in truth other
properties do in every individual instance accompany, and in
almost all instances modify, the property thus exclusively pre-
dicated. The denial, therefore, is a mere fiction, or supposition,
made for the purpose of excluding the consideration of those
modifying circumstances, when their influence is of too trifling
amount to be worth considering, or adjourning it, when impor-
tant, to a more convenient moment.

From these considerations it would appear that Deductive
or Demonstrative Sciences are all, without exception, Induc-
tive Sciences ; that their evidence is that of experience ; but
that they are also, in virtue of the peculiar character of one
indispensable portion of the general formula according to
which their inductions are made, Hypothetical Sciences.
Their conclusions are only true on certain suppositions, which
are, or ought to be, approximations to the truth, but are seldom,
if ever, exactly true; and to this hypothetical character is to
be ascribed the peculiar certainty, which is supposed to be
inherent in demonstration.

What we have now asserted, however, cannot be received
as universally true of Deductive or Demonstrative Sciences,
until verified by being applied to the most remarkable of all
those sciences, that of Numbers ; the theory of the Calculus :
Arithmetic and Algebra. It is harder to believe of the doc-
trines of this science than of any other, either that they are
not truths a priori, but experimental truths, or that their
peculiar certainty is owing to their being not absolute but only
conditional truths. This, therefore, is a case which merits
examination apart; and the more so, because on this subject
we have a double set of doctrines to contend with ; that of the
a priori philosophers on one side ; and on the other, a theory
the most opposite to theirs, which was at one time very gene-

19—2

REASONING.

• rally received, and is still far from being altogether exploded,
among metaphysicians.

§ 2. This theory attempts to solve the difficulty appa-
rently inherent in the case, by representing the propositions
of the science of numbers as merely verbal, and its processes
as simple transformations of language, substitutions of one
expression for another. The proposition, Two and one is
equal to three, according to these writers, is not a truth, is
not the assertion of a really existing fact, but a definition of
the word three; a statement that mankind have agreed to use
the name three as a sign exactly equivalent to two and one ;
to call by the former name whatever is called by the other
more clumsy phrase. According to this doctrine, the longest
process in algebra is but a succession of changes in termi-
nology, by which equivalent expressions are substituted one
for another ; a series of translations of the same fact, from
1 one into another language ; though how, after such a series
. of translations, the fact itself comes out changed (as when we
demonstrate a new geometrical theorem by algebra,) they
have not explained ; and it is a difficulty which is fatal to their
theory.

It must be acknowledged that there are peculiarities in the
processes of arithmetic and algebra which render the theory
in question very plausible, and have not unnaturally made
those sciences the stronghold of Nominalism. The doctrine
that we can discover facts, detect the hidden processes of
nature, by an artful manipulation of language, is so contrary
to common sense, that a person must have made some advances
in philosophy to believe it: men fly to so paradoxical a
belief to avoid, as they think, some even greater difficulty,
which the vulgar do not see. What has led many to believe
that reasoning is a mere verbal process, is, that no other
theory seemed reconcileable with the nature of the Science of
Numbers. For we do not carry any ideas along with us when
we use the symbols of arithmetic or of algebra. In a geome-
trical demonstration we have a mental diagram, if not one on
paper ; AB, AC, are present to our imagination as lines, in-

DEMONSTRATION*, AND NECESSARY TRUTHS. 293

tersecting other lines, forming an angle with one another, and
the like ; but not so a and b. These may represent lines or
any other magnitudes, but those magnitudes are never thought
of; nothing is realized in our imagination but a and &. The
ideas which, on the particular occasion, they happen to repre-
sent, are banished from the mind during every intermediate
part of the process, between the beginning, when the premises
are translated from things into signs, and the end, when the
conclusion is translated back from signs into things. Nothing,
then, being in the reasoner's mind but the symbols, what can
seem more inadmissible than to contend that the reasoning pro-
cess has to do with anything more ? We seem to have come
to one of Bacon's Prerogative Instances; an experimentum
crucis on the nature of reasoning itself.

Nevertheless, it will appear on consideration, that this
apparently so decisive instance is no instance at all ; that there
is in every step of an arithmetical or algebraical calculation a
real induction, a real inference of facts from facts; and that
what disguises the induction is simply its comprehensive nature,
and the consequent extreme generality of the language. All
numbers must be numbers of something : there are no such
things as numbers in the abstract. Ten must mean ten bodies,
or ten sounds, or ten beatings of the pulse. But though num-
bers must be numbers of something, they may be numbers of
anything. Propositions, therefore, concerning numbers, have
the remarkable peculiarity that they are propositions concerning
all things whatever; all objects, all existences of every kind,
known to our experience. All things possess quantity ; con-
sist of parts which can be numbered ; and in that character
possess all the properties which are called properties of numbers.
That half of four is two, must be true whatever the word four
represents, whether four hours, four miles, or four pounds
weight. We need only conceive a thing divided into four equal
parts, (and all things may be conceived as so divided,) to be
able to predicate of it every property of the number four, that
is, every arithmetical proposition in which the number four
stands on one side of the equation. Algebra extends the
generalization still farther: every number represents that par-

294 REASONING.

ticular number of all things without distinction, but every
algebraical symbol does more, it represents all numbers with-
out distinction. As soon as we conceive a thing divided into
equal parts, without knowing into what number of parts, we
may call it a or x, and apply to it, without danger of error,
every algebraical formula in the books. The proposition,
2 (a + 6) = 2 a + 2 I, is a truth co-extensive with all nature.
Since then algebraical truths are true of all things whatever,
and not, like those of geometry, true of lines only or of an-
gles only, it is no wonder that the symbols should not excite
in our minds ideas of any things in particular. When we de-
monstrate the forty-seventh proposition of Euclid, it is not
necessary that the words should raise in us an image of all
right-angled triangles, but only of some one right-angled
triangle : so in algebra we need not, under the symbol a,
picture to ourselves all things whatever, but only some one
thing; why not, then, the letter itself? The mere written
characters, a, b, x, y, z, serve as well for representatives of
Things in general, as any more complex and apparently
more concrete conception. That we are conscious of them,
however in their character of things, and not of mere signs,
is evident from the fact that our whole process of reasoning
is carried on by predicating of them the properties of things.
In resolving an algebraic equation, by what rules do we
proceed ? By applying at each step to a, ft, and x, the pro-
position that equals added to equals make equals ; that equals
taken from equals leave equals; and other propositions-
founded on these two. These are not properties of language,
or of signs as such, but of magnitudes, which is as much as
to say, of all things. The inferences, therefore, which are
successively drawn, are inferences concerning things, not sym-
bols ; though as any Things whatever will serve the turn,
there is no necessity for keeping the idea of the Thing at ail
distinct, and consequently the process of thought may, in this
case, be allowed without danger to do what all processes of
thought, when they have been performed often, will do if per-
mitted, namely, to become entirely mechanical. Hence the
general language of algebra comes to be used familiarly with-

DEMONSTRATION', AND NECESSARY TRUTHS. 295

out exciting ideas, as all other general language is prone to
do from mere habit, though in no other case than this can it
be done with complete safety. But when we look back to see
from whence the probative force of the process is derived, we
find that at every single step, unless we suppose ourselves to
be thinking and talking of the things, and not the mere sym-
bols, the evidence fails.

There is another circumstance, which, still more than that
which we have now mentioned, gives plausibility to the notion
that the propositions of arithmetic and algebra are merely
verbal. That is, that when considered as propositions respect-
ing Things, they all have the appearance of being identical
propositions. The assertion, Two and one is equal to three,
considered as an assertion respecting objects, as for instance
" Two pebbles and one pebble are equal to three pebbles,"
does not affirm equality between two collections of pebbles,
but absolute identity. It affirms that if we put one pebble to
two pebbles, those very pebbles are three. The objects, there-
fore, being the very same, and the mere assertion that "ob-
jects are themselves " being insignificant, it seems but natural
to consider the proposition, Two and one is equal to three,
as asserting mere identity of signification between the two
names.

This, however, though it looks so plausible, will not bear
examination. The expression "two pebbLes and one pebble,"
and the expression, " three pebbles," stand indeed for the same
aggregation of objects, but they by no means stand for the
same physical fact. They are names of the same objects, but
of those objects in two different states : though they denote
the same things, their connotation is different. Three pebbles
in two separate parcels, and three pebbles in one parcel, do
not make the same impression on our senses ; and the asser-
tion that the very same pebbles may by an alteration of place
and arrangement be made to produce either the one set of sen-
sations or the other, though a very familiar proposition, is not
an identical one. It is a truth known to us by early and con-
stant experience : an inductive truth ; and such truths are the
foundation of the science of Number. The fundamental truths

296 REASONING.

of:that science all rest on the evidence of sense; they are
proved by showing to our eyes and our fingers that any given
number of objects, ten balls for example, may by separation
and re-arrangement exhibit to our senses all the different sets
of numbers the sum of which is equal to ten. All the improved
methods of teaching arithmetic to children proceed on a
knowledge of this fact. All who wish to carry the child's
mind along with them in learning arithmetic ; all who wish to
teach numbers, and not mere ciphers — now teach it through
the evidence of the senses, in the manner we have described.

We may, if we please, call the proposition, " Three is two
and one," a definition of the number three, and assert that
arithmetic, as it has been asserted that geometry, is a science
founded on definitions. But they are definitions in the
geometrical sense, not the logical; asserting not the meaning
of a term only, but along with it an observed matter of fact.
The proposition, "A circle is a figure bounded by aline which
has all its points equally distant from a point within it," is
called the definition of a circle ; but the proposition from which
so many consequences follow, and which is really a first
principle in geometry, is, that figures answering to this de-
scription exist. And thus we may call " Three is two and
one " a definition of three ; but the calculations which depend
on that proposition do not follow from the definition itself,
but from an arithmetical theorem presupposed in it, namely,
that collections of objects exist, which while they impress
the senses thus, °0°, may be separated into two parts, thus,
oo o. This proposition being granted, we term all such
parcels Threes, after which the enunciation of the above
mentioned physical fact will serve also for a definition of the
word Three.

The Science of Number is thus no exception to the conclu-
sion we previously arrived at, that the processes even of de-
ductive sciences are altogether inductive, and that their first
.principles are generalizations from experience. It remains
to be examined whether this science resembles geometry in
the further circumstance, that some of its inductions are not
exactly true ; and that the peculiar certainty ascribed to it, on
account of which its propositions are called Necessary Truths,

DEMONSTRATION/ AND NECESSARY TRUTHS. 297

is fictitious and hypothetical, being true in no other sense than
that those propositions legitimately follow from the hypothesis
of the truth of premises which are avowedly mere approxima-
tions to truth.

§ 3. The inductions of arithmetic are of two sorts : first,
those which we have just expounded, such as One and one are
two, Two and one are three, &c., which may be called the
definitions of the various numbers, in the improper or geome-
trical sense of the word Definition; and secondly, the two
following axioms : The sums of equals are equal, The diffe-
rences of equals are equal. These two are sufficient; for the
corresponding propositions respecting unequals may be proved
from these, by a reductio ad absurdum.

These axioms, and likewise the so-called definitions, are, as
has already been said, results of induction ; true of all objects
whatever, and, as it may seem, exactly true, without the hypo-
thetical assumption of unqualified truth where an approxima-
tion to it is all that exists. The conclusions, therefore, it will
naturally be inferred, are exactly true, and the science of
number is an exception to other demonstrative sciences in this,
that the categorical certainty which is predicable of its demon-
strations is independent of all hypothesis.

On more accurate investigation, however, it will be found
that, even in this case, there is one hypothetical element in the
ratiocination. In all propositions concerning numbers, a con-
dition is implied, without which none of them would be true ;
and that condition is an assumption which may be false. The
condition, is that 1=1; that all the numbers are numbers of
the same or of equal units. Let this be doubtful, and not one of
the propositions of arithmetic will hold true. How can we
know that one pound and one pound make two pounds, if one
of the pounds may be troy, and the other avoirdupois ? They
may not make two pounds of either, or of any weight. Plow
can we know that a forty-horse power is always equal to itself,
unless we assume that all horses are of equal strength ? It is
certain that 1 is always equal in number to 1 ; and where the
mere number of objects, or of the parts of an object, without
supposing them to be equivalent in any other respect, is all

298

REASONING.

that is material, the conclusions of arithmetic, so far as they
go to that alone, are true without mixture of hypothesis.
There are such cases in statistics ; as, for instance, an inquiry
into the amount of the population of any country. It is
indifferent to that inquiry whether they are grown people or
children, strong or weak, tall or short ; the only thing we want
to ascertain is their number. But whenever, from equality or
inequality of number, equality or inequality in any other
respect is to be inferred, arithmetic carried into such inquiries
becomes as hypothetical a science as geometry. All units
must be assumed to be equal in that other respect ; and this is
never accurately true, for one actual pound weight is not
exactly equal to another, nor one measured mile's length to
another ; a nicer balance, or more accurate measuring instru-
ments, would always detect some difference.

What is commonly called mathematical certainty, therefore,
which comprises the twofold conception of unconditional truth
and perfect accuracy, is not an attribute of all mathematical
truths, but of those only which relate to pure Number, as dis-
tinguished from Quantity in the more enlarged sense ; and
only so long as we abstain from supposing that the numbers
are a precise index to actual quantities. The certainty usually
ascribed to the conclusions of geometry, and even to those of
mechanics, is nothing whatever but certainty of inference. We
can have full assurance of particular results under particular
suppositions, but we cannot have the same assurance that these
suppositions are accurately true, nor that they include all the
data which may exercise an influence over the result in any
given instance.

§ 4. It appears, therefore, that the method of all Deduc-
tive Sciences is hypothetical. They proceed by tracing the
consequences of certain assumptions ; leaving for separate con-
sideration whether the assumptions are true or not, and if not
exactly true, whether they are a sufficiently near approxima-
tion to the truth. The reason is obvious. Since it is only in
questions of pure number that the assumptions are exactly
true, and even there, only so long as no conclusions except
purely numerical ones are to be founded on them ; it must, in

DEMONSTRATION, AND NECESSARY TRUTHS. 299"

all other cases of deductive investigation, form a part of the
inquiry, to determine how much the assumptions want of being
exactly true in the case in hand. This is generally a matter
of observation, to be repeated in every fresh case; or if it has
to be settled by argument instead of observation, may require
in every different case different evidence, and present every
degree of difficulty, from the lowest to the highest. But the
other part of the process — namely, to determine what else may
be concluded if we find, and in proportion as we lind, the as-
sumptions to be true — may be performed once for all, and the
results held ready to be employed as the occasions turn up for
use. We thus do all beforehand that can be so done, and leave
the least possible work to be performed when cases arise and
press for a decision. This inquiry into the inferences which
can be drawn from assumptions, is what properly constitutes
Demonstrative Science.

It is of course quite aspracticable to arrive at new conclusions
from facts assumed, as from facts observed ; from fictitious, as
from real, inductions. Deduction, as we have seen, consists of
a series of inferences in this form — a is a mark of b, b of c, c
of d, therefore a is a mark of d, which last may be a truth
inaccessible to direct observation. In like manner it is allow-
able to say, suppose that a were a mark of b, b of c, and c ofd,
a would be a mark of d, which last conclusion was not thought
of by those who laid down the premises. A system of pro-
positions as complicated as geometry might be deduced from
assumptions which are false; as was done by Ptolemy,
Descartes, and others, in their attempts to explain syntheti-
cally the phenomena of the solar system on the supposition
that the apparent motions of the heavenly bodies were the real
motions, or were produced in some way more or less different
from the true one. Sometimes the same thing is knowingly
done, for the purpose of showing the falsity of the assumption;
which is called a reductio ad absurdum. In such cases, the
reasoning is as follows : a is a mark of b, and b of c ; now if
c were also a mark of d, a would be a mark of d ; but d is
known to be a mark of the absence of a; consequently a
would be a mark of its own absence, which is a contradiction ;
therefore c is not a mark of d.

800

REASONING.

§ 5. It has even been held by some writers, that all ratio-
cination rests in the last resort on a reductio ad absurclum ;
since the way to enforce assent to it, in case of obscurity,
would be to show that if the conclusion be denied we must
deny some one at least of the premises, which, as they are all
supposed true, would be a contradiction. »And in accordance
with this, many have thought that the peculiar nature of the
evidence of ratiocination consisted in the impossibility of
admitting the premises and rejecting the conclusion without a
contradiction in terms. This theory, however, is inadmissible
as an explanation of the grounds on which ratiocination itself
rests. If any one denies the conclusion notwithstanding his
admission of the premises, he is not involved in any direct and
express contradiction until he is compelled to deny some
premise ; and he can only be forced to do this by a reductio ad
absurdum, that is, by another ratiocination : now, if he denies
the validity of the reasoning process itself, he can no more
be forced to assent to the second syllogism than to the first.
In truth, therefore, no one is ever forced to a contradiction in
terms : he can only be forced to a contradiction (or rather an
infringement) of the fundamental maxim of ratiocination,
namely, that whatever has a mark, has what it is a mark of;
or, (in the case of universal propositions,) that whatever is a
mark of anything, is a mark of whatever else that thing is a
mark of. For in the case of every correct argument, as soon
as thrown into the syllogistic form, it is evident without the
aid of any other syllogism, that he who, admitting the pre-
mises, fails to draw the conclusion, does not conform to the
above axiom.

We have now proceeded as far in the theory of Deduction
as we can advance in the present stage of our inquiry. Any
further insight into the subject requires that the foundation
shall have been laid of the philosophic theory of Induction
itself; in which theory that of Deduction, as a mode of Induc-
tion, which we have now shown it to be, will assume sponta-
neously the place which belongs to it, and will receive its share
of whatever light may be thrown upon the great intellectual
operation of which it forms so important a part.

CHAPTER VII.

EXAMINATION OF SOME OPINIONS OPPOSED TO THE
PRECEDING DOCTRINES.

§ 1. POLEMICAL discussion is foreign to the plan of this
work. But an opinion which stands in need of much illustra-
tion, can often receive it most effectually, and least tediously,
in the form of a defence against objections. And on subjects
concerning which speculative minds are still divided, a writer
does but half his duty by stating his own doctrine, if he does
not also examine, and to the best of his ability judge, those
of other thinkers.

In the dissertation which Mr. Herbert Spencer has prefixed
to his, in many respects, highly philosophical treatise on the
Mind,* he criticises some of the doctrines of the two preceding
chapters, and propounds a theory of his own on the subject of
first principles. Mr. Spencer agrees with me in considering
axioms to be " simply our earliest inductions from experience."
But he differs from me " widely as to the worth of the test of
inconceivableness." He thinks that it is the ultimate test of
all beliefs. He arrives at this conclusion by two steps. First,
we never can have any stronger ground for believing anything,
than that the belief of it " invariably exists." Whenever any
fact or proposition is invariably believed ; that is, if I under-
stand Mr. Spencer rightly, believed by all persons, and by one-
self at all times ; it is entitled to be received as one of the
primitive truths, or original premises of our knowledge.
Secondly, the criterion by which we decide whether anything
is invariably believed to be true, is our inability to conceive it
as false. " The inconceivability of its negation is the test by
which we ascertain whether a given belief invariably exists or

* Principles of Paydiology.

302 REASONING.

not." " For our primary beliefs, the fact of invariable exis-
tence, tested by an abortive effort to cause their non-existence,
is the only reason assignable." He thinks this the sole ground
of our belief in our own sensations. If I believe that I feel
cold, I only receive this as true because I cannot conceive
that I am not feeling cold. " While the proposition remains
true, the negation of it remains inconceivable." There are
numerous other beliefs which Mr. Spencer considers to rest on
the same basis ; being chiefly those, or apart of those, which
the metaphysicians of the Reid and Stewart school consider as
truths of immediate intuition. That there exists a material
world ; that this is the very world which we directly and imme-
diately perceive, and not merely the hidden cause of our per-
ceptions ; that Space, Time, Force, Extension, Figure, are not
modes of our consciousness, but objective realities ; are
regarded by Mr. Spencer as truths known by the inconceiva-
bleness of their negatives. We cannot, he says, by any effort,
conceive these objects of thought as mere states of our mind ;
as not having an existence external to us. Their real exis-
tence is, therefore, as certain as our sensations themselves.
The truths which are the subject of direct knowledge, being,
according to this doctrine, known to be truths only by the
inconceivability of their negation ; and the truths which are
not the object of direct knowledge, being known as inferences
from those which are ; and those inferences being believed to
follow from the premises, only because we cannot conceive
them not to follow ; inconceivability is thus the ultimate
ground of all assured beliefs.

Thus far, there is no very wide difference between Mr.
Spencer's doctrine and the ordinary one of philosophers of the
intuitive school, from Descartes to Dr. Whewell; but at this
point Mr. Spencer diverges from them. For he does not, like
them, set up the test of inconceivability as infallible. On the
contrary, he holds that it may be fallacious, not from any fault
in the test itself, but because "men have mistaken for incon-
ceivable things, some things which were not inconceivable."
And he himself, in this very book, denies not a few proposi-
tions usually regarded as among the most marked examples of

THEORIES CONCERNING AXIOMS. 303

.

truths whose negations are inconceivahle. But occasional
failure, he says, is incident to all tests. If such failure vitiates
'" the test of inconceivahleness," it " must similarly vitiate all
tests whatever. We consider ail inference logically drawn
from established premises to he true. Yet in millions of cases
men have heen wrong in the inferences they have thought thus
•drawn. Do we therefore argue that it is absurd to consider
an inference true on no other ground than that it is logically
drawn from established premises ? No : we say that though
men may have taken for logical inferences, inferences that
were not logical, there nevertheless are logical inferences, and
that we are justified in assuming the truth of what seem to us
such, until better instructed. Similarly, though men may
have thought some things inconceivable which were not so,
there may still be inconceivable things ; and the inability to
conceive the negation of a thing, may still be our best warrant
for believing it. ... Though occasionally it may prove an
imperfect test, yet, as our most certain beliefs are capable of
no better, to doubt any one belief because we have no higher
guarantee for it, is really to doubt all beliefs." Mr. Spencer's
doctrine, therefore, does not erect the curable, but only the
incurable limitations of the human conceptive faculty, into
laws of the outward universe.

§ 2. The doctrine, that " a belief which is proved by the
inconceivableness of its negation to invariably exist, is true,"
Mr. Spencer enforces by two arguments, one of which may be
distinguished as positive, and the other as negative.

The positive argument is, that every such belief represents
the aggregate of all past experience. " Conceding the entire
truth of" the " position, that during any phase of human pro-
gress, the ability or inability to form a specific conception
wholly depends on the experiences men have had ; and that,
by a widening of their experiences, they may, by and by, be
enabled to conceive things before inconceivable to them, it
may still be argued that as, at any time, the best warrant
men can have for a belief is the perfect agreement of all pre-
existing experience in support of it, it follows that, at any

REASONING.

• time, the inconceivableness of. its negation is the deepest test
any belief admits of. ... Objective facts are ever im-
pressing themselves upon us ; our experience is a register of
these objective facts ; and the inconceivableness of a thing
implies that it is wholly at variance -with the register. Even
were this all, it is not clear how, if every truth is primarily
inductive, any better test of truth could exist. But it must be
remembered that whilst many of these facts, impressing them-
selves upon us, are occasional ; whilst others again are very
general; some are universal and unchanging. These universal
and unchanging facts are, by the hypothesis, certain to estab-
lish beliefs of which the negations are inconceivable ; whilst
the others are not certain to do this ; and if they do, subsequent
facts will reverse their action. Hence if, after an immense
accumulation of experiences, there remain beliefs of which the
negations are still inconceivable, most, if not all of them, must
correspond to universal objective facts. If there be ...
certain absolute uniformities in nature ; if these uniformities
produce, as they must, absolute uniformities in our experience;
and if ... these absolute uniformities in our experience
disable us from conceiving the negations of them ; then
answering to each absolute uniformity in nature which we can
cognize, there must exist in us a belief of which the negation
is inconceivable, and which is absolutely true. In this wide
range of cases subjective inconceivableness must correspond to
objective impossibility. Further experience will produce cor-
respondence where it may not yet exist; and we may expect
the correspondence to become ultimately complete. In nearly
all cases this test of inconceivableness must be valid now;"
(I wish I could think we were so nearly arrived at omniscience)
" and where it is not, it still expresses the net result of our
experience up to the present time ; which is the most that any
test con do."

To this I answer, first, that it is by no means true that the
inconceivability, by us, of the negative of a proposition proves
all, or even any, " pre-existing experience" to be in favour of
the affirmative. There may have been no such pre-existing
experiences, but only a mistaken supposition of experience.

THEORIES CONCERNING AXIOMS. 305

How did the inconceivability of antipodes prove that expe-
rience had given any testimony against their possibility ? How
did the incapacity men felt of conceiving sunset otherwise than
as a motion of the sun, represent any " net result" of expe-
rience in support of its being the sun and not the earth that
moves ? It is not experience that is represented, it is only a
superficial semblance of experience. The only thing proved
with regard to real experience, is the negative fact, that men
have not had it of the kind which would have made the incon-
ceivable proposition conceivable.

Next : Even if it were true that inconceivableness repre-
sents the net result of all past experience, why should we
stop at the representative when we can get at the thing
represented? If our incapacity to conceive the negation
of a given supposition is proof of its truth, because proving
that our experience has hitherto been uniform in its favour,
the real evidence for the supposition is not the inconceivable-
ness, but the uniformity of experience. Now this, which is the
substantial and only proof, is directly accessible. We are not
obliged to presume it from an incidental consequence. If all
past experience is in favour of a belief, let this be stated, and
the belief openly rested on that ground : after which the
question arises, what that fact may be worth as evidence of its
truth ? For uniformity of experience is evidence in very
different degrees : in some cases it is strong evidence, in others
weak, in others it scarcely amounts to evidence at all. That
all metals sink in water, was an uniform experience, from the
origin of the human race to the discovery of potassium in the
present century by Sir Humphry Davy. That all swans are
white, was an uniform experience down to the discovery of
Australia. In the few cases in which uniformity of experience
does amount to the strongest possible proof, as with such pro-
positions as these, Two straight lines cannot inclose a space,
Every event has a cause, it is not because their negations are
inconceivable, which is not always the fact ; but because the
experience, which has been thus uniform, pervades all nature.
It will be shown in the following Book that none of the con-
clusions either of induction or of deduction can be considered
VOL. i. 20

306 REASONING.

certain, except as far as their truth is shown to be inseparably
bound up with truths of this class.

I maintain then, first, that uniformity of past experience is
very far from being universally a criterion of truth. But
secondly, inconceivableness is still farther from being a test
even of that test. Uniformity of contrary experience is only
one of many causes of inconceivability. Tradition handed
down from a period of more limited knowledge, is one of the
commonest. The mere familiarity of one mode of production
of a phenomenon, often suffices to make every other mode
appear inconceivable. Whatever connects two ideas by a
strong association may, and continually does, render their
separation in thought impossible ; as Mr. Spencer, in other
parts of his speculations, frequently recognises. It was not
for want of experience that the Cartesians were unable to con-
ceive that one body could produce motion in another without
contact. They had as much experience of other modes of pro-
ducing motion, as they had of that mode. The planets had
revolved, and heavy bodies had fallen, every hour of their lives.
But they fancied these phenomena to be produced by a hidden
machinery which they did not see, because without it they
were unable to conceive what they did see. The inconceiv-
ableness, instead of representing their experience, dominated
and overrode their experience. Without dwelling farther on
what I have termed the positive argument of Mr. Spencer ia
support of his criterion of truth, I pass to his negative
argument, on which he lays more stress.

§ 3. The negative argument is, that, whether inconceiv-
ability be good evidence or bad, no stronger evidence is to be
obtained. That what is inconceivable cannot be true, is pos-
tulated in every act of thought. It is the foundation of all our
original premises. Still more it is assumed in all conclusions
from those premises. The invariability of belief, tested by the
inconceivableness of its negation, "is our sole warrant for
every demonstration. Logic is simply a systematization of
the process by which we indirectly obtain this warrant for
beliefs that do not directly possess it. To gain the strongesl

THEORIES CONCERNING AXIOMS. 307

conviction possible respecting any complex fact, we either
analytically descend from it by successive steps, each of which
we unconsciously test by the inconceivableness of its negation,
until we reach some axiom or truth which we have similarly
tested ; or we synthetically ascend from such axiom or truth
by such steps. In either case we connect some isolated belief,
with a belief which invariably exists, by a series of interme-
diate beliefs which invariably exist." The following passage
sums up the theory : " When we perceive that the negation of
the belief is inconceivable, we have all possible warrant for
asserting the invariability of its existence : and in asserting
this, we express alike our logical justification of it,
and the inexorable necessity we are under of holding it. ...
We have seen that this is the assumption on which every con-
clusion whatever ultimately rests. We have no other guaran-
tee for the reality of consciousness, of sensations, of personal
existence ; we have no other guarantee for any axiom ; we
have no other guarantee for any step in a demonstration.
Hence, as being taken for granted in every act of the under-
standing, it must be regarded as the Universal Postulate.'
But as this postulate which we are under an " inexorable
necessity " of holding true, is sometimes false ; as " beliefs
that once were shown by the inconceivableness of their nega-
tions to invariably exist, have since been found untrue," and
as " beliefs that now possess this character may some day share
the same fate ;" the canon of belief laid down by Mr. Spencer
is, that "the most certain conclusion" is that " which involves
the postulate the fewest times." Eeasoning, therefore, never
ought to prevail against one of the immediate beliefs (the
belief in Matter, in the outward reality of Extension, Space,
and the like), because each of these involves the postulate only
once ; while an argument, besides involving it in the premises,
involves it again in every step of the ratiocination, no one of
the successive acts of inference being recognised as valid ex-
cept because we cannot conceive the conclusion not to follow
from the premises.

It will be convenient to take the last part of this argu-
ment first. In every reasoning, according to Mr. Spencer,

20—2

308 REASONING.

the assumption of the postulate is renewed at every step. At
each inference we judge that the conclusion follows from the
premises, our sole warrant for that judgment heing that we
cannot conceive it not to follow. Consequently if the postu-
late is fallible, the conclusions of reasoning are more vitiated by
that uncertainty than direct intuitions ; and the disproportion
is greater, the more numerous the steps of the argument.

To test this doctrine, let us first suppose an argument
consisting only of a single step, which would be represented
by one syllogism. This argument does rest on an assumption,
and we have seen in the preceding chapters what the assump-
tion is. It is, that whatever has a mark, has what it is a
mark of. The evidence of this axiom I shall not consider at
present ;* let us suppose it (with Mr. Spencer) to be the in-
conceivableness of its reverse.

Let us now add a second step to the argument: we require,
what ? Another assumption ? No : the same assumption a
second time ; and so on to a third, and a fourth. I confess I
do not see how, on Mr. Spencer's own principles, the repeti-
tion of the assumption at all weakens the force of the argu-
ment. If it were necessary the second time to assume some
other axiom, the argument would no doubt be weakened,
since it would be necessary to its validity that both axioms
should be true, and it might happen that one was true and
not the other : making two chances of error instead of one.
But since it is the same axiom, if it is true once it is true
every time ; and if the argument, being of a hundred links,
assumed the axiom a hundred times, these hundred assump-
tions would make but one chance of error among them all.
It is satisfactory that we are not obliged to suppose the
deductions of pure mathematics to be among the most uncer-
tain of argumentative processes, which on Mr. Spencer's
theory they could hardly fail to be, since they are the longest.
But the number of steps in an argument does not subtract

* Mr. Spencer is mistaken in supposing rne to claim any peculiar " neces-
sity " for this axiom as compared with others. I have corrected the expressions
which led him into that misapprehension of my meaning.

THEORIES CONCERNING AXIOMS. 309

from its reliableness, if no new premises, of an uncertain cha-
racter, are taken up by the way.*

* Mr. Spencer, in recently returning to the subject (Principles of Psycho-
logy, new edition, ch. xii. "The Test of Relative Validity,") makes two
answers to the preceding remarks. One is :

' ' Were an argument formed by repeating the same proposition over and
over again, it would be true that any intrinsic fallibility of the postulate
would not make the conclusion more untrustworthy than the first step. But
an argument consists of unlike propositions. Now since Mr. Mill's criticism
on the Universal Postulate is that in some cases, which he names, it has proved
to be an untrustworthy test ; it follows that in any argument consisting of
heterogeneous propositions, there is a risk, increasing as the number of propo-
sitions increases, that some one of them belongs to this class of cases, and is
wrongly accepted because of the inconceivableness of its negation."

No doubt : but this supposes new premises to be taken in. The point we
are discussing is the fallibility not of the premises, but of the reasoning, as
distinguished from the premises. Now the validity of the reasoning depends
always upon the same axiom, repeated (in thought) "over and over again,"
viz. that whatever has a mark, has what it is a mark of. Even, therefore, on
the assumption that this axiom rests ultimately on the Universal Postulate,
and that, the Postulate not being wholly trustworthy, the axiom may be one
of the cases of its failure ; all the risk there is of this is incurred at the very
first step of the reasoning, and is not added to, however long may be the
series of subsequent steps.

I am here arguing, of course, from Mr. Spencer's point of view. From
my own the case is still clearer ; for, in my view, the truth that whatever has
a mark has what it is a mark of, is wholly trustworthy, and derives none of
its evidence from so very untrustworthy a test as the inconceivability of the
negative.

Mr. Spencer's second answer is valid up to a certain point ; it is, that every
prolongation of the process involves additional chances of casual error, from
carelessness in the reasoning operation. This is an important consideration in
the private speculations of an individual reasoner ; and even with respect to
mankind at large, it must be admitted that, though mere oversights in the
syllogistic process, like errors of addition in an account, are special to the
individual, and seldom escape detection, confusion of thought produced (for
example) by ambiguous terms has led whole nations or ages to accept fallacious
reasoning as valid. But this very fact points to causes of error so much more
dangerous than the mere length of the process, as quite to vitiate the doctrine
that the "test of the relative validities of conflicting conclusions " is the
number of times the fundamental postulate is involved. On the contrary,
the subjects on which the trains of reasoning are longest, and the assumption,
therefore, oftenest repeated, are in general those which are best fortified
against the really formidable causes of fallacy ; aa in the example already given
of mathematics.

310 REASONING.

To speak next of the premises. Our assurance of their
truth, whether they he generalities or individual facts, is
grounded, in Mr. Spencer's opinion, on the inconceivableness
of their heing false. It is necessary to advert to a double
meaning of the word inconceivable, which Mr. Spencer is
aware of, and would sincerely disclaim founding an argument
upon, but from which his case derives no little advantage
notwithstanding.- By inconceivableness is sometimes meant,
inability to form or get rid of an idea ; sometimes, inability to
form or get rid of a belief. The former meaning is the most
conformable to the analogy of language ; for a conception
always means an idea, and never a belief. The wrong meaning
of "inconceivable" is, however, fully as frequent in philosophical
discussion as the right meaning, and the intuitive school of
metaphysicians could not well do without either. To illustrate
the difference, we will take two contrasted examples. The early
physical speculators considered antipodes incredible, because
inconceivable. But antipodes were not inconceivable in the
primitive sense of the word. An idea of them could be formed
without difficulty : they could be completely pictured to the
mental eye. What was difficult, and as it then seemed, impos-
sible, was to apprehend them as believable. The idea could be
put together, of men sticking on by their feet to the under side
of the earth ; but the belief would follow, that they must fall
off. Antipodes were not unimaginable, but they were un-
believable.

On the other hand, when I endeavour to conceive an end
to extension, the two ideas refuse to come together. When I
attempt to form a conception of the last point of space, I can-
not help figuring to myself a vast space beyond that last point.
The combination is, under the conditions of our experience,
unimaginable. This double meaning of inconceivable it is
very important to bear in mind, for the argument from incon-
ceivableness almost always turns on the alternate substitution
of each of those meanings for the other.

In which of these two senses does Mr. Spencer employ the
term, when he makes it a test of the truth of a proposition
that its negation is inconceivable ? Until Mr. Spencer ex-

THEORIES CONCERNING AXIOMS. 311

pressly stated the contrary, I inferred from the course of his
argument, that he meant unbelievable. He has, however, in
a paper published in the fifth number of the Fortnightly
Review, disclaimed this meaning, and declared that by an in-
conceivable proposition he means, now and always, " one of
which the terms cannot, by any effort, be brought before con-
sciousness in that relation which the proposition asserts
between them — a proposition of which the subject and predi-
cate offer an insurmountable resistance to union in thought."
We now, therefore, know positively that Mr. Spencer always
endeavours to use the word inconceivable in this, its proper,
sense : but it may yet be questioned whether his endeavour is
always successful ; whether the other, and popular use of the
word does not sometimes creep in with its associations, and
prevent him from maintaining a clear separation between the
two. When, for example, he says, that when I feel cold, I
cannot conceive that I am not feeling cold, this expression
cannot be translated into "I cannot conceive myself not feel-
ing cold," for it is evident that I can : the word conceive, there-
fore, is here used to express the recognition of a matter of fact
— the perception of truth or falsehood ; which I apprehend to
be exactly the meaning of an act of belief, as distinguished
from simple conception. Again, Mr. Spencer calls the attempt
to conceive something which is inconceivable, " an abortive
effort to cause the non-existence" not of a conception or mental
representation, but of a belief. There is need, therefore, to
revise a considerable part of Mr. Spencer's language, if it is to
be kept always consistent with his definition of inconceivability.
But in truth the point is of little importance ; since inconceiva-
bility, in Mr. Spencer's theory, is only a test of truth, inasmuch
as it is a test of believability. The inconceivableness of a
supposition is the extreme case of its unbelievability. This is
the very foundation of Mr. Spencer's doctrine. The invaria-
bility of the belief is with him the real guarantee. The
attempt to conceive the negative, is made in order to test the
inevitableness of the belief. It should be called, an attempt
to believe the negative. When Mr. Spencer says that while
looking at the sun a man cannot conceive that he is looking

312 REASONING.

into darkness, he should have said that a man cannot believe
that he is doing so. For it is surely possible, in broad daylight,
to imagine oneself looking into darkness.* As Mr. Spencer
himself says, speaking of the belief of our own existence :
" That he might not exist, he can conceive well enough; but
that he does not exist, he finds it impossible to conceive," i.e.
to believe. So that the statement resolves itself into this : That
I exist, and that I have sensations, I believe, because I cannot
helieve otherwise. And in this case every one will admit that
the impossibility is real. Any one's present sensations, or other
states of subjective consciousness, that one person inevitably
believes. They are facts known per se : it is impossible to
ascend beyond them. Their negative is really unbelievable,
and therefore there is never any question about believing it.
Mr. Spencer's theory is not needed for these truths.

But according to Mr. Spencer there are other beliefs,
relating to other things than our own subjective feelings, for
which we have the same guarantee — which are, in a similar
manner, invariable and necessary. With regard to these other
beliefs, they cannot be necessary, since they do not always
exist. There have been, and are, many persons who do not
believe the reality of an external world, still less the reality of
extension and figure as the forms of that external world ; who
do not believe that space and time have an existence indepen-
dent of the mind — nor any other of Mr. Spencer's objective
intuitions. The negations of these alleged invariable beliefs
are not unbelievable, for they are believed. It may be main-
tained, without obvious error, that we cannot imagine tangible
objects as mere states of our own and other people's con-
sciousness ; that the perception of them irresistibly suggests to
us the idea of something external to ourselves : and I am not
in a condition to say that this is not the fact (though I do not

* Mr. Spencer makes a distinction between conceiving myself looking into
darkness, and conceiving that I am then and there looking into darkness. To
me it seems that this change of the expression to the form I am, just marsjs
the transition from concep tion to belief, and that the phrase " to conceive that
/ am," or " that anything ?'«," is not consistent with using the word conceive
in its rigorous sense.

THEORIES CONCERNING AXIOMS. 313

think any one is entitled to affirm it of any person besides
himself) . But many thinkers have believed, whether they could
conceive it or not, that what we represent to ourselves as ma-
terial objects, are mere modifications of consciousness ; complex
feelings of touch and of muscular action. Mr. Spencer may
think the inference correct from the unimaginable to the
unbelievable, because he holds that belief itself is but the per-
sistence of an idea, and that what we can succeed in imagining
we cannot at the moment help apprehending as believable.
But of what consequence is it what we apprehend at the
moment, if the moment is in contradiction to the permanent
state of our mind? A person who has been frightened when
an infant by stories of ghosts, though he disbelieves them in
after years (and perhaps never believed them), may be unable
all his life to be in a dark place, in circumstances stimulating
to the imagination, without mental discomposure. The idea
of ghosts, with all its attendant terrors, is irresistibly called
up in his mind by the outward circumstances. Mr. Spencer
may say, that while he is under the influence of this terror he
does not disbelieve in ghosts, but has a temporary and uncon-
trollable belief in them. Be it so ; but allowing it to be so,
which would it be truest to say of this man on the whole —
that he believes in ghosts, or that he does not believe in them ?
Assuredly that he does not believe in them. The case is
similar with those who disbelieve a material world. Though
they cannot get rid of the idea ; though while looking at a
solid object they cannot help having the conception, and
therefore, according to Mr. Spencer's metaphysics, the mo-
mentary belief, of its externality ; even at that moment they
would sincerely deny holding that belief: and it would be
incorrect to call them other than disbelievers of the doc-
trine. The belief therefore is not invariable ; and the test of
inconceivableness fails in the only cases to which there could
ever be any occasion to apply it.

That a thing may be perfectly believable, and yet may not
have become conceivable, and that we may habitually believe
one side of an alternative, and conceive only in the other, is
familiarly exemplified in the state of mind of educated persons

314 REASONING.

respecting sunrise and sunset. All educated persons either
know by investigation, or believe on the authority of science,
that it is the earth and not the sun which moves : but there
are probably few who habitually conceive the phenomenon
otherwise than as the ascent or descent of the sun. Assuredly
no one can do so without a prolonged trial ; and it is probably
not easier now than in the first generation after Copernicus.
Mr. Spencer does not say, " In looking at sunrise it is impos-
sible not to conceive that it is the sun which moves, therefore
this is what everybody believes, and we have all the evidence
for it that we can have for any truth." Yet this would be an
exact parallel to his doctrine about the belief in matter.

The existence of matter, and other Noumena, as dis-
tinguished from the phenomenal world, remains a question of
argument, as it was before ; and the very general, but neither
necessary nor universal, belief in them, stands as a psychological
phenomenon to be explained, either on the hypothesis of its
truth, or on some other. The belief is not a conclusive proof
of its own truth, unless there are no such things as idola tribus ;
but, being a fact, it calls on antagonists to show, from what
except the real existence of the thing believed, so general and
apparently spontaneous a belief can have originated. And its
opponents have never hesitated to accept this challenge.*
The amount of their success in meeting it will probably
determine the ultimate verdict of philosophers on the ques-
tion.

§ 4. In a revision, or rather reconstruction, of his
" Principles of Psychology," as one of the stages or platforms in
the imposing structure of hi s System of Philosophy, Mr. Spencer
has presumed what he justly terms f the "amicable con-
troversy that has been long pending between us;" expressing at
the same time a regret, which I cordially share, that " this
lengthened exposition of a single point of difference, unaccom-

* I have myself accepted the contest, and fought it out on this battle-
ground, in the eleventh chaper of An Examination of Sir William Hamilton's
Philosophy.

t chap. xi.

THEORIES CONCERNING AXIOMS. 315

parried by an exposition of the numerous points of concur-
rence, unavoidably produces an appearance of dissent very far
greater than that which exists." I believe, with Mr. Spencer,
that the difference between us, if measured by our conclusions,
is " superficial rather than substantial ;" and the value I at-
tach to so great an amount of agreement, in the field of analytic
psychology, with a thinker of his force and depth, is such as I
can hardly overstate. But I also agree with him that the dif-
ference which exists in our premises is one of " profound im-
portance, philosophically considered ;" and not to be dismissed
while any part of the case of either of us has not been fully
examined and discussed.

In his present statement of the Universal Postulate, Mr.
Spencer has exchanged his former expression, " beliefs which
invariably exist," for the following : " cognitions of which the
predicates invariably exist along with their subjects." And
he says that " an abortive effort to conceive the negation of a
proposition, shows that the cognition expressed is one of which
the predicate invariably exists along with its subject; and the
discovery that the predicate invariably exists along with its
subject, is the discovery that this cognition is one we are com-
pelled to accept." Both these premises of Mr. Spencer's
syllogism I am able to assent to, but in different senses of the
middle term. If the invariable existence of the predicate along
with its subject, is to be understood in the most obvious
meaning, as an existence in actual Nature, or in other words,
in our objective, or sensational, experience, I of course admit
that this, once ascertained, compels us to accept the propo-
sition : but then I do not admit that the failure of an attempt
to conceive the negative, proves the predicate to be always
coexistent with the subject in actual Mature. If, on the other
hand (which I believe to be Mr. Spencer's meaning) the inva-
riable existence of the predicate along with the subject is to
be understood only of our conceptive faculty, i.e. that the one
is inseparable from the other in our thoughts ; then, indeed,
the inability to separate the two ideas proves their inseparable
conjunction, here and now, in the mind which has failed in the
attempt; but this inseparability in thought does not prove a

316 REASONING.

corresponding inseparability in fact ; nor even in the thoughts
of other people, or of the same person in a possible future.

" That some propositions have been wrongly accepted as
true, because their negations were supposed inconceivable
when they were not," does not, in Mr. Spencer's opinion, " dis-
prove the validity of the test;" not only because any test
whatever " is liable to yield untrue results, either from inca-
pacity or from carelessness in those who use it," but because
the propositions in question " were complex propositions, not
to be established by a test applicable to propositions no further
decomposable." " A test legitimately applicable to a simple
proposition, the subject and predicate of which are in direct
relation, cannot be legitimately applied to a complex propo-
sition, the subject and predicate of which are indirectly re-
lated through the many simple propositions implied." " That
things which are equal to the same thing are equal to one
another, is a fact which can be known by direct comparison

of actual or ideal relations But that the square of the

hypothenuse of a right angled triangle equals the sum of the
squares of the other two sides, cannot be known immediately
by comparison of two states of consciousness : here the truth
can be reached only mediately, through a series of simple
judgments respecting the likenesses or unlikenesses of cer-
tain relations." Moreover, even when the proposition admits
of being tested by immediate consciousness, people often
neglect to do it A schoolboy, in adding up a column of
figures, will say " 35 and 9 are 4G," though this is contrary to
the verdict which consciousness gives when 35 and 9 are
really called up before it ; but this is not done. And not only
schoolboys, but men and thinkers, do not always " distinctly
translate into their equivalent states of consciousness the
words they use."

It is but just to give Mr. Spencer's doctrine the benefit of
the limitation he claims — viz. that it is only applicable to
propositions which are assented to on simple inspection, with-
out any intervening media of proof. But this limitation does
not exclude some of the most marked instances of propositions
now known to be false or groundless, but whose negative was

THEORIES CONCERNING AXIOMS. 317

once found inconceivable : such as, that in sunrise and sunset
it is the sun which moves; that gravitation may exist
without an intervening medium ; and even the case of anti-
podes. The distinction drawn by Mr. Spencer is real ; but, in
the case of the propositions classed by him as complex, con-
sciousness, until the media of proof are supplied, gives no ver-
dict at all : it neither declares the equality of the square of
the hypothenuse with the sum of the squares of the sides
to be inconceivable, nor their inequality to be inconceivable.
But in all the three cases which I have just cited, the incon-
ceivability seems to be apprehended directly; no train of argu-
ment was needed, as in the case of the square of the hypo-
thenuse, to obtain the verdict of consciousness on the point.
Neither is any of the three a case like that of the schoolboy's
mistake, in which the mind was never really brought into con-
tact with the proposition. They are cases in which one of
two opposite predicates, mero adspectu, seemed to be incom-
patible with the subject, and the other, therefore, to be proved
always to exist with it*

As now limited by Mr. Spencer, the ultimate cognitions fit

* In one of the three cases, Mr. Spencer, to my no small surprise, thinks
that the belief of mankind "cannot be rightly said to have undergone" the change
I allege. Mr. Spencer himself still thinks we are unable to conceive gravita-
tion acting through empty space. " If an astronomer avowed that he could
conceive gravitative force as exercised through space absolutely void, my
private opinion would be that he mistook the nature of conception. Conception
implies representation. Here the elements of the representation are the two
bodies and an agency by which either affects the other. To conceive this
agency is to represent it in some terms derived from our experiences —
that is, from our sensations. As this agency gives us no sensations, we are
obliged (if we try to conceive it) to use symbols idealized from our sensa-
tions— imponderable units forming a medium."

If Mr. Spencer means that the action of gravitation gives us no sensations,
the assertion is one than which I have not seen, in the writings of philoso-
phers, many more startling. What other sensation do we need than the sensa-
tion of one body moving towards another? "The elements of the representa-
tion " are not two bodies and an " agency," but two bodies and an effect ;
viz. the fact of their approaching one another. If we are able to conceive a
vacuum, is there any difficulty in conceiving a body falling to the earth
through it ?

318 REASONING.

to be submitted to bis test are only tbose of so universal and
elementary a character as to be represented in tbe earliest and
most unvarying experience, or apparent experience, of all man-
kind. In such cases the inconceivability of the negative, if
real, is accounted for by the experience : and why (I have
asked) should the truth be tested by the inconceivability, when
we can go further back for proof — namely, to the experience
itself? To this Mr. Spencer answers, that the experiences
cannot be all recalled to mind, and if recalled, would be of
unmanageable multitude. To test a proposition by experience
seems to him to mean that " before accepting as certain the
proposition that any rectilineal figure must have as many angles
as it has sides," I have " to think of every triangle, square,
pentagon, hexagon, &c., which I have ever seen, and to verify
the asserted relation in each case." I can only say, with sur-
prise, that I do not understand this to be the meaning of an
appeal to experience. It is enough to know that one has been
seeing the fact all one's life, and has never remarked any in-
stance to the contrary, and that other people, with every op-
portunity of observation, unanimously declare the same thing.
It is true, even this experience may be insufficient, and so it
might be even if I could recal to mind every instance of it ; but
its insufficiency, instead of being brought to light, is disguised, if
instead of sifting the experience itself, I appeal to a test which
bears no relation to the sufficiency of the experience, but, at
the most, only to its familiarity. These remarks do not lose
their force even if we believe, with Mr. Spencer, that mental
tendencies originally derived from experience impress them-
selves permanently on the cerebral structure and are trans-
mitted by inheritance, so that modes of thinking which are
acquired by the race become innate and a priori in the indi-
vidual, thus representing, in Mr. Spencer's opinion, the expe-
rience of his progenitors, in addition to his own. All that
would follow from this is, that a conviction might be really in-
nate, i.e. prior to individual experience, and yet not be ti'ue,
since the inherited tendency to accept it may have been origi-
nally the result of other causes than its truth.

Mr. Spencer would have a much stronger case, if he could

THEORIES CONCERNING AXIOMS. 319

really show that the evidence of Seasoning rests on the Postu-
late, or, in other words, that we believe that a conclusion
follows from premises only because we cannot conceive it not
to follow. But this statement seems to me to be of the same
kind as one I have previously commented on, viz. that I be-
lieve I see light, because I cannot, while the sensation remains,
conceive that I am looking into darkness. Both these state-
ments seem to me incompatible with the meaning (as very
rightly limited by Mr. Spencer) of the verb to conceive. To
say that when I apprehend that A is B and that B is C, I
cannot conceive that A is not C, is to my mind merely to say
that I am compelled to believe that A is C. If to
conceive be taken in its proper meaning, viz. to form a
mental representation, I may be able to conceive A as
not being C. After assenting, with full understanding, to the
Copernican proof that it is the earth and not the sun that
moves, I not only can conceive, or represent to myself, sunset
as a motion of the sun, but almost every one finds this concep-
tion of sunset easier to form, than that which they nevertheless
know to be the true one.

§ 5. Sir William Hamilton holds as I do, that incon-
ceivability is no criterion of impossibility. "There is no
ground for inferring a certain fact to be impossible, merely from
our inability to conceive its possibility." " Things there are
which may, nay must, be true, of which the understanding is
wholly unable to construe to itself the possibility."* Sir
William Hamilton is however a firm believer in the ci priori
character of many axioms, and of the sciences deduced from
them ; and is so far from considering those axioms to rest on
the evidence of experience, that he declares certain of them to
be true even of Noumena — of the Unconditioned — of which
it is one of the principal aims of his philosophy to prove that
the nature of our faculties debars us from having any know-
ledge. The axioms to which he attributes this exceptional
emancipation from the limits which confine all our other

* Discussions, &c., 2nd ed. p. 624.

320 REASONING.

possibilities of knowledge ; the chinks through which, as he
represents, one ray of light finds its way to us from behind the
curtain which veils from us the mysterious world of Things in
themselves, — are the two principles, which he terms, after the
schoolmen, the Principle of Contradiction, and the Principle
of Excluded Middle : the first, that two contradictory pro-
positions cannot both be true ; the second, that they cannot
both be false. Armed with these logical weapons, we may
boldly face Things in themselves, and tender to them the
double alternative, sure that they must absolutely elect one or
the other side, though we may be for ever precluded from
discovering which. To take his favourite example, we cannot
conceive the infinite divisibility of matter, and we cannot
conceive a minimum, or end to divisibility : yet one or the
other must be true.

As I have hitherto said nothing of the two axioms in
question, those of Contradiction and of Excluded Middle, it
is not unseasonable to consider them here. The former asserts
that an affirmative proposition and the corresponding negative
proposition cannot both be true ; which has generally been
held to be intuitively evident. Sir William Hamilton and the
Germans consider it to be the statement in words of a form or
law of our thinking faculty. Other philosophers, not less
deserving of consideration, deem it to be an identical proposi-
tion ; an assertion involved in the meaning of terms; a mode
of defining Negation, and the word Not.

I am able to go one step with these last. An affirmative
assertion and its negative are not two independent assertions,
connected with each other only as mutually incompatible.
That if the negative be true, the affirmative must be false,
really is a mere identical proposition ; for the negative pro-
position asserts nothing but the falsity of the affirmative, and
has no other sense or meaning whatever. The Principium
Contradictionis should therefore put off the ambitious
phraseology which gives it the air of a fundamental antithesis
pervading nature, and should be enunciated in the simpler
form, that the same proposition cannot at the same time be
false and true. But I can go no farther with the Nominalists ;

THEORIES CONCERNING AXIOMS. 321

for I cannot look upon this last as a merely verbal proposition.
I consider it to be, like other axioms, one of our first and
most familiar generalizations from experience. The original
foundation of it I take to be, that Belief and Disbelief are
two different mental states, excluding one another. This we
know by the simplest observation of our own minds. And if
we carry our observation outwards, we also find that light and
darkness, sound and silence, motion and quiescence, equality
and inequality, preceding and following, succession and
simultaneousness, any positive phenomenon whatever and its
negative, are distinct phenomena, pointedly contrasted, and the
one always absent where the other is present. I consider the
maxim in question to be a generalization from all these
facts.

In like manner as the Principle of Contradiction (that one
of two contradictories must be false) means that an assertion
cannot be both true and false, so the Principle of Excluded
Middle, or that one of two contradictories must be true, means
that an assertion must be either true or false : either the affir-
mative is true, or otherwise the negative is true, which means
that the affirmative is false. I cannot help thinking this
principle a surprising specimen of a so-called necessity of
Thought, since it is not even true, unless with a large qualifi-
cation. A proposition must be either true or false, provided
that the predicate be one which can in any intelligible sense
be attributed to the subject; (and as this is always assumed
to be the case in treatises on logic, the axiom is always laid
down there as of absolute truth). "Abracadabra is a second
intention" is neither true nor false. Between the true and the
false there is a third possibility, the Unmeaning : and this
alternative is fatal to Sir William Hamilton's extension of the
maxim to Noumena. That Matter must either have a minimum
of divisibility or be infinitely divisible, is more than we can
ever know. For in the first place, Matter, in any other than
the phenomenal sense of the term, may not exist: and it will
scarcely be said that a non-entity must be either infinitely or
finitely divisible. In the second place, though matter, con-
sidered as the occult cause of our sensations, do really exist,
VOL. i. 21

REASONING.

yet what we call divisibility may be an attribute only of our
sensations of sight and touch, and not of their uncognizable
cause. Divisibility may not be predicable at all, in any intel-
ligible sense, of Things in themselves, nor therefore of
Matter in itself; and the assumed necessity of being
either infinitely or finitely divisible, may be an inapplicable
alternative.

On this question I am happy to have the full concurrence
of Mr. Herbert Spencer, from whose paper in the Fortnightly
Review I extract the following passage. The germ of an idea
identical with that of Mr. Spencer may be found in the present
chapter, about a page back, but in Mr. Spencer it is not am
undeveloped thought, but a philosophical theory.

" When remembering a certain thing as in a certain place,
the place and the thing are mentally represented together;
while to think of the non-existence of the thing in that place
implies a consciousness in which the place is represented, but
not the thing. Similarly, if instead of thinking of an object
as colourless, we think of its having colour, the change con-
sists in the addition to the concept of an element that was
before absent from it — the object cannot bethought of first as
red and then as not red, without one component of the thought
being totally expelled from the mind by another. The law of
the Excluded Middle, then, is simply a generalization of the
universal experience that some mental states are directly de-
structive of other states. It formulates a certain absolutely
constant law, that the appearance of any positive mode of con-
sciousness cannot o^cur without excluding a correlative negative
mode ; and that the negative mode cannot occur without ex-
cluding the correlative positive mode : the antithesis of posi-
tive and negative being, indeed, merely an expression of this
experience. Hence it follows that if consciousness is not in
one of the two modes it must be in the other." *

* Professor Bain (Logic, \. 16) identifies the Principle of Contradiction
with his Law of Relativity, viz., that " everything that can bethought of, every
affirmation that can be made, has an opposite or counternotion or affirmation ;"
a proposition which is one of the general results of the whole body of human

THEORIES CONCERNING AXIOMS. 323

I must here close this supplementary chapter, and with it
the Second Book. The theory of Induction, in the most com-
prehensive sense of the term, will form the subject of the
Third.

experience. For further considerations respecting the axioms of Contradiction
and Excluded Middle, see the twenty -first chapter of A n Examination of Sir
William Hamilton s Philosophy.

21—2

BOOK III.

OF INDUCTION.

"According to the doctrine now stated, the highest, or rather the only
proper object of physics, is to ascertain those established conjunctions of suc-
cessive events, which constitute the order of the universe ; to record the
phenomena which it exhibits to our observations, or which it discloses to
our experiments ; and to refer these phenomena to their general laws." —
D. STEWABT, Elements of the Philosophy of the Human Mind, voL ii. chap. iv.
sect. 1.

CHAPTER I.

PRELIMINARY OBSERVATIONS ON INDUCTION IN
GENERAL.

§ 1. THE portion of the present inquiry upon which we
are now about to enter, may be considered as the principal,
both from its surpassing in intricacy all the other branches,
and because it relates to a process which has been shown in
the preceding Book to be that in which the investigation of
nature essentially consists. We have found that all Inference,
consequently all Proof, and all discovery of truths not self-
evident, consists of inductions, and the interpretation of induc-
tions : that all our knowledge, not intuitive, comes to us
exclusively from that source. What Induction is, therefore,
and what conditions render it legitimate, cannot but be deemed
the main question of the science of logic — the question which
includes all others. It is, however, one which professed writers
on logic have almost entirely passed over. The generalities of
the subject have not been altogether neglected by metaphysi-
cians; but, for want of sufficient acquaintance with the processes
by which science has actually succeeded in establishing general
truths, their analysis of the inductive operation, even when un-
exceptionable as to correctness, has not been specific enough
to be made the foundation of practical rules, which might be
for induction itself what the rules of the syllogism are for the
interpretation of induction : while those by whom physical
science has been carried to its present state of improvement—-
and who, to arrive at a complete theory of the process, needed
only to generalize, and adapt to all varieties of problems, the
methods which they themselves employed in their habitual
pursuits — never until very lately made any serious attempt to
philosophize on the subject, nor regarded the mode in which

328

INDUCTION.

they arrived at their conclusions as deserving of study, inde-
pendently of the conclusions themselves.

§ 2. For the purposes of the present inquiry, Induction
may be defined, the operation of discovering and proving general
propositions. It is true that (as already shown) the process of
indirectly ascertaining individual facts, is as truly inductive as
that by which we establish general truths. But it is not a
different kind of induction ; it is a form of the very same pro-
cess : since, on the one hand, generals are but collections of
particulars, definite in kind but indefinite in number ; and on
the other hand, whenever the evidence which we derive from
observation of known cases justifies us in drawing an inference
respecting even one unknown case, we should on the same
evidence be justiQed in drawing a similar inference with respect
to a whole class of cases. The inference either does not hold
at all, or it holds in all cases of a certain description ; in all
cases which, in certain definable respects, resemble those we
have observed.

If these remarks are just ; if the principles and rules of in-
ference are the same whether we infer general propositions or
individual facts ; it follows that a complete logic of the sciences
would be also a complete logic of practical business and com-
mon life. Since there is no case of legitimate inference from
experience, in which the conclusion may not legitimately be a
general proposition ; an analysis of the process by which
general truths are arrived at, is virtually an analysis of all in-
duction whatever. Whether we are inquiring into a scientific
principle or into an individual fact, and whether we proceed by
experiment or by ratiocination, every step in the train
of inferences is essentially inductive, and the legitimacy
of the induction depends in both cases on the same con-
ditions.

True it is that in the case of the practical inquirer, who is
endeavouring to ascertain facts not for the purposes of science
but for those of business, such for instance as the advocate or
the judge, the chief difficulty is one in which the principles of
induction will afford him no assistance. It lies not in making

INDUCTION IN GENERAL. 329

his inductions, but in the selection of them ; in choosing from
among all general propositions ascertained to be true, those
which furnish marks by which he may trace whether the given
subject possesses or not the predicate in question. In arguing
a doubtful question of fact before a jury, the general propositions
or principles to which the advocate appeals are mostly, in them-
selves, sufficiently trite, and assented to as soon as stated : his
skill lies in bringing his case under those propositions or prin-
ciples ; in calling to mind such of the known or received maxims
of probability as admit of application to the case in hand, and
selecting from among them those best adapted to his object.
Success is here dependent on natural or acquired sagacity, aided
by knowledge of the particular subject, and of subjects allied
with it. Invention, though it can be cultivated, cannot be re-
duced to rule ; there is no science which will enable a man to
bethink himself of that which will suit his purpose.

But when he has thought of something, science can tell him
whether that which he has thought of will suit his purpose or
not. The inquirer or arguer must be guided by his own know-
ledge and sagacity in the choice of the inductions out of which
he will construct his argument. But the validity of the argu-
ment when constructed, depends on principles and must be
tried by tests which are the same for all descriptions of inquiries,
whether the result be to give A an estate, or to enrich science
with a new general truth. In the one case and in the other,
the senses, or testimony, must decide on the individual facts ;
the rules of the syllogism will determine whether, those facts
being supposed correct, the case really falls within the formulae
of the different inductions under which it has been successively
brought; and finally, the legitimacy of the inductions them-
selves must be decided by other rules, and these it is now our
purpose to investigate. If this third part of the operation be,
in many of the questions of practical life, not the most, but the
least arduous portion of it, we have seen that this is also
the case in some great departments of the field of science ; in
all those which are principally deductive, and most of all in
mathematics ; where the inductions themselves fire few in
number, and so obvious and elementary that they seem to

330 INDUCTION.

stand in no need of the evidence of experience, while to com-
bine them so as to prove a given theorem or solve a problem,
may call for the utmost powers of invention and contrivance
with which our species is gifted.

If the identity of the logical processes which prove parti-
cular facts and those which establish general scientific truths,
required any additional confirmation, it would be sufficient to
consider that in many branches of science, single facts have to
be proved, as well as principles ; facts as completely individual
as any that are debated in a court of justice; but which are
proved in the same manner as the other truths of the science,
and without disturbing in any degree the homogeneity of its
method. A remarkable example of this is afforded by astronomy.
The individual facts on which that science grounds its most im-
portant deductions, such facts as the magnitudes of the bodies
of the solar system, their distances from one another, the figure
of the earth, and its rotation, are scarcely any of them accessible
to our means of direct observation : they are proved indirectly,
by the aid of inductions founded on other facts which we
can more easily reach. For example, the distance of the
moon from the earth was determined by a very circuitous
process. The share which direct observation had in the
work consisted in ascertaining, at one and the same instant,
the zenith distances of the moon, as seen from two points
very remote from one another on the earth's surface. The
ascertainment of these angular distances ascertained their sup-
plements ; and since the angle at the earth's centre subtended
by the distance between the two places of observation was de-
ducible by spherical trigonometry from the latitude and longi-
tude of those places, the angle at the moon subtended by the
same line became the fourth angle of a quadrilateral of which
the other three angles were known. The four angles being thus
ascertained, and two sides of the quadrilateral being radii of the
earth; the two remaining sides and the diagonal, or in other
words, the moon's distance from the two places of observation
and from the centre of the earth, could be ascertained, at least
in terms of the earth's radius, from elementary theorems of
geometry. At each step in this demonstration a new induction

INDUCTION IN GENERAL. 331

is taken in, represented in the aggregate of its results by a
genei-al proposition.

Not only is the process by which an individual astrono-
mical fact was thus ascertained, exactly similar to those by
which the same science establishes its general truths, but also
(as we have shown to be the case in all legitimate reasoning)
a general proposition might have been concluded instead of a
single fact. In strictness, indeed, the result of the reasoning
is a general proposition ; a theorem respecting the distance,
not of the moon in particular, but of any inaccessible object;
showing in what relation that distance stands to certain other
quantities. And although the moon is almost the only heavenly
body the distance of which from the earth can really be thus
ascertained, this is merely owing to the accidental circum-
stances of the other heavenly bodies, which render them inca-
pable of affording such data as the application of the theorem
requires ; for the theorem itself is as true of them as it is of
the moon.*

* Dr. Whewell thinks it improper to apply the term Induction to any
operation not terminating in the establishment of a general truth. Induction,
he says (Philosophy of Discovery, p. 245), "is not the same thing as experience
and observation. Induction is experience or observation consciously looked at
in a general form. This consciousness and generality are necessary parts of
that knowledge which is science." And he objects (p. 241) to the mode in
which the word Induction, is employed in this work, as an undue extension of
that term "not only to the cases in which the general induction is consciously
applied to a particular instance, but to the cases in which the particular instance
is dealt with by means of experience in that rude sense in which experience can
be asserted of brutes, and in which of course we can in no way imagine that the
law is possessed or understood as a general proposition." This use of the term
he deems a "confusion of knowledge with practical tendencies."

I disclaim, as strongly as Dr. Whewell can do, the application of such terms
as induction, inference, or reasoning, to operations performed by mere instinct,
that is, from an animal impulse, without the exertion of any intelligence. But
I perceive no ground for confining the use of those terms to cases in which the
inference is drawn in the forms and with the precautions required by scientific
propriety. To the idea of Science, an express recognition and distinct appre-
hension of general laws as such, is essential : but nine-tenths of the conclusions
drawn from experience in the course of practical life, are drawn without any
such recognition : they are direct inferences from known cases, to a case sup-
posed to be similar. I have endeavoured to show that this is not only as legi-
timate an operation, but substantially the same operation, as that of ascending

•332 INDUCTION.

We shall fall into no error, then, if in treating of Induction,
we limit our attention to the establishment of general proposi-
tions. The principles and rules of Induction as directed to this
end, are the principles and rules of all Induction ; and the logic
of Science is the universal Logic, applicable to all inquiries in
which man can angage.

from known cases to a general proposition ; except that the latter process has
one great security for correctness which the former does not possess. In science,
the inference must necessarily pass through the intermediate stage of a general
proposition, because Science wants its conclusions for record, and not for in-
stantaneous use. But the inferences drawn for the guidance of practical affairs,
by persons who would often be quite incapable of expressing in unexceptionable
terms the corresponding generalizations, may and frequently do exhibit intel-
lectual powers quite equal to any which have ever been displayed in science :
and if these inferences are not inductive, what are they ? The limitation im-
posed on the term by Dr. Whewell seems perfectly arbitrary; neither justified
by any fundamental distinction between what he includes and what he desires
to exclude, nor sanctioned by usage, at least from the time of Reid and Stewart,
the principal legislators (as far as the English language is concerned) of modem
metaphysical terminology.

CHAPTER II.

OF INDUCTIONS IMPROPERLY SO CALLED.

§ 1. INDUCTION, then, is that operation of the mind, by
which we infer that what we know to be true in a particular
case or cases, will be true in all cases which resemble the former
in certain assignable respects. In other words, Induction is
the process by which we conclude that what is true of certain
individuals of a class is true of the whole class, or that what
is true at certain times will be true in similar circumstances at
all times.

This definition excludes from the meaning of the term In-
duction, various logical operations, to which it is not unusual
to apply that name.

Induction, as above defined, is a process of inference ; it
proceeds from the known to the unknown ; and any operation
involving no inference, any process in which what seems the
conclusion is no wider than the premises from which it is
drawn, does not fall within the meaning of the term. Yet in
the common books of Logic we find this laid down as the
most perfect, indeed the only quite perfect, form of induction.
In those books, every process which sets out from a less
general and terminates in a more general expression, — which
admits of being stated in the form, " This and that A are B,
therefore every A is B," — is called an induction, whether any-
thing be really concluded or not : and the induction is asserted
not to be perfect, unless every single individual of the class
A is included in the antecedent, or premise : that is, unless
what we affirm of the class has already been ascertained to be
true of every individual in it, so that the nominal conclusion
is not really a conclusion, but a mere reassertion of the pre-
mises. If we were to say, All the planets shine by the sun's
light, from observation of each separate planet, or All the

334 INDUCTION.

Apostles were Jews, because this is true of Peter, Paul, John,
and every other apostle, — these, and such as these, would, in
the phraseology in question, be called perfect, and the only
perfect, Inductions. This, however, is a totally different kind
of induction from ours ; it is not an inference from facts known
to facts unknown, but a mere short-hand registration of facts
known. The two simulated arguments which we have quoted,
are not generalizations ; the propositions purporting to be
conclusions from them, are not really general propositions.
A general proposition is one in which the predicate is affirmed
or denied of an unlimited number of individuals ; namely, all,
whether few or many, existing or capable of existing, which
possess the properties connoted by the subject of the proposi-
tion. " All men are mortal" does not mean all now living,
but all men past, present, and to come. When the significa-
tion of the term is limited so as to render it a name not for
any and every individual falling under a certain general de-
scription, but only for each of a number of individuals desig-
nated as such, and as it were counted off individually, the
proposition, though it may be general in its language, is no
general proposition, but merely that number of singular pro-
positions, written in an abridged character. The operation
may be very useful, as most forms of abridged notation are ;
but it is no part of the investigation of truth, though often
bearing an important part in the preparation of the materials
for that investigation.

As we may sum up a definite number of singular proposi-
tions in one proposition, which will be apparently, but not
really, general, so we may sum up a definite number of general
propositions in one proposition, which will be apparently, but
not really, more general. If by a separate induction applied
to every distinct species of animals, it has been established
that each possesses a nervous system, and we affirm thereupon
that all animals have a nervous system ; this looks like a
generalization, though as the conclusion merely affirms of all
what has already been affirmed of each, it seems to tell us
nothing but what we knew before. A distinction however
must be made. If in concluding that all animals have a

INDUCTIONS IMPROPERLY SO CALLED. 335

nervous system, we mean the same thing and no more as if
we had said " all known animals," the proposition . is not
general, and the process by which it is arrived at is not in-
duction. But if our meaning is that the observations made
of the various species of animals have discovered to us a law
of animal nature, and that we are in a condition to say that a
nervous system will be found even in animals yet undiscovered,
this indeed is an induction ; but in this case the general pro-
position contains more than the sum of the special proposi-
tions from which it is inferred. The distinction is still more
forcibly brought out when we consider, that if this real gene-
ralization be legitimate at all, its legitimacy probably does not
require that we should have examined without exception every
known species. It is the number and nature of the instances,
and not their being the whole of those which happen to be
known, that makes them sufficient evidence to prove a general
law : while the more limited assertion, which stops at all
known animals, cannot be made unless we have rigorously
verified it in every species. In like manner (to return to a
former example) we might have inferred, not that all the
planets, but that all planets, shine by reflected light: the
former is no induction ; the latter is an induction, and a bad
one, being disproved by the case of double stars — self-luminous
bodies which are properly planets, since they revolve round a
centre.

§ 2. There are several processes used in mathematics
which require to be distinguished from Induction, being not
unfrequently called by that name, and being so far similar to
Induction properly so called, that the propositions they lead
to are really general propositions. For example, when we
have proved with respect to the circle, that a straight line
cannot meet it in more than two points, and when the same
thing has been successively proved of the ellipse, the parabola,
and the hyperbola, it may be laid down as an universal pro-
perty of the sections of the cone. The distinction drawn in
the two previous examples can have no place here, there being
no difference between all known sections of the cone and all

336 INDUCTION.

sections, since a cone demonstrably cannot be intersected by
a plane except in one of these four lines. It would be diffi-
cult, therefore, to refuse to the proposition arrived at, the name
of a generalization, since there is no room for any generaliza-
tion beyond it. But there is no induction, because there is no
inference : the conclusion is a mere summing up of what was
asserted in the various propositions from which it is drawn.
A case somewhat, though not altogether, similar, is the proof
of a geometrical theorem by means of a diagram. Whether
the diagram be on paper or only in the imagination, the de-
monstration (as formerly observed*) does not prove directly the
general theorem ; it proves only that the conclusion, which
the theorem asserts generally, is true of the particular triangle
or circle exhibited in the diagram ; but since we perceive that
in the same way in which we have proved it of that circle, it
might also be proved of any other circle, we gather up into
one general expression all the singular propositions susceptible
of being thus proved, and embody them in an universal pro-
position. Having shown that the three angles of the triangle
ABC are together equal to two right angles, we conclude that
this is true of every other triangle, not because it is true of
ABC, but for the same reason which proved it to be true
of ABC. If this were to be called Induction, an appropriate
name for it would be, induction by parity of reasoning. But
the term cannot properly belong to it; the characteristic
quality of Induction is wanting, since the truth obtained,
though really general, is not believed on the evidence of par-
ticular instances. We do not conclude that all triangles have
the property because some triangles have, but from the ulterior
demonstrative evidence which was the ground of our conviction
in the particular instances.

There are nevertheless, in mathematics, some examples of
so-called Induction, in which the conclusion does bear the
appearance of a generalization grounded on some of the par-
ticular cases included in it. A mathematician, when he has
calculated a sufficient number of the terms of an algebraical

* Supra, p. 219.

INDUCTIONS IMPROPERLY SO CALLED. 337

or arithmetical series to have ascertained what is called the law
of the series, does not hesitate to fill up any number of the
succeeding terms without repeating the calculations. But I
apprehend he only does so when it is apparent from a priori
considerations (which might he exhibited in the form of
demonstration) that the mode of formation of the subsequent
terms, each from that which preceded it, must be similar to
the formation of the terms which have been already calculated.
And when the attempt has been hazarded without the sanction
of such general considerations, there are instances on record in
which it has led to false results.

It is said that Newton discovered the binomial theorem by
induction ; by raising a binomial successively to a certain
number of powers, and comparing those powers with one
another until he detected the relation in which the algebraic
formula of each power stands to the exponent of that power,
and to the two terms of the binomial. The fact is not im-
probable : but a mathematician like Newton, who seemed to
arrive per saltum at principles and conclusions that ordinary
mathematicians only reached by a succession of steps, certainly
could not have performed the comparison in question without
being led by it to the a priori ground of the law ; since any
one who understands sufficiently the nature of multiplication
to venture upon multiplying several lines of symbols at one
operation, cannot but perceive that in raising a binomial to a
power, the coefficients must depend on the laws of permuta-
tion and combination : and as soon as this is recognised, the
theorem is demonstrated. Indeed, when once it was seen that
the law prevailed in a few of the lower powers, its identity
with the law of permutation would at once suggest the con-
siderations which prove it to obtain universally. Even,
therefore, such cases as these, are but examples of what I
have called Induction by parity of reasoning, that is, not really
Induction, because not involving inference of a general propo-
sition from particular instances.

§ 3. There remains a third improper use of the term
Induction, which it is of real importance to clear up, because
VOL. i. 22

3'38 INDUCTION.

the theory of Induction has heen, in no ordinary degree, con-
fused by it, and because the confusion is exemplified in the
most recent and elaborate treatise on the inductive philosophy
which exists in our language. The error in question is that
of confounding a mere description, by general terms, of a set
of observed phenomena, with an induction from them.

Suppose that a phenomenon consists of parts, and that
these parts are only capable of being observed separately, and
as it were piecemeal. When the observations have been made,
there is a convenience (amounting for many purposes to a
necessity) in obtaining a representation of the phenomenon as
a whole, by combining, or as we may say, piecing these
detached fragments together. A navigator sailing in the
midst of the ocean discovers land : he cannot at first, or
by any one observation, determine whether it is a continent
or an island ; but he coasts along it, and after a few days finds
himself to have sailed completely round it : he then pronounces
it an island. Now there was no particular time or place of
observation at which he could perceive that this land was
entirely surrounded by water : he ascertained the fact by a
succession of partial observations, and then selected a general
expression which summed up in two or three words the
whole of what he so observed. But is there anything of the
nature of an induction in this process ? Did he infer anything
that had not been observed, from something else which had ?
Certainly not. He had observed the whole of what the pro-
position asserts. That the land in question is an island, is
not an inference from the partial facts which the navigator saw
in the course of his circumnavigation ; it is the facts them-
selves ; it is a summary of those facts ; the description of a
complex fact, to which those simpler ones are as the parts of
a whole.

Now there is, I conceive, no difference in kind between this
simple operation, and that by which Kepler ascertained the
nature of the planetary orbits : and Kepler's operation, all at
least that was characteristic in it, was not more an inductive
act than that of our supposed navigator.

The object of Kepler was to determine the real path de-

INDUCTIONS IMPROPERLY SO CALLED. 339

scribed by each of the planets, or let us say by the planet Mars
(since it was of that body that he first established the two of
his three laws which did not require a comparison of planets).
To do this there was no other mode than that of direct obser-
vation : and all which observation could do was to ascertain a
great number of the successive places of the planet ; or rather,
of its apparent places. That the planet occupied successively
all these positions, or at all events, positions which produced
the same impressions on the eye, and that it passed from one
of these to another insensibly, and without any apparent
breach of continuity ; thus much the senses, with the aid of
the proper instruments, could ascertain. What Kepler did
more than this, was to find what sort of a curve these different
points would make, supposing them to be all joined together.
He expressed the whole series of the observed places of Mars
by what Dr. Whewell calls the general conception of an
ellipse. This operation was far from being as easy as that of
the navigator who expressed the series of his observations on
successive points of the coast by the general conception of an
island. But it is the very same sort of operation ; and if the
one is not an induction but a description, this must also be
true of the other.

The only real induction concerned in the case, consisted in
inferring that because the observed places of Mars were cor-
rectly represented by points in an imaginary ellipse, therefore
Mars would continue to revolve in that same ellipse; and in
concluding (before the gap had been filled up by further obser-
vations) that the positions of the planet during the time which
intervened between two observations, must have coincided with
the intermediate points of the curve. For these were facts
which had not been directly observed. They were inferences
from the observations; facts inferred, as distinguished from
facts seen. But these inferences were so far from being a part
of Kepler's philosophical operation, that they had been drawn
long before he was born. Astronomers had long known that
the planets periodically returned to the same places. When
this had been ascertained, there was no induction left for
Kepler to make, nor did he make any further induction-

22—2

340 INDUCTION.

He merely applied his new conception to the facts inferred,
as he did to the facts observed. Knowing already that
the planets continued to move in the same paths ; when he
found that an ellipse correctly represented the past path, he
knew that it would represent the future path. In finding a
compendious expression for the one set of facts, he found
one for the other : hut he found the expression only, not the in-
ference ; nor did he (which is the true test of a general truth)
add anything to the power of prediction already possessed.

§ 4. The descriptive operation which enables a number of
details to be summed up in a single proposition, Dr. Whewell,
by an aptly chosen expression, has termed the Colligation of
Facts. In most of his observations concerning that mental
process I fully agree, and would gladly transfer all that por-
tion of his book into my own pages. I only think him mis-
taken in setting up this kind of operation, which according to
the old and received meaning of the term, is not induction at
all, as the type of induction generally ; and laying down,
throughout his work, as principles of induction, the principles
of mere colligation.

Dr. Whewell maintains that the general proposition which
binds together the particular facts, and makes them, as it were,
one fact, is not the mere sum of those facts, hut something
more, since there is introduced a conception of the mind, which
did not exist in the facts themselves. " The particular facts,"
says he,* " are not merely brought together, but there is a
new element added to the combination by the very act of
thought by which they are combined. . . . When the
Greeks, after long observing the motions of the planets, saw
that these motions might be rightly considered as produced by
the motion of one wheel revolving in the inside of another
wheel, these wheels were creations of their minds, added to the
facts which they perceived by sense. And even if the wheels
were no longer supposed to be material, but were reduced
to mere geometrical spheres or circles, they were not the

* Novum Organum Renovatum, pp. 72, 73.

INDUCTIONS IMPROPERLY SO CALLED. 341

less products of the mind alone, — something additional to the
facts observed. The same is the case in all other discoveries.
The facts are known, but they are insulated and unconnected,
till the discoverer supplies from his own store a principle of
connexion. The pearls are there, but they will not hang to-
gether till some one provides the string."

Let me first remark that Dr. Whewell, in this passage,
blends together, indiscriminately, examples of both the processes
which I am endeavouring to distinguish from one another.
When the Greeks abandoned the supposition that the plane-
tary motions were produced by the revolution of material
wheels, and fell back upon the idea of " mere geometrical
spheres or circles," there was more in this change of opinion
than the mere substitution of an ideal curve for a physical
one. There was the abandonment of a theory, and the replace-
ment of it by a mere description. No one would think of
calling the doctrine of material wheels a mere description.
That doctrine was an attempt to point out the force by which
the planets were acted upon, and compelled to move in their
orbits. But when, by a great step in philosophy, the mate-
riality of the wheels was discarded, and the geometrical forms
alone retained, the attempt to account for the motions was
given up, and what was left of the theory was a mere descrip-
tion of the orbits. The assertion that the planets were carried
round by wheels revolving in the inside of other wheels, gave
place to the proposition, that they moved in the same lines
which would be traced by bodies so carried : which was a mere
mode of representing the sum of the observed facts ; as Kep-
ler's was another and a better mode of representing the same
observations.

It is true that for these simply descriptive operations, as
well as for the erroneous inductive one, a conception of the
mind was required. The conception of an ellipse must have
presented itself to Kepler's mind, before he could identify the
planetary orbits with it. According to Dr. Whewell. the con-
ception was something added to the facts. He expresses him-
self as if Kepler had put something into the facts by his mode
of conceiving them. But Kepler did no such thing. The

342 INDUCTION.

ellipse was in the facts before Kepler recognised it ; just as the
island was an island before it had been sailed round. Kepler
did not put what he had conceived into the facts, but saiu it iu
them. A conception implies, and corresponds to, something
conceived : and though the conception itself is not in the facts,
but in our mind, yet if it is to convey any knowledge relating
to them, it must be a conception of something which really is
in the facts, some property which they actually possess, and
which they would manifest to our senses, if our senses were
able to take cognizance of it. If, for instance, the planet left
behind it in space a visible track, and if the observer were in a
fixed position at such a distance from the plane of the orbit
as would enable him to see the whole of it at once, he would
see it to be an ellipse; and if gifted with appropriate instru-
ments and powers of locomotion, he could prove it to be such
by measuring its different dimensions. Nay, further: if the
track were visible, and he were so placed that he could see all
parts of it in succession, but not all of them at once, he might
be able, by piecing together his successive observations, to dis-
cover both that it was an ellipse and that the planet moved in
it. The case would then exactly resemble that of the naviga-
tor who discovers the land to be an island by sailing round it.
If the path was visible, no one I think would dispute that to
identify it with an ellipse is to describe it : and I cannot see
why any difference should be made by its not being directly
an object of sense, when every point in it is as exactly ascer-
tained as if it were so.

Subject to the indispensable condition which has just beeu
stated, I do not conceive that the part which conceptions
have in the operation of studying facts, has ever been
overlooked or undervalued. No one ever disputed that in
order to reason about anything we must have a conception
of it ; or that when we include a multitude of things under a
general expression, there is implied in the expression a
conception of something common to those things. But it
by no means follows that the conception is necessarily pre-
existent, or constructed by the mind out of its own materials.
If the facts are rightly classed under the conception, it is

INDUCTIONS IMPROPERLY SO CALLED. 343

because there is in the facts themselves something of which
the conception is itself a copy ; and which if we cannot
directly perceive, it is because of the limited power of our
organs, and not because the thing itself is not there. The
conception itself is often obtained by abstraction from the
very facts which, in Dr. Whewell's language, it is afterwards
called in to connect. This he himself admits, when he ob-
serves, (which he does on several occasions,) how great a
service would be rendered to the science of physiology by the
philosopher " who should establish a precise, tenable, and con-
sistent conception of life."* Such a conception can only be
abstracted from the phenomena of life itself ; from the very
facts which it is put in requisition to connect. In other cases,
no doubt, instead of collecting the conception from the very
phenomena which we are attempting to colligate, we select it
from among those which have been previously collected by
abstraction from other facts. In the instance of Kepler's laws,
the latter was the case. The facts being out of the reach of
being observed, in any such manner as would have enabled the
senses to identify directly the path of the planet, the concep-
tion requisite for framing a general description of that path
could not be collected by abstraction from the observations
themselves ; the mind had to supply hypotheticaiiy, from
among the conceptions it had obtained from other portions
of its experience, some one which would correctly represent
the series of the observed facts. It had to frame a supposition
respecting the general course of the phenomenon, and ask
itself, If this be the general description, what will the details
be ? and then compare these with the details actually observed.
If they agreed, the hypothesis would serve for a description of
the phenomenon : if not, it was necessarily abandoned, and
another tried. It is such a case as this which gives rise to the
doctrine that the mind, in framing the descriptions, adds
something of its own which it does not find in the facts.

Yet it is a fact surely, that the planet does describe an
ellipse ; and a fact which we could see, if we had adequate
visual organs and a suitable position. Not having these

* Novum Organum Renovatum, p. 32.

344 INDUCTION.

advantages, but possessing the conception of an ellipse, or (to
express the meaning in less technical language) knowing what
an ellipse was, Kepler tried whether the observed places of
the planet were consistent with such a path. He found they
were so; and he, consequently, asserted as a fact that the
planet moved in an ellipse. But this fact, which Kepler did
not add to, but found in, the motions of the planet, namely,
that it occupied in succession the various points in the circum-
ference of a given ellipse, was the very fact, the separate parts
of which had been separately observed ; it was the sum of the
different observations.

Having stated this fundamental difference between my
opinion and that of Dr. Whewell, I must add, that his account
of the manner in which a conception is selected, suitable to
express the facts, appears to me perfectly just. The experience
of all thinkers will, I believe, testify that the process is
tentative ; that it consists of a succession of guesses ; many
being rejected, until one at last occurs fit to be chosen. We
know from Kepler himself that before hitting upon the " con-
ception " of an ellipse, he tried nineteen other imaginary paths,
which, finding them inconsistent with the observations, he was
obliged to reject. But as Dr. Whewell truly says, the suc-
cessful hypothesis, though a guess, ought generally to be
called, not a lucky, but a skilful guess. The guesses which
serve to give mental unity and wholeness to a chaos of
scattered particulars, are accidents which rarely occur to any
minds but those abounding in knowledge and disciplined in
intellectual combinations.

How far this tentative method, so indispensable as a means
to the colligation of facts for purposes of description, admits
of application to Induction itself, and what functions belong
to it in that department, will be considered in the chapter of
the present Book which relates to Hypotheses. On the pre-
sent occasion we have chiefly to distinguish this process of
Colligation from Induction properly so called ; and that the
distinction may be made clearer, it is well to advert to a
curious and interesting remark, which is as strikingly true of
ithe former operation, as it appears to me unequivocally false
of the latter.

INDUCTIONS IMPROPERLY SO CALLED. 345

In different stages of the progress of knowledge, philoso-
phers have employed, for the colligation of the same order of
facts, different conceptions. The early rude observations of
the heavenly bodies, in which minute precision was neither
attained nor sought, presented nothing inconsistent with the
representation of the path of a planet as an exact circle, having
the earth for its centre. As observations increased in accuracy,
facts were disclosed which were not reconcileable with this
simple supposition : for the colligation of those additional
facts, the supposition was varied ; and varied again and again
as facts became more numerous and precise. The earth was
removed from the centre to some other point within the circle ;
the planet was supposed to revolve in a smaller circle called an
epicycle, round an imaginary point which revolved in a circle
round the earth : in proportion as observation elicited fresh
facts contradictory to these representations, other epicycles and
other excentrics were added, producing additional complica-
tion ; until at last Kepler swept all these circles away, and
substituted the conception of an exact ellipse. Even this is
found not to represent with complete correctness the accurate
observations of the present day, which disclose many slight
deviations from an orbit exactly elliptical. Now Dr. Whewell
has remarked that these successive general expressions, though
apparently so conflicting, were all correct : they all answered
the purpose of colligation ; they all enabled the mind to repre-
sent to itself with facility, and by a simultaneous glance, the
whole body of facts at the time ascertained : each in its turn
served as a correct description of the phenomena, so far as the
senses had up to that time taken cognizance of them. If a
necessity afterwards arose for discarding one of these general
descriptions of the planet's orbit, and framing a different
imaginary line, by which to express the series of observed
positions, it was because a number of new facts had now been
added, which it was necessary to combine with the old facts
into one general description. But this did not affect the
correctness of the former expression, considered as a general
statement of the only facts which it was intended to represent.
And so true is this, that, as is well remarked by M. Comte, these

346 INDUCTION.

ancient generalizations, even the rudest and most imperfect of
them, that of uniform movement in a circle, are so far from
being entirely false, that they are even now habitually em-
ployed by astronomers when only a rough approximation to
correctness is required. " L'astronomie moderne, en de-
trnisant sans retour les hypotheses primitives, envisagees
comme lois reelles du monde, a soigneusement maintenu leur
valeur positive et permanente, la propriete de represeuter com-
modement les phenomenes quand il s'agit d'une premiere
ebauche. Nos ressources a cet egard sont meme bien plus
etendues, precisement a cause que nous ne nous faisons aucune
illusion sur la realite des hypotheses ; ce qui nous permet
d'employer sans scrupule, en chaque cas, celle que nousjugeons
la plus avantageuse."*

Dr. Whewell's remark, therefore, is philosophically correct.
Successive expressions for the colligation of observed facts, or
in other words, successive descriptions of a phenomenon as a
whole, which has been observed only in parts, may, though
conflicting, be all correct as far as they go. But it would
surely be absurd to assert this of conflicting inductions.

The scientific study of facts may be undertaken for three
different purposes : the simple description of the facts ; their
explanation ; or their prediction : meaning by prediction,
the determination of the conditions under which similar facts
may be expected again to occur. To the first of these three
operations the name of Induction does not properly belong :
to the other two it does. Now, Dr. Whewell's observation is
true of the first alone. Considered as a mere description, the
circular theory of the heavenly motions represents perfectly
well their general features : and by adding epicycles without
limit, those motions, even as now known to us, might be ex-
pressed with any degree of accuracy that might be required.
The elliptical theory, as a mere description, would have a great
advantage in point of simplicity, and in the consequent facility
of conceiving it and reasoning about it; but it would not
really be more true than the other. Different descriptions,

* Gours de Philosophic Positive, vol. ii. p. 202.

INDUCTIONS IMPROPERLY SO CALLED. 31-7

therefore, may be all true : but not, surely, different explana-
tions. The doctrine that the heavenly bodies moved by a
virtue inherent in their celestial nature ; the doctrine that they
were moved by impact, (which led to the hypothesis of vor-
tices as the only impelling force capable of whirling bodies in
circles,) and the Newtonian doctrine, that they are moved by
the composition of a centripetal with an original projectile
force ; all these are explanations, collected by real induction
from supposed parallel cases ; and they were all successively
received by philosophers, as scientific truths on the subject of
the heavenly bodies. Can it be said of these, as was said of
the different descriptions, that they are all true as far as they
go ? Is it not clear that only one can be true in any degree,
and the other two must be altogether false? So much for
explanations : let us now compare different predictions : the
first, that eclipses will occur when one planet or satellite is so
situated as to cast its shadow upon another ; the second, that
they will occur when some great calamity is impending over
mankind. Do these two doctrines only differ in the degree
of their truth, as expressing real facts with unequal degrees of
accuracy ? Assuredly the one is true, and the other absolutely
false.*

* Dr. Whewell, in his reply, contests the distinction here drawn, and main-
tains, that not only different descriptions, but different explanations of a
phenomenon, may all be true. Of the three theories respecting the motions of
the heavenly bodies, he says (Philosophy of Discovery, p. 231) : " Undoubtedly
all these explanations may be true and consistent with each other, and would
be so if each had been followed out so as to show in what manner it could be
made consistent with the facts. And this was, in reality, in a great measure
done. The doctrine that the heavenly bodies were moved by vortices was
successfully modified, so that it came to coincide in its results with the doctrine

of an inverse-quadratic centripetal force When this point was reached,

the vortex was merely a machinery, well or ill devised, for producing such a
centripetal force, and therefore did not contradict the doctrine of a centripetal
force. Newton himself does not appear to have been averse to explaining
gravity by impulse. So little is it true that if one theory be true the other
must be false. The attempt to explain gravity by the impulse of streams of
particles flowing through the universe in all directions, which I have men-
tioned in the Philosophy, is so far from being inconsistent with the Newtonian
theory, that it is founded entirely upon it. And even with regard to the
doctrine, that the heavenly bodies move by an inherent virtue; if this doctrine

348

INDUCTION.

In every way, therefore, it is evident that to explain in-
duction as the colligation of facts by means of appropriate
conceptions, that is, conceptions which will really express them,
is to confound mere description of the observed facts with in-
ference from those facts, and ascribe to the latter what is a
characteristic property of the former.

had been maintained in any such way that it was brought to agree with the
facts, the inherent virtue must have had its laws determined ; and then it
would have been found that the virtue had a reference to the central body ; and
so, the ' inherent virtue ' must have coincided in its effect with the Newtonian
force ; and then, the two explanations would agree, except so far as the word
'inherent' was concerned. And if such a part of an earlier theory as this
word inherent indicates, is found to be untenable, it is of course rejected in the
transition to later and more exact theories, in Inductions of this kind, as well
as in what Mr. Mill calls Descriptions. There is, therefore, still no validity
discoverable in the distinction which Mr. Mill attempts to draw between
descriptions like Kepler's law of elliptical orbits, and other examples of
induction."

If the doctrine of vortices had meant, not that vortices existed, but only
that the planets moved in the same manner as if they had been whirled by
vortices ; if the hypothesis had been merely a mode of representing the facts,
not an attempt to account for them ; if, in short, it bad been only a Descrip-
tion ; it would, no doubt, have been reconcileable with the Newtonian theory.
The vortices, however, were not a mere aid to conceiving the motions of the
planets, but a supposed physical agent, actively impelling them ; a material fact,
which might be true or not true, but could not be both true and not true.
According to Descartes' theory it was true, according to Newton's it was not
true. Dr. Whewell probably means that since the phrases, centripetal and
projectile force, do not declare the nature but only the direction of the forces,
the Newtonian theory does not absolutely contradict any hypothesis which may
be framed respecting the mode of their production. The Newtonian theory,
regarded as a mere description of the planetary motions, does not ; but the
Newtonian theory as an explanation of them does. For in what does the
explanation consist ? In ascribing those motions to a general law which obtains
between all particles of matter, and in identifying this with the law by which
bodies fall to the ground. If the planets are kept in their orbits by a force
which draws the particles composing them towards every other particle of
matter in the solar system, they are not kept in those orbits by the impulsive
force of certain streams of matter which whirl them round. The one
explanation absolutely excludes the other. Either the planets are not moved
by vortices, or they do not move by a law common to all matter. It is impos-
sible that both opinions can be true. As well might it be said that there is no
contradiction between the assertions, that a man died because somebody killed
him, and that he died a natural death.

So, again, the theory that the planets move by a virtue inherent in their

INDUCTIONS IMPROPERLY SO CALLED. 349

There is, however, between Colligation and Induction, a
real correlation, which it is important to conceive correctly.
Colligation is not always induction ; hut induction is always
colligation. The assertion that the planets move in ellipses,
was but a mode of representing observed facts ; it was but a
colligation ; while the assertion that they are drawn, or tend,

celestial nature, is incompatible with either of the two others : either that of
their being moved by vortices, or that which regards them as moving by a
property which they have in common with the earth and all terrestrial bodies.
Dr. Whewell says that the theory of an inherent virtue agrees with Newton's
when the word inherent is left out, which of course it would be (he says) if
"found to be untenable." But leave that out, and where is the theory ? The
word inherent is the theoiy. When that is omitted, there remains nothing ex-
cept that the heavenly bodies move " by a virtue," i.e. by a power of some sort ;
or by virtue of their celestial nature, which directly contradicts the doctrine
that terrestrial bodies fall by the same law.

If Dr. Whewell is not yet satisfied, any other subject will serve equally well
to test his doctrine. He will hardly say that there is no contradiction between
the emission theory and the undulatory theory of light ; or that there can be
both one and two electricities ; or that the hypothesis of the production of
the higher organic forms by development from the lower, and the supposition
of separate and successive acts of creation, are quite reconcileable ; or that the
theory that volcanoes are fed from a central fire, and the doctrines which
ascribe them to chemical action at a comparatively small depth below the earth's
surface, are consistent with one another, and all true as far as they go.

If different explanations of the same fact cannot both be true, still less,
surely, can different predictions. Dr. Whewell quarrels (on what ground it is
not necessary here to consider) with the example I had chosen on this point,
and thinks an objection to an illustration a sufficient answer to a theory.
Examples not liable to his objection are easily found, if the proposition that
conflicting predictions cannot both be true, can be made clearer by any examples.
Suppose the phenomenon to be a newly-discovered comet, and that one astro-
nomer predicts its return once in every 300 years — another once in every 400 :
can they both be right ? When Columbus predicted that by sailing constantly
westward he should in time return to the point from which he set out, while
others asserted that he could never do so except by turning back, were both he
and his opponents true prophets ? Were the predictions which foretold the
wonders of railways and steamships, and those which averred that the Atlantic-
could never be crossed by steam navigation, nor a railway train propelled ten
miles an hour, both (in Dr. Whewell's words) " true, and consistent with one
another " ?

Dr. Whewell sees no distinction between holding contradictory opinions o
a question of fact, and merely employing different analogies to facilitate the
conception of the same fact. The case of different Inductions belongs to the
former class, that of different Descriptions to the latter.

350 INDUCTION.

towards the sun, was the statement of a new fact, inferred
by induction. But the induction, once made, accomplishes
the purposes of colligation likewise. It brings the same
facts, which Kepler had connected by his conception of an
ellipse, under the additional conception of bodies acted upon
by a central force, and serves therefore as a new bond of
connexion for those facts ; a new principle for their classifi-
cation.

Further, the descriptions which are improperly confounded
with induction, are nevertheless a necessary preparation for
induction ; no less necessary than correct observation of the
facts themselves. Without the previous colligation of detached
observations by means of one general conception, we could
never have obtained any basis for an induction, except in the
case of phenomena of very limited compass. We should not be
able to affirm any predicates at all, of a subject incapable of
being observed otherwise than piecemeal : much less could we
extend those predicates by induction to other similar subjects.
Induction, therefore, always presupposes, not only that the
necessary observations are made with the necessary accuracy,
but also that the results of these observations are, so far as
practicable, connected together by general descriptions, en-
abling the mind to represent to itself as wholes whatever
phenomena are capable of being so represented.

§ 5. Dr. Whewell has replied at some length to the pre-
ceding observations, re-stating his opinions, but without (as
far as I can perceive) adding anything material to his former
arguments. Since, however, mine have not had the good for-
tune to make any impression upon him, I will subjoin a few re-
marks, tending to show more clearly in what our difference of
opinion consists, as well as, in some measure, to account
for it.

Nearly all the definitions of induction, by writers of autho-
rity, make it consist in drawing inferences from known cases
to unknown ; affirming of a class, a predicate which has been
found true of some cases belonging to the class ; concluding
because some things have a certain property, that other things

INDUCTIONS IMPROPERLY SO CALLED. J351

which resemble them have the same property — or because a
thing has manifested a property at a certain time, that it has
and will have that property at other times.

It will scarcely be contended that Kepler's operation was
an Induction in this sense of the term. The statement, that
Mars moves in an elliptical orbit, was no generalization from
individual cases to a class of cases. Neither was it an exten-
sion to all time, of what had been found true at some particu-
lar time. The whole amount of generalization which the case
admitted of, was already completed, or might have been so.
Long before the elliptic theory was thought of, it had been
ascertained that the planets returned periodically to the same
apparent places ; the series of these places was, or might have
been, completely determined, and the apparent course of each
planet marked out on the celestial globe in an uninterrupted
line. Kepler did not extend an observed truth to other cases
than those in which it had been observed : he did not widen
the subject of the proposition which expressed the observed
facts. The alteration he made was in the predicate. Instead
of saying, the successive places of Mars are so and so, he
summed them up in the statement, that the successive places
of Mars are points in an ellipse. It is true, this statement, as
Dr. Whewell says, was not the sum of the observations merely;
it was the sum of the observations seen under a new point of
view.* But it was not the sum of more than the observations,
as a real induction is. It took in no cases but those which
had been actually observed, or which could have been inferred
from the observations before the new point of view presented
itself. There was not that transition from known cases to
unknown, which constitutes Induction in the original and
acknowledged meaning of the term.

Old definitions, it is true, cannot prevail against new
knowledge : and if the Keplerian operation, as a logical pro-
cess, be really identical with what takes place in acknowledged
induction, the definition of induction ought to be so widened
as to take it in ; since scientific language ought to adapt itself

* Phil, of Discov. p. 256.

352 INDUCTION.

to the true relations which subsist between the things it is
employed to designate. Here then it is that I am at issue
with Dr. Whewell. He does think the operations identical.
He allows of no logical process in any case of induction,
other than what there was in Kepler's case, namely, guessing
until a guess is found which tallies with the facts; and accord-
ingly, as we shall see hereafter, he rejects all canons of induc-
tion, because it is not by means of them that we guess. Dr.
Whewell's theory of the logic of science would be very perfect
if it did not pass over altogether the question of Proof. But
in my apprehension there is such a thing as proof, and induc-
tions differ altogether from descriptions in their relation to
that element. Induction is proof; it is inferring something
unobserved from something observed : it requires, therefore,
an appropriate test of proof; and to provide that test, is the
special purpose of inductive logic. When, on the contrary,
we merely collate known observations, and, in Dr. Whewell's
phraseology, connect them by means of a new conception ; if
the conception does serve to connect the observations, we have
all we want. As the proposition in which it is embodied pre-
tends to no other truth than what it may share with many
other modes of representing the same facts, to be consistent
with the facts is all it requires : it neither needs nor admits of
proof; though it may serve to prove other things, inasmuch
as, by placing the facts in mental connexion with other facts,
not previously seen to resemble them, it assimilates the case to
another class of phenomena, concerning which real Inductions
have already been made. Thus Kepler's so-called law brought
the orbit of Mars into the class ellipse, and by doing so,
proved alt the properties of an ellipse to be true of the orbit :
but in this proof Kepler's law supplied the minor premise, and
not (as is the case with real Inductions) the major.

Dr. Whewell calls nothing Induction where there is not a
new mental conception introduced, and everything induction
where there is. But this is to confound two very different
things, Invention and Proof. The introduction of a new con-
ception belongs to Invention : and invention may be required
in any operation, but is the essence of none. A new concep-

INDUCTIONS IMPROPERLY SO CALLED. 353

tion may be introduced for descriptive purposes, arid so it may
for inductive purposes. But it is so far from constituting
induction, that induction does not necessarily stand in need of
it. Most inductions require no conception but what was pre-
sent in every one of the particular instances on which the
induction is grounded. That all men are mortal is surely an
inductive conclusion ; yet no new conception is introduced
by it. Whoever knows that any man has died, has all the
conceptions involved in the inductive generalization. But
Dr. Whewell considers the process of invention which con-
sists in framing a new conception consistent with the facts,
to be not merely a necessary part of all induction, but the
whole of it.

The mental operation which extracts from a number of
detached observations certain general characters in which the
observed phenomena resemble one another, or resemble other
known facts, is what Bacon, Locke, and most subsequent
metaphysicians, have understood by the word Abstraction. A
general expression obtained by abstraction, connecting known
facts by means of common characters, but without concluding
from them to unknown, may, I think, with strict logical cor-
rectness, be termed a Description ; nor do I know in what
other way things can ever be described. My position, how-
ever, does not depend on the employment of that particular
word ; I am quite content to use Dr. Whewell's term Colli-
gation, or the more general phrases, " mode of representing,
or of expressing, phenomena :" provided it be clearly seen
that the process is not Induction, but something radically
different.

What more may usefully be said on the subject of Colliga-
tion, or of the correlative expression invented by Dr. Whewell,
the Explication of Conceptions, and generally on the subject
of ideas and mental representations as connected with the
study of facts, will find a more appropriate place in the Fourth
Book, on the Operations Subsidiary to Induction : to which I
must refer the reader for the removal of any difficulty which
the present discussion may have left

VOL. I.

CHAPTEK III.

OF THE GROUND OF INDUCTION.

§ 1. INDUCTION properly so called, as distinguished from
those mental operations, sometimes though improperly desig-
nated by the name, which I have attempted in the preceding
chapter to characterize, may, then, be summarily defined as
Generalization from Experience. It consists in inferring from
some individual instances in which a phenomenon is observed
to occur, that it occurs in all instances of a certain class ;
namely, in all which resemble the former,- in what are regarded
as the material circumstances.

In what way the material circumstances are to be distin-
guished from those which are immaterial, or why some of the
circumstances are material and others not so, we are not yet
ready to point out. We must first observe, that there is a
principle implied in the very statement of what Induction is ;
an assumption with regard to the course of nature and the
order of the universe ; namely, that there are such things in
nature as parallel cases ; that what happens once, will, under
a sufficient degree of similarity of circumstances, happen again,
and not only again, but as often as the same circumstances
recur. This, I say, is an assumption, involved in every case of
induction. And, if we consult the actual course of nature, we
find that the assumption is warranted. The universe, so far
as known to us, is so constituted, that whatever is true in any
one case, is true in all cases of a certain description ; the only
difficulty is, to find what description.

This universal fact, which is our warrant for all inferences
from experience, has been described by different philosophers
in different forms of language : that the course of nature is
uniform ; that the universe is governed by general laws ; and

GROUND OF INDUCTION. 355

the like. One of the most usual of these modes of expression,
but also one of the most inadequate, is that which has been
brought into familiar use by the metaphysicians of the school
of Reid and Stewart. The disposition of the human mind to
generalize from experience, — a propensity considered by these
philosophers as an instinct of our nature, — they usually de-
scribe under some such name as " our intuitive conviction that
the future will resemble the past." Now it has been well
pointed out by Mr. Bailey,* that (whether the tendency be or
not an original and ultimate element of our natu/e), Time, in
its modifications of past, present, and future, has no concern
either with the belief itself, or with the grounds of it. We
believe that fire will burn to-morrow, because it burned to-day
and yesterday ; but we believe, on precisely the same grounds,
that it burned before we were born, and that it burns this very
day in Cochin-China. It is not from the past to the future,
as past and future, 'that we infer, but from the known to the
unknown ; from facts observed to facts unobserved ; from what
we have perceived, or been directly conscious of, to what has
not come within our experience. In this last predicament is
the whole region of the future ; but also the vastly greater
portion of the present and of the past.

Whatever be the most proper mode of expressing it, the
proposition that the course of nature is uniform, is the funda-
mental principle, or general axiom, of Induction. It would yet
be a great error to offer this large generalization as any expla-
nation of the inductive process. On the contrary, I hold it to
be itself an instance of induction, and induction by no means
of the most obvious kind. Far from being the first induction
we make, it is one of the last, or at all events one of those
which are latest in attaining strict philosophical accuracy. As
a general maxim, indeed, it has scarcely entered into the minds
of any but philosophers ; nor even by them, as we shall have
many opportunities of remarking, have its extent and limits
been always very justly conceived. The truth is, that this
great generalization is itself founded on prior generalizations.

* Essays on the Pursuit of Truth.

23—2

356 INDUCTION.

The obscurer laws of nature were discovered by means of it,
but the more obvious ones must have been understood and as-
sented to as general truths before it was ever heard of. We
should never have thought of affirming that all phenomena
take place according to general laws, if we had not first arrived,
in the case of a great multitude of phenomena, at some know-
ledge of the laws themselves ; which could be done no other-
wise than by induction. In what sense, then, can a principle,
which is so far from being our earliest induction, be regarded
as our warrant for all the others ? In the only sense, in which
(as we have already seen) the general propositions which we
place at the head of our reasonings when we throw them into
syllogisms, ever really contribute to their validity. As Arch-
bishop Whately remarks, every induction is a syllogism with
the major premise suppressed ; or (as I prefer expressing it)
every induction may be thrown into the form of a syllogism,
by supplying a major premise. If this be actually done, the
principle which we are now considering, that of the uniformity
of the course of nature, will appear as the ultimate major pre-
mise of all inductions, and will, therefore, stand to all inductions
in the relation in which, as has been shown at so much length,
the major proposition of a syllogism always stands to the
conclusion ; not contributing at all to prove it, but being a
necessary condition of its being proved ; since no conclusion
is proved, for which there cannot be found a true major
premise.*

* In the first edition a note was appended at this place, containing some
criticism on Archbishop Whately's mode of conceiving the relation between
Syllogism and Induction. In a subsequent issue of his Logic, the Archbishop
made a reply to the criticism, which induced me to cancel part of the note,
incorporating the remainder in the text. In a still later edition, the Archbishop
observes in a tone of something like disapprobation, that the objections, " doubt-
less from their being fully answered and found untenable, were silently sup-
pressed," and that hence he might appear to some of his readers to be combating
a shadow. On this latter point, the Archbishop need give himself no uneasi-
ness. His readers, I make bold to say, will fully credit his mere affirmation
that the objection.1; have actually been made.

But as he seems to think that what he terms the suppression of the objec-
tions ought not to have been made "silently," I now break that silence, and
state exactly what it is that I suppressed, and why. I suppressed that alone

GROUND OP INDUCTION. 357

The statement, that the uniformity of the course of nature
is the ultimate major premise in all casses of induction, may be
thought to require some explanation. The immediate major
premise in every inductive argument, it certainly is not. Of
that, Archbishop Whately's must be held to be the correct
account. The induction, " John, Peter, &c. are mortal, there-
fore all mankind are mortal," may, as he justly says, be thrown
into a syllogism by prefixing as a major premise (what is at
any rate a necessary condition of the validity of the argument)
namely, that what is true of John, Peter, &c. is true of all
mankind. But how came we by this major premise ? It is
not self-evident; nay, in all cases of unwarranted generaliza-
tion, it is not true. How, then, is it arrived at ? Necessarily
either by induction or ratiocination ; and if by induction, the
process, like all other inductive arguments, may be thrown into
the form of a syllogism. This previous syllogism it is, there-
fore, necessary to construct. There is, in the long run, only
one possible construction. The real proof that what is true of
John, Peter, &c. is true of all mankind, can only be, that
a different supposition would be inconsistent with the uni-
formity which we know to exist in the course of nature.

which might be regarded as personal criticism on the Archbishop. I had im-
puted to him the having omitted to ask himself a particular question. I found
that he had asked himself the question, and could give it an answer consistent
with his own theory. I had also, within the compass of a parenthesis, hazarded
some remarks on certain general characteristics of Archbishop Whately as a
philosopher. These remarks, though their tone, I hope, was neither disrespect-
ful nor arrogant, I felt, on reconsideration, that I was hardly entitled to make ;
least of all, when the instance which I had regarded as an illustration of them,
failed, as I now saw, to bear them out. The real matter at the bottom of the
whole dispute, the different view we take of the function of the major premise,
remains exactly where it was ; and so far was I from thinking that my opinion
had been fully "answered " and was "untenable," that in the same edition in
which I cancelled the note, I not only enforced the opinion by further argu- t
ments, but answered (though without naming him) those of the Archbishop.

For not having made this statement before, I do not think it needful to
apologize. It would be attaching very great importance to one's smallest say-
ings, to think a formal retractation requisite every time that one falls into an
error. Nor is Archbishop Whately's well-earned fame of so tender a quality as
to require that in withdrawing a slight criticism on him I should have been
bound to offer a public amende for having made it.

358 INDUCTION.

Whether there would be this inconsistency or not, may be
a matter of long and delicate inquiry ; but unless there would,
we have no sufficient ground for the major of the inductive
syllogism. It hence appears, that if we throw the whole
course of any inductive argument into a series of syllogisms,
we shall arrive by more or fewer steps at an ultimate syllogism,
which will have for its major premise the principle, or axiom,
of the uniformity of the course of nature.*

It was not to be expected that in the case of this axiom,
any more than of other axioms, there should be unanimity
among thinkers with respect to the grounds on which it is to
be received as true. I have already stated that I regard it as
itself a generalization from experience. Others hold it to be a
principle which, antecedently to any verification by experience,
we are compelled by the constitution of our thinking faculty to
assume as true. Having so recently, and at so much length,
combated a similar doctrine as applied to the axioms of mathe-
matics, by arguments which are in a great measure applicable
to the present case, I shall defer the more particular discussion
of this controverted point in regard to the fundamental axiom
of induction, until a more advanced period of our inquiry.t

* But though it is a condition of the validity of every induction that there
be uniformity in the course of nature, it is not a necessary condition that the
uniformity should pervade all nature. It is enough that it pervades the par-
ticular class of phenomena to which the induction relates. An induction con-
cerning the motions of the planets, or the properties of the magnet, would not
be vitiated though we were to suppose that wind and weather are the sport of
chance, provided it be assumed that astronomical and magnetic phenomena are
under the dominion of general laws. Otherwise the early experience of man-
kind would have rested on a very weak foundation ; for in the infancy of science
it could not be known that all phenomena are regular in their course.

Neither would it be correct to say that every induction by which we infer
any truth, implies the general fact of uniformity as foreknown, even in reference
to the kind of phenomena concerned. It implies, cither that this general fact
is already known, or that we may now know it : as the conclusion, the Duke of
Wellington is mortal, drawn from the instances A, B, and C, implies either that
we have already concluded all men to be mortal, or that we are now entitled to
do so from the same evidence. A vast amount of confusion and paralogism
respecting the grounds of Induction would be dispelled by keeping in view these
simple considerations.

t Infra, chap. xxi.

GROUND OF INDUCTION. 359

At present it is of more importance to understand thoroughly
the import of the axiom itself. For the proposition, that the
course of nature is uniform, possesses rather the brevity suit-
able to popular, than the precision requisite in philosophical
language : its terms require to be explained, and a stricter
than their ordinary signification given to them, before the truth
of the assertion can be admitted.

§ 2. Every person's consciousness assures him that he
does not always expect uniformity in the course of events ; he
does not always believe that the unknown will be similar to
the known, that the future will resemble the past. Nobody
believes that the succession of rain and fine weather will be
the same in every future year as in the present. Nobody ex-
pects to have the same dreams repeated every night. On the
contrary, everybody mentions it as something extraordinary,
if the course of nature is constant, and resembles itself, in these
particulars. To look for constancy where constancy is not to
be expected, as for instance that a day which has once brought
good fortune will always be a fortunate day, is justly accounted
superstition.

The course of nature, in truth, is not only uniform, it is
also infinitely various. Some phenomena are always seen to
recur in the very same combinations in which we met with
them at first; others seem altogether capricious; while some,
which we had been accustomed to regard as bound down ex-
clusively to a particular set of combinations, we unexpectedly
find detached from some of the elements with which we had
hitherto found them conjoined, and united to others of quite
a contrary description. To an inhabitant of Central Africa,
fifty years ago, no fact probably appeared to rest on more
uniform experience than this, that all human beings are black.
To Europeans, not many years ago, the proposition, All swans
are white, appeared an equally unequivocal instance of uni-
formity in the course of nature. Further experience has proved
to both that they were mistaken ; but they had to wait fifty
centuries for this experience. During that long time, mankind

360 INDUCTION.

believed in an uniformity of the course of nature where no such
uniformity really existed.

According to the notion which the ancients entertained of
induction, the foregoing were cases of as legitimate inference
as any inductions whatever. In these two instances, in which,
the conclusion being false, the ground of inference must have
been insufficient, there was, nevertheless, as much ground for
it as this conception of induction admitted of. The induction
of the ancients has been well described by Bacon, under the
name of " Inductio per enumeratiouem simplicem, ubi non
reperitur instantia contradictoria." It consists in ascribing
the character of general truths to all propositions which are
true in every instance that we happen to know of. This is the
kind of induction which is natural to the mind when unaccus-
tomed to scientific methods. The tendency, which some call
an instinct, and which others account for by association, to
infer the future from the past, the known from the unknown,
is simply a habit of expecting that what has been found true
once or several times, and never yet found false, will be found
true again. Whether the instances are few or many, conclu-
sive or inconclusive, does not much affect the matter : these
are considerations which occur only on reflection; the un-
prompted tendency of the mind is to generalize its experience,
provided this points all in one direction ; provided no other
experience of a conflicting character comes unsought. The
notion of seeking it, of experimenting, for it, of interrogating
nature (to use Bacon's expression) is of much later growth.
The observation of nature, by uncultivated intellects, is purely
passive : they accept the facts which present themselves,
without taking the trouble of searching for more : it is a
superior mind only which asks itself what facts are needed to
enable it to come to a safe conclusion, and then looks out for
these.

But though we have always a propensity to generalize
from unvarying experience, we are not always warranted in
doing so. Before we can be at liberty to conclude that some-
thing is universally true because we have never known an
instance to the contrary, we must have reason to believe that

GROUND OF INDUCTION. 36]

if there were in nature any instances to the contrary, we
should have known of them. This assurance, in the great
majority of cases, we cannot have, or can have only in a very
moderate degree. The possibility of having it, is the founda-
tion on which we shall see hereafter that induction by simple
enumeration may in some remarkable cases amount practically
to proof.* No such assurance, however, can be had, on any
of the ordinary subjects of scientific inquiry. Popular notions
are usually founded on induction by simple enumeration ; in
science it carries us but a little way. We are forced to begin
with it; we must often rely on it provisionally, in the absence
of means of more searching investigation. But, for the accu-
rate study of nature, we require a surer and a more potent
instrument.

It was, above all, by pointing out the insufficiency of this
rude and loose conception of Induction, that Bacon merited
the title so generally awarded to him, of Founder of the In-
ductive Philosophy. The value of his own contributions to
a more philosophical theory of the subject has certainly been
exaggerated. Although (along with some fundamental errors)
his writings contain, more or less fully developed, several of
the most important principles of the Inductive Method, physical
investigation has now far outgrown the Baconian conception
of Induction. Moral and political inquiry, indeed, are as yet
far behind that conception. The current and approved modes
of reasoning on these- subjects are still of the same vicious
description against which Bacon protested ; the method almost
exclusively employed by those professing to treat such matters
inductively, is the very inductio per enumerationem simplicem
which he condemns ; and the experience which we hear so
confidently appealed to by all sects, parties, and interests, is
still, in his own emphatic words, mera palpatio.

§ 3. In order to a better understanding of the problem
which the logician must solve if he would establish a scientific
theory of Induction, let us compare a few cases of incorrect

* Infra, chap. xxi. xxii.

362

INDUCTION.

inductions with others which are acknowledged to be legiti-
mate. Some, we know, which were believed for centuries to
be correct, were nevertheless incorrect. That all swans are
white, cannot have been a good induction, since the conclu-
sion has turned out erroneous. The experience, however, on
which the conclusion rested, was genuine. From the earliest
records, the testimony of the inhabitants of the known world
was unanimous on the point. The uniform experience, there-
fore, of the inhabitants of the known world, agreeing in a
common result, without one known instance of deviation from
that result, is not always sufficient to establish a general
conclusion.

But let us now turn to an instance apparently not very
dissimilar to this. Mankind were wrong, it seems, in con-
cluding that all swans were white : are we also wrong, when
we conclude that alt men's heads grow above their shoulders,
and never below, in spite of the conflicting testimony of the
naturalist Pliny ? As there were black swans, though civi-
lized people had existed for three thousand years on the earth
without meeting with them, may there not also be " men
whose heads do grow beneath their shoulders," notwith-
standing a rather less perfect unanimity of negative testimony
from observers ? Most persons would answer No ; it was
more credible that a bird should vary in its colour, than that
men should vary in the relative position of their principal
organs. And there is no doubt that in so saying they would
be right : but to say why they are right, would be impossible,
without entering more deeply than is usually done, into the
true theory of Induction.

Again, there are cases in which we reckon with the most
unfailing confidence upon uniformity, and other cases in which
we do not count upon it at all. In some we feel complete
assurance that the future will resemble the past, the unknown
be precisely similar to the known. In others, however
invariable may be the result obtained from the instances
which have been observed, we draw from them no more than
a very feeble presumption that the like result will hold in all
other cases. That a straight line is the shortest distance

GROUND OF INDUCTION. 363

between two points, we do not doubt to be true even in the
region of the fixed stars.* When a chemist announces the
existence and properties of a newly-discovered substance, if
we confide in his accuracy, we feel assured that the conclu-
sions he has arrived at will hold universally, though the
induction be founded but on a single instance. We do not
withhold our assent, waiting for a repetition of the experi-
ment; or if we do, it is from a doubt whether the one experi-
ment was properly made, not whether if properly made it
would be conclusive. Here, then, is a general law of nature,
inferred without hesitation from a single instance ; an universal
proposition from a singular one. Now mark another case, and
contrast it with this. Not all the instances which have been
observed since the beginning of the world, in support of the
general proposition that all crows are black, would be deemed
a sufficient presumption of the truth of the proposition, to
outweigh the testimony of one unexceptionable witness who
should affirm that in some region of the earth not fully ex-
plored, he had caught and examined a crow, and had found it
to be grey.

Why is a single instance, in some cases, sufficient for a com-
plete induction, while in others, myriads of concurring in-
stances, without a single exception known or presumed, go
such a very little way towards establishing an universal propo-
sition ? Whoever can answer this question knows more of the
philosophy of logic than the wisest of the ancients, and has
solved the problem of induction.

* In strictness, wherever the present constitution of space exists ; which we
have ample reason to believe that it does in the region of the fixed stars.

CHAPTER IV.

OF LAWS OF NATURE.

§ 1. IN the contemplation of that uniformity in the course
of nature, which is assumed in every inference from experi-
ence, one of the first observations that present themselves is,
that the uniformity in question is not properly uniformity, but
uniformities. The general regularity results from the coexis-
tence of partial regularities. The course of nature in general
is constant, because the course of each of the various pheno-
mena that compose it is so. A certain fact invariably occurs
whenever certain circumstances are present, and does not occur
when they are absent ; the like is true of another fact ; and
so on. From these separate threads of connexion between
parts of the great whole which we term nature, a general
tissue of connexion unavoidably weaves itself, by which the
whole is held together. If A is always accompanied by D,
B by E, and C by F, it follows that A B is accompanied by
D E, A C by D F, B C by E F, and finally A B C by D E
F; and thus the general character of regularity is produced,,
which, along with and in the midst of infinite diversity, per-
vades all nature.

The first point, therefore, to be noted in regard to what is
called the uniformity of the course of nature, is, that it is itself
a complex fact, compounded of all the separate uniformities-
which exist in respect to single phenomena. These various
uniformities, when ascertained by what is regarded as a suffi-
cient induction, \ve call in common parlance, Laws of Nature.
Scientifically speaking, that title is employed in a more re-
stricted sense, to designate the uniformities when reduced to
their most simple expression. Thus in the illustration already
employed, there were seven uniformities ; all of which, if con-
sidered sufficiently certain, would, in the more lax application

LAWS OF NATURE. 365

of the term, be called laws of nature. But of the seven, three
alone are properly distinct and independent : these being pre-
supposed, the others follow of course. The three first, there-
fore, according to the stricter acceptation, are called laws of
nature ; the remainder not ; because they are in truth mere
cases of the three first ; virtually included in them ; said,
therefore, to result from them : whoever affirms those three has
already affirmed all the rest.

To substitute real examples for symbolical ones, the fol-
lowing are three uniformities, or call them laws of nature :
the law that air has weight, the law that pressure on a fluid is
propagated equally in all directions, and the law that pressure
in one direction, not opposed by equal pressure in the contrary
direction, produces motion, which does not cease until equili-
brium is restored. From these three uniformities we should
be able to predict another uniformity, namely, the rise of the
mercury in the Torricellian tube. This, in the stricter use of
the phrase, is not a law of nature. It is the result of laws of
nature. It is a case of each and every one of the three laws :
and is the only occurrence by which they could all be fulfilled.
If the mercury were not sustained in the barometer, and sus-
tained at such a height that the column of mercury were equal
in weight to a column of the atmosphere of the same diameter;
here would be a case, either of the air not pressing upon the
surface of the mercury with the force which is called its weight,
or of the downward pressure on the mercury not being propa-
gated equally in an upward direction, or of a body pressed in
one direction and not in the direction opposite, either not
moving in the direction in which it is pressed, or stopping
before it had attained equilibrium. If we knew, therefore, the
three simple laws, but had never tried the Torricellian experi-
ment, we might deduce its result from those laws. The known
weight of the air, combined with the position of the appa-
ratus, would bring the mercury within the first of the three
inductions ; the first induction would bring it within the
second, and the second within the third, in the manner which
we characterized in treating of Ratiocination. We should
thus come to know the more complex uniformity, indepen-

366 INDUCTION.

dently of specific experience, through our knowledge of the
simpler ones from which it results ; though, for reasons which
will appear hereafter, verification by specific experience would
still be desirable, and might possibly be indispensable.

Complex uniformities which, like this, are mere cases of
simpler ones, and have, therefore, been virtually affirmed in
affirming those, may with propriety be called laws, but can
scarcely, in the strictness of scientific speech, be termed Laws
of Nature. It is the custom in science, wherever regularity of
any kind can be traced, to call the general proposition which
expresses the nature of that regularity, a law ; as when, in
mathematics, we speak of the law of decrease of the successive
terms of a converging series. But the expression law of
nature has generally been employed with a sort of tacit refe-
rence to the original sense of the word law, namely, the ex-
pression of the will of a superior. When, therefore, it appeared
that any of the uniformities which were observed in nature,
would result spontaneously from certain other uniformities, no
separate act of creative will being supposed necessary for the
production of the derivative uniformities, these have not usually
been spoken of as laws of nature. According to one mode
of expression, the question, What are the laws of nature? may
be stated thus : — What are the fewest and simplest as-
sumptions, which being granted, the whole existing order of
nature would result ? Another mode of stating it would be
thus : What are the fewest general propositions from which
all the uniformities which exist in the universe might be de-
ductively inferred ?

Every great advance which marks an epoch in the progress
of science, has consisted in a step made towards the solution
of this problem. Even a simple colligation of inductions
already made, without any fresh extension of the inductive
inference, is already an advance in that direction. When
Kepler expressed the regularity which exists in the observed
motions of the heavenly bodies, by the three general proposi-
tions called his laws, he, in so doing, pointed out three simple
suppositions which, instead of a much greater number, would
suffice to construct the whole scheme of the heavenly motions,
so far as it was known up to that time. A similar and still

LAWS OF NATURE. 367

greater step was made when these laws, which at first did not
seem to be included in any more general truths, were dis-
covered to be cases of the three laws of motion, as obtaining
among bodies which mutually tend towards one another with
a certain force, and have had a certain instantaneous impulse
originally impressed upon them. After this great discovery,
Kepler's three propositions, though still called laws, would
hardly, by any person accustomed to use language with pre-
cision, be termed laws of nature : that phrase would be reserved
for the simpler and more general laws into which Newton is
said to have resolved them.

According to this language, every well-grounded inductive
generalization is either a law of nature, or a result of laws of
nature, capable, if those laws are known, of being predicted
from them. And the problem of Inductive Logic may be
summed up in two questions : how to ascertain the laws of
nature ; and how, after having ascertained them, to follow
them into their results. On the other hand, we must not
suffer ourselves to imagine that this mode of statement amounts
to a real analysis, or to anything but a mere verbal transfor-
mation of the problem; for the expression, Laws of Nature,
means nothing but the uniformities which exist among natural
phenomena (or, in other words, the results of induction), when
reduced to their simplest expression. It is, however, some-
thing to have advanced so far, as to see that the study of
nature is the study of laws, not a law ; of uniformities, in the
plural number : that the different natural phenomena have
their separate rules or modes of taking place, which, though
much intermixed and entangled with one another, may, to a
certain extent, be studied apart : that (to resume our former
metaphor) the regularity which exists in nature is a web com-
posed of distinct threads, and only to be understood by tracing
each of the threads separately ; for which purpose it is often
necessary to unravel some portion of the web, and exhibit the
fibres apart. The rules of experimental inquiry are the con-
trivances for unravelling the web.

§ 2. In thus attempting to ascertain the general order of
nature by ascertaining the particular order of the occurrence

368 INDUCTION.

of each one of the phenomena of nature, the most scientific
proceeding can be no more than an improved form of that
which was primitively pursued by the human understanding,
while undirected by science. When mankind first formed the
idea of studying phenomena according to a stricter and surer
method than that which they had in the first instance spon-
taneously adopted, they did not, conformably to the well-
meant but impracticable precept of Descartes, set out from
the supposition that nothing had been already ascertained.
Many of the uniformities existing among phenomena are so
constant, and so open to observation, as to force themselves
upon involuntary recognition. Some facts are so perpetually
and familiarly accompanied by certain others, that mankind
learnt, as children learn, to expect the one where they found
the other, long before they knew how to put their expectation
into words by asserting, in a proposition, the existence of a
connexion between those phenomena. No science was needed
to teach that food nourishes, that water drowns, or quenches
thirst, that the sun gives light and heat, that bodies fall to
the ground. The first scientific inquirers assumed these and
the like as known truths, and set out from them to discover
others which were unknown : nor were they wrong in so doing,
subject, however, as they afterwards began to see, to an ulte-
rior revision of these spontaneous generalizations themselves,
when the progress of knowledge pointed out limits to them,
or showed their truth to be contingent on some circumstance
not originally attended to. It will appear, I think, from
the subsequent part of our inquiry, that there is no logical
fallacy in this mode of proceeding ; but we may see already
that any other mode is rigorously impracticable : since it is
impossible to frame any scientific method of induction, or
test of the correctness of inductions, unless on the hypothesis
that some inductions deserving of reliance have been already
made.

Let us revert, for instance, to one of our former illustra-
tions, and consider why it is that, with exactly the same
amount of evidence, both negative and positive, we did not
reject the assertion that there are black swans, while we
should refuse credence to any testimony which asserted that

LAWS OF NATURE. 369

there were men wearing their heads underaeath their shoulders.
The first assertion was more credible than the latter. But
why more credible ? So long as neither phenomenon had
been actually witnessed, what reason was there for finding the
one harder to be believed than the other ? Apparently because
there is less constancy in the colours of animals, than in the
general structure of their anatomy. But how do we know
this ? Doubtless, from experience. It appears, then, that we
need experience to inform us, in what degree, and in what
cases, or sorts of cases, experience is to be relied on. Expe-
rience must be consulted in order to learn from it under what
circumstances arguments from it will be valid. We have no
ulterior test to which we subject experience in general; but
we make experience its own test. Experience testifies, that
among the uniformities which it exhibits or seems to exhibit,
some are more to be relied on than others ; and uniformity,
therefore, maybe presumed, from any given number of instances,
with a greater degree of assurance, in proportion as the case
belongs to a class in which the uniformities have hitherto been
found more uniform.

This mode of correcting one generalization by means of
another, a narrower generalization by a wider, which common
sense suggests and adopts in practice, is the real type
of scientific Induction. All that art can do is but to give
accuracy and precision to this process, and adapt it to all
varieties of cases, without any essential alteration in its
principle.

There are of course no means of applying such a test as
that above described, unless we already possess a general
knowledge of the prevalent character of the uniformities
existing throughout nature. The indispensable foundation,
therefore, of a scientific formula of induction, must be a
survey of the inductions to which mankind have been con-
ducted in unscientific practice ; with the special purpose of
ascertaining what kinds of uniformities have been found per-
fectly invariable, pervading all nature, and what are those
which have been found to vary with difference of time, place,
or other changeable circumstances.

VOL. i. 24

370 INDUCTION.

§ 3. The necessity of such a survey is confirmed by the
consideration, that the stronger inductions are the touchstone
to which we always endeavour to bring the weaker. If we
find any means of deducing one of the less strong inductions
from stronger ones, it acquires, at once, all the strength of
those from which it is deduced ; and even adds to that
strength ; since the independent experience on which the
weaker induction previously rested, becomes additional evi-
dence of the truth of the better established law in which it is
now found to be included. We may have inferred, from his-
torical evidence, that the uncontrolled power of a monarch,
of an aristocracy, or of the majority, will often be abused :
but we are entitled to rely on this generalization with much
greater assurance when it is shown to be a corollary from still
better established facts ; the very low degree of elevation of
character ever yet attained by the average of mankind, and
the little efficacy, for the most part, of the modes of education
hitherto practised, in maintaining the predominance of reason
and conscience over the selfish propensities. It is at the same
time obvious that even these more general facts derive an acces-
sion of evidence from the testimony which history bears to the
effects of despotism. The strong induction becomes still
stronger when a weaker one has been bound up with it.

On the other hand, if an induction conflicts with stronger
inductions, or with conclusions capable of being correctly
deduced from them, then, unless on reconsideration it should
appear that some of the stronger inductions have been
expressed with greater universality than their evidence war-
rants, the weaker one must give way. The opinion so long
prevalent that a comet, or any other unusual appearance in
the heavenly regions, was the precursor of calamities to
mankind, or to those at least who witnessed it ; the belief in
the veracity of the oracles of Delphi or Dodona; the reliance
on astrology, or on the weather-prophecies in almanacks, were
doubtless inductions supposed to be grounded on experience :*

* Dr. Whewell (Phil, of Discov., p. 246) will not allow these and similar
erroneous judgments to be called inductions; inasmuch as such superstitious

LAWS OF NATURE. 371

and faith in such delusions seems quite capable of holding out
against a great multitude of failures, provided it be nourished
by a reasonable number of casual coincidences between the
prediction and the event. What has really put an end to
these insufficient inductions, is their inconsistency with the
stronger inductions subsequently obtained by scientific inquiry,
respecting the causes on which terrestrial events really depend ;
and where those scientific truths have not yet penetrated, the
same or similar delusions still prevail.

It may be affirmed as a general principle, that all induc-
tions, whether strong or weak, which can be connected by
ratiocination, are confirmatory of one another; while any
•which lead deductively to consequences that are incompatible,
become mutually each other's test, showing that one or other
must be given up, or at least more guardedly expressed. In
the case of inductions which confirm each other, the one which

fancies " were not collected from the facts by seeking a law of their occurrence,
but were suggested by an imagination of the anger of superior powers, shown
by such deviations from the ordinary course of nature." I conceive the ques-
tion to be, not in what manner these notions were at first suggested, but by
what evidence they have, from time to time, been supposed to be substantiated.
If the believers in these erroneous opinions bad been put on their defence, they
would have referred to experience: to the comet which preceded the assassina-
tion of Julius Csesar, or to oracles and other prophecies known to have been
fulfilled. It is by such appeals to facts that all analogous superstitions, even in
our day, attempt to justify themselves ; the supposed evidence of experience is
necessary to their hold on the mind. I quite admit that the influence of such
coincidences would not be what it is, if strength were not lent to it by an
antecedent presumption ; but this is not peculiar to such cases; preconceived'
notions of probability form part of the explanation of many other cases of
belief on insufficient evidence. The d, priori prejudice does not prevent the
erroneous opinion from being sincerely regarded as a legitimate conclusion front
experience ; though it improperly predisposes the mind to that interpretation of
experience.

Thus much in defence of the sort of examples objected to. But it would
be easy to produce instances, equally adapted to the purpose, and in which no
antecedent prejudice is at all concerned. "For many ages," says Archbishop
Whately, "all farmers and gardeners were firmly convinced — and convinced
of their knowing it by experience — that the crops would never turn out good
unless the seed were sown during the increase of the moon." This was
induction, but bad induction ; just as a vicious syllogism is reasoning, but bad
reasoning.

24-— 2

372 INDUCTION.

/

becomes a conclusion from ratiocination rises to at least the
level of certainty of the weakest of those from "which it is
deduced ; while in general all are more or less increased in
certainty. Thus the Torricellian experiment, though a mere
case of three more general laws, not only strengthened greatly
the evidence on which those laws rested, hut converted one of
them (the weight of the atmosphere) from a still doubtful gene-
ralization into a completely established doctrine.

If, then, a survey of the uniformities which have been
ascertained to exist in nature, should point out some which,
as far as any human purpose requires certainty, may be con-
sidered quite certain and quite universal ; then by means of
these uniformities we may be able to raise multitudes of other
inductions to the same point in the scale. For if we can show,
with respect to any inductive inference, that either it must be
true, or one of these certain and universal inductions must admit
of an exception ; the former generalization will attain the same
certainty, and indefeasibleness within the bounds assigned to it,
which are the attributes of the latter. It will be proved to be
Ji law ; and if not a result of other and simpler laws, it will be
ft law of nature.

There are such certain and universal inductions ; and it is
because there are such, that a Logic of Induction is possible.

CHAPTER V.

OF THE LAW OF UNIVERSAL CAUSATION.

§ 1. THE phenomena of nature exist in two distinct
relations to one another ; that of simultaneity, and that of
succession. Every phenomenon is related, in an uniform man-
ner, to some phenomena that coexist with it, and to some that
have preceded and will follow it.

Of the uniformities which exist among synchronous pheno-
mena, the most important, on every account, are the laws of
number ; and next to them those of space, or, in other words,
of extension and figure. The laws of number are common to
synchronous and successive phenomena. That two and two
make four, is equally true whether the second two follow the
first two or accompany them. It is as true of days and years
as of feet and inches. The laws of extension and figure (in
other words, the theorems of geometry, from its lowest to its
highest branches) are, on the contrai'y, laws of simultaneous
phenomena only. The various parts of space, and of the
objects which are said to fill space, coexist; and the unvarying
laws which are the subject of the science of geometry, are an
expression of the mode of their coexistence.

This is a class of laws, or in other words, of uniformities,
for the comprehension and proof of which it is not necessary
to suppose any lapse of time, any variety of facts or events suc-
ceeding one another. The propositions of geometry are inde-
pendent of the succession of events. All things which possess
extension, or, in other words, which fill space, are subject to
geometrical laws. Possessing extension, they possess figure ;
possessing figure, they must possess some figure in particular,
and have all the properties which geometry assigns to that
figure. If one body be a sphere and another a cylinder, of
equal height and diameter, the one will be exactly two-thirds

374 INDUCTION.

of the other, let the nature and quality of the material be
what it will. Again, each body, and each point of a body,
must occupy some place or position among other bodies ; and
the position of two bodies relatively to each other, of whatever
nature the bodies be, may be unerringly inferred from the
position of each of them relatively to any third body.

In the laws of number, then, and in those of space, we re-
cognise in the most unqualified manner, the rigorous univer-
sality of which we are in quest. Those laws have been in all
ages the type of certainty, the standard of comparison for all
inferior degrees of evidence. Their invariability is so perfect,
that it renders us unable even to conceive any exception to
them ; and philosophers have been led, though (as I have en-
deavoured to show) erroneously, to consider their evidence as
lying not in experience, but in the original constitution of the
intellect. If, therefore, from the laws of space and number,
we were able to deduce uniformities of any other description,
this would be conclusive evidence to us that those other uni-
formities possessed the same rigorous certainty. But this we
cannot do. From laws of space and number alone, nothing
can be deduced but laws of space and number.

Of all truths relating to phenomena, the most valuable to
us are those which relate to the order of their succession. On
a knowledge of these is founded every reasonable anticipation
of future facts, and whatever power we possess of influencing
those facts to our advantage. Even the laws of geometry are
chiefly of practical importance to us as being a portion of the
premises from which the order of the succession of phenomena
may be inferred. Inasmuch as the motion of bodies, the
action of forces, and the propagation of influences of all sorts,
take place in certain lines and over definite spaces, the proper-
ties of those lines and spaces are an important part of the laws
to which those phenomena are themselves subject. Again,
motions, forces, or other influences, and times, are numerable
quantities ; and the properties of number are applicable to
them as to all other things. But though the laws of number
and space are important elements in the ascertainment of uni-
formities of succession, they can do nothing towards it when

LAW OF CAUSATION. 375

taken by themselves. They can only be made instrumental
to that purpose when we combine with them additional premises,
expressive of uniformities of succession already known. By
taking, for instance, as premises these propositions, that bodies
acted upon by an instantaneous force move with uniform velo-
city in straight lines ; that bodies acted upon by a conti-
nuous force move with accelerated velocity in straight lines ;
and that bodies acted upon by two forces in different directions
move in the diagonal of a parallelogram, whose sides repre-
sent the direction and quantity of those forces ; we may by
combining these truths with propositions relating to the pro-
perties of straight lines and of parallelograms, (as that a triangle
is half a parallelogram of the same base and altitude,) deduce
another important uniformity of succession, viz., that a body
moving round a centre of force describes areas proportional to
the times. But unless there had been laws of succession in
our premises, there could have been no truths of succession in
our conclusions. A similar remark might be extended to every
other class of phenomena really peculiar ; and, had it been
attended to, would have prevented many chimerical attempts
at demonstrations of the indemonstrable, and explanations
which do not explain.

It is not, therefore, enough for us that the laws of space,
which are only laws of simultaneous phenomena, and the laws
of number, which though true of successive phenomena do not
relate to their succession, possess the rigorous certainty and
universality of which we are in search. We must endeavour
to find some law of succession which has those same attributes,
and is therefore fit to be made the foundation of processes for
discovering, and of a test for verifying, all other uniformities
of succession. This fundamental law must resemble the truths
of geometry in their most remarkable peculiarity, that of never
being, in any instance whatever, defeated or suspended by any
change of circumstances.

Now among all those uniformities in the succession 01
phenomena, which common observation is sufficient to bring
to light, there are very few which have any, even apparent,
pretension to this rigorous indefeasibility : and of those few,

376 INDUCTION.

one only has been found capable of completely sustaining it.
In that one, however, we recognise a law which is universal
also in another sense ; it is coextensive with the entire field of
successive phenomena, all instances whatever of succession
being examples of it. This law is the Law of Causation.
The truth that every fact which has a beginning has a cause,
is coextensive with human experience.

This generalization may appear to some minds not to
amount to much, since after all it asserts only this : " it is a
law, that every event depends on some law : " " it is a law,
that there is a law for everything." We must not, however,
conclude that the generality of the principle is merely verbal ;
it will be found on inspection to be no vague or unmeaning
assertion, but a most important and really fundamental truth.

§ 2. The notion of Cause being the root of the whole
theory of Induction, it is indispensable that this idea should,
at the very outset of our inquiry, be, with the utmost practi-
cable degree of precision, fixed and determined. If, indeed,
it were necessary for the purpose of inductive logic that the
strife should be quelled, which has so long raged among the
different schools of metaphysicians, respecting the origin and
analysis of our idea of causation; the promulgation, or at least
the general reception, of a true theory of induction, might be
considered desperate for a long time to come. But the science
of the Investigation of Truth by means of Evidence, is hap-
pily independent of many of the controversies which perplex
the science of the ultimate constitution of the human mind,
and is under no necessity of pushing the analysis of mental
phenomena to that extreme limit which alone ought to satisfy
a metaphysician.

I premise, then, that when in the course of this inquiry I
speak of the cause of any phenomenon, I do not mean a cause
which is not itself a phenomenon ; I make no research into
the ultimate or ontological cause of anything. To adopt a
distinction familiar in the writings of the Scotch metaphysi-
cians, and especially of Reid, the causes with which I concern
myself are not efficient, but physical causes. They are causes

LAW OF CAUSATION. 377

in that sense alone, in which one physical fact is said to be the
cause of another. Of the efficient causes of phenomena, or
whether any such causes exist at all, I am not called upon to
give an opinion. The notion of causation is deemed, by the
schools of metaphysics most in vogue at the present moment,
to imply a mysterious and most powerful tie, such as cannot,
or at least does not, exist between any physical fact and that
other physical fact on which it is invariably consequent, and
which is popularly termed its cause : and thence is deduced
the supposed necessity of ascending higher, into the essences
and inherent constitution of things, to find the true cause,
the cause which is not only followed by, but actually produces,
the effect. No such necessity exists for the purposes of the
present inquiry, nor will any such doctrine be found in the
following pages. The only notion of a cause, which the
theory of induction requires, is such a notion as can be gained
from experience. The Law- of Causation, the recognition
of which is the main pillar of inductive science, is but the
familiar truth, that invariability of succession is found by
observation to obtain between every fact in nature and some
other fact which has preceded it ; independently of all consi-
derations respecting the ultimate mode of production of phe-
nomena, and of every other question regarding the nature of
" Things in themselves."

Between the phenomena, then, which exist at any instant,
and the phenomena which exist at the succeeding instant,
there is an invariable order of succession ; and, as we said in
speaking of the general uniformity of the course of nature,
this web is composed of separate fibres ; this collective order
is made up of particular sequences, obtaining invariably
among the separate parts. To certain facts, certain facts
always do, and, as we believe, will continue to, succeed. The
invariable antecedent is termed the cause ; the invariable con-
sequent, the effect. And the universality of the law of causa-
tion consists in this, that every consequent is connected in
this manner with some particular antecedent, or set of ante-
cedents. Let the fact be what it may, if it has begun to exist,
it was preceded by some fact or facts, with which it is in-

378

INDUCTION.

variably connected. For every event there exists some com-
bination of objects or events, some given concurrence of cir-
cumstances, positive and negative, the occurrence of which
is always followed by that phenomenon. We may not have
found out what this concurrence of circumstances may be ; but
we never doubt that there is such a one, and that it never
occurs without having the phenomenon in question as its effect
or consequence. On the universality of this truth depends
the possibility of reducing the inductive process to rules. The
undoubted assurance we have that there is a law to be found
if we only knew how to find it, will be seen presently to be the
source from which the canons of the Inductive Logic derive
their validity.

§ 3. It is seldom, if ever, between a consequent and a
single antecedent, that this invariable sequence subsists. It
is usually between a consequent and the sum of several ante-
cedents ; the concurrence of all of them being requisite to
produce, that is, to be certain of being followed by, the con-
sequent. In such cases it is very common to single out one
only of the antecedents under the denomination of Cause,
calling the others merely Conditions. Thus, if a person eats
of a particular dish, and dies in consequence, that is, would
not have died if he had not eaten of it, people would be apt
to say that eating of that dish was the cause of his death.
There needs not, however, be any invariable connexion between
eating of the dish and death ; but there certainly is, among
the circumstances which took place, some combination or other
on which death is invariably consequent : as, for instance, the
act of eating of the dish, combined with a particular bodily
constitution, a particular state of present health, and perhaps
even a certain state of the atmosphere ; the whole of which
circumstances perhaps constituted in this particular case the
conditions of the phenomenon, or, in other words, the set of
antecedents which determined it, and but for which it would
not. have happened. The real Cause, is the whole of these
antecedents ; and we have, philosophically speaking, no right
to give the name of cause to one of them, exclusively of the

LAW OF CAUSATION. 379

others. What, in the case we have supposed, disguises the
incorrectness of the expression, is this : that the various con-
ditions, except the single one of eating the food, were not
events (that is, instantaneous changes, or successions of in-
stantaneous changes) but states, possessing more or less of
permanency ; and might therefore have preceded the effect by
an indefinite length of duration, for want of the event which
was requisite to complete the required concurrence of con-
ditions : while as soon as that event, eating the food, occurs,
no other cause is waited for, but the effect begins imme-
diately to take place : and hence the appearance is presented
of a more immediate and close connexion between the effect
and that one antecedent, than between the effect and the
remaining conditions. But though we may think proper to
give the name of cause to that one condition, the fulfilment
of which completes the tale, and brings about the effect with-
out further delay; this condition has really no closer relation
to the effect than any of the other conditions has. All the
conditions were equally indispensable to the production of the
consequent ; and the statement of the cause is incomplete,
unless in some shape or other we introduce them all. A man
takes mercury, goes out of doors, and catches cold. We say,
perhaps, that the cause of his taking cold was exposure to the
air. It is clear, however, that his having taken mercury may
have been a necessary condition of his catching cold; and
though it might consist with usage to say that the cause of his
attack was exposure to the air, to be accurate we ought to
say that the cause was exposure to the air while under the
effect of mercury.

If we do not, when aiming at accuracy, enumerate all the
conditions, it is only because some of them will in most cases
be understood without being expressed, or because for the
purpose in view they may without detriment be overlooked.
For example, when we say, the cause of a man's death was
that his foot slipped in climbing a ladder, we omit as a thing
unnecessary to be stated the circumstance of his weight,
though quite as indispensable a condition of the effect which
took place. When we say that the assent of the crown to a

380 INDUCTION.

bill makes it law, we mean that the assent, being never given
until all the other conditions are fulfilled, makes up the sum
of the conditions, though no one now regards it as the prin-
cipal one. When the decision of a legislative assembly has
been determined by the casting vote of the chairman, we
sometimes say that this one person was the cause of all the
effects which resulted from the enactment. Yet we do not
really suppose that his single vote contributed more to the
result than that of any other person who voted in the affirma-
tive ; but, for the purpose we have in view, which is to insist
on his individual responsibility, the part which any other
person had in the transaction is not material.

In all these instances the fact which was dignified with
the name of cause, was the one condition which came last into
existence. But it must not be supposed that in the employ-
ment of the term this or any other rule is always adhered to.
Nothing can better show the absence of any scientific ground
for the distinction between the cause of a phenomenon and
its conditions, than the capricious manner in which \ve select
from among the conditions that which we choose to denomi-
nate the cause. However numerous the conditions may be,
there is hardly any of them which may not, according to the
purpose of our immediate discourse, obtain that nominal pre-
eminence. This will be seen by analysing the conditions of
some one familiar phenomenon. For example, a stone thrown
into water falls to the bottom. What are the conditions of
this event ? In the first place there must be a stone, and
water, and the stone must be thrown into the water ; but these
suppositions forming part of the enunciation of the pheno-
menon itself, to include them also among the conditions would
be a vicious tautology ; and this class of conditions, therefore,
have never received the name of cause from any but the Aris-
totelians, by whom they were called the material cause, causa
materialis. The next condition is, there must be an earth :
and accordingly it is often said, that the fall of a stone is
caused by the earth ; or by a power or property of the earth,
or a force exerted by the earth, all of which are merely round-
about ways of saying that it is caused by the earth ; or, lastly,

LAW OF CAUSATION. 381

the earth's attraction ; which also is only a technical mode of
saying that the earth causes the motion, with the additional
particularity that the motion is towards the earth, which is
not a character of the cause, but of the effect. Let us now
pass to another condition. It is not enough that the earth
should exist ; the body must be within that distance from it,
in which the earth's attraction preponderates over that of any
other body. Accordingly we may say, and the expression
would be confessedly correct, that the cause of the stone's
falling is its being within the sphere of the earth's attraction.
We proceed to a further condition. The stone is immersed in
water : it is therefore a condition of its reaching the ground,
that its specific gravity exceed that of the surrounding fluid,
or in other words that it surpass in weight an equal volume of
water. Accordingly any one would be acknowledged to speak
correctly who said, that the cause of the stone's going to the
bottom is its exceeding in specific gravity the fluid in which it
is immersed.

Thus we see that each and every condition of the pheno-
menon may be taken in its turn, and, with equal propriety in
common parlance, but with equal impropriety in scientific dis-
course, may be spoken of as if it were the entire cause. And
in practice, that particular condition is usually styled the cause,
whose share in the matter is superficially the most conspi-
cuous, or whose requisiteness to the production of the effect
we happen to be insisting on at the moment. So great is the
force of this last consideration, that it sometimes induces us
to give the name of cause even to one of the negative condi-
tions. We say, for example, The army was surprised because
the sentinel was off his post. But since the sentinel's absence
was not what created the enemy, or put the soldiers asleep,
how did it cause them to be surprised ? All that is really
meant is, that the event would not have happened if he had
been at his duty. His being off his post was no producing
cause, but the mere absence of a preventing cause : it was
simply equivalent to his non-existence. From nothing, from
a mere negation, no consequences can proceed. All effects
are connected, by the law of causation, with some set o-f"

•382 INDUCTION.

positive conditions ; negative ones, it is true, being almost
always required in addition. In other words, every fact or
phenomenon which has a beginning, invariably arises when
some certain combination of positive facts exists, provided
certain other positive facts do not exist.

There is, no doubt, a tendency (which our first example,
that of death from taking a particular food, sufficiently illus-
trates) to associate the idea of causation with the proximate
antecedent event, rather than with any of the antecedent states,
or permanent facts, which may happen also to be conditions
of the phenomenon ; the reason being that the event not only
exists, but begins to exist immediately previous ; while the
other conditions may have pre-existed for an indefinite time.
And this tendency shows itself very visibly in the different
logical fictions which are resorted to, even by men of science,
to avoid the necessity of giving the name of cause to anything
which had existed for an indeterminate length of time before
the effect. Thus, rather than say that the earth causes the
fall of bodies, they ascribe it to a force exerted by the earth,
or an attraction by the earth, abstractions which they can
represent to themselves as exhausted by each effort, and there-
fore constituting at each successive instant a fresh fact,
simultaneous with, or only immediately preceding, the effect.
Inasmuch as the coming of the circumstance which completes
the assemblage of conditions, is a change or event, it thence
happens that an event is always the antecedent in closest
apparent proximity to the consequent : and this may account
for the illusion which disposes us to look upon the proximate
event as standing more peculiarly in the position of a cause
than any of the antecedent states. But even this peculiarity,
of being in closer proximity to the effect than any other of its
conditions, is, as we have already seen, far from being neces-
sary to the common notion of a cause ; with which notion, on
the contrary, any one of the conditions, either positive or
negative, is found, on occasion, completely to accord.*

* The assertion, that any and every one of the conditions of a phenomenon
may be and is, on some occasions and for some purposes, spoken of as the
cause, has been disputed by an intelligent reviewer of this work in the Pros-

LAW OF CAUSATION. 383

The cause, then, philosophically speaking, is the sum total
of the conditions, positive and negative taken together ; the
whole of the contingencies of every description, which heing
realized, the consequent invariably follows. The negative

pective Review (the predecessor of the justly esteemed National Review], who
maintains that "we always apply the word cause rather to that element in the
antecedents which exercises force, and which would tend at all times to pro-
duce the same or a similar effect to that which, under certain conditions, it
would actually produce." And he says, that "every one would feel" the
expression, that the cause of a surprise was the sentinel's being off his post, to
be incorrect ; but that the "allurement or force which drew him off his post,
might be so called, because in doing so it removed a resisting power which
would have prevented the surprise." I cannot think that it would be wrong
to say, that the event took place because the sentinel was absent, and yet
right to say that it look place because he was bribed to be absent. Since the
only direct effect of the bribe was his absence, the bribe could be called the
remote cause of the surprise, only on the supposition that the absence was the
proximate cause ; nor does it seem to me that any one (who had not a theory
to support) would use the one expression and reject the other.

The reviewer observes, that when a person dies of poison, his possession of
bodily organs is a necessary condition, but that no one would ever speak of it
as the cause. I admit the fact ; but I believe the reason to be, that the occa-
sion could never arise for so speaking of it ; for when in the inaccuracy of
common discourse we are led to speak of some one condition of a phenomenon
as its cause, the condition so spoken of is always one which it is at least pos-
sible that the hearer may require to be informed of. The possession of .bodily
organs is a known condition, and to give that as the answer, when asked the
cause of a person's death, would not supply the information sought. Once
conceive that a doubt could exist as to his having bodily organs, or that he
were to be compared with some being who had them not, and cases may be
imagined in which it might be said that his possession of them was the cause
of his death. If Faust and Mephistopheles together took poison, it might be
said that Faust died because he was a human being, and had a body, while
Mephistopheles survived because he was a spirit.

It is for the same reason that no one (as the reviewer remarks) "calls the
cause of a leap, the muscles or sinews of the body, though they are necessary
conditions ; nor the cause of a self-sacrifice, the knowledge which was neces-
sary for it ; nor the cause of writing a book, that a man has time for it, which
is a necessary condition." These conditions (besides that they are antecedent
states, and not proximate antecedent events, and are therefore never the condi-
tions in closest apparent proximity to the effect) are all of them so obviously
implied, that it is hardly possible there should exist that necessity for insisting
on them, which alone gives occasion for speaking of a single condition as if it
were the cause. Wherever this necessity exists in regard to some one condi-
tion, and does not exist in regard to any other, I conceive that it is consistent
with usage, when scientific accuracy is not aimed at, to apply the name cause

384 INDUCTION.

conditions, however, of any phenomenon, a special enumeration
of which would generally be very prolix, may be all summed
up under one head, namely, the absence of preventing or
counteracting causes. The convenience of this mode of
expression is mainly grounded on the fact, that the effects of
any cause in counteracting another cause may in most cases
be, with strict scientific exactness, regarded as a mere exten-
sion of its own proper and separate effects. If gravity retards
the upward motion of a projectile, and deflects it into a para-
bolic trajectory, it produces, in so doing, the very same kind

to that one condition. If the only condition which can be supposed to be
unknown is a negative condition, the negative condition may be spoken of as
the cause. It might be said that a person died for want of medical advice :
though this would not be likely to be said, unless the person was already
understood to be ill, and in order to indicate that this negative circumstance
was what made the illness fatal, and not the weakness of his constitution, or
the original virulence of the disease. It might be said that a person was
drowned because he could not swim ; the positive condition, namely, that he
fell into the water, being already implied iu the word drowned. And here let
me remark, that his falling into the water is in this case the only positive con-
dition : all the conditions not expressly or virtually included in this (as that he
could not swim, that nobody helped him, and so forth) are negative. Yet, if
it were simply said that the cause of a man's death was falling into the water,
there would be quite as great a sense of impropriety in the expression, as there
would be if it were said that the cause was his inability to swim ; because, though
the one condition is positive and the other negative, it would be felt that neither
of them was sufficient, without the other, to produce death.

With regard to the assertion that nothing is termed the cause, except the
element which exerts active force ; I waive the question as to the meaning of
active force, and accepting the phrase in its popular sense, I revert to a former
example, and I ask, would it be more agreeable to custom to say that a man
fell because his foot slipped in climbing a ladder, or that he fell because of his
weight ? for his weight, and not the motion of his foot, was the active force
which determined his fall. If a person walking out in a frosty day, stumbled
and fell, it might be said that he stumbled because the ground was slippery, or
because he was not sufficiently careful ; but few people, I suppose, would say,
that he stumbled because he walked. Yet the only active force concerned was
that which he exerted in walking : the others were mere negative conditions ;
but they happened to be the only ones which there could be any necessity to
state ; for he walked, most likely, in exactly his usual manner, and the nega-
tive conditions made all the difference. Again, if a person were asked why the
army of Xerxes defeated that of Leonidas, he would probably say, because
they were a thousand times the number ; but I do not think he would say, it
was because they fought, though that was the element of active force. To

LAW OF CAUSATION. 885

of effect, and even (as mathematicians know) the same quan-
tity of effect, as it does in its ordinary operation of causing
the fall of bodies when simply deprived of their support. If
an alkaline solution mixed with an acid destroys its sourness,
and prevents it from reddening vegetable blues, it is because
the specific effect of the alkali is to combine with the acid,
and form a compound with totally different qualities. This
property, which causes of all descriptions possess, of prevent-
ing the effects of other causes by virtue (for the most part) of
the same laws according to which they produce their own,*
enables us, by establishing the general axiom that all causes
are liable to be counteracted in their effects by one another,
to dispense with the consideration of negative conditions
entirely, and limit the notion of cause to the assemblage of
the positive conditions of the phenomenon : one negative
condition invariably understood, and the same in all

boiTow another example, used by Mr. Grove and by Mr. Baden Powell, the
opening of floodgates is said to be the cause of the flow of water; yet the
active force is exerted by the water itself, and opening the floodgates merely
supplies a negative condition. The reviewer adds, " there are some conditions
absolutely passive, and yet absolutely necessary to physical phenomena, viz. the
relations of space and time ; and to these no one ever applies the word cause
without being immediately arrested by those who hear him." Even from this
statement I am compelled to dissent. Few persons would feel it incongruous
to say (for example) that a secret became known because it was spoken of when
A. B. was within hearing ; which is a condition of space : or that the cause
why one of two particular trees is taller than the other, is that it has been
longer planted ; which is a condition of time.

* There are a few exceptions ; for there are some properties of objects
which seem to be purely preventive ; as the property of opaque bodies, by
which they intercept the passage of light. This, as far as we are able to under-
stand it, appears an instance not of one cause counteracting another by the
same law whereby it produces its own effects, but of an agency which manifests
itself in no other way than in defeating the effects of another agency. If we
knew on what other relations to light, or on what peculiarities of structure,
opacity depends, we might find that this is only an apparent, not a real,
exception to the general proposition in the text. In any case it needs not
affect the practical application. The formula which includes all the negative
conditions of an effect in the single one of the absence of counteracting causes,
is not violated by such cases as this ; though, if all counteracting agencies were
of this description, there would be no purpose served by employing the
formula.

VOL. I. 25

886 INDUCTION.

instances (namely, the absence of counteracting causes) being
sufficient, along with the sum of the positive conditions, to
make up the whole set of circumstances on which the pheno-
menon is dependent.

§ 4. Among the positive conditions, as we have seen that
there are some to which, in common parlance, the term cause
is more readily and frequently awarded, so there are others to
which it is, in ordinary circumstances, refused. In most cases
of causation a distinction is commonly drawn between some-
thing which acts, and some other thing which is acted upon ;
between an agent and a patient. Both of these, it would be
universally allowed, are conditions of the phenomenon ; but it
would be thought absurd to call the latter the cause, that title
being reserved for the former. The distinction, however,
vanishes on examination, or rather is found to be only verbal ;
arising from an incident of mere expression, namely, that the
object said to be acted upon, and which is considered as the
scene in which the effect takes place, is commonly included in
the phrase by which the effect is spoken of, so that if it were
also reckoned as part of the cause, the seeming incongruity
would arise of its being supposed to cause itself. In the
instance which we have already had, of falling bodies, the
question was thus put : What is the cause which makes a stone
fall ? and if the answer had been " the stone itself," the
expression would have been in apparent contradiction to the
meaning of the word cause. The stone, therefore, is conceived
as the patient, and the earth (or, according to the common
and most unphilosophical practice, an occult quality of the
earth) is represented as the agent or cause. But that there is
nothing fundamental in the distinction may be seen from this,
that it is quite possible to conceive the stone as causing its
own fall, provided the language employed be such as to save
the mere verbal incongruity. We might say that the stone
moves towards the earth by the properties of the matter com-
posing it; and according to this mode of presenting the
phenomenon, the stone itself might without impropriety be
called the agent ; though, to save the established doctrine

LAW OF CAUSATION. 3S7

of the inactivity of matter, men usually prefer here also to
ascribe the effect to an occult quality, and say that the cause
is not the stone itself, but the tveight or gravitation of the
stone.

Those who have contended for a radical distinction be-
tween agent and patient, have generally conceived the agent
as that which causes some state of, or some change in the
state of, another object which is called the patient. But
a little reflection will show that the licence we assume of
speaking of phenomena as states of the various objects which
take part in them, (an artifice of which so much use has been
made by some philosophers, Brown in particular, for the ap-
parent explanation of phenomena,) is simply a sort of logical
fiction, useful sometimes as one among several modes of
expression, but which should never be supposed to be the
enunciation of a scientific truth. Even those attributes of
an object which might seem with greatest propriety to be
called states of the object itself, its sensible qualities, its
colour, hardness, shape, and the like, are in reality (as no
one has pointed out more clearly than Brown himself)
phenomena of causation, in which the substance is distinctly
the agent, or producing cause, the patient being our own
organs, and those of other sentient beings. What we call
states of objects, are always sequences into which the
objects enter, generally as antecedents or causes : and things
are never more active than in the production of those phe-
nomena in which they are said to be acted upon. Thus,
in the example of a stone falling to the earth, according to
the theory of gravitation the stone is as much an agent as
the earth, which not only attracts, but is itself attracted by,
the stone. In the case of a sensation produced in our organs,
the laws of our organization, and even those of our minds, are
as directly operative in determining the effect produced, as the
laws of the outward object. Though we call prussic acid the
agent of a person's death, the whole of the vital and organic
properties of the patient are as actively instrumental as the
poison, in the chain of effects which so rapidly terminates his
sentient existence. In the process of education, we may

25—2

388 INDUCTION.

call the teacher the agent, and the scholar only the material
acted upon ; yet in truth all the facts which pre-existed in
the scholar's mind exert either co-operating or counteracting
agencies in relation to the teacher's efforts. It is not light
alone which is the agent in vision, hut light coupled with the
active properties of the eye and hrain, and with those of the
visible object. The distinction between agent and patient is
merely verbal : patients are always agents ; in a great pro-
portion, indeed, of all natural phenomena, they are so to
such a degree as to react forcibly on the causes which acted
upon them : and even when this is not the case, they con-
tribute, in the same manner as any of the other conditions, to
the production of the effect of which they are vulgarly treated
as the mere theatre. All the positive conditions of a phe-
nomenon are alike agents, alike active ; and in any expression
of the cause which professes to be complete, none of them can
with reason be excluded, except such as have already been
implied in the words used for describing the effect ; nor by
including even these would there be incurred any but a merely
verbal impropriety.

§ 5. There is a case of causation which calls for separate
notice, as it possesses a peculiar feature, and presents a
greater degree of complexity than the common case. It often
happens that the effect, or one of the effects, of a cause, is,
not to produce of itself a certain phenomenon, but to fit
something else for producing it. In other words, there is a
case of causation in which the effect is to invest an object
with a certain property. When sulphur, charcoal, and nitre
are put together in certain proportions and in a certain
manner, the effect is, not an explosion, but that the mixture
acquires a property by which, in given circumstances, it will
explode. The various causes, natural and artificial, which
educate the human body or the human mind, have for their
principal effect, not to make the body or mind immediately
do anything, but to endow it with certain properties — in
other words, to give assurance that in given circumstances
certain results will take place in it, or as consequences of it.

LAW OF CAUSATION. 389

Physiological agencies often have for the chief part of their
operation to predispose the constitution to some mode of
action. To take a simpler instance than all these : putting
a coat of white paint upon a wall does not merely produce in
those who see it done, the sensation of white ; it confers on
the wall the permanent property of giving that kind of sen-
sation. Regarded in reference to the sensation, the putting on
of the paint is a condition of a condition ; it is a condition of
the wall's causing that particular fact. The wall may have
heeu painted years ago, hut it has acquired a property which
has lasted till now and will last longer ; the antecedent con-
dition necessary to enable the wall to become in its turn a
condition, has been fulfilled once for all. In a case like this,
where the immediate consequent in the sequence is a property
produced in an object, no one now supposes the property
to be a substantive entity "inherent" in the object. What
has been produced is what, in other language, may be called a
state of preparation in an object for producing an effect.
The ingredients of the gunpowder have been brought into a
stafe of preparation for exploding as soon as the other con-
ditions of an explosion shall have occurred. In the case of
the gunpowder, this state of preparation consists in a certain
collocation of its particles relatively to one another. In the
example of the wall, it consists in a new collocation of two
things relatively to each other — the wall and the paint. In
the example of the moulding influences on the human mind,
its being a collocation at all is only conjectural : for, even on
the materialistic hypothesis, it would remain to be proved that
the increased facility with which the brain sums up a column
of figures when it has been long trained to calculation, is the
result of a permanent new arrangement of some of its material
particles. We must, therefore, content ourselves with what
we know, and must include among the effects of causes, the
capacities given to objects of being causes of other effects.
This capacity is not a real thing existing in the objects ; it is
but a name for our conviction that they will act in a particular
manner when certain new circumstances arise. We may
invest this assurance of future events with a fictitious objec-

390

INDUCTION.

tive existence, by calling it a state of the object. But unless
the state consists, as in the case of the gunpowder it does, in
a collocation of particles, it expresses no present fact ; it is
but the contingent future fact brought back under another
name.

It may be thought that this form of causation requires us
to admit an exception to the doctrine that the conditions of a
phenomenon — the antecedents required for calling it into
existence — must all be found among the facts immediately,
not remotely, preceding its commencement. But what we
have arrived at is not a correction, it is only an explanation,
of that doctrine. In the enumeration of the conditions
required for the occurrence of any phenomenon, it always has
to be included that objects must be present, possessed of
given properties. It is a condition of the phenomenon explo-
sion that an object should be present, of one or other of
certain kinds, which for that reason are called explosive.
The presence of one of these' objects is a condition imme-
diately precedent to the explosion. The condition which is
not immediately precedent is the cause which produced,' not
the explosion, but the explosive property. The conditions of
the explosion itself were all present immediately before it took
place, and the general law, therefore, remains intact.

§ 6. It now remains to advert to a distinction which is of
first-rate importance both for clearing up the notion of cause,
and for obviating a very specious objection often made against
the view which we have taken of the subject.

When we define the cause of anything (in the only sense
in which the present inquiry has any concern with causes) to
be "the antecedent which it invariably follows," we do not use
this phrase as exactly synonymous with " the antecedent which
it invariably has followed in our past experience." Such a
mode of conceiving causation would be liable to the objection
very plausibly urged by Dr. Reid, namely, that according to
this doctrine night must be the cause1 of day, and day the
cause of night ; since these phenomena have invariably
succeeded one another from the beginning of the world.

LAW OF CAUSATION. 391

But it is necessary to our using the word cause, that we
should believe not only that the antecedent always has
been followed by the consequent, but that, as long as the
present constitution of things * endures, it always tvill be so.
And this would not be true of day and night. We do not
believe that night will be followed by day under all imaginable
circumstances, but only that it will be so provided the sun
rises above the horizon. If the sun ceased to rise, which,
for aught we know, may be perfectly compatible with the
general laws of matter, night would be, or might be, eternal.
On the other hand, if the sun is above the horizon, his light
not extinct, and no opaque body between us and him, we
believe firmly that unless a change takes place in the pro-
perties of matter, this combination of antecedents will be
followed by the consequent, day ; that if the combination of
antecedents could be indefinitely prolonged, it would be
always day ; and that if the same combination had always
existed, it would always have been day, quite independently
of night as a previous condition. Therefore is it that we do
not call night the cause, nor even a condition, of day. The
existence of the sun (or some such luminous body), and there
being no opaque medium in a straight line f between that
body and the part of the earth where we are situated, are the
sole conditions ; and the union of these, without the addition
of any superfluous circumstance, constitutes the cause. This
is what writers mean when they say that the notion of cause
involves the idea of necessity. If there be any meaning
which confessedly belongs to the term necessity, it is uncon-

* I mean by this expression, the ultimate laws of nature (whatever they
may be) as distinguished from the derivative laws and from the collocations.
The diurnal revolution of the earth (for example) is not a part of the constitu-
tion of things, because nothing can be so called which might possibly be termi-
nated or altered by natural causes.

t I use the words " straight line " for brevity and simplicity. In reality
the line in question is not exactly straight, for, from the effect of refraction,
we actually see the sun for a short interval during which the opaque mass of
the earth is interposed in a direct line between the sun and our eyes ; thus
realizing, though but to a limited extent, the coveted desideratum of seeing
round a corner.

392 INDUCTION.

ditionalness. That which is necessary, that which must be,
means that which will be, whatever supposition we may make
in regard to all other things. The succession of day and
night evidently is not necessary in this sense. It is con-
ditional on the occurrence of other antecedents. That which
will be followed by a given consequent when, and only when,
some third circumstance also exists, is not the cause, even
though no case should ever have occurred in which the phe-
nomenon took place without it.

Invariable sequence, therefore, is not synonymous with
causation, unless the sequence, besides being invariable, is
unconditional. There are sequences, as uniform in past expe-
rience as any others whatever, which yet we do not regard as
cases of causation, but as conjunctions in some sort accidental.
Such, to an accurate thinker, is that of day and night. The
one might have existed for any length of time, and the other
not have followed the sooner for its existence ; it follows only
if certain other antecedents exist; and where those ante-
cedents existed, it would follow in any case. No one, pro-
bably, ever called night the cause of day; mankind must so
soon have arrived at the very obvious generalization, that the
state of general illumination which we call day would follow
from the presence of a sufficiently luminous body, whether
darkness had preceded or not.

We may define, therefore, the cause of a phenomenon, to
be the antecedent, or the concurrence of antecedents, on which
it is invariably and unconditionally consequent. Or if we adopt
the convenient modification of the meaning of the word cause,
which confines it to the assemblage of positivp conditions
without the negative, then instead of " unconditionally," we
must say, " subject to no other than negative conditions."

To some it may appear, that the sequence between night
and day being invariable in our experience, we have as much
ground in this case as experience can give in any case, for
recognising the two phenomena as cause and effect; and that
to say that more is necessary — to require a belief that the
succession is unconditional, or in other words that it would be
invariable under all changes of circumstances, is to acknow-

LAW OF CAUSATION. 393

ledge in causation an element of belief not derived from expe-
rience. The answer to this is, that it is experience itself
which teaches us that one uniformity of sequence is condi-
tional and another unconditional. When we judge that the
succession of night and day is a derivative sequence, depend-
ing on something else, we proceed on grounds of experience.
Jt is the evidence of experience which convinces us that day
could equally exist without being followed by night, and that
night could equally exist without being followed by day. To
say that these beliefs are " not generated by our mere obser-
vation of sequence,"* is to forget that twice in every twenty-
four hours, when the sky is clear, we have an experimentum
crucis that the cause of day is the sun. We have an experi-
mental knowledge of the sun which justifies us on experi-
mental grounds in concluding, that if the sun were always
above the horizon there would be day, though there had been
no night, and that if the sun were always below the horizon
there would be night, though there had been no day. We
thus know from experience that the succession of night and
day is not unconditional. Let me add, that the antecedent
which is only conditionally invariable, is not the invariable
antecedent. Though a fact may, in experience, have always
been followed by another fact, yet if the remainder of our
experience teaches us that it might not always be so followed,
or if the experience itself is such as leaves room for a possibi-
lity that the known cases may not correctly represent all pos-
sible cases, the hitherto invariable antecedent is not accounted
the cause ; but why ? Because we are not sure that it is the
invariable antecedent.

Such cases of sequence as that of day and night not only
do not contradict the doctrine which resolves causation into
invariable sequence, but are necessarily implied in that
doctrine. It is evident, that from a limited number of uncon-
ditional sequences, there will result a much greater number of
conditional ones. Certain causes being given, that is, certain
antecedents which are unconditionally followed by certain
-consequents; the mere coexistence of these causes will give

* Second Burnett Prize Essay, by Principal Tulloch, p. 25.

394

INDUCTION.

rise to an unlimited number of additional uniformities. If
two causes exist together, the effects of both will exist toge-
ther ; and if many causes coexist, these causes (by what we
shall term hereafter the intermixture of their laws) will give
rise to new effects, accompanying or succeeding one another
in some particular order, which order will be invariable while
the causes continue to coexist, but no longer. The motion
of the earth in a given orbit round the sun, is a series of
changes which follow one another as antecedents and conse-
quents, and will continue to do so while the sun's attraction,
and the force with which the earth tends to advance in a
direct line through space, continue to coexist in the same
quantities as at present. But vary either of these causes, and
this particular succession of motions would cease to take
place. The series of the earth's motions, therefore, though
a case of sequence invariable within the limits of human expe-
rience, is not a case of causation. It is not unconditional.

This distinction between the relations of succession which
so far as we know are unconditional, and those relations,
whether of succession or of coexistence, which, like the earth's
motions, or the succession of day and night, depend on the
existence or on the coexistence of other antecedent facts — •
corresponds to the great division which Dr. Whewell and
other writers have made of the field of science, into the inves-
tigation of what they term the Laws of Phenomena, and the
investigation of causes; a phraseology, as I conceive, not
philosophically sustainable, inasmuch as the ascertainment of
causes, such causes as the human faculties can ascertain,
namely, causes which are themselves phenomena, is, therefore,
merely the ascertainment of other and more universal Laws
of Phenomena. And let me here observe, that Dr. Whewell,
and in some degree even Sir John Herschel, seem to have
misunderstood the meaning of those writers who, like M.
Comte, limit the sphere of scientific investigation to Laws of
Phenomena, and speak of the inquiry into causes as vain and
futile. The causes which M. Comte designates as inacces-
sible, are efficient causes. The investigation of physical, as
opposed to efficient, causes (including the study of all the

LAW OF CAUSATION. 895

active forces in Nature, considered as facts of observation) is
as important a part of M. Comte's conception of science as of
Dr. Whewell's. His objection to the word cause is a mere matter
of nomenclature, in whicb, as a matter of nomenclature, I
consider him to be entirely wrong. "Those," it is justly
remarked by Mr. Bailey,* "who, like M. Comte, object to
designate events as causes, are objecting without any real
ground to a mere but extremely convenient generalization, to
a very useful common name, the employment of which
involves, or needs involve, no particular theory." To which
it may be added, that by rejecting this form of expression,
M. Comte leaves himself without any term for marking a
distinction which, however incorrectly expressed, is not only
real, but is one of the fundamental distinctions in science ;
indeed it is on this alone, as we shall hereafter find, that the
possibility rests of framing a rigorous Canon of Induction.
And as things left without a name are apt to be forgotten, a
Canon of that description is not one of the many benefits
which the philosophy of Induction has received from M.
Comte's great powers.

§ 7. Does a cause always stand with its effect in the
relation of antecedent and consequent ? Do we not often say
of two simultaneous facts that they are cause and effect — as
when we say that fire is the cause of warmth, the sun and
moisture the cause of vegetation, and the like? Since a
cause does not necessarily perish because its effect has been
produced, the two things do very generally coexist ; and there
are some appearances, and some common expressions, seeming
to imply not only that causes may, but that they must, be
contemporaneous with their effects. Cessante causa cessat et
ejfcctus, has been a dogma of the schools: the necessity for
the continued existence of the cause in order to the continu-
ance of the effect, seems to have been once a generally received
doctrine. Kepler's numerous attempts to account for the
motions of the heavenly bodies on mechanical principles, were
rendered abortive by his always supposing that the agency

* Letters on the Philosophy of the Human Mind, First Series, p. 21P.

396 INDUCTION.

which set those bodies in motion must continue to operate in
order to keep up the motion which it at first produced. Yet
there were at all times many familiar instances of the con-
tinuance of effects, long after their causes had ceased. A coup
de soleil gives a person brain fever : will the fever go off as
soon as he is moved out of the sunshine ? A sword is run
through his body : must the sword remain in his body in
order that he may continue dead ? A ploughshare once
made, remains a ploughshare, without any continuance of
heating and hammering, and even after the man who heated
and hammered it has been gathered to his fathers. On the
other hand, the pressure which forces up the mercury in an
exhausted tube must be continued in order to sustain it in
the tube. This (it may be replied) is because another force
is acting without intermission, the force of gravity, which
would restore it to its level, unless counterpoised by a force
equally constant. But again : a tight bandage causes pain,
which pain will sometimes go off as soon as the bandage is
removed. The illumination which the sun diffuses over the
earth ceases when the sun goes down.

There is, therefore, a distinction to be drawn. The con-
ditions which are necessary for the first production of a phe-
nomenon, are occasionally also necessary for its continuance ;
though more commonly its continuance requires no condition
except negative ones. Most things, once produced, continue
as they are, until something changes or destroys them ; but
some require the permanent presence of the agencies which
produced them at first. These may, if we please, be considered
as instantaneous phenomena, requiring to be renewed at each
instant by the cause by which they were at first generated.
Accordingly, the illumination of any given point of space
has always been looked upon as an instantaneous fact, which
perishes and is perpetually renewed as long as the necessary
conditions subsist. If we adopt this language we avoid the
necessity of admitting that the continuance of the cause is
ever required to maintain the effect. We may say, it is not
required to maintain, but to reproduce, the effect, or else to
counteract some force tending to destroy it. And this may be

LAW OF CAUSATION. 397

a convenient phraseology. But it is only a phraseology. The
fact remains, that in some cases (though those are a minority)
the continuance of the conditions which produced an effect is
necessary to the continuance of the effect.

As to the ulterior question, whether it is strictly necessary
that the cause, or assemblage of conditions, should precede,
by ever so short an instant, the production of the effect, (a
question raised and argued with much ingenuity by Sir John
Herschel in an Essay already quoted,*) the inquiry is of no
consequence for our present purpose. There certainly are
cases in which the effect follows without any interval per-
ceptible by our faculties ; and when there is an interval, we
cannot tell by how many intermediate links imperceptible to
us that interval may really be filled up. But even granting
that an effect may commence simultaneously with its cause,
the view I have taken of causation is in no way practically
affected. Whether the cause and its effect be necessarily suc-
cessive or not, the beginning of a phenomenon is what implies
a cause, and causation is the law of the succession of phe-
nomena. If these axioms be granted, we can afford, though
I see no necessity for doing so, to drop the words antecedent
and consequent as applied to cause and effect. I have no
objection to define a cause, the assemblage of phenomena,
which occurring, some other phenomenon invariably com-
mences, or has its origin. Whether the effect coincides in
point of time with, or immediately follows, the hindmost of its
conditions, is immaterial. At all events it does not precede
it ; and when we are in doubt, between two co-existent phe-
nomena, which is cause and which effect, we rightly deem the
question solved if we can ascertain which of them preceded
the other.

§ 8. It continually happens that several different phe-
nomena, which are not in the slightest degree dependent or
conditional on one another, are found all to depend, as the
phrase is, on one and the same agent; in other words, one

* Essays, pp. 206-208.

398 INDUCTION.

and the same phenomenon is seen to be followed by several
sorts of effects quite heterogeneous, but which go on simul-
taneously one with another; provided, of course, that all other
conditions requisite for each of them also exist. Thus, the
sun produces the celestial motions, it produces daylight, and
it produces heat. The earth causes the fall of heavy bodies,
and it also, in its capacity of a great magnet, causes the phe-
nomena of the magnetic needle. A crystal of galena causes
the sensations of hardness, of weight, of cubical form, of grey
colour, and many others between which we can trace no inter-
dependence. The purpose to which the phraseology of Pro-
perties and Powers is specially adapted, is the expression of
this sort of cases. When the same phenomenon is followed
(either subject or not to the presence of other conditions) by
effects of different and dissimilar orders, it is usual to say that
each different sort of effect is produced by a different property
of the cause. Thus we distinguish the attractive or gravitative
property of the earth, and its magnetic property: the gravita-
tive, lurainiferous, and calorific properties of the sun : the colour,
shape, weight, and hardness of a crystal. These are mere
phrases, which explain nothing, and add nothing to our know-
ledge of the subject ; but, considered as abstract names denoting
the connexion between the different effects produced and the
object which produces them, they are a very powerful instru-
ment of abridgment, and of that acceleration of the process of
thought which abridgment accomplishes.

This class of considerations leads to a conception which
we shall find to be of great importance, that of a Permanent
Cause, or original natural agent. There exist in nature a
number of permanent causes, which have subsisted ever since
the human race has been in existence, and for an indefinite
and probably an enormous length of time previous. The sun,
the earth, and planets, with their various constituents, air,
water, and other distinguishable substances, whether simple or
compound, of which nature is made up, are such Permanent
Causes. These have existed, and the effects or consequences
which they were fitted to produce have taken place (as often
as the other conditions of the production met,) from the very

LAW OF CAUSATION. 399

beginning of our experience. But we can give no account of

the origin of the Permanent Causes themselves. Why these

particular natural agents existed originally and no others, or

why they are commingled in such and such proportions, and

distributed in such and such a manner throughout space, is a

question we cannot answer. More than this : we can discover

nothing regular in the distribution itself; we can reduce it to

no uniformity, to no law. There are no means by which, from

the distribution of these causes or agents in one part of space,

we could conjecture whether a similar distribution prevails in

another. The coexistence, therefore, of Primeval Causes,

ranks, to us, among merely casual concurrences : and all those

sequences or coexistences among the effects of several such

causes, which, though invariable while those causes coexist,

would, if the coexistence terminated, terminate along with it,

we do not class as cases of causation, or laws of nature : we

can only calculate on finding these sequences or coexistences

where we know by direct evidence, that the natural agents on

the properties of which they ultimately depend, are distributed

in the requisite manner. These Permanent Causes are not

always objects ; they are sometimes events, that is to say,

periodical cycles of events, that being the only mode in which

events can possess the property of permanence. Not only, for

instance, is the earth itself a permanent cause, or primitive

natural agent, but the earth's rotation is so too : it is a cause

which has produced, from the earliest period, (by the aid of

other necessary conditions,) tLa succession of day and night,

the ebb and flow of the sea, and many other effects, while, as

we can assign no cause (except conjecturally) for the rotation

itself, it is entitled to be ranked as a primeval cause. It is,

however, only the origin of the rotation which is mysterious

to us : once begun, its continuance is accounted for by the first

law of motion (that of the permanence of rectilinear motion

once impressed) combined with the gravitation of the parts of

the earth towards one another.

All phenomena without exception which begin to exist,
that is, all except the primeval causes, are effects either imme-
diate or remote of those primitive facts, or of some combinu-

400 INDUCTION*.

tion of them. There is no Thing produced, no event happen-
ing, in the known universe, which is not connected hy an
uniformity, or invariable sequence, with some one or more of
the phenomena which preceded it ; insomuch that it will happen
again as often as those phenomena occur again, and as no other
phenomenon having the character of a counteracting cause
shall coexist. These antecedent phenomena, again, were con-
nected in a similar manner with some that preceded them ; and
so on, until we reach, as the ultimate step attainable hy us,
either the properties of some one primeval cause, or the con-
junction of several. The whole of the phenomena of nature
were therefore the necessary, or in other words, the uncondi-
tional, consequences of some former collocation of the Perma-
nent Causes.

The state of the whole universe at any instant, we believe
to be the consequence of its state at .the previous instant ;
insomuch that one who knew all the agents which exist at the
present moment, their collocation in space, and all their pro-
perties, in other words, the laws of their agency, could predict
the whole subsequent history of the universe, at least unless
some new volition of a power capable of controlling the uni-
verse should supervene.* And if any particular state of the

* To the universality which mankind are agreed in ascribing to the Law of
Causation, there is one claim of exception, one disputed case, that of the
Human Will ; the determinations of which, a large class of metaphysicians are
not willing to regard as following the causes called motives, according to as
strict laws as those which they suppose to exist in the world of mere matter.
This controverted point will undergo a special examination when we come to
treat particularly of the Logic of the Moral Sciences (Book vi. ch. 2). In the
meantime I may remark that these metaphysicians, who, it must be observed,
ground the main part of their objection on the supposed repugnance of the
doctrine in question to our consciousness, seem to me to mistake the fact which
consciousness testifies against. What is really in contradiction to consciousness,
they would, I think, on strict self-examination, find to be, the application to
human actions and volitions of the ideas involved in the common use of the
term Necessity; which I agree with them in objecting to. But if they would
consider that by saying that a person's actions necessarily follow from his
character, all that is really meant (for no more is meant in any case whatever
of causation) is that he invariably does act in conformity to his character, and
that any one who thoroughly knew his character could certainly predict how

LAW OF CAUSATION. 401

entire universe could ever recur a second time, all subsequent
states would return too, and history would, like a circulating
decimal of many figures, periodically repeat itself: —

Jam redit et virgo, redeunt Saturnia regna. . . .
Alter erit turn Tiphys, et altera quae vehat Argo
Delectos heroas ; erunt quoque altera bella,
Atque iterum ad Trojam magnus inittetur Achilles.

And though things do not really revolve in this eternal round,
the whole series of events in the history of the universe, past
and future, is not the less capable, in its own nature, of being
constructed a priori by any one whom we can suppose ac-
quainted with the original distribution of all natural agents,
and with the whole of their properties, that is, the laws of suc-
cession existing between them and their effects: saving the far
more than human powers of combination and calculation which
would be required, even in one possessing the data, for the
actual performance of the task.

§ 9. Since everything which occurs is determined by
laws of causation and collocations of the original causes, it
follows that the coexistences which are observable among effects
cannot be themselves the subject of any similar set of laws,
distinct from laws of causation. Uniformities there are, as well
of coexistence as of succession, among effects ; but these must
in all cases be a mere result either of the identity or of the
coexistence of their causes; if the causes did not coexist,
neither could the effects. And these causes being also effects
of prior causes, and these of others, until we reach the primeval
causes, it follows that (except in the case of effects which
can be traced immediately or remotely to one and the same
cause) the coexistences of phenomena can in no case be uni-
versal, unless the coexistences of the primeval causes to which
the effects are ultimately traceable, can be reduced to an uni-
versal law : but we have seen that they cannot. There are,
accordingly, no original and independent, in other words no

he would act in any supposable case ; they probably would not find Una
doctrine either contrary to their experience or revolting to their feelings. And
no more than this is contended for by any one but an Asiatic fatalist.

VOL. i. 26

402

INDUCTION.

unconditional, uniformities of coexistence, between effects of
different causes; if they coexist, it is only because tbe causes
have casually coexisted. The only independent and uncondi-
tional coexistences which are sufficiently invariable to have
any claim to the character of laws, are between different and
mutually independent effects of the same cause ; in other words,
between different properties of the same natural agent. This
portion of the Laws of Nature will be treated of in the latter
part of the present Book, under the name of the Specific Pro-
perties of Kinds.

§ 10. Since the first publication of the present treatise,
the sciences of physical nature have made a great advance in
generalization, through the doctrine known as the Conserva-
tion or Persistence of Force. This imposing edifice of theory,
the building and laying out of which has for some time been
the principal occupation of the most systematic minds among
physical enquirers, consists of two stages : one, of ascertained
fact, the other containing a large element of hypothesis.

To begin with the first. It is proved by numerous facts,
both natural and of artificial production, that agencies which
had been regarded as distinct and independent sources of
force — heat, electricity, chemical action, nervous and muscular
action, momentum of moving bodies — are interchangeable, in
definite and fixed quantities, with one another. It had long
been known that these dissimilar phenomena had the power,
under certain conditions, of producing one another : what is
new in the theory is a more accurate estimation of what this
production consists in. What happens is, that the whole or
part of the one kind of phenomena disappears, and is replaced
by phenomena of one of the other descriptions, and that there
is an equivalence in quantity between the phenomena that
have disappeared and those which have been produced, insomuch
that if the process be reversed, the very .same quantity which
had disappeared will reappear, without increase or diminu-
tion. Thus, the amount of heat which will raise the tem-
perature of a pound of water one degree of the thermometer,
will, if expended, say in the expansion of steam, lift a weight

LAW OF CAUSATION. 403

of 772 pounds one foot, or a weight of one pound 772 feet:
and the same exact quantity of heat can, by certain means, be
recovered, through the expenditure of exactly that amount of
mechanical motion.

The establishment of this comprehensive law has led to a
change in the language in which the scientific world had been
accustomed to speak of what are called the Forces of nature.
Before this correlation between phenomena most unlike one
another had been ascertained, their unlikeness had caused
them to be referred to so many distinct forces. Now that they
are known to be convertible into one another without loss,
they are spoken of as all of them results of one and the same
force, manifesting itself in different modes. This force (it is
said) can only produce a limited and definite quantity of effect,
but always does produce that definite quantity ; and produces
it, according to circumstances, in one or another of the forms,
or divides it among several, but so as (according to a scale
of numerical equivalents established by experiment) always to
make up the same sum : and no one of the manifestations can
be produced, save by the disappearance of the equivalent
quantity of another, which in its turn, in appropriate circum-
stances, will reappear undiminished. This mutual interchange-
ability of the forces of nature, according to fixed numerical
equivalents, is the part of the new doctrine which rests on
irrefragable fact.

To make the statement true, however, it is necessary to
add, that an indefinite and perhaps immense interval of time
may elapse between the disappearance of the force in one form
and its reappearance in another. A stone thrown up into the
air with a given force, and falling back immediately, will, by
the time it reaches the earth, recover the exact amount of
mechanical momentum which was expended in throwing it
up, deduction being made of a small portion of motion which
has been communicated to the air. But if the stone has lodged
on a height, it may not fall back for years, or perhaps ages,
and until it does, the force expended in raising it is temporarily
lost, being represented only by what, in the language ot the
new theory, is called potential energy. The coal imbedded in

26—2

404 INDUCTION.

the earth is considered by the theory as a vast reservoir of
force, which has remained dormant for many geological
periods, and will so remain until, by being burnt, it gives out
the stored-up force in the form of heat. Yet it is not sup-
posed that this force is a material thing which can be confined
by bounds, as used to be thought of latent heat when that
important phenomenon was first discovered. What is meant
is that when the coal does at last, by combustion, generate a
quantity of heat (transformable like all other heat into mecha-
nical momentum, and the other forms of force), this extrication
of heat is the reappearance of a force derived from the sun's
rays, expended myriads of ages ago in the vegetation of the
organic substances which were the material of the coal.

Let us now pass to the higher stage of the theory of Con-
servation of Force ; the part which is no longer a generalization
of proved fact, but a combination of fact and hypothesis.
Stated in few words, it is as follows : That the Conservation
of Force is really the Conservation of Motion ; that in the
various interchanges between the forms of force, it is always
motion that is transformed into motion. To establish this, it
is necessary to assume motions which are hypothetical. The
supposition is, that there are motions which manifest them-
selves to our senses only as heat, electricity, &c., being
molecular motions ; oscillations, invisible to us, among the
minute particles of bodies ; and that these molecular motions
are transmutable into molar motions (motions of masses), and
molar motions into molecular. Now there is a real basis of fact
for this supposition : we have positive evidence of the existence
of molecular motion in these manifestations of force. In the
case of chemical action, for instance, the particles separate and
form new combinations, often with a great visible disturbance
of the mass. In the case of heat, the evidence is equally con-
clusive, since heat expands bodies (that is, causes their particles
to move from one another) ; and if of sufficient amount, changes
their mode of aggregation from solid to liquid, or from liquid to
gaseous. Again, the mechanical actions which produce heat —
friction, and the collision of bodies — must from the nature of the
case produce a shock, that is, an internal motion of particles,

LAW OF CAUSATION. 405

which indeed, we find, is often so violent as to break them per-
manently asunder. Such facts are thought to warrant the
inference, that it is not, as was supposed, heat that causes
the motion of particles, but the motion of particles that causes
heat; the original cause of both being the previous motion
(whether molar or molecular — collision of bodies or combustion
of fuel) which formed the heating agency. This inference
already contains hypothesis : but at least the supposed cause,
the intestine motion of molecules, is a vera causa. But in
order to reduce the Conservation of Force to Conservation of
Motion, it was necessary to attribute to motion the heat pro-
pagated, through apparently empty space, from the sun.
This required the supposition (already made for the expla-
nation of the laws of light) of a subtle ether pervading space,
which, though impalpable to us, must have the property
which constitutes matter, that of resistance, since waves are
propagated through it by an impulse from a given point.
The ether must be supposed (a supposition not required by the
theory of light) to penetrate into the minute interstices of all
bodies. The vibratory motion supposed to b« taking place in
the heated mass of the sun, is considered as imparted from
that mass to the particles of the surrounding ether, and
through them to the particles of the same ether in the inter-
stices of terrestrial bodies; and this, too, with a sufficient me-
chanical force to throw the particles of those bodies intoastate of
similar vibration, producing the expansion of their mass, and the
sensation of heat in sentient creatures. All this is hypothesis,
though, of its legitimacy as hypothesis, I do not mean to ex-
press any doubt. It would seem to follow as a consequence
from this theory, that Force may and should be defined, matter
in motion. This definition, however, will not stand, for, as
has already been seen, the matter needs not be in actual motion.
It is not necessary to suppose that the motion afterwards
manifested, is actually taking place among the molecules of
the coal during its sojourn in the earth ; * certainly not in
the stone which is at rest on the eminence to which it has

* I believe, however, the accredited authorities do suppose that molecular
motion, equivalent in amount to that which will be manifested in the combus-

406 INDUCTION.

been raised. The true definition of Force must be, not motion,
but Potentiality of Motion ; and what the doctrine, if esta-
blished, amounts to, is, not that there is at all times the same
quantity of actual motion in the universe ; but that the possi-
bilities of motion are limited to a definite quantity, -which can-
not be added to, but which cannot be exhausted ; and that all
actual motion which takes place in Nature is a draft upon this
limited stock. It needs not all of it have ever existed as
actual motion. There is a vast amount of potential motion in
the universe in the form of gravitation, which it would be a
great abuse of hypothesis to suppose to have been stored up
by the expenditure of an equal amount of actual motion in
some former state of the universe. Nor does the motion pro-
duced by gravity take place, so far as we know, at the expense
of any other motion, either molar or molecular.

It is proper to consider whether the adoption of this theory
as a scientific truth, involving as it does a change in the con-
ception hitherto entertained of the most general physical
agencies, requires any modification in the view I have taken
of Causation as a law of nature. As it appears to me, none
whatever. The manifestations which the theory regards as
modes of motion, are as much distinct and separate phe-
nomena when referred to a single force, as when attributed
to several. Whether the phenomenon is called a transfor-
mation of force or the generation of one, it has its own set or
sets of antecedents, with which it is connected by invariable
and unconditional sequence ; and that set, or those sets, of
antecedents, are its cause. The relation of the Conservation
theory to the principle of Causation is discussed in much
detail, and very instructively, by Professor Bain, in the second
volume of his Logic. The chief practical conclusion drawn
by him, bearing on Causation, is, that we must distinguish in
the assemblage of conditions which constitutes the Cause of a
phenomenon, two elements : one, the presence of a force ; the
other, the collocation or position of objects which is required

tion of the coal, is actually taking place during the whole of the long interval,
if not in the coal, yet in the oxygen which will then combine with it. But how
purely hypothetical this supposition is, need hardly be remarked ; I venture
to say, unnecessarily and extravagantly hypothetical.

LAW OF CAUSATION. 407

in order that the force may undergo the particular transinu-
tatiou which constitutes the phenomenon. Now, it might
always have been said with acknowledged correctness, that a
force and a collocation were both of them necessary to pro-
duce any phenomenon. The law of causation is, that
change can only be produced by change. Along with any
number of stationary antecedents, which are collocations,
there must be at least one changing antecedent, which is a
force. To produce a bonfire, there must not only be fuel, and
air, and a spark, which are collocations, but chemical action
between the air and the materials, which is a force. To grind
corn, there must be a certain collocation of the parts com-
posing a mill, relatively to one another and to the corn ; but
there must also be the gravitation of water, or the motion of
wind, to supply a force. But as the force in these cases was
regarded as a property of the objects in which it is embodied,
it seemed tautology to say that there must be the collocation
and the force. As the collocation must be a collocation of
objects possessing the force-giving property, the collocation,
so understood, included the force.

How, then, shall we have to express these facts, if the
theory be finally substantiated that all Force is reducible to a
previous Motion ? We shall have to say, that one of the con-
ditions of every phenomenon is an antecedent Motion. But
it will have to be explained that this needs not be actual
motion. The coal which supplies the force exerted in com-
bustion is not shown to have been exerting that force in
the form of molecular motion in the pit; it was not even
exerting pressure. The stone on the eminence is exerting a
pressure, but only equivalent to its weight, not to the addi-
tional momentum it would acquire by falling. The ante-
cedent, therefore, is not a force in action ; and we can still
only call it a property of the objects, by which they would
exert a force on the occurrence of a fresh collocation. The
collocation, therefore still includes the force. The force said
to be stored up, is simply a particular property which the
object has acquired. The cause we are in search of, is a col-
location of objects possessing that particular property. When

408 INDUCTION.

indeed we inquire further into the cause from which they
derive that property, the new conception introduced by
the Conservation theory comes in : the property is itself an
effect, and its cause, according to the theory, is a former
motion of exactly equivalent amount, which has been impressed
on the particles of the body, perhaps at some very distant
period. But the case is simply one of those we have already
considered, in which the efficacy of a cause consists in its
investing an object with a property. The force said to be laid
up, and merely potential, is no more a really existing thing
than any other properties of objects are really existing things.
The expression is a mere artifice of language, convenient for
describing the phenomena : it is unnecessary to suppose that
any thing has been in continuous existence except an abstract
potentiality. A force suspended in its operation, neither
manifesting itself by motion nor by pressure, is not an
existing fact, but a name for our conviction that in appro-
priate circumstances a fact would take place. We know that
a pound weight, were it to fall from the earth into the sun,
would acquire in falling a momentum equal to millions of
pounds ; but we do not credit the pound weight with more of
actually existing force than is equal to the pressure it is now
exerting on the earth, and that is exactly a pound. We
might as well say that a force of millions of pounds exists in a
pound, as that the force which will manifest itself when the
coal is burnt is a real thing existing in the coal. What is
fixed in the coal is only a certain property: it has become fit
to be the antecedent of an effect called combustion, which
partly consists in giving out, under certain conditions, a given
definite quantity of heat.

We thus see that no new general conception of Causation
is introduced by the Conservation theory. The indestructi-
bility of Force no more interferes with the theory of Causation
than the indestructibility of Matter, meaning by matter, the
element of resistance in the sensible world. It only enables
us to understand better than before the nature and laws of
some of the sequences.

This better understanding, however, enables us, with Mr.

LAW OF CAUSATION. 409

Bain, to admit, as one of the tests for distinguishing causatioti
from mere concomitance, the expenditure or transfer of energy.
If the effect, or any part of the effect, to be accounted for,
consists in putting matter in motion, then any of the objects
present which has lost motion has contributed to the effect ;
and this is the true meaning of the proposition that the cause
is that one of the antecedents which exerts active force.

§11. It is proper in this place to advert to a rather
ancient doctrine respecting causation, which has been revived
during the last few years in many quarters, and at present gives
more signs of life than any other theory of causation at variance
with that set forth in the preceding pages.

According to the theory in question, Mind, or to speak
more precisely, Will, is the only cause of phenomena. The
type of Causation, as well as the exclusive source from which
we derive the idea, is our own voluntary agency. Here, and
here only (it is said) we have direct evidence of causation. We
know that we can move our bodies. Respecting the pheno-
mena of inanimate nature, we have no other direct knowledge
than that of antecedence and sequence. But in the case of
our voluntary actions, it is affirmed that we are conscious
of power before we have experience of results. An act of
volition, whether followed by an effect or not, is accompanied
by a consciousness of effort, " of force exerted, of power in
action, which is necessarily causal, or causative." This feel-
ing of energy or force, inherent in an act of will, is knowledge
a priori; assurance, prior to experience, that we have the
power of causing effects. Volition, therefore, it is asserted, is
something more than an unconditional antecedent; it is a
cause, in a different sense from that in which physical pheno-
mena are said to cause one another : it is an Efficient Cause.
From this the transition is easy to the further doctrine, that
Volition is the sole Efficient Cause of all phenomena. " It is
inconceivable that dead force could continue unsupported for
a moment beyond its creation. We cannot even conceive of
change or phenomena without the energy of a mind." " The
word action " itself, says another writer of the same school,

410 INDUCTION.

" has no real significance except when applied to the doings of
an intelligent agent. Let any one conceive, if he can, of any
power, energy, or force, inherent in a lump of matter." Phe-
nomena may have the semblance of being produced by phy-
sical causes, but they are in reality produced, say these writers,
by the immediate agency of mind. All things which do not
proceed from a human (or, I suppose, an animal) will, pro-
ceed, they say, directly from divine will. The earth is not
moved by the combination of a centripetal and a projectile
force ; this is but a mode of speaking, which serves to facili-
tate our conceptions. It is moved by the direct volition of an
omnipotent Being, in a path coinciding with that which we
deduce from the hypothesis of these two forces.

As I have so often observed, the general question of the
existence of Efficient Causes does not fall within the limits of
our subject: but a theory which represents them as capable of
being subjects of human knowledge, and which passes off as
efficient causes what are only physical or phenomenal causes,
belongs as much to Logic as to Metaphysics, and is a fit sub-
ject for discussion here.

To my apprehension, a volition is not an efficient, but
simply a physical cause. Our will causes our bodily actions
in the same sense, and in no other, in which cold causes ice,
or a spark causes an explosion of gunpowder. The volition,
a state of our mind, is the antecedent ; the motion of our limbs
in conformity to the volition, is the consequent. This sequence
I conceive to be not a subject of direct consciousness, in the
sense intended by the theory. The antecedent, indeed, and
the consequent, are subjects of consciousness. But the con-
nexion between them is a subject of experience. I cannot
admit that our consciousness of the volition contains in itself
any a priori knowledge that the muscular motion will follow.
If our nerves of motion were paralysed, or our muscles stiff
and inflexible, and had been so all our lives, I do not see the
slightest ground for supposing that we should ever (unless by
information from other people) have known anything of voli-
tion as a physical power, or been conscious of any tendency
in feelings of our mind to produce motions of our body, or of

LAW OF CAUSATION. 411

other bodies. I will not undertake to say whether we should
in that case have had the physical feeling which I suppose is
meant when these writers speak of " consciousness of effort :"
I see no reason why we should not; since that physical feeling
is probably a state of nervous sensation beginning and ending
in the brain, without involving the motory apparatus : but we
certainly should not have designated it by any term equivalent
to effort, since effort implies consciously aiming at an end,
which we should not only in that case have had no reason to
do, but could not even have had the idea of doing. If con-
scious at all of this peculiar sensation, we should have been
conscious of it, I conceive, only as a kind of uneasiness, ac-
companying our feelings of desire.

It is well argued by Sir William Hamilton against the
theory in question, that it " is refuted by the consideration
that between the overt fact of corporeal, movement of which
we are cognisant, and the internal act of mental determination
of which we are also cognisant, there intervenes a numerous
series of intermediate agencies of which we have no knowledge ;
and, consequently, that we can have no consciousness of any
causal connexion between the extreme links of this chain, the
volition to move and the limb moving, as this hypothesis
asserts. No one is immediately conscious, for example, of
moving his arm through his volition. Previously to this
ultimate movement, muscles, nerves, a multitude of solid and
fluid parts, must be set in motion by the will, but of this
motion we know, from consciousness, absolutely nothing. A
person struck with paralysis is conscious of no inability in his
limb to fulfil the determinations of his will ; and it is only
after having willed, and finding that his limbs do not obey his
volition, that he learns by this experience, that the external
movement does not follow the internal act. But as the para-
lytic learns after the volition that his limbs do not obey his
mind ; so it is only after volition that the man in health learns,
that his limbs do obey the mandates of his will."*

* Lectures on Metaphysics, vol. ii. Lect. xxxix. pp. 391-2.
I regret that I cannot invoke the authority of Sir William Hamilton in
favour of my own opinions on Causation, as I can against the particular theory

412

INDUCTION'.

Those against whom I am contending have never pro-
duced, and do not pretend to produce, any positive evidence*
that the power of our will to move our bodies would be known
to us independently of experience. What they have to say
on the subject is, that the production of physical events by a
•will seems to carry its own .explanation with it, while the
action of matter upon matter seems to require something else
to explain it; and is even, according to them, "inconceivable"
on any other supposition than that some will intervenes be-
tween the apparent cause and its apparent effect. They thus
rest their case on an appeal to the inherent laws of our con-
ceptive faculty ; mistaking, as I apprehend, for the laws of
that faculty its acquired habits, grounded on the spontaneous
tendencies of its uncultured state. The succession between
the will to move a limb and the actual motion is one of the
most direct and instantaneous of all sequences which come

which I am now combating. But that acute thinker has a theory of Causation
peculiar to himself, which has never yet, as far as I know, been analytically
examined, but which, I venture to think, admits of as complete refutation as
any one of the false or insufficient psychological theories which strew the ground
in such numbers under his potent metaphysical scythe. (Since examined and
controverted in the sixteenth chapter of An Examination of Sir William
Hamilton's Philosophy.)

* Unless we are to consider as such the following statement, by one of the
writers quoted in the text : "In the case of mental exertion, the result to be
accomplished is preconsidered or meditated, and is therefore known d priori,
or before experience." — (Bowen's Lowell Lectures on the Application of Meta-
physical and Ethical Science to tke Evidence of Religion, Boston, 1849.) This
is merely saying that when we will a thing we have an idea of it. But to have
an idea of what we wish to happen, does not imply a prophetic knowledge that
it will happen. Perhaps it will be said that the first time we exerted our will,
when we had of course no experience of any of the powers residing in us, we
nevertheless must already have known that we possessed them, since we cannot
will that which we do not believe to be in our power. But the impossibility is
perhaps in the words only, and not in the facts ; for we may desire what we do
not know to be in our power ; and finding by experience that our bodies move
according to our dtsire, we may then, and only then, pass into the more com-
plicated mental state which is termed will.

After all, even if we had an instinctive knowledge that our actions would
follow our will, this, as Brown remarks, would prove nothing as to the nature
of Causation. Our knowing, previous to experience, that an antecedent will
be followed by a certain consequent, would not prove the relation between them
to be anything more than antecedence and consequence.

LAW OF CAUSATION'. 413

under our observation, and is familiar to every moment's ex-
perience from our earliest infancy; more familiar than any
succession of events exterior to our bodies, and especially
more so tban any otber case of the apparent origination (as
distinguished from the mere communicalion) of motion. Now,
it is the natural tendency of the mind to be always attempting
to facilitate its conception of unfamiliar facts by assimilating
them to others which are familiar. Accordingly, our voluntary
acts, being the most familiar to us of all cases of causation,
are, in the infancy and early youth of the human race, spon-
taneously taken as the type of causation in general, and all
phenomena are supposed to be directly produced by the will
of some sentient being. This original Fetichism I shall not
characterize in the words of Hume, or of any follower of Hume,
but in those of a religious metaphysician, Dr. Reid, in order
more effectually to show the unanimity which exists on the
subject among all competent thinkers.

" When we turn our attention to external objects, and
begin to exercise our rational faculties about them, we find that
there are some motions and changes in them which we have
power to produce, and that there are many which must have
some other cause. Either the objects must have life and active
power, as we have, or they must be moved or changed by
something that has life and active power, as external objects
are moved by us.

" Our first thoughts seem to be, that the objects in which
we perceive such motion have understanding and active power
as we have. ' Savages/ says the Abbe Raynal, ' wherever they
see motion which they cannot account for, there they suppose
a soul." All men may be considered as savages in this respect,
until they are capable of instruction, and of using their facul-
ties in a more perfect manner than savages do.

" The Abbe Raynal's observation is sufficiently confirmed,
both from fact, and from the structure of all languages.

" Rude nations do really believe sun, moon, and stars,
earth, sea, and air, fountains, and lakes, to have understanding
and active power. To pay homage to them, and implore their
favour, is a kind of idolatry natural to savages.

414 INDUCTION.

"All languages carry in their structure the marks of their
being formed when this belief prevailed. The distinction of
verbs and participles into active and passive, which is found in
all languages, must have been originally intended to distin-
guish what is really active from what is merely passive ; and
in all languages, we find active verbs applied to those objects,
in which, according to the Abbe Kaynal's observation, savages
suppose a soul.

" Thus we say the sun rises and sets, and comes to the
meridian, the moon changes, the sea ebbs and flows, the winds
blow. Languages were formed by men who believed these
objects to have life and active power in themselves. It was
therefore proper and natural to express their motions and
changes by active verbs.

" There is no surer way of tracing the sentiments of nations
before they have records, than by the structure of their lan-
guage, which, notwithstanding the changes produced in it by
time, will always retain some signatures of the thoughts of
those by whom it was invented. When we find the same sen-
timents indicated in the structure of all languages, those senti-
ments must have been common to the human species when
languages were invented.

" When a few, of superior intellectual abilities, find leisure
for speculation, they begin to philosophize, and soon discover,
that many of those objects which at first they believed to be
intelligent and active are really lifeless and passive. This is
a very important discovery. It elevates the mind, emancipates
from many vulgar superstitions, and invites to further disco-
veries of the same kind.

" As philosophy advances, life and activity in natural
objects retires, and leaves them dead and inactive. Instead of
moving voluntarily, we find them to be moved necessarily ;
instead of acting, we find them to be acted upon ; and Nature
appears as one great machine, where one wheel is turned by
another, that by a third ; and how far this necessary succes-
sion may reach, the philosopher does not know."*

* Reid's Essays on the Active Powers, Essay iv. ch. 3.

LAW OF CAUSATION'. 415

There is, then, a spontaneous tendency of the intellect to
account to itself for all cases of causation by assimilating them
to the intentional acts of voluntary agents like itself. This is
the instinctive philosophy of the human mind in its earliest
stage, before it has become familiar with any other invariable
sequences than those between its own volitions or those of other
human beings and their voluntary acts. As the notion of fixed
laws of succession among external phenomena gradually
establishes itself, the propensity to refer all phenomena to vo-
luntary agency slowly gives way before it. The suggestions,
however, of daily life continuing to be more powerful than
those of scientific thought, the original instinctive philosophy
maintains its ground in the mind, underneath the growths
obtained by cultivation, and keeps up a constent resistance to
their throwing their roots deep into the soil. The theory
against which I am contending derives its nourishment from
that substratum. Its strength does not lie in argument, but
in its affinity to an obstinate tendency of the infancy of the
human mind.

That this tendency, however, is not the result of an inhe-
rent mental law, is proved by superabundant evidence. The
history of science, from its earliest dawn, shows that mankind
have not been unanimous in thinking either that the action of
matter upon matter was not conceivable, or that the action of
mind upon matter was. To some thinkers, and some schools
of thinkers, both in ancient and in modern times, this last has
appeared much more inconceivable than the former. Sequences
entirely physical and material, as soon as they had become
sufficiently familiar to the human mind, came to be thought
perfectly natural, and were regarded not only as needing no
explanation themselves, but as being capable of affording it to
others, and even of serving as the ultimate explanation of
things in general.

One of the ablest recent supporters of the Volitional
theory has furnished an explanation, at once historically true
and philosophically acute, of the failure of the Greek philoso-
phers in physical inquiry, in which, as I conceive, he uncon-
sciously depicts his own state of mind. " Their stumbling-

416 INDUCTION.

block was one as to the nature of the evidence they had to
expect for their conviction. . . . They had not seized the
idea that they must not expect to understand the processes of
outward causes, but only their results : and consequently, the
whole physical philosophy of the Greeks was an attempt to
identify mentally the effect with its cause, to feel after some
not only necessary but natural connexion, where they meant
by natural that which would per se carry some presumption
to their own mind. . . . They wanted to see some reason
why the physical antecedent should produce this particular
consequent, and their only attempts were in directions where
they could find such reasons."* In other words, they were not
content merely to know that one phenomenon was always fol-
lowed by another ; they thought that they had not attained
the true aim of science, unless they could perceive something
in the nature of the one phenomenon from which it might
have been known or presumed previous to trial that it would
be followed by the other: just what the writer, who has so
clearly pointed out their error, thinks that he perceives in the
nature of the phenomenon Volition. And to complete the
statement of the case, he should have added that these early
speculators not only made this their aim, but were quite satis-
fied with their success in it ; not only sought for causes which
should carry in their mere statement evidence of their effi-
ciency, but fully believed that they had found such causes.
The reviewer can see plainly that this was an error, because he
does not believe that there exist any relations between material
phenomena which can account for their producing one another :
but the very fact of the persistency of the Greeks in this error,
shows that their minds were in a very different state : they
were able to derive from the assimilation of physical facts to
other physical facts, the kind of mental satisfaction which we
connect with the word explanation, and which the reviewer
would have us think can only be found in referring phenomena
to a will. When Thales and Hippo held that moisture was
the universal cause, and external element, of which all other
things were but the infinitely various sensible manifestations ;

* Prospective Review for February 1850.

LAW OP CAUSATION. 417

when Anaximenes predicated the same thing of air, Pythagoras
of numbers, and the like, they all thought that they had found
a real explanation ; and were content to rest in this explana-
tion as ultimate. The ordinary sequences of the external
universe appeared to them, no less than to their critic, to be
inconceivable without the supposition of some universal agency
to connect the antecedents with the consequents ; but they did
not think that Volition, exerted by minds, was the only agency
which fulfilled this requirement. Moisture, or air, or numbers,
carried to their minds a precisely similar impression of making
intelligible what was otherwise inconceivable, and gave the
same full satisfaction to the demands of their conceptive
faculty.

It was not the Greeks alone, who "wanted to see some
reason why the physical antecedent should produce this par-
ticular consequent," some connexion " which would per se
carry some presumption to their own mind." Among modern
philosophers, Leibnitz laid it down as a self-evident principle
that all physical causes without exception must contain in
their own nature something which makes it intelligible that
they should be able to produce the effects which they do pro-
duce. Far from admitting Volition as the only kind of cause
which carried internal evidence of its own power, and as the
real bond of connexion between physical antecedents and their
consequents, he demanded some naturally and per se efficient
physical antecedent as the bond of connexion between Volition
itself and its effects. He distinctly refused to admit the will
of God as a sufficient explanation of anything except miracles ;
and insisted upon finding something that would account better
for the phenomena of nature than a mere reference to divine
volition.*

Again, and conversely, the action of mind upon matter
(which, we are now told, not only needs no explanation itself,
but is the explanation of all other effects), has appeared to
some thinkers to be itself the grand inconceivability. It was
to get over this very difficulty that the Cartesians invented the

* Vide supra, p. 276, note.
VOL. I. 27

418 INDUCTION.

system of Occasional Onuses. They could not conceive that
thoughts in a mind could produce movements in a body, or
that bodily movements could produce thoughts. They could
see no necessary connexion, no relation a priori, between a
motion and a thought. And as the Cartesians, more than any
other school of philosophical speculation before or since, made
their own minds the measure of all things, and refused, on
principle, to believe that Nature had done what they were
unable to see any reason why she must do, they affirmed it to
be impossible that a material and a mental fact could be causes
one of another. They regarded them as mere Occasions on
which the real agent, God, thought fit to exert his power as a
Cause. When a man wills to move his foot, it is not his will
that moves it, but God (they said) moves it on the occasion of
his will. God, according to this system, is the only efficient
cause, not qua mind, or qua endowed with volition, but qua
omnipotent. This hypothesis was, as I said, originally sug-
gested by the supposed inconceivability of any real mutual
action between Mind and Matter : but it was afterwards extended
to the action of Matter upon Matter, for on a nicer examina-
tion they found this inconceivable too, and therefore, according
to their logic, impossible. The deus ex machind was ulti-
mately called in to produce a spark on the occasion of a flint
and steel coming together, or to break an egg on the occasion
of its falling on the ground.

All this, undoubtedly, shows that it is the disposition of
mankind in general, not to be satisfied with knowing that one
fact is invariably antecedent and another consequent, but to
look out for something which may seem to explain their being
so. But we also see that this demand may be completely satisfied
by an agency purely physical, provided it be much more familiar
than that which it is invoked to explain. To Thales and
Anaximenes, it appeared inconceivable that the antecedents
which we see in nature, should produce the consequents ; but
perfectly natural that water, or air, should produce them. The
writers whom I oppose declare this inconceivable, but can con-
ceive that mind, or volition, is per se an efficient cause: while
the Cartesians could not conceive even that, but peremptorily

LAW OF CAUSATION. 419

declared that no mode of production of any fact whatever was
conceivable, except the direct agency of an omnipotent heing.
Thus giving additional proof of what finds new confirmation
in every stage of the history of science : that both what
persons can, and what they cannot, conceive, is very much an
affair of accident, and depends altogether on their experience,
and their habits of thought; that by cultivating the requisite
associations of ideas, people may make themselves unable to
conceive any given thing ; and may make themselves able to
conceive most things, however inconceivable these may at first
appear : and the same facts in each person's mental history
which determine what is or is not conceivable to him, deter-
mine also which among the various sequences in nature will
appear to him so natural and plausible, as to need no other
proof of their existence; to be evident by their own light,
independent equally of experience and of explanation.

By what rule is any one to decide between one theory of
this description and another ? The theorists do not direct us
to any external evidence ; they appeal each to his own sub-
jective feelings. One says, the succession C, B, appears to me
more natural, conceivable, and credible per se, than the suc-
cession A, B ; you are therefore mistaken in thinking that B
depends upon A ; I am certain, though I can give no other
evidence of it, that C comes in between A and B, and is the
real and only cause of B. The other answers — the successions
C, B, and A, B, appear to me equally natural and conceivable,
or the latter more so than the former : A is quite capable of
producing B without any other intervention. A third agrees
with the first in being unable to conceive that A can produce
B, but finds the sequence D, B, still more natural than C, B,
or of nearer kin to the subject matter, and prefers his D theory
to the C theory. It is plain that there is no universal law-
operating here, except the law that each person's conceptions
are governed and limited by his individual experiences and
habits of thought. We are warranted in saying of all three,
what each of them already believes of the other two, namely,
that they exalt into an original law of the human intellect
and of outward nature, one particular sequence of phenomena,

27—2

420 INDUCTION.

which appears to them more natural and more conceivable
than other sequences, only because it is more familiar. And
from this judgment I am unable to except the theory, that
Volition is an Efficient Cause.

I am unwilling to leave the subject without adverting to
the additional fallacy contained in the corollary from this
theory; in the inference that because Volition is an efficient
cause, therefore it is the only cause, and the direct agent in
producing even what is apparently produced by something
else. Volitions are not known to produce anything directly
except nervous action, for the will influences even the muscles
only through the nerves. Though it were granted, then, that
every phenomenon has an efficient, and not merely a pheno-
menal cause, and that volition, in the case of the peculiar
phenomena which are known to be produced by it, is that
efficient cause ; are we therefore to say, with these writers,
that since we know of no other efficient cause, and ought not
to assume one without evidence, there is no other, and volition
is the direct cause of all phenomena ? A more outrageous
stretch of inference could hardly be made. Because among
the infinite variety of the phenomena of nature there is one,
namely, a particular mode of action of certain nerves, which
has for its cause, and as we are now supposing for its efficient
cause, a state of our mind ; and because this is the only effi-
cient cause of which we are conscious, being the only one of
which in the nature of the case we can be conscious, since it
is the only one which exists within ourselves; does this justify
us in concluding that all other phenomena must have the
same kind of efficient cause with that one eminently special,
narrow, and peculiarly human or animal, phenomenon ? The
nearest parallel to this specimen of generalization is suggested
by the recently revived controversy on the old subject of
Plurality of Worlds, in which the contending parties have
been eo conspicuously successful in overthrowing one another.
Here also we have experience only of a single case, that of the
world in which we live, but that this is inhabited we know
absolutely, and without possibility of doubt. Now if on this
evidence any one were to infer that every heavenly body

LAW OF CAUSATION. 421

without exception, sun, planet, satellite, cornet, fixed star or
nebula, is inhabited, and must be so from the inherent consti-
tution of things, his inference would exactly resemble that of
the writers who conclude that because volition is the efficient
cause of our own bodily motions, it must be the efficient cause
of everything else in the universe. It is true there are cases
in which, with acknowledged propriety, we generalize from a
single instance to a multitude of instances. But they must
be instances which resemble the one known instance, and not
such as have no circumstance in common with it except that
of being instances. I have, for example, no direct evidence
that any creature is alive except myself : yet I attribute, with
full assurance, life and sensation to other human beings and
animals. But I do not conclude that all other things are
alive merely because I am. I ascribe to certain other
creatures a life like my own, because they manifest it by the
same sort of indications by which mine is manifested. I find
that their phenomena and mine conform to the same laws,
and it is for this reason that I believe both to arise from a
similar cause. Accordingly I do not extend the conclusion
beyond the grounds for it. Earth, fire, mountains, trees, are
remarkable agencies, but their phenomena do not conform
to the same laws as my actions do, and I therefore do not
believe earth or fire, mountains or trees, to possess animal
life. But the supporters of the Volition Theory ask us to
infer that volition causes everything, for no reason except that
it causes one particular thing ; although that one pheno-
menon, far from being a type of all natural phenomena, is
eminently peculiar ; its laws bearing scarcely any resemblance
to those of any other phenomenon, whether of inorganic or of
organic nature.

NOTE SUPPLEMENTARY TO THE PRECEDING CHAPTER.

The author of the Second Burnett Prize Essay (Dr. Tulloch), who has em-
ployed a considerable number of pages in controverting the doctrines of the
preceding chapter, has somewhat surprised me by denying a fact, which I
imagined too well known to require proof — that there have been philosophers
who found in physical explanations of phenomena the same complete mental

422 INDUCTION.

satisfaction which we are told is only given by volitional explanation, and others
who denied the Volitional Theory on the same ground of inconceivability on
which it is defended. The assertion of the Essayist is countersigned still more
positively by an able reviewer of the Essay :* "Two illustrations," says the
reviewer, "are advanced by Mr. Mill: the case of Thales and Anaximenes,
stated by him to have maintained, the one Moisture and the other Air to be the
origin of all things ; and that of Descartes and Leibnitz, whom he asserts to
have found the action of Mind upon Matter the grand inconceivability. In
counterstatement as to the first of these cases the author shows — what we be-
lieve now hardly admits of doubt — that the Greek philosophers distinctly recog-
nised as beyond and above their primal material source, the VOVQ, or Divine Intel-
ligence, as the efficient and originating Source of all : and as to the second, by
proof that it was the mode, not the fact, of that action on matter, which was
represented as inconceivable."

A greater quantity of historical error has sel Joni been comprised in a single
sentence. With regard to Thales, the assertion that he considered water as
a mere material in the hands of VOVQ rests on a passage of Cicero de datura
Deorum : and whoever will refer to any of the accurate historians of philoso-
phy, will find that they treat this as a mere fancy of Cicero, resting on no
authority, opposed to all the evidence ; and make surmises as to the manner
in which Cicero may have been led into the error. (See Eitter, vol. i. p. 211,
2nd ed. ; Brandis, vol. i. pp. 118-9, 1st ed. ; Preller, Historia, Philosophies
Grceco-flomancE, p. 10. " Schiefe Ansicht, durchaus zu verwerfen ;" "augen-
scheinlich folgernd statt zu berichten :" "quibus vera suntentia Thaletis plane
detorquetur ;" are the expressions of these writers.) As for Anaximenes, he
even according to Cicero, maintained, not that air was the material out of
which God made the world, but that the air was a god : " Anaximenes aera
deum statuit :" or according to St. Augustine, that it was the material out of
which the gods were made ; "non tamenab ipsis [Diis] aerem factum, sed ipsos
ex acre ortos credidit." Those who are not familiar with the metaphysical
terminology of antiquity, must not be misled by finding it stated that Anaxi-
menes attributed i|/ux>) (translated soul, or life) to his universal element, the
air. The Greek philosophers acknowledged several kinds of 4/v\rj, the nutritive,
the sensitive, and the intellective.^ Even the moderns, with admitted correct-
ness, attribute life to plants. As far as we can make out the meaning of Anaxi-
menes, he made choice of Air as the universal agent, on the ground that it is
perpetually in motion, without any apparent cause external to itself : so that
he conceived it as exercising spontaneous force, and as the principle of life and
activity in all things, men and gods inclusive. If this be not representing it as
the Efficient Cause, the dispute altogether has no meaning.

If either Anaximenes, or Thales, or any of their cotemporaries, had held the
doctrine that VOVQ was the Efficient Cause, that doctrine could not have been
reputed, as it was throughout antiquity, to have originated with Anaxagoras.
The testimony of Aristotle, in the first book of his Metaphysics, is perfectly
decisive with respect to these early speculations. After enumerating four

* Westminster Review for October 1855.

f See the whole doctrine in Aristotle de Animd : where the 0pt7rrtio) ^wx4
is treated as exactly equivalent to Optwrixr) Svvaftts.

LAW OF CAUSATION. 423

kinds of causes, or rather four different meanings of the word Cause, viz. the
Essence of a thing, the Matter of it, the Origin of Motion (Efficient Cause),
and the End or Final Cause, he proceeds to say, that most of the early philo-
sophers recognised only the second kind of Cause, the Matter of a thing, roc fv
vXtjg tlcei fiovciQ tf>i)Qr}aav apx«C fivai iravTwv. As his first example he
specifies Thales, whom he describes as taking the lead in this view of the sub-
ject, 6 rjjc roiavTTis dpxny°G <f>i\ooo<pias, and goes on to Hippon, Anaximenes,
Diogenes (of Apollonia), Hippasus of Metapontum, Heraclitus, and Empe-
docles. Anaxagoras, however, (he proceeds to say,) taught a different doc-
trine, as we know, and it is alleged that Hermotimus of Clazomense taught it
before him. Anaxagoras represented, that even if these various theories of
the universal material were true, there would be need of some other cause to
account for the transformations of the material, since the material cannot
originate its own changes : ov yap £n TO yt viroKcipivov O.UTO iroul /j.sra^d\\tii>
iavro' \ijio S' oiov ovre r!> KvXov ovre o xaXicoe alnog TOV [iiTafidXXtiv
iKartpov avTwv, oi'fe iroitl TO fj.tr %vX v K\ivrjv o Se \a\KO<; dvfipidvTa, tiXX'
frtpov TI T?I£ /j£ra/3oX?}c; ainov, viz., the other kind of cause, oQiv »} dpxn r>)G
Kivt'jtrtuc —an Efficient Cause. Aristotle expresses great approbation of this
doctrine (which he says made its author appear the only sober man among
persons raving, olov vr]<j>tav t<j>rtvt) Trap' flicfj XiyovTac; roue irpoTtpov); but
while describing the influence which it exercised over subsequent speculation,
he remarks that the philosophers against whom this, as he thinks, insuperable
difficulty was urged, had not felt it to be any difficulty : otdiv tSva\tpdvav iv
iavTolg. It is surely unnecessary to say more in proof of the matter of fact
which Dr. Tullich and his reviewer disbelieve.

Having pointed out what he thinks the error of these early speculators hi
not recognising the need of an efficient cause, Aristotle goes on to mention two
other efficient causes to which they might have had recourse, instead of intel
licence : TV^T], chance, and rd avTOfidrov, spontaneity. He indeed puts these
aside as not sufficiently worthy causes for the order in the universe, ovF av T<£
aitroparip nai Ty Tv%y TOOOVTOV iiriTptyai 7rpay/^a (caXwg tlxtv. but he does
not reject them as incapable of producing any effect, but only as incapable of
producing that effect. He himself recognises TVX*I and TO avTopaTov as co-
ordinate agents with Mind in producing the phenomena of the universe ; the
department allotted to them being composed of all theclasses of phenomena which
are not supposed to fullow any uniform law. By thus including Chance among
efficient causes, Aristotle fell into an error which philosophy has now outgrown,
but which is by no means so alien to the spirit even of modern speculation as
it may at first sight appear. Up to quite a recent period philosophers went on
ascribing, and many of them have not yet ceased to ascribe, a real existence to
the results of abstraction. Chance could make out as good a title to that dig-
nity as many other of the mind's abstract creations : it had had a name given
to it, and why should it not be a reality ? As for Tb avTOftdrov, it is recognised
even yet as one of the modes of origination of phenomena, by all those thinkers
who maintain what is called the Freedom of the Will. The same self-deter-
mining power which that doctrine attributes to volitions, was supposed by the
ancients to be possessed also by some other natural phenomena : a circum-
stance which throws considerable light on more than one of the supposed

424 INDUCTION.

invincible necessities of belief. I have introduced it here, because this belief
of Aristotle, or rather of the Greek philosophers generally, is as fatal as the
doctrines of Thales and the Ionic school, to the theory that the human mind is
compelled by its constitution to conceive volition as the origin of all force, and
the efficient cause of all phenomena.*

With regard to the modern philosophers (Leibnitz and the Cartesians) whom I
had cited as having maintained that the action of mind upon matter, so far from
being the only conceivable origin of material phenomena, is itself inconceivable ;
the attempt to rebut this argument by asserting that the mode, not the fact, of
the action of mind on matter was represented as inconceivable, is an abuse of
the privilege of writing confidently about authors without reading them : for
any knowledge whatever of Leibnitz would have taught those who thus speak
of him, that the inconceivability of the mode, and the impossibility of the
thing, were in his mind convertible expressions. What was bis famous Prin-
ciple of the Sufficient Reason, the very corner stone of his Philosophy, from
which the Preestablished Harmony, the doctrine of Monads, and all the opinions

* It deserves notice that the parts of nature which Aristotle regards as
presenting evidence of design, are the Uniformities : the phenomena in so far
as reducible to law. Tvx'n and rb avro^urov satisfy him as explanations of the
variable element in phenomena, but their occurring according to a fixed rule
can only, to his conceptions, be accounted for by an Intelligent Will. The
common, or what may be called the instinctive, religious interpretation of
nature, is the reverse of this. The events in which men spontaneously see the
hand of a supernatural being, are those which cannot, as they think, be
reduced to a physical law. What they can distinctly connect with physical
causes, and especially what they can predict, though of course ascribed to an
Author of Nature if they already recognise such an author, might be con-
ceived, they think, to arise from a blind fatality, and in any case do not appear
to them to bear so obviously the mark of a divine will. And this distinction
has been countenanced by eminent writers on Natural Theology, in particular
by Dr. Chalmers : who thinks that though design is present everywhere, the
irresistible evidence of it is to be found not in the laws of nature but in the
collocations, i.e. in the part of nature in which it is impossible to trace any
law. A few properties of dead matter might, he thinks, conceivably account
for the regular and invariable succession of effects and causes ; but that the
different kinds of matter have been so placed as to promote beneficent ends, is
what he regards as the proof of a Divine Providence. Mr. Baden Powell, in
his Essay entitled "Philosophy of Creation," has returned to the point of
view of Aristotle and the ancients, and vigorously reasserts the doctrine that
the indication of design in the universe is not special adaptations, but Unifor-
mity and Law, these being the evidences of mind, and not what appears to
us to be a provision for our uses. While I decline to express any opinion here on
this vexata qucestio, I ought not to mention Mr. Powell's volume without the
acknowledgment due to the philosophic spirit which pervades generally
the three Essays composing it, forming in the case of one of them (the " Unity
of Worlds") an honourable contrast with the other dissertations, so far as they
have come under my notice, which have appeared on either side of that con-
troversy.

LAW OF CAUSATION. 425

most characteristic of Leibnitz, were corollaries ? It was, that nothing exists,
the existence of which is not capable of being proved and explained d priori ;
the proof and explanation in the case of contingent facts being derived from
the nature of their causes ; which could not be the causes unless there was
something in their nature showing them to be capable of producing those par-
ticular effects. And this " something " which accounts for the production of
physical effects, he was able to find in many physical causes, but could not find
it in any finite minds, which therefore he unhesitatingly asserted to be incapable
of producing any physical effects whatever. "On ne saurait concevoir," he
says, " une action re'ciproque de la matiere et de Intelligence 1'une sur Pautre,"
and there is therefore (he contends) no choice but between the Occasional Causes
of the Cartesians, and his own Preestablished Harmony, according to which
there is no more connexion between our volitions and our muscular actions
than there is between two clocks which are wound up to strike at the same
instant. But he felt no similar difficulty as to physical causes : and throughout
his speculations, as in the passage I have already cited respecting gravitation,
he distinctly refuses to consider as part of the order of nature any fact which is
oot explicable from the nature of its physical cause.

With regard to the Cartesians (not Descartes ; I did not make that mistake,
though the reviewer of Dr. Tulloch's Essay attributes it to me) I take a passage
almost at random from Malebranche, who is the best known of the Cartesians,
and, though not the inventor of the system of Occasional Causes, is its princi-
pal expositor. In Part 2, chap. 3, of his Sixth Book, having first said that
matter cannot have the power of moving itself, he proceeds to argue that neither
can mind have the power of moving it. "Quand on examine 1'idee que Ton a
de tous les esprits finis, on ne voit point de liaison ne"cessaire entre leur volonte"
et le mouvement de quelque corps que ce soit, on voit au contraire qu'il n'y en
a point, et qu'il n'y en peut avoir ;" (there is nothing in the idea of finite mind
which can account for its causing the motion of a body ;) " on doit aussi con-
clure, si on veut raisonner selon ses lumieres, qu'il n'y a aucun esprit cre'e' qui
puisse remuer quelque corps que ce soit comme cause veritable ou principale, de
me"me que 1'on a dit qu'aucun corps ne se pouvait remuer soi-meme :" thus the
idea of Mind is according to him as incompatible as the idea of Matter with the
exercise of active force. But when, he continues, we consider not a created
but a Divine Mind, the case is altered ; for the idea of a Divine Mind includes
omnipotence ; and the idea of omnipotence does contain the idea of being able
to move bodies. Thus it is the nature of omnipotence which renders the motion
of bodies even by the divine mind credible or conceivable, while, so far as
depended on the mere nature of mind, it would have been inconceivable and
incredible. If Malebranche had not believed in an omnipotent being, he would
have held all action of mind on body to be a demonstrated impossibility.*

A doctrine more precisely the reverse of the Volitional theory of causation

* In the words of Fontenelle, another celebrated Cartesian, "les philosophea
aussi bien que le peuple avaient cru que I'ame et le corps agissaient re"ellernent
et physiquement 1'un sur 1'autre. Descartes vint, qui prouva que leur nature
ne permettait point cette sorte de communication veritable, et qu'ils n'en pou-
vaient avoir qu'une apparente, dont Dieu e"tait le Me"diateur." ((Euvres de
Fontenelle, ed. 1767, torn. v. p. 534.)

426

INDUCTION.

cannot well be imagined. The Volitional theory is, that we know by intuition
or by direct experience the action of our own mental volitions on matter ; that
we may hence infer all other action upon matter to be that of volition, and
might thus know, without any other evidence, that matter is under the govern-
ment of a divine mind. Leibnitz and the Cartesians, on the contrary, maintain
that our volitions do not and cannot act upon matter, and that it is only the
existence of an all-governing Being, and that Being omnipotent, which can
account for the sequence between our volitions and our bodily actions. When
we consider that each of these two theories, which, as theories of causation,
stand at the opposite extremes of possible divergence from one another, invokes
not only as its evidence, but as its sole evidence, the absolute inconceivability
of any theory but itself, we are enabled to measure the worth of this kind of
evidence : and when we find the Volitional theory entirely built upon the asser-
tion that by our mental constitution we are compelled to recognise our volitions
as efficient causes, and then find other thinkers maintaining that we know that
they are not and cannot be such causes, and cannot conceive them to be so,
I think we have a right to say, that this supposed law of our mental constitu-
tion does not exist.

Dr. Tulloch (pp. 45-7) thinks it a sufficient answer to this, that Leibnitz
and the Cartesians were Theists, and believed the will of God to be an efficient
cause. Doubtless they did, and the Cartesians even believed (though Leibnitz
did not) that it is the only such cause. Dr. Tulloch mistakes the nature of the
question. I was not writing on Theism, as Dr. Tulloch is, but against a par-
ticular theory of causation, which, if it be unfounded, can give no effective sup-
port to Theism or to anything else. T found it asserted that volition is the
only efficient cause, on the ground that no other efficient cause is conceivable.
To this assertion I oppose the instances of Leibnitz and of the Cartesians, who
affirmed with equal positiveness that volition as an efficient cause is itself not
conceivable, and that omnipotence, which renders all things conceivable, can
alone take away the impossibility. This I thought, and think, a conclusive
answer to the argument on which this theory of causation avowedly depends.
But I certainly did not imagine that Theism was bound up with that theory ;
nor expected to be charged with denying Leibnitz and the Cartesians to be
Theists because I denied that they held the theory.

CHAPTER VI.

ON THE COMPOSITION OF CAUSES.

§ 1. To complete the general notion of causation on
which the rules of experimental inquiry into the laws of nature
must be founded, one distinction still remains to be pointed
out : a distinction so radical, and of so much importance, as
to require a chapter to itself.

The preceding discussions have rendered us familiar with
the case in which several agents, or causes, concur as condi-
tions to the production of an effect; a case, in truth, almost
universal, there being very few effects to the production of
which no more than one agent contributes. Suppose, then,
that two different agents, operating jointly, are followed, under
a certain set of collateral conditions, by a given effect. If
either of these agents, instead of being joined with the other,
had operated alone, under the same set of conditions in all
other respects, some effect would probably have followed ;
which would have been different from the joint effect of the
two, and more or less dissimilar to it. Now, if we happen to
know what would be the effect of each cause when acting
separately from the other, we are often able to arrive deduc-
tively, or a priori, at a correct prediction of what will arise
from their conjunct agency. To render this possible, it is
only necessary that the same law which expresses the effect
of each cause acting by itself, shall also correctly express the
part due to that cause, of the effect which follows from the
two together. This condition is realized in the extensive and
important class of phenomena commonly called mechanical,
namely the phenomena of the communication of motion (or
of pressure, which is tendency to motion) from one body to

428 INDUCTION.

another. In this important class of cases of causation, one
cause never, properly speaking, defeats or frustrates another ;
both have their full effect. If a body is propelled in two direc-
tions by two forces, one tending to drive it to the north and
the other to the east, it is caused to move in a given time
exactly as far in both directions as the two forces would
separately have carried it ; and is left precisely where it -would
have arrived if it had been acted upon first by one of the two
forces, and afterwards by the other. This law of nature is
called, in dynamics, the principle of the Composition of
Forces : and in imitation of that well-chosen expression, I
shall give the name of the Composition of Causes to the
principle which is exemplified in all cases in which the joint
effect of several causes is identical with the sum of their se-
parate effects.

This principle, however, by no means prevails in all de-
partments of the field of nature. The chemical combination
of two substances produces, as is well known, a third substance
•with properties different from those of either of the two sub-
stances separately, or of both of them taken together. Not a
trace of the properties of hydrogen or of oxygen is observable
in those of their compound, water. The taste of sugar of
lead is not the sum of the tastes of its component elements,
acetic acid and lead or its oxide; nor is the colour of blue
vitriol a mixture of the colours of sulphuric acid and copper.
This explains why mechanics is a deductive or demonstrative
science, and chemistry not. In the one, we can compute the
effects of combinations of causes, whether real or hypothetical,
from the laws which we know to govern those causes when
acting separately ; because they continue to observe the same
laws when in combination which they observed when separate :
whatever would have happened in consequence of each cause
taken by itself, happens when they are together, and we have
only to cast up the results. Not so in the phenomena which
are the peculiar subject of the science of chemistry. There,
most of the uniformities to which the causes conformed when
separate, cease altogether when they are conjoined; and we
are not, at least in the present state of our knowledge, able to

COMPOSITION OF CAUSES. 429

foresee what result will follow from any new combination, until
we have tried the specific experiment.

If this be true of chemical combinations, it is still more
true of those far more complex combinations of elements
which constitute organized bodies ; and in which those extra-
ordinary new uniformities arise, which are called the laws of
life. All organized bodies are composed of parts similar to
those composing inorganic nature, and which have even them-
selves existed in an inorganic state ; but the phenomena of
life, which result from the juxtaposition of those parts in a
certain manner, bear no analogy to any of the effects which
would be produced by the action of the component substances
considered as mere physical agents. To whatever degree we
might imagine our knowledge of the properties of the several
ingredients of a living body to be extended and perfected, it
is certain that no mere summing up of the separate actions of
those elements will ever amount to the action of the living
body itself. The tongue, for instance, is, like all other parts
of the animal frame, composed of gelatine, fibrin, and other
products of the chemistry of digestion, but from no knowledge
of the properties of those substances could we ever predict
that it could taste, unless gelatine or fibrin could themselves
taste ; for no elementary fact can be in the conclusion, which
was not in the premises.

There are thus two different modes of the conjunct action
of causes; from which arise two modes of conflict, or mutual
interference, between laws of nature. Suppose, at a given
point of time and space, two or more causes, which, if they
acted separately, would produce effects contrary, or at least
conflicting with each other ; one of them tending to undo,
wholly or partially, what the other tends to do. Thus, the
expansive force of the gases generated by the ignition of gun-
powder tends to project a bullet towards the sky, while its
gravity tends to make it fall to the ground. A stream running
into a reservoir at one end tends to fill it higher and higher,
while a drain at the other extremity tends to empty it. Now,
in such cases as these, even if the two causes which are in
joint action exactly annul one another, still the laws of both

430 INDUCTION.

are fulfilled ; the effect is the same as if the drain had heen
open for half an hour first,* and the stream had flowed in for
as long afterwards. Each agent produced the same amount
of effect as if it had acted separately, though the contrary
effect which was taking place during the same time obliterated
it as fast as it was produced. Here then are two causes, pro-
ducing by their joint operation an effect which at first seems
quite dissimilar to those which they produce separately, but
which on examination proves to be really the sum of those
separate effects. It will be noticed that we here enlarge the
idea of the sum of two effects, so as to include what is com-
monly called their difference, but which is in reality the result
of the addition of opposites; a conception to which mankind
are indebted for that admirable extension of the algebraical
calculus, which has so vastly increased its powers as an instru-
ment of discovery, by introducing into its reasonings (with
the sign of subtraction prefixed, and under the name of Nega-
tive Quantities) every description whatever of positive pheno-
mena, provided they are of such a quality in reference to those
previously introduced, that to add the one is equivalent to
subtracting an equal quantity of the other.

There is, then, one mode of the mutual interference of
laws of nature, in which, even when the concurrent causes an-
nihilate each other's effects, each exerts its full efficacy accord-
ing to its own law, its law as a separate agent. But in the
other description of cases, the agencies which are brought to-
gether cease entirely, and a totally different set of phenomena
arise : as in the experiment of two liquids which, when mixed
in certain proportions, instantly become, not a larger amount
of liquid, but a solid mass.

§ 2. This difference between the case in which the joint
effect of causes is the sum of their separate effects, and the

* I omit, for simplicity, to take into account the effect, in this latter
case, of the diminution of pressure, in diminishing the flow of water through
the drain ; which evidently in no waj' affects the truth or applicability of the
principle, since when the two causes act simultaneously the conditions of that
diminution of pressure do not arise.

COMPOSITION OF CAUSES. 431

case in which it is heterogeneous to them ; between laws which
work together without alteration, and laws which, when called
upon to work together, cease and give place to others ; is one
of the fundamental distinctions in nature. The former case,
that of the Composition of Causes, is the general one ; the
other is always special and exceptional. There are no objects
which do not, as to some of their phenomena, obey the prin-
ciple of the Composition of Causes ; none that have not some
laws which are rigidly fulfilled in every combination into
which the objects enter. The weight of a body, for instance,
is a property which it retains in all the combinations in which
it is placed. The weight of a chemical compound, or of an
organized body, is equal to the sum of the weights of the
elements which compose it. The weight either of the ele-
ments or of the compound will vary, if they be carried farther
from their centre of attraction, or brought nearer to it ; but
whatever affects the one affects the other. They always remain
precisely equal. So again, the component parts of a vegetable
or animal substance do not lose their mechanical and chemical
properties as separate agents, when, by a peculiar mode of
juxtaposition, they, as an aggregate whole, acquire physiolo-
gical or vital properties in addition. Those bodies continue,
as before, to obey mechanical and chemical laws, in so far as
the operation of those laws is not counteracted by the new
laws which govern them as organized beings. When, in short,
a concurrence of causes takes place which calls into action
new laws bearing no analogy to any that we can trace in the
separate operation of the causes, the new laws, while they
supersede one portion of the previous laws, may coexist with
another portion, and may even compound the effect of those
previous laws with their own.

Again, laws which were themselves generated in the second
mode, may generate others in the first. Though there are
laws which, like those of chemistry and physiology, owe their
existence to a breach of the principle of Composition of Causes,
it does not follow that these peculiar, or as they might be
termed, heteropathic laws, are not capable of composition with
one another. The causes which by one combination have

432 INDUCTION.

had their laws altered, may carry their new laws with them
unaltered into their ulterior combinations. And hence there
is no reason to despair of ultimately raising chemistry and
physiology to the condition of deductive sciences ; for though
it is impossible to deduce all chemical and physiological truths
from the laws or properties of simple substances or elementary
agents, they may possibly be deducible from laws which com-
mence when these elementary agents are brought together into
some moderate number of not very complex combinations.
The Laws of Life will never be deducible from the mere laws
of the ingredients, but the prodigiously complex Facts of Life
may all be deducible from comparatively simple laws of life ;
which laws (depending indeed on combinations, but on com-
paratively simple combinations, of antecedents) may, in more
complex circumstances, be strictly compounded with one an-
other, and with the physical and chemical laws of the ingre-
dients. The details of the vital phenomena, even now, afford
innumerable exemplifications of the Composition of Causes ;
and in proportion as these phenomena are more accurately
studied, there appears more reason to believe that the same
laws which operate in the simpler combinations of circum-
stances do, in fact, continue to be observed in the more com-
plex. This will be found equally true in the phenomena of
mind ; and even in social and political phenomena, the results
of the laws of mind. It is in the case of chemical phenomena
that the least progress has yet been made in bringing the
special laws under general ones from which they may be de-
duced ; but there are even in chemistry many circumstances
to encourage the hope that such general laws will hereafter be
discovered. The different actions of a chemical compound
will never, undoubtedly, be found to be the sums of the actions
of its separate elements ; but there may exist, between the
properties of the compound and those of its elements, some
constant relation, which, if discoverable by a sufficient induc-
tion, would enable us to foresee the sort of compound which
•will result from a new combination before we have actually
tried it, and to judge of what sort of elements some new sub-
stance is compounded before we have analysed it. The law

COMPOSITION OF CAUSES. 433

of definite proportions, first discovered in its full generality by
Dalton, is a complete solution of this problem in one, though
but a secondary aspect, that of quantity : and in respect to
quality, we have already some partial generalizations, sufficient
to indicate the possibility of ultimately proceeding farther.
We can predicate some common properties of the kind of com-
pounds which result from the combination, in each of the
small number of possible proportions, of any acid whatever
with any base. We have also the curious law, discovered by
Berthollet, that two soluble salts mutually decompose one
another whenever the new combinations which result produce
an insoluble compound, or one less soluble than the two
former. Another uniformity is that called the law of isomor-
phism ; the identity of the crystalline forms of substances
which possess in common certain peculiarities of chemical
composition.* Thus it appears that even heteropathic laws,
such laws of combined agency as are not compounded of the
laws of the separate agencies, are yet, at least in some cases,
derived from them according to a fixed principle. There may,
therefore, be laws of the generation of laws from others dis-
similar to them; and in chemistry, these undiscovered laws of
the dependence of the properties of the compound on the pro-
perties of its elements, may, together with the laws of the
elements themselves, furnish the premises by which the science
is perhaps destined one day to be rendered deductive.

It would seem, therefore, that there is no class of pheno-
mena in which the Composition of Causes does not obtain :
that as a general rule, causes in combination produce exactly
the same effects as when acting singly : but that this rule,
though general, is not universal : that in some instances, at
some particular points in the transition from separate to
united action, the laws change, and an entirely new set of
effects are either added to, or take the place of, those which

* Professor Bain adds several other well-established chemical generaliza-
tions: " The laws that simple substances exhibit the strongest affinities; that
compounds are more fusible than their elements ; that combination tends to a
lower state of matter from gas down to solid ;" and some general propositions
concerning the circumstances which facilitate or resist chemical combination,
(Logic, ii. 254).

VOL. I. 28

434 INDUCTION.

arise from the separate agency of the same causes : the laws
of these new effects being again susceptible of composition, to
an indefinite extent, like the laws which they superseded.

§ 3. That effects are proportional to their causes is laid
down by some writers as an axiom in the theory of causation ;
and great use is sometimes made of this principle in reason-
ings respecting the laws of nature, though it is encumbered
with many difficulties and apparent exceptions, which much
ingenuity has been expended in showing not to be real ones.
This proposition, in so far as it is true, enters as a particular
case into the general principle of the Composition of Causes ;
the causes compounded being, in this instance, homogeneous;
in which case, if in any, their joint effect might be expected
to be identical .with the sum of their separate effects. If a
force equal to one hundred weight will raise a certain body
along an inclined plane, a force equal to two hundred weight
will raise two bodies exactly similar, and thus the effect is
proportional to the cause. But does not a force equal to two
hundred weight actually contain in itself two forces each equal
to one hundred weight, which, if employed apart, would sepa-
rately raise the two bodies in question ? The fact, therefore,
that when exerted jointly they raise both bodies at once,
results from the Composition of Causes, and is a mere in-
stance of the general fact that mechanical forces are subject
to the law of Composition. And so in every other case which
can be supposed. For the doctrine of the proportionality of
effects to their causes cannot of course be applicable to cases
in which the augmentation of the cause alters the kind of
effect ; that is, in which the surplus quantity superadded to
the cause does not become compounded with it, but the two
together generate an altogether new phenomenon. Suppose
that the application of a certain quantity of heat to a body
merely increases its bulk, that a double quantity melts it, and
a triple quantity decomposes it : these three effects being
heterogeneous, no ratio, whether corresponding or not to that
of the quantities of heat applied, can be established between
them. Thus the supposed axiom of the proportionality of

COMPOSITION OF CAUSES. 435

effects to their causes fails at the precise point where the prin-
ciple of the Composition of Causes also fails ; viz. where the
concurrence of causes is such as to determine a change in the
properties of the hody generally, and render it subject to new
laws, more or less dissimilar to those to which it conformed in
its previous state. The recognition, therefore, of any such
law of proportionality, is superseded hy the more comprehen-
sive principle, in which as much of it as is true is implicitly
asserted.*

The general remarks on causation, which seemed necessary
as an introduction to the theory of the inductive process, may
here terminate. That process is essentially an inquiry into
cases of causation. All the uniformities which exist in the
succession of phenomena, and most of the uniformities in
their co-existence, are either, as we have seen, themselves laws

* Professor Bain (Logic, ii. 39) points out a class of cases, other than that
spoken of in the text, which he thinks must be regarded as an exception to the
Composition of Causes. ' ' Causes that merely make good the collocation for
bringing a prime mover into action, or that release a potential force, do not
follow any such rule. One man may direct a gun upon a fort as well as three :
two sparks are not more effectual than one in exploding a barrel of gunpowder.
In medicine there is a certain dose that answers the end ; and adding to it does
no more good."

I am not sure that these cases are really exceptions. The law of Composi-
tion of Causes, I think, is really fulfilled, and the appearance to the contrary
is produced by attending to the remote instead of the immediate effect of the
causes. In the cases mentioned, the immediate effect of the causes in action is
a collocation, and the duplication of the cause does double the quantity of col-
location. Two men could raise the gun to the required angle twice as quickly
as one, though one is enough. Two sparks put two sets of particles of the
gunpowder into the state of intestine motion which makes them explode, though
one is sufficient. It is the collocation itself that does not, by being doubled,
always double the effect ; because in many cases a certain collocation, once
obtained, is all that is required for the production of the whole amount of effect
which can be produced at all at the given time and place. Doubling the collo-
cation with difference of time and place, as by pointing two guns, or exploding
a second barrel after the first, does double the effect. This remark applies still
more to Mr. Bain's third example, that of a double dose of medicine : for a
double dose of an aperient does purge more violently, and a double dose of
laudanum does produce longer and sounder sleep. But a double purging, or a
double amount of narcotism, may have remote effects different in kind from the
effect of the smaller amount, reducing the case to that of heteropathic lawSi
discussed in the text.

28—2

436 INDUCTION.

of causation, or consequences resulting from, and corollaries
capable of being deduced from, such laws. If we could deter-
mine what causes are correctly assigned to what effects, and
what effects to what causes, we should be virtually acquainted
with the whole course of nature. All those uniformities
which are mere results of causation might then be explained
and accounted for ; and every individual fact or event might
be predicted, provided we had the requisite data, that is, the
requisite knowledge of the circumstances which, in the par-
ticular instance, preceded it.

To ascertain, therefore, what are the laws of causation
which exist in nature ; to determine the effect of every cause,
and the causes of all effects, — is the main business of Induction ;
and to point out how this is done is the chief object of
Inductive Logic.

CHAPTER VII.

OF OBSERVATION* AND EXPERIMENT.

§ J . IT results from the preceding exposition, that the
process of ascertaining what consequents, in nature, are inva-
riahly connected with what antecedents, or in other words
what phenomena are related to each other as causes and
effects, is in some sort a process of analysis. That every
fact which begins to exist has a cause, and that this cause
must be found in some fact or concourse of facts which imme-
diately preceded the occurrence, may be taken for certain.
The whole of the present facts are the infallible result of all
past facts, and more immediately of all the facts which
existed at the moment previous. Here, then, is a great
sequence, which we know to be uniform. If the whole prior
state of the entire universe could again recur, it would again
be followed by the present state. The question is, how to
resolve this complex uniformity into the simpler uniformities
which compose it, and assign to each portion of the vast
antecedent the portion of the consequent which is attendant
on it.

This operation, which we have called analytical, inasmuch
as it is the resolution of a complex whole into the component
elements, is more than a merely mental analysis. No mere
contemplation of the phenomena, and partition of them by
the intellect alone, will of itself accomplish the end we have
now in view. Nevertheless, such a mental partition is an
indispensable first step. The order of nature, as perceived at
a first glance, presents at every instant a chaos followed by
another chaos. We must decompose each chaos into single
facts. We must learn to see in the chaotic antecedent a mul-
titude of distinct antecedents, in the chaotic consequent a
multitude of distinct consequents. This, supposing it done,

438 INDUCTION.

will not of itself tell us on which of the antecedents each con-
sequent is invariably attendant. To determine that point, we
must endeavour to effect a separation of the facts from one
another, not in our minds only, hut in nature. The mental
analysis, however, must take place first. And every one knows
that in the mode of performing it, one intellect differs im-
mensely from another. It is the essence of the act of observing;
for the observer is not he who merely sees the thing which is
before his eyes, but he who sees what parts that thing is com-
posed of. To do this well is a rare talent. One person, from
inattention, or attending only in the wrong place, overlooks
half of what he sees ; another sets down much more than he
sees, confounding it with what he imagines, or with what he
infers ; another takes note of the kind of all the circumstances,
but being inexpert in estimating their degree, leaves the quan-
tity of each vague and uncertain ; another sees indeed the
whole, but makes such an awkward division of it into parts,
throwing things into one mass which require to be separated,
and separating others which might more conveniently be con-
sidered as one, that the result is much the same, sometimes
even worse, than if no analysis had been attempted at all. It
would be possible to point out what qualities of mind, and
modes of mental culture, fit a person for being a good observer :
that, however, is a question not of Logic, but of the Theory of
Education, in the most enlarged sense of the term. There is
not properly an Art of Observing. There may be rules for
observing. But these, like rules for inventing, are properly
instructions for the preparation of one's own mind ; for put-
ting it into the state in which it will be most fitted to observe,
or most likely to invent. They are, therefore, essentially rules
of self-education, which is a different thing from Logic. They
do not teach how to do the thing, but how to make ourselves
capable of doing it. They are an art of strengthening the
litnbs, not an art of using them.

The extent and minuteness of observation which may be
requisite, and the degree of decomposition to which it may be
necessary to carry the mental analysis, depend on the par-
ticular purpose in view. To ascertain the state of the whole

OBSERVATION AND EXPERIMENT. 439

universe at any particular moment is impossible, but would
also be useless. In making chemical experiments, we do not
think it necessary to note the position of the planets ; because
experience has shown, as a very superficial experience is suffi-
cient to show, that in such cases that circumstance is not
material to the result : and accordingly, in the ages when
men believed in the occult influences of the heavenly bodies,
it might have been unphilosophical to omit ascertaining the
precise condition of those bodies at the moment of the expe-
riment. As to the degree of minuteness of the mental sub-
division, if we were obliged to break down what we observe
into its very simplest elements, that is, literally into single
facts, it would be difficult to say where we should find them :
we can hardly ever affirm that our divisions of any kind have
reached the ultimate unit. But this, too, is fortunately un-
necessary. The only object of the mental separation is to
suggest the requisite physical separation, so that we may
either accomplish it ourselves, or seek for it in nature; and
we have done enough when we have carried the subdivision as
far as the point at which we are able to see what observations
or experiments we require. It is only essential, at whatever
point our mental decomposition of facts may for the present
have stopped, that we should hold ourselves ready and able to
carry it farther as occasion requires, and should not allow the
freedom of our discriminating faculty to be imprisoned by the
swathes and bands of ordinary classification ; as was the case
with all early speculative inquirers, not excepting the Greeks,
to whom it seldom occurred that what was called by one abstract
name might, in reality, be several phenomena, or that there
was a possibility of decomposing the facts of the universe
into any elements but those which ordinary language already
recognised.

§ 2. The different antecedents and consequents, being,
then, supposed to be, so far as the case requires, ascertained
and discriminated from one another ; we are to inquire which
is connected with which. In every instance which comes
under our observation, there are many antecedents and many

440 INDUCTION'.

consequents. If those antecedents could not be severed from
one another except in thought, or if those consequents never
were found apart, it would be impossible for us to distinguish
[a posteriori at least) the real laws, or to assign to any cause
its effect, or to any effect its cause. To do so, we must be
able to meet with some of the antecedents apart from the rest,
and observe what follows from them ; or some of the conse-
quents, and observe by what they are preceded. We must,
in short, follow the Baconian rule of varying the circum-
stances. This is, indeed, only the first rule of physical inquiry,
and not, as some have thought, the sole rule ; but it is the
foundation of all the rest.

For the purpose of varying the circumstances, we may
have recourse (according to a distinction commonly made)
either to observation or to experiment ; we may either find
an instance in nature suited to our purposes, or, by an arti-
ficial arrangement of circumstances, make one. The value of
the instance depends on what it is in itself, not on the mode in
which it is obtained : its employment for the purposes of in-
duction depends on the same principles in the one case and in
the other; as the uses of money are the same whether it is
inherited or acquired. There is, in short, no difference in
kind, no real logical distinction, between the two processes of
investigation. There are, however, practical distinctions to
which it is of considerable importance to advert.

§ 3. The first and most obvious distinction between
Observation and Experiment is, that the latter is an immense
extension of the former. It not only enables us to produce
a much greater number of variations in the circumstances
than nature spontaneously offers, but also, in thousands of
cases, to produce the precise sort of variation which we are in
want of for discovering the law of the phenomenon; a service
which nature, being constructed on a quite different scheme
from that of facilitating our studies, is seldom so friendly as
to bestow upon us. For example, in order to ascertain what
principle in the atmosphere enables it to sustain life, the
variation we require is that a living animal should be immersed

OBSERVATION AND EXPERIMENT. 441

in each component element of the atmosphere separately. But
nature does not supply either oxygen or azote in a separate
state. We are indebted to artificial experiment for our know-
ledge that it is the former, and not the latter, which supports
respiration ; and for our knowledge of the very existence of
the two ingredients.

Thus far the advantage of experimentation over simple
observation is universally recognised : all are aware that it
enables us to obtain innumerable combinations of circum-
stances which are not to be found in nature, and so add to
nature's experiments a multitude of experiments of our own.
But there is another superiority (or, as Bacon would have ex-
pressed it, another prerogative) of instances artificially obtained
over spontaneous instances, — of our own experiments over
even the same experiments when made by nature, — which is
not of less importance, and which is far from being felt and
acknowledged in the same degree.

When we can produce a phenomenon artificially, we can
take it, as it were, home with us, and observe it in the midst
of circumstances with which in all other respects we are accu-
rately acquainted. If we desire to know what are the effects
of the cause A, and are able to produce A by means at our
disposal, we can generally determine at our own discretion, so
far as is compatible with the nature of the phenomenon A, the
whole of the circumstances which shall be present along with
it : and thus, knowing exactly the simultaneous state of every-
thing else which' is within the reach of A's influence, we have
only to observe what alteration is made in that state by the
presence of A.

For example, by the electric machine we can produce,
in the midst of known circumstances, the phenomena
which nature exhibits on a grander scale in the form of
lightning and thunder. Now let any one consider what
amount of knowledge of the effects and laws of electric agency
mankind could have obtained from the mere observation of
thunderstorms, and compare it with that which they have
gained, and may expect to gain, from electrical and galvanic
experiments. This example is the more striking, now that we

442 INDUCTION.

have reason to believe that electric action is of all natural
phenomena (except heat) the most pervading and universal,
which, therefore, it might antecedently have been supposed
could stand least in need of artificial means of production to
enable it to be studied ; while the fact is so much the contrary,
that without the electric machine, the Leyden jar, and the
voltaic battery, we probably should never have suspected the
existence of electricity as one of the great agents in nature ;
the few electric phenomena we should have known of would
have continued to be regarded either as supernatural, or as a
sort of anomalies and eccentricities in the order of the
universe.

When we have succeeded in insulating the phenomenon
which is the subject of inquiry, by placing it among known
circumstances, we may produce further variations of circum-
stances to any extent, and of such kinds as we think best
calculated to bring the laws of the phenomenon into a clear
light. By introducing one well-defined circumstance after
another into the experiment, we obtain assurance of the
manner in which the phenomenon behaves under an indefinite
variety of possible circumstances. Thus, chemists, after
having obtained some newly-discovered substance in a pure
state (that is, having made sure that there is nothing present
which can interfere with and modify its agency,) introduce
various other substances, one by one, to ascertain whether it
will combine with them, or decompose them, and with what
result ; and also apply heat, or electricity, or pressure, to dis-
cover what will happen to the substance under each of these
circumstances.

But if, on the other hand, it is out of our power to pro-
duce the phenomenon, and we have to seek for instances in
which nature produces it, the task before us is very different.

Instead of being able to choose what the concomitant cir-
cumstances shall be, we now have to discover what they are ;
which, when we go beyond the simplest and most accessible
cases, it is next to impossible to do, with any precision and
completeness. Let us take, as an exemplification of a pheno-
menon which we have no means of fabricating artificially, a

OBSERVATION AND EXPERIMENT. 443

human mind. Nature produces many ; but the consequence
of our not being able to produce them by art is, that in every
instance in which we see a human mind developing itself, or
acting upon other things, we see it surrounded and obscured
by an indefinite multitude of unascertainable circumstances,
rendering the use of the common experimental methods almost
delusive. We may conceive to what extent this is true, if we
consider, among other things, that whenever nature produces
a human mind, she produces, in close connexion with it, a
body ; that is, a vast complication of physical facts, in no two
cases perhaps exactly similar, and most of which (except the
mere structure, which we can examine in a sort of coarse
way after it has ceased to act), are radically out of the reach
of our means of exploration. If, instead of a human mind,
we suppose the subject of investigation to be a human society
or State, all the same difficulties recur in a greatly augmented
degree.

We have thus already come within sight of a conclusion,
which the progress of the inquiry will, I think, bring before
us with the clearest evidence : namely, that in the sciences
which deal with phenomena in which artificial experiments are
impossible (as in the case of astronomy), or in which they
have a very limited range (as in mental philosophy, social
science, and even physiology) induction from direct experience
is practised at a disadvantage in most cases equivalent to im-
practicability : from which it follows that the methods of those
sciences, in order to accomplish anything worthy of attain-
ment, must be to a great extent, if not principally, deductive.
This is already known to be the case with the first of the
sciences we have mentioned, astronomy ; that it is not gene-
rally recognised as true of the others, is probably one of the
reasons why they are not in a more advanced state.

§ 4. If what is called pure observation is at so great a
disadvantage, compared with artificial experimentation, in one
department of the direct exploration of phenomena, there is
another branch in which the advantage is all on the side of the
former.

444 INDUCTION*,

Inductive inquiry having for its object to ascertain what
causes are connected with what effects, we may begin this
search at either end of the road which leads from the one
point to the other : we may either inquire into the effects of a
given cause, or into the causes of a given effect. The fact
that light blackens chloride of silver might have been disco-
vered either by experiments on light, trying what effect it would
produce on various substances, or by observing that portions
of the chloride had repeatedly become black, and inquiring
into the circumstances. The effect of the urali poison might
have become known either by administering it to animals, or
by examining how it happened that the wounds which the
Indians of Guiana inflict with their arrows prove so uniformly
mortal. Now it is manifest from the mere statement of the
examples, without any theoretical discussion, that artificial
experimentation is applicable only to the former of these
modes of investigation. We can take a cause, and try what it
will produce : but we cannot take an effect, and try what it
will be produced by. We can only watch till we see it pro-
duced, or are enabled to produce it by accident.

This would be of little importance, if it always depended
on our choice from which of the two ends of the sequence we
would undertake our inquiries. But we have seldom any
option. As we can only travel from the known to the un-
known, we are obliged to commence at whichever end we are
best acquainted with. If the agent is more familiar to us than
its effects, we watch for, or contrive, instances of the agent,
under such varieties of circumstances as are open to us, and
observe the result. If, on the contrary, the conditions on
which a phenomenon depends are obscure, but the phenomenon
itself familiar, we must commence our inquiry from the effect.
If we are struck with the fact that chloride of silver has been
blackened, and have no suspicion of the cause, we have no
resource but to compare instances in which the fact has
chanced to occur, until by that comparison we discover that in
all those instances the substances had been exposed to light.
If we knew nothing of the Indian arrows but their fatal effect,
accident alone could turn our attention to experiments on the

OBSERVATION AND EXPERIMENT. 445

urali ; in the regular course of investigation, we could only
inquire, or try to observe, what had been done to the arrows in
particular instances.

Wherevei', having nothing to guide us to the cause, we
are obliged to set out from the effect, and to apply the rule of
varying the circumstances to the consequents, not the ante-
cedents, we are necessarily destitute of the resource of artificial
experimentation. We cannot, at our choice, obtain conse-
quents, as we can antecedents, under any set of circumstances
compatible with their nature. There are no means of pro-
ducing effects but through their causes, and by the supposi-
tion the causes of the effect in question are not known to us.
We have, therefore, no expedient but to study it where it offers
itself spontaneously. If nature happens to present us with
instances sufficiently varied in their circumstances, and if we
are able to discover, either among the proximate antecedents
or among some other order of antecedents, something which
is always found when the effect is found, however various the
circumstances, and never found when it is not ; we may dis-
cover, by mere observation without experiment, a real uni-
formity in nature.

But though this is certainly the most favourable case for
sciences of pure observation, as contrasted with those in which
artificial experiments are possible, there is in reality no case
which more strikingly illustrates the inherent imperfection of
direct induction when not founded on experimentation. Sup-
pose that, by a comparison of cases of the effect, we have
found an antecedent which appears to be, and perhaps is, in-
variably connected with it : we have not yet proved that ante-
cedent to be the cause, until we have reversed the process, and
produced the effect by means of that antecedent. If we can
produce the antecedent artificially, and if, when we do so, the
effect follows, the induction is complete ; that antecedent is
the cause of that consequent.* But we have then added the

* Unless, indeed, the consequent was generated, not by the antecedent, but
by the means employed to produce the antecedent. As, however, these means
are under our power, there is so far a probability that they are also sufficiently
within our knowledge, to enable us to judge whether that could be the case or not.

446 INDUCTION.

evidence of experiment to that of simple observation. Until
we had done so, we had only proved invariable antecedence
within the limits of experience, but not unconditional ante-
cedence, or causation. Until it had been shown by the actual
production of the antecedent under known circumstances,
and the occurrence thereupon of the consequent, that the
antecedent was really the condition on which it depended ;
the uniformity of succession which was proved to exist between
them might, for aught we knew, be (like the succession of day
and night) not a case of causation at all ; both antecedent and
consequent might be successive stages of the effect of an ulte-
rior cause. Observation, in short, without experiment (sup-
posing no aid from deduction) can ascertain sequences and
coexistences, but cannot prove causation.

In order to see these remarks verified by the actual state
of the sciences, we have only to think of the condition of
natural history. In zoology, for example, there is an immense
number of uniformities ascertained, some of coexistence,
others of succession, to many of which, notwithstanding con-
siderable variations of the attendant circumstances, we know
not any exception : but the antecedents, for the most part, are
such as we cannot artificially produce ; or if we can, it is only
by setting in motion the exact process by which nature pro-
duces them ; and this being to us a mysterious process, of
which the main circumstances are not only unknown but un-
observable, we do not succeed in obtaining the antecedents
under known circumstances. What is the result? That on
this vast subject, which affords so much and such varied scope
for observation, we have made most scanty progress in ascer-
taining any laws of causation. We know not with certainty,
in the case of most of the phenomena that we find conjoined,
which is the condition of the other; which is cause, and
which effect, or whether either of them is so, or they are not
rather conjunct effects of causes yet to be discovered, complex
results of laws hitherto unknown.

Although some of the foregoing observations may be, in
technical strictness of arrangement, premature in this place, it
seemed that a few general remarks on the difference between

OBSERVATION AND EXPERIMENT. 447

sciences of mere observation and sciences of experimentation,
and the extreme disadvantage under which directly inductive
inquiry is necessarily carried on in the former, were the best
preparation for discussing the methods of direct induction ; a
preparation rendering superfluous much that must otherwise
have been introduced, with some inconvenience, into the heart
of that discussion. To the consideration of these methods
we now proceed.

CHAPTER VIII.

OF THE FOUR METHODS OF EXPERIMENTAL INQUIRY.

§ 1. THE simplest and most obvious modes of singling
out from among the circumstances which precede or follow a
phenomenon, those with which it is really connected hy an
invariable law, are two in number. One is, by comparing
together different instances in which the phenomenon occurs.
The other is, by comparing instances in which the phenomenon
does occur, with instances in other respects similar in which
it does not. These two methods may be respectively deno-
minated, the Method of Agreement, and the Method of Dif-
ference.

In illustrating these methods, it will be necessary to bear
in mind the twofold character of inquiries into the laws of
phenomena ; which may be either inquiries into the cause of
a given effect, or into the effects or properties of a given cause.
We shall consider the methods in their application to either
order of investigation, and shall draw our examples equally
from both.

We shall denote antecedents by the large letters of the
alphabet, and the consequents corresponding to them by the
small. Let A, then, be an agent or cause, and let the object
of our inquiry be to ascertain what are the effects of this cause.
If we can either find, or produce, the agent A in such varieties
of circumstances, that the different cases have no circumstance
in common except A ; then whatever effect we find to be pro-
duced in all our trials, is indicated as the effect of A. Sup-
pose, for example, that A is tried along with B and C, and
that the effect is a b c ; and suppose that A is next tried with
D and E, but without B and C, and that the effect is a d e.
Then we may reason thus : b and c are not effects of A, for
they were not produced by it in the second experiment; nor

THE FOUR EXPERIMENTAL METHODS. 449

are d and e, for they were not produced in the first. Whatever
is really the effect of A must have been produced in both
instances; now this condition is fulfilled by no circumstance
except a. The phenomenon a cannot have been the effect of
B or C} since it was produced where they were not ; nor of D
or E, since it was produced where they were not. Therefore
it is the effect of A.

For example, let the antecedent A be the contact of an
alkaline substance and an oil. This combination being tried
under several varieties of circumstances, resembling each other
in nothing else, the results agree in the production of a greasy
and detersive or saponaceous substance : it is therefore con-
cluded that the combination of an oil and an alkali causes the
production of a soap. It is thus we inquire, by the Method of
Agreement, into the effect of a given cause.

In a similar manner we may inquire into the cause of a
given effect. Let a be the effect. Here, as shown in the
last chapter, we have only the resource of observation without
experiment : we cannot take a phenomenon of which we know
not the origin, and try to find its mode of production by pro-
ducing it: if we succeeded in such a random trial it could only
be by accident. But if we can observe a in two different com-
binations, a b c and ade; and if we know, or can discover,
that the antecedent circumstances in these cases respectively
were ABC and ADE; we may conclude by a reasoning
similar to that in the preceding example, that A is the ante-
cedent connected with the consequent a by a law of causation.
B and C, we may say, cannot be causes of a, since on its
second occurrence they were not present ; nor are D and E,
for they were not present on its first occurrence. A, alone of
the five circumstances, was found among the antecedents of a
in both instances.

For example, let the effect a be crystallization. We com-
pare instances in which bodies are known to assume crystalline
structure, but which have no other point of agreement ; and we
find them to have one, and as far as we can observe, only one,
antecedent in common : the deposition of a solid matter from
a liquid state, either a state of fusion or of solution. We con-
VOL. i. 29

450 INDUCTION.

elude, therefore, that the solidification of a substance from a
liquid state is an invariable antecedent of its crystallization.

In this example we may go farther, and say, it is not only
the invariable antecedent but the cause ; or at least the proxi-
mate event which completes the cause. For in this case we
are able, after detecting the antecedent A, to produce it arti-
ficially, and by finding that a follows it, verify the result of
our induction. The importance of thus reversing the proof
was strikingly manifested when by keeping a phial of water
charged with siliceous particles undisturbed for years, a
chemist (I believe Dr. Wollaston) succeeded in obtaining
crystals of quartz ; and in the equally interesting experiment
in which Sir James Hall produced artificial marble by the
cooling of its materials from fusion under immense pressure :
two admirable examples of the light which may be thrown upon
the most secret processes of nature by well-contrived interro-
gation of her.

But if we cannot artificially produce the phenomenon A,
the conclusion that it is the cause of a remains subject to
very considerable doubt. Though an invariable, it may not
be the unconditional antecedent of a, but may precede it as
day precedes night or night day. This uncertainty arises from
the impossibility of assuring ourselves that A is the only im-
mediate antecedent common to both the instances. If we
could be certain of having ascertained all the invariable ante-
cedents, we might be sure that the unconditional invariable
antecedent, or cause, must be found somewhere among them.
Unfortunately it is hardly ever possible to ascertain all the
antecedents, unless the phenomenon is one which we can pro-
duce artificially. Even then, the difficulty is merely lightened,
not removed : men knew how to raise water in pumps long
before they adverted to what was really the operating circum-
stance in the means they employed, namely, the pressure of
the atmosphere on the open surface of the water. It is, how-
ever, much easier to analyse completely a set of arrangements
made by ourselves, than the whole complex mass of the
agencies which nature happens to be exerting at the moment
of the production of a given phenomenon. We may overlook

THE FOUR EXPERIMENTAL METHODS. 451

some of the material circumstances in an experiment with an
electrical machine ; hut we shall, at the worst, he hetter ac-
quainted with them than with those of a thunder-storm.

The mode of discovering and proving laws of nature, which
we have now examined, proceeds on the following axiom :
Whatever circumstances can be excluded, without prejudice to
the phenomenon, or can he ahsent notwithstanding its
presence, is not connected with it in the way of causation.
The casual circumstances being thus eliminated, if only one
remains, that one is the cause which we are in search of: if
more than one, they either are, or contain among them, the
cause ; and so, mutatis mutandis, of the effect. As this method
proceeds by comparing different instances to ascertain in
what they agree, I have termed it the Method of Agreement:
and we may adopt as its regulating principle the following
canon : —

FIRST CANON.

If two or more instances of the phenomenon under investi-
gation have only one circumstance in common, the circumstance
in which alone all the instances agree, is the cause (or effect)
of the given phenomenon.

Quitting for the present the Method of Agreement, to
which we shall almost immediately return, we proceed to a
still more potent instrument of the investigation of nature, the
method of Difference.

§ 2. In the Method of Agreement, we endeavoured to
obtain instances which agreed in the given circumstance but
differed in every other : in the present method we require, on
the contrary, two instances resembling one another in every
other respect, but differing in the presence or absence of the
phenomenon we wish to study. If our object be to discover
the effects of an agent A, we must procure A in some set of
ascertained circumstances, as ABC, and having noted the
effects produced, compare them with the effect of the remain-
ing circumstances B C, when A is absent. If the effect of
A B Cisafcc, and the effect of BC, b c, it is evident that the effect
of A is a. So again, if we begin at the other end, and desire

29—2

452 INDUCTION.

to investigate the cause of an effect a, we must select an in-
stance, as abc, in which the effect occurs, and in which the
antecedents were ABC, and we must look out for another
instance in which the remaining circumstances, b c, occur
without a. If the antecedents, in that instance, are B C, we
know that the cause of a must be A : either A alone, or A in
conjunction with some of the other circumstances present.

It is scarcely necessary to give examples of a logical
process to which we owe almost all the inductive conclusions
we draw in daily life. When a man is shot through the
heart, it is by this method we know that it was the gun-shot
which killed him : for he was in the fulness of life immediately
before, all circumstances being the same, except the wound.

The axioms implied in this method are evidently the fol-
lowing. Whatever antecedent cannot be excluded without
preventing the phenomenon, is the cause, or a condition, of
that phenomenon : Whatever consequent can be excluded,
with no other difference in the antecedents than the absence
of a particular one, is the effect of that one. Instead of
comparing different instances of a phenomenon, to discover
in what they agree, this method compares an instance of its
occurrence with an instance of its non-occurrence, to discover
in what they differ. The canon which is the regulating
principle of the Method of Difference may be expressed as
follows :

SECOND CANON.

If an instance in which the phenomenon under investiga-
tion occurs, and an instance in which it does not occur, have
every circumstance in common save one, that one occurring only
in the former; the circumstance in which alone the two in-
stances differ, is the effect, or the cause, or an indispensable
part of the cause, of the phenomenon.

§ 3. The two methods which we have now stated have
many features of resemblance, but there are also many dis-
tinctions between them. Both are methods of elimination,
This term (employed in the theory of equations to denote the
process by which one after another of the elements of a question

THE FOUR EXPERIMENTAL METHODS. 453

is excluded, and the solution made to depend on the relation
between the remaining elements only) is well suited to express
the operation, analogous to this, which has been understood
since the time of Bacon to be the foundation of experimental
inquiry : namely, the successive exclusion of the various cir-
cumstances which are found to accompany a phenomenon in a
given instance, in order to ascertain what are those among
them which can be absent consistently with the existence of
the phenomenon. The method of Agreement stands on the
ground that whatever can be eliminated, is not connected with
the phenomenon by any law. The Method of Difference has
for its foundation, that whatever cannot be eliminated, is con-
nected with the phenomenon by a law.

Of these methods, that of Difference is more particularly
a method of artificial experiment; while that of Agreement is
more especially the resource employed where experimentation
is impossible. A few reflections will prove the fact, and point
out the reason of it.

It is inherent in the peculiar character of the Method of
Difference, that the nature of the combinations which it
requires is much more strictly defined than in the Method of
Agreement. The two instances which are to be compared
with one another must be exactly similar, in all circumstances
except the one which we are attempting to investigate : they
must be in the relation of A B C and B C, or of a b c and b c.
It is true that this similarity of circumstances needs not
extend to such as are already known to be immaterial to the
result. And in the case of most phenomena we learn at once,
from the commonest experience, that most of the coexistent
phenomena of the universe may be either present or absent
without affecting the given phenomenon ; or, if present, are
present indifferently when the phenomenon does not happen
and when it does. Still, even limiting the identity which is
required between the two instances, ABC and B C, to such
circumstances as are not already known to be indifferent ; it is
very seldom that nature affords two instances, of which we
can be assured that they stand in this precise relation to one
another. In the spontaneous operations of nature there is

454 INDUCTION.

generally such complication and such obscurity, they are
mostly either on so overwhelmingly large or on so inaccessibly
minute a scale, we are so ignorant of a great part of the facts
which really take place, and even those of which we are not
ignorant are so multitudinous, and therefore so seldom exactly
alike in any two cases, that a spontaneous experiment, of the
kind required by the Method of Difference, is commonly not
to be found. When, on the contrary, we obtain a phenomenon
by an artificial experiment, a pair of instances such as the
method requires is obtained almost as a matter of course, pro-
vided the process does not last a long time. A certain state
of surrounding circumstances existed before we commenced
the experiment ; this is B C. We then introduce A ; say,
for instance, by merely bringing an object from another part
of the room, before there has been time for any change in
the other elements. It is, in short (as M. Comte observes),
the very nature of an experiment, to introduce into the pre-
existing state of circumstances a change perfectly definite.
We choose a previous state of things with which we are well
acquainted, so that no unforeseen alteration in that state is
likely to pass unobserved ; and into this we introduce, as
rapidly as possible, the phenomenon which we wish to study ;
so that in general we are entitled to feel complete assurance
that the pre-existing state, and the state which we have pro-
duced, differ in nothing except the presence or absence of that
phenomenon. If a bird is taken from a cage, and instantly
plunged into carbonic acid gas, the experimentalist may be
fully assured (at all events after one or two repetitious) that
no circumstance capable of causing suffocation had supervened
in the interim, except the change from immersion in the
atmosphere to immersion in carbonic acid gas. There is one
doubt, indeed, which may remain in some cases of this de-
scription ; the effect may have been produced not by the change,
but by the means employed to produce the change. The pos-
sibility, however, of this last supposition generally admits of
being conclusively tested by other experiments. It thus
appears that in the study of the various kinds of phenomena
which we can, by our voluntary agency, modify or control, we

THE FOUR EXPERIMENTAL METHODS. 455

can in general satisfy the requisitions of the Method of Dif-
ference ; but that by the spontaneous operations of nature
those requisitions are seldom fulfilled.

The reverse of this is the case with the Method of Agree-
ment. We do not here require instances of so special and de-
terminate a kind. Any instances whatever, in which nature
presents us with a phenomenon, may be examined for the
purposes of this method ; and if all such instances agree in
anything, a conclusion of considerable value is already attained.
We can seldom, indeed, be sure that the one point of agree-
ment is the only one ; but this ignorance does not, as in the
Method of Difference, vitiate the conclusion ; the certainty of
the result, as far as it goes, is not affected. WTe have ascer-
tained one invariable antecedent or consequent, however many
other invariable antecedents or consequents may still remain
unascertained. If A B C, A D E, A EG, are all equally
followed by a, then a is an invariable consequent of A. If
a & c, a d e, afg, all number A among their antecedents, then
A is connected as an antecedent, by some invariable law, with
a. But to determine whether this invariable antecedent is a
cause, or this invariable consequent an effect, we must be able,
in addition, to produce the one by means of the other ; or, at
least, to obtain that which alone constitutes our assurance of
having produced anything, namely, an instance in which the
effect, a, has come into existence, with no other change in the
pre-existing circumstances than the addition of A. And this,
if we can do it, is an application of the Method of Difference,
not of the Method of Agreement.

It thus appears to be by the Method of Difference alone
that we can ever, in the way of direct experience, arrive with
certainty at causes. The Method of Agreement leads only
to laws of phenomena (as some writers call them, but impro-
perly, since laws of causation are also laws of phenomena) :
that is, to uniformities, which either are not laws of causation,
or in which the question of causation must for the present
remain undecided. The Method of Agreement is chiefly to
be resorted to, as a means of suggesting applications of the
Method of Difference (as in the last example the comparison

456 INDUCTION.

of A B C, A D E, A F G, suggested that A was the antece
dent on which to try the experiment whether it could produce
a) ; or as an inferior resource, in case the Method of Difference
is impracticable ; which, as we hefore showed, generally arises
from the impossibility of artificially producing the phenomena.
And hence it is that the Method of Agreement, though appli-
cable in principle to either case, is more emphatically the
method of investigation on those subjects where artificial ex-
perimentation is impossible : because on those it is, generally,
our only resource of a directly inductive nature ; while, in the
phenomena which we can produce at pleasure, the Method of
Difference generally affords a more efficacious process, which
will ascertain causes as well as mere laws.

§ 4. There are, however, many cases in which, though
our power of producing the phenomenon is complete, the
Method of Difference either cannot be made available at all,
or not without a previous employment of the Method of
Agreement. This occurs when the agency by which we can
produce the phenomenon is not that of one single antecedent,
but a combination of antecedents, which we have no power of
separating from each other, and exhibiting apart. For instance,
suppose the subject of inquiry to be the cause of the double
refraction of light. We can produce this phenomenon at
pleasure, by employing any one of the many substances which
are known to refract light in that peculiar manner. But if,
taking one of those substances, as Iceland spar for example,
we wish to determine on which of the properties of Iceland
spar this remarkable phenomenon depends, we can make no
use, for that purpose, of the Method of Difference ; for we
cannot find another substance precisely resembling Iceland
spar except in some one property. The only mode, therefore,
of prosecuting this inquiry is that afforded by the Method of
Agreement ; by which, in fact, through a comparison of all
the known substances which have the property of doubly re-
fracting light, it was ascertained that they agree in the circum-
stance of being crystalline substances; and though the con-
verse does not hold, though all crystalline substances have

THE FOUR EXPERIMENTAL METHODS. 457

not the property of double refraction, it was concluded, with
reason, that there is a real connexion between these two pro-
perties ; that either crystalline structure, or the cause which
gives rise to that structure, is one of the conditions of double
refraction.

Out of this employment of the Method of Agreement arises
a peculiar modification of that method, which is sometimes of
great avail in the investigation of nature. In cases similar to
the above, in which it is not possible to obtain the precise pair
of instances which our second canon requires — instances agree-
ing in every antecedent except A, or in every consequent except
a ; we may yet be able, by a double employment of the Method
of Agreement, to discover in what the instances which contain
A or a, differ from those which do not.

If we compare various instances in which a occurs, and
find that they all have in common the circumstance A, and
(as far as can be observed) no other circumstance, the Method
of Agreement, so far, bears testimony to a connexion between
A and a. In order to convert this evidence of connexion into
proof of causation by the direct Method of Difference, we
ought to be able, in some one of these instances, as for example
ABC, to leave out A, and observe whether by doing so, a is
prevented. Now supposing (what is often the case) that we
are not able to try this decisive experiment ; yet, provided we
can by any means discover what would be its result if we
could try it, the advantage will be the same. Suppose, then,
that as we previously examined a variety of instances in which
a occurred, and found them to agree in containing A, so we
now observe a variety of instances in which a does not occur,
and find them agree in not containing A ; which establishes,
by the Method of Agreement, the same connexion between the
absence of A and the absence of a, which was before esta-
blished between their presence. As, then, it had been shown
that whenever A is present a is present, so it being now shown
that when A is taken away a is removed along with it, we
have by the one proposition A B C, a b c, by the other B C,
b c, the positive and negative instances which the Method of
Difference requires.

458 INDUCTION.

This method may be called the Indirect Method of Dif-
ference, or the Joint Method of Agreement and Difference;
and consists in a double employment of the Method of Agree-
ment, each proof being independent of the other, and corro-
borating it. But it is not equivalent to a proof by the direct
Method of Difference. For the requisitions of the Method of
Difference are not satisfied, unless we can be quite sure either
that the instances affirmative of a, agree in no antecedent
whatever but A, or that the instances negative of a agree in
nothing but the negation of A. Now if it were possible,
which it never is, to have this assurance, we should not need
the joint method ; for either of the two sets of instances
separately, would then be sufficient to prove causation. This
indirect method, therefore, can only be regarded as a great
extension and improvement of the Method of Agreement, but
not as participating in the more cogent nature of the Method
of Difference. The following may be stated as its canon : —

THIRD CANON.

If two or more instances in which the phenomenon occurs
have only one circumstance in common, while two or more
instances in which it does not occur have nothing in common
save the absence of that circumstance ; the circumstance in
which alone the two sets of instances differ, is the effect, or the
cause, or an indispensable part of the cause, of the phenomenon.

We shall presently see that the Joint Method of Agree-
ment and Difference constitutes, in another respect not yet
adverted to, an improvement upon the common Method of
Agreement, namely, in being unaffected by a characteristic
imperfection of that method, the nature of which still remains
to be pointed out. But as we cannot enter into this expo-
sition without introducing a new element of complexity into
this long and intricate discussion, I shall postpone it to a sub-
sequent chapter, and shall at once proceed to a statement of
two other methods, which will complete the enumeration of
the means which mankind possess for exploring the laws of
nature by specific observation and experience.

THE FOUR EXPERIMENTAL METHODS. 459

§ 5. The first of these has been aptly denominated the
Method of Residues. Its principle is very simple. Sub-
ducting from any given phenomenon all the portions which,
by virtue of preceding inductions, can be assigned to known
causes, the remainder will be the effect of the antecedents
which had been overlooked, or of which the effect was as yet
an unknown quantity.

Suppose, as before, that we have the antecedents ABC,
followed by the consequents a b c, and that by previous induc-
tions (founded, we will suppose, on the Method of Difference)
we have ascertained the causes of some of these effects, or the
effects of some of these causes ; and are thence apprised that
the effect of A is a, and that the effect of B is b. Subtracting
the sum of these effects from the total phenomenon, there
remains c, which now, without any fresh experiments, we may
know to be the effect of C. This Method of Residues is in
truth a peculiar modification of the Method of Difference. If
the instance ABC, a b c, could have been compared with a
single instance A B, a b, we should have proved C to be the
cause of c, by the common process of the Method of Diffe-
rence. In the present case, however, instead of a single
instance A B, we have had to study separately the causes
A -and B, and to infer from the effects which they produce
separately, what effect they must produce in the case ABC
where they act together. Of the two instances, therefore,
which the Method of Difference requires, — the one positive,
the other negative, — the negative one, or that in which the
given phenomenon is absent, is not the direct result of obser-
vation and experiment, but has been arrived at by deduction.
As one of the forms of the Method of Difference, the Method
of Residues partakes of its rigorous certainty, provided the
previous inductions, those which gave the effects of A and B,
were obtained by the same infallible method, and provided we
are certain that C is the only antecedent to which the residual
phenomenon c can be referred ; the only agent of which we
had not already calculated and subducted the effect. But as
we can never be quite certain of this, the evidence derived
from the Method of Residues is not complete unless we can

460 INDUCTION.

obtain C artificially and try it separately, or unless its agency,
when once suggested, can be accounted for, and proved deduc-
tively, from known laws.

Even with these reservations, the Method of Residues is
one of the most important among our instruments of disco-
very. Of all the methods of investigating laws of nature,
this is the most fertile in unexpected results : often informing
us of sequences in which neither the cause nor the effect were
sufficiently conspicuous to attract of themselves the attention
of observers. The agent C may be an obscure circumstance,
not likely to have been perceived unless sought for, nor likely
to have been sought for until attention had been awakened by
the insufficiency of the obvious causes to account for the whole
of the effect. And c may be so disguised by its intermixture
with a and b, that it would scarcely have presented itself spon-
taneously as a subject of separate study. Of these uses of
the method, we shall presently cite some remarkable examples.
The canon of the Method of Residues is as follows: —

FOURTH CANON.

Subduct from any phenomenon such part as is known by
previous inductions to be the effect of certain antecedents, and
the residue of the phenomenon is the effect of the remaining
antecedents.

§ 6. There remains a class of laws which it is impracti-
cable to ascertain by any of the three methods which I have
attempted to characterize ; namely, the laws of those Perma-
nent Causes, or indestructible natural agents, which it is im-
possible either to exclude or to isolate ; which we can neither
hinder from being present, nor contrive that they shall be pre-
sent alone. It would appear at first sight that we could by no
means separate the effects of these agents from the effects of
those other phenomena with which they cannot be prevented
from coexisting. In respect, indeed, to most of the perma-
nent causes, no such difficulty exists; since though we cannot
eliminate them as coexisting facts, we can eliminate them as
influencing agents, by simply trying our experiment in a local
situation beyond the limits of their influence. The pendulum,

THE FOUR EXPERIMENTAL METHODS. 461

for example, has its oscillations disturbed by the vicinity of a
mountain : we remove the pendulum to a sufficient distance
from the mountain, and the disturbance ceases : from these
data we can determine by the Method of Difference, the amount
of effect due to the mountain ; and beyond a certain distance
everything goes on precisely as it would do if the mountain
exercised no influence whatever, which, accordingly, we, with
sufficient reason, conclude to be the fact.

The difficulty, therefore, in applying the methods already
treated of to determine the effects of Permanent Causes, is
confined to the cases in which it is impossible for us to get
out of the local limits of their influence. The pendulum can
be removed from the influence of the mountain, but it cannot
be removed from the influence of the earth : we cannot take
away the earth from the pendulum, nor the pendulum from
the earth, to ascertain whether it would continue to vibrate
if the action which the earth exerts upon it were withdrawn.
On what evidence, then, do we ascribe its vibrations to the
earth's influence ? Not on any sanctioned by the Method of
Difference ; for one of the two instances, the negative instance,
is wanting. Nor by the Method of Agreement ; for though
all pendulums agree in this, that during their oscillations
the earth is always present, why may we not as well ascribe
the phenomenon to the sun, which is equally a coexistent
fact in all the experiments ? It is evident that to establish
even so simple a fact of causation as this, there was required
some method over and above those which we have yet ex-
amined.

As another example, let us take the phenomenon Heat.
Independently of all hypothesis as to the real nature of the
agency so called, this fact is certain, that we are unable to
exhaust any body of the whole of its heat. It is equally cer-
tain, that no one ever perceived heat not emanating from a
body. Being unable, then, to separate Body and Heat, we
cannot effect such a variation of circumstances as the fore-
going three methods require ; we cannot ascertain, by those
methods, what portion of the phenomena exhibited by any
body is due to the heat contained in it. If we could observe

INDUCTION.

a body with its heat, and the same hody entirely divested of
heat, the Method of Difference would show the effect due to
the heat, apart from that due to the hody. If we could observe
heat under circumstances agreeing in nothing but heat, and
therefore not characterized also by the presence of a body, we
could ascertain the effects of heat, from an instance of heat
with a body and an instance of heat without a body, by the
Method of Agreement ; or we could determine by the Method
of Difference what effect was due to the body, when the
remainder which was due to the heat would be given by the
Method of Residues. But we can do none of these things ;
and without them the application of any of the three methods
to the solution of this problem would be illusory. It would
be idle, for instance, to attempt to ascertain the effect of heat
by subtracting from the phenomena exhibited by a body, all
that is due to its other properties ; for as we have never been
able to observe any bodies without a portion of heat in them,
effects due to that heat might form a part of the very results,
which we were affecting to subtract in order that the effect of
heat might be shown by the residue.

If, therefore, there were no other methods of experimental
investigation than these three, we should be unable to deter-
mine the effects due to heat as a cause. But we have still a
resource. Though we cannot exclude an antecedent altogether,
we may be able to produce, or nature may produce for us,
some modification in it. By a modification is here meant, a
change in it, not amounting to its total removal. If some
modification in the antecedent A is always followed by a
change in the consequent a, the other consequents b and c
remaining the same ; or vice versd, if every change in a is
found to have been preceded by some modification in A, none
being observable in any of the other antecedents ; we may
safely conclude that a is, wholly or in part, an effect traceable
to A, or at least in some way connected with it through causa-
tion. For example, in the case of heat, though we cannot
expel it altogether from any body, we can modify it in quantity,
we can increase or diminish it ; and doing so, we find by the
various methods of experimentation or observation already

THE FOUR EXPERIMENTAL METHODS. 463

treated of, that such increase or diminution of heat is followed
by expansion or contraction of the body. In this manner we
arrive at the conclusion, otherwise unattainable by us, that one
of the effects of heat is to enlarge the dimensions of bodies ;
or what is the same thing in other words, to widen the dis-
tances between their particles.

A change in a thing, not amounting to its total removal,
that is, a change which leaves it still the same thing it was,
must be a change either in its quantity, or in some of its
variable relations to other things, of which variable relations
the principal is its position in space. In the previous example,
the modification which was produced in the antecedent was an
alteration in its quantity. Let us now suppose the question to
be, what influence the moon exerts on the surface of the earth.
We cannot try an experiment in the absence of the moon, so
as to observe what terrestrial phenomena her annihilation
would put an end to ; but when we find that all the variations
in the position of the moon are followed by corresponding
variations in the time and place of high water, the place being
always either the part of the earth which is nearest to, or that
which is most remote from, the moon, we have ample evidence
that the moon is, wholly or partially, the cause which deter-
mines the tides. It very commonly happens, as it does in this
instance, that the variations of an effect are correspondent, or
analogous, to those of its cause ; as the moon moves farther
towards the east, the high water point does the same : but this
is not an indispensable condition ; as may be seen in the same
example, for along with that high water point there is at the
same instant another high water point diametrically opposite
to it, and which, therefore, of necessity, moves towards the
west, as the moon, followed by the nearer of the tide waves,
advances towards the east : and yet both these motions are
equally effects of the moon's motion.

That the oscillations of the pendulum are caused by the
earth, is proved by similar evidence. Those oscillations take
place between equidistant points on the two sides of a line,
which, being perpendicular to the earth, varies with every
variation in the earth's position, either in space or relatively to

464 INDUCTION.

the object. Speaking accurately, we only know by the method
now characterized, that all terrestrial bodies tend to the earth,
and not to some unknown fixed point lying in the same direc-
tion. In every twenty-four hours, by the earth's rotation, the
line drawn from the body at right angles to the earth coincides
successively with all the radii of a circle, and in the course of
six months the place of that circle varies by nearly two
hundred millions of miles ; yet in all these changes of the
earth's position, the line in which bodies tend to fall continues
to be directed towards it : which proves that terrestrial gravity
is directed to the earth, and not, as was once fancied by some,
to a fixed point of space.

The method by which these results were obtained, may be
termed the Method of Concomitant Variations : it is regulated
by the following canon : —

FIFTH CANON.

Whatever phenomenon varies in any manner whenever
another phenomenon varies in some particular manner, is
either a cause or an effect of that phenomenon, or is connected
with it through some fact of causation.

The last clause is subjoined, because it by no means follows
when two phenomena accompany each other in their variations,
that the one is cause and the other effect. The same thing
may, and indeed must happen, supposing them to be two dif-
ferent effects of a common cause : and by this method alone it
would never be possible to ascertain which of the suppositions
is the true one. The only way to solve the doubt would be
that which we have so often adverted to, viz. by endeavouring
to ascertain whether we can produce the one set of variations
by means of the other. In the case of heat, for example, by
increasing the temperature of a body we increase its bulk, but
by increasing its bulk we do not increase its temperature ; on
the contrary, (as in the rarefaction of air under the receiver of
an air-pump,) we generally diminish it : therefore heat is not
an effect, but a cause, of increase of bulk. If we cannot our-
selves produce the variations, we must endeavour, though it is
an attempt which is seldom successful, to find them produced

THE FOUR EXPERIMENTAL METHODS.

by nature in some case in which the pre-existing circumstances
are perfectly known to us.

It is scarcely necessary to say, that in order to ascertain
the uniform concomitance of variations in the effect with varia-
tions in the cause, the same precautions must he used as in
any other case of the determination of an invariable sequence.
We must endeavour to retain all the other antecedents un-
changed, while that particular one is subjected to the requisite
series of variations ; or in other words, that we may be war-
ranted in inferring causation from concomitance of variations,
the concomitance itself must be proved by the Method of
Difference.

It might at first appear that the Method of Concomitant
Variations assumes a new axiom, or law of causation in
general, namely, that every modification of the cause is fol-
lowed by a change in the effect. And it does usually happen
that when a phenomenon A causes a phenomenon a, any
variation in the quantity or in the various relations of A, is
uniformly followed by a variation in the quantity or relations
of a. To take a familiar instance, that of gravitation. The
sun causes a certain tendency to motion in the earth ; here
we have cause and effect; but that tendency is towards the
sun, and therefore varies in direction as the sun varies in the
relation of position ; and moreover the tendency varies in
intensity, in a certain numerical correspondence to the sun's
distance from the earth, that is, according to another relation
of the sun. Thus we see that there is not only an invariable
connexion between the sun and the earth's gravitation, but
that two of the relations of the sun, its position with respect
to the earth and its distance from the earth, are invariably
connected as antecedents with the quantity and direction of
the earth's gravitation. The cause of the earth's gravitating
at all, is simply the sun ; but the cause of its gravitating with
a given intensity and in a given direction, is the existence of
the sun in a given direction and at a given distance. It is not
strange that a modified cause, which is in truth a different
cause, should produce a different effect.

Although it is for the most part true that a modification
VOL. i. 30

466 INDUCTION.

of the cause is followed by a modification of the effect, the
Method of Concomitant Variations does not, however, pre-
suppose this as an axiom. It only requires the converse pro-
position ; that anything on whose modifications, modifications
of an effect are invariably consequent, must be the cause (or
connected with the cause) of that effect ; a proposition, the
truth of which is evident ; for if the thing itself had no influ-
ence on the effect, neither could the modifications of the
thing have any influence. If the stars have no power over
the fortunes of mankind, it is implied in the very terms, that
the conjunctions or oppositions of different stars can have no
such power.

Although the most striking applications of the Method of
Concomitant Variations take place in the cases in which the
Method of Difference, strictly so called, is impossible, its use
is not confined to those cases ; it may often usefully follow
after the Method of Difference, to give additional precision to
a solution which that has found. When by the Method of
Difference it has first been ascertained that a certain object
produces a certain effect, the Method of Concomitant Varia-
tions may be usefully called in, to determine according to
what law the quantity or the different relations of the effect
follow those of the cause.

§ 7. The case in which this method admits of the most
extensive employment, is that in which the variations of the
cause are variations of quantity. Of such variations we may
in general affirm with safety, that they will be attended not
only with variations, but with similar variations, of the effect :
the proposition, that more of the cause is followed by more of
the effect, being a corollary from the principle of the Compo-
sition of Causes, which, as we have seen, is the general rule of
causation ; cases of the opposite description, in which causes
change their properties on being conjoined with one another,
being, on the contrary, special and exceptional. Suppose,
then, that when A changes in quantity, a also changes in
quantity, and in such a manner that we can trace the nume-
rical relation which the changes of the one bear to such

THE FOUR EXPERIMENTAL METHODS. 467

changes of the other as take place within our limits of obser-
vation. We may then, with certain precautions, safely con-
clude that the same numerical relation will hold beyond those
limits. If, for instance, we find that when A is double, a is
double; that when A is treble or quadruple, a is treble or
quadruple ; we may conclude that if A were a half or a third,
a would be a half or a third, and finally, that if A were anni-
hilated, a would be annihilated ; and that a is wholly the
effect of A, or wholly the effect of the same cause with A. And
so with any other numerical relation according to which A and
a would vanish simultaneously ; as, for instance, if a were
proportional to the square of A. If, on the other hand, a is
not wholly the effect of A, but yet varies when A varies, it is
probably a mathematical function not of A alone, but of A
and something else: its changes, for example, may be such as
would occur if part of it remained constant, or varied on some
other principle, and the remainder varied in some numerical
relation to the variations of A. In that case, when A dimi-
nishes, a will be seen to approach not towards zero, but
towards some other limit: and when the series of variations is
such as to indicate what that limit is, if constant, or the law of
its variation if variable, the limit will exactly measure how
much of a is the effect of some other and independent cause,
and the remainder will be the effect of A (or of the cause of A).
These conclusions, however, must not be drawn without
certain precautions. In the first place, the possibility of
drawing them at all, manifestly supposes that we are ac-
quainted not only with the variations, but with the absolute
quantities both of A and a. If we do not know the total
quantities, we cannot, of course, determine the real numerical
relation according to which those quantities vary. It is there-
fore an error to conclude, as some have concluded, that because
increase of heat expands bodies, that is, increases the distance
between their particles, therefore the distance is wholly the
effect of heat, and that if we could entirely exhaust the body
of its heat, the particles would be in complete contact. This
is no more than a guess, and of the most hazardous sort, not
a legitimate induction : for since we neither know how much

30—2

468 INDUCTION.

heat there is in any body, nor what is the real distance
between any two of its particles, we cannot judge whether the
contraction of the distance does or does not follow the dimi-
nution of the quantity of heat according to such a numerical
relation that the two quantities would vanish simulta-
neously.

In contrast with this, let us consider a case in which the
absolute quantities are known ; the case contemplated in the
first law of motion ; viz. that all bodies in motion continue to
move in a straight line with uniform velocity until acted upon
by some new force. This assertion is in open opposition to
first appearances ; all terrestrial objects, when in motion,
gradually abate their velocity and at last stop ; which accord-
ingly the ancients, with their inductio per enumerationem sim-
plicem, imagined to be the law. Every moving body, how-
ever, encounters various obstacles, as friction, the resistance of
the atmosphere, £c., which we know by daily experience to be
causes capable of destroying motion. It was suggested that
the whole of the retardation might be owing to these causes.
How was this inquired into ? If the obstacles could have
been entirely removed, the case would have been amenable to
the Method of Difference. They could not be removed, they
could only be diminished, and the case, therefore, admitted
only of the Method of Concomitant Variations. This accord-
ingly being employed, it was found that even,- diminution of
the obstacles diminished the retardation of the motion : and
inasmuch as in this case (unlike the case of heat) the total
quantities both of the antecedent and of the consequent were
known ; it was practicable to estimate, with an approach to
accuracy, both the amount of the retardation and the amount
of the retarding causes, or resistances, and to judge how near
they both were to being exhausted ; and it appeared that the
effect dwindled as rapidly, and at each step was as far on the
road towards annihilation, as the cause was. The simple
oscillation of a weight suspended from a fixed point, and moved
a little out of the perpendicular, which in ordinary circum-
stances lasts but a few minutes, was prolonged in Borda's ex-
periments to more than thirty hours, by diminishing as much

THE FOUR EXPERIMENTAL METHODS. 469

as possible the friction at the point of suspension, and by
making the body oscillate in a space exhausted as nearly as
possible of its air. There could therefore be no hesitation in
assigning the whole of the retardation of motion to the in-
fluence of the obstacles; and since, after subducting this
retardation from the total phenomenon, the remainder was an
uniform velocity, the result was the proposition known as the
first law of motion.

There is also another characteristic uncertainty affecting
the inference that the law of variation which the quantities
observe within our limits of observation, will hold beyond
those limits. There is of course, in the first instance, the
possibility that beyond the limits, and in circumstances there-
fore of which we have no direct experience, some counteract-
ing cause might develop itself; either a new agent, or a new
property of the agents concerned, which lies dormant in the
circumstances we are able to observe. This is an element of
uncertainty which enters largely into all our predictions of
effects ; but it is not peculiarly applicable to the Method of
Concomitant Variations. The uncertainty, however, of which
I am about to speak, is characteristic of that method ; espe-
cially in the cases in which the extreme limits of our observa-
tion are very narrow, in comparison with the possible variations
in the quantities of the phenomena. Any one who has the
slightest acquaintance with mathematics, is aware that very
different laws of variation may produce numerical results which
differ but slightly from one another within narrow limits; and
it is often only when the absolute amounts of variation are
considerable, that the difference between the results given by
one law and by another becomes appreciable. When, there-
fore, such variations in the quantity of the antecedents as we
have the means of observing, are small in comparison with
the total quantities, there is much danger lest we should mis-
take the numerical law, and be led to miscalculate the varia-
tions which would take place beyond the limits ; a miscalcula-
tion which would vitiate any conclusion respecting the de-
pendence of the effect upon the cause, that could be founded
on those variations. Examples are not wanting of such mis-

INDUCTION.

takes. " The formulae," says Sir John Herschel,* " which
have been empirically deduced for the elasticity of steam, (till
very recently,) and those for the resistance of fluids, and other
similar subjects," when relied on beyond the limits of the ob-
servations from which they were deduced, " have almost inva-
riably failed to support the theoretical structures which have
been erected on them."

In this uncertainty, the conclusion we may draw from the
concomitant variations of a and A, to the existence of an
invariable and exclusive connexion between them, or to the
permanency of the same numerical relation between their varia-
tions when the quantities are much greater or smaller than
those which we have had the means of observing, cannot be
considered to rest on a complete induction. All that in such
a case can be regarded as proved on the subject of causa-
tion is, that there is some connexion between the two pheno-
mena; that A, or something which can influence A, must be
one of the causes which collectively determine a. We may,
however, feel assured that the relation which we have observed
to exist between the variations of A and a, will hold true in
all cases which fall between the same extreme limits; that is,
wherever the utmost increase or diminution in which the result
has been found by observation to coincide with the law, is not
exceeded.

The four methods which it has now been attempted to de-
scribe, are the only possible modes of experimental inquiry —
of direct induction a posteriori, as distinguished from deduc-
tion : at least, I know not, nor am able to imagine, any
others. And even of these, the Method of Residues, as we
have seen, is not independent of deduction ; though, as it also
requires specific experience, it may, without impropriety, be
included among methods of direct observation and experiment.

These, then, with such assistance as can be obtained from
Deduction, compose the available resources of the human mind
for ascertaining the laws of the succession of phenomena.
Before proceeding to point out certain circumstances, by which

* Discourse on the Study of Natural Philosophy, p. 179.

THE FOUR EXPERIMENTAL METHODS. 471

the employment of these methods is subjected to an immense
increase of complication and of difficulty, it is expedient to
illustrate the use of the methods, by suitable examples drawn
from actual physical investigations. These, accordingly, will
form the subject of the succeeding chapter.

CHAPTER IX.

MISCELLANEOUS EXAMPLES OF THE FOUR METHODS.

§ 1. I SHALL select, as a first example, an interesting
speculation of one of the most eminent of theoretical chemists,
Baron Liebig. The object in view, is to ascertain the imme-
diate cause of the death produced by metallic poisons.

Arsenious acid, and the salts of lead, bismuth, copper, and
mercury, if introduced into the animal organism, except in
the smallest doses, destroy life. These facts have long
been known, as insulated truths of the lowest order of gene-
ralization ; but it was reserved for Liebig, by an apt employ-
ment of the first two of our methods of experimental inquiry,
to connect these truths together by a higher induction,
pointing out what property, common to all these deleterious
substances, is the really operating cause of their fatal eifect.

When solutions of these substances are placed in suffi-
ciently close contact with many animal products, albumen,
milk, muscular fibre, and animal membranes, the acid or salt
leaves the water in which it was dissolved, and enters into com-
bination with the animal substance : which substance, after
being thus acted upon, is found to have lost its tendency to
spontaneous decomposition, or putrefaction.

Observation also shows, in cases where death has been
produced by these poisons, that the parts of the body with
which the poisonous substances have been brought into con-
tact, do not afterwards putrefy.

And, finally, when the poison has been supplied in too
small a quantity to destroy life, eschars are produced, that is,
certain superficial portions of the tissues are destroyed, which
are afterwards thrown off by the reparative process taking
place in the healthy parts.

These three sets of instances admit of being treated accord-

EXAMPLES OF THE FOUR METHODS. 473

ing to the Method of Agreement. In all of them the metallic
compounds are brought into contact with the substances which
compose the human or animal body ; and the instances do not
seem to agree in any other circumstance. The remaining
antecedents are as different, and even opposite, as they could
possibly be made ; for in some the animal substances exposed
to the action of the poisons are in a state of life, in others
only in a state of organization, in others not even in that.
And what is the result which follows in all the cases ? The
conversion of the animal substance (by combination with
the poison) into a chemical compound, held together by so
powerful a force as to resist the subsequent action of the
ordinary causes of decomposition. Now, organic life (the
necessary condition of sensitive life) consisting in a continual
state of decomposition and recompositiou of the different
organs and tissues ; whatever incapacitates them for this
decomposition destroys life. And thus the proximate cause
of the death produced by this description of poisons, is
ascertained, as far as the Method of Agreement can ascer-
tain it.

Let us now bring our conclusion to the test of the Method
of Difference. Setting out from the cases already mentioned,
in which the antecedent is the presence of substances forming
with the tissues a compound incapable of putrefaction, (and
a fortiori incapable of the chemical actions which constitute
life,) and the consequent is death, either of the whole organism,
or of some portion of it; let us compare with these cases
other cases, as much resembling them as possible, but in
which that effect is not produced. And, first, " many inso-
luble basic salts of arsenious acid are known not to be poi-
sonous. The substance called alkargen, discovered by Bunsen,
which contains a very large quantity of arsenic, and approaches
very closely in composition to the organic arseuious compounds
found in the body, has not the slightest injurious action upon
the organism." Now when these substances are brought into
contact with the tissues in any way, they do not combine with
them ; they do not arrest their progress to decomposition.
As far, therefore, as these instances go, it appears that when

474 INDUCTION.

the effect is absent, it is by reason of tbe absence of that ante-
cedent which we had already good ground for considering as
the proximate cause.

But the rigorous conditions of the Method of Difference
are not yet satisfied ; for we cannot be sure that these un-
poisonous bodies agree with the poisonous substances in every
property, except the particular one, of entering into a difficultly
decomposable compound with the animal tissues. To render
the method strictly applicable, we need an instance, not of a
different substance, but of one of the very same substances, in
circumstances which would prevent it from forming, with the
tissues, the sort of compound in question ; and then, if death
does not follow, our case is made out. Now such instances
are afforded by the antidotes to these poisons. For example,
in case of poisoning by arsenious acid, if hydrated peroxide of
iron is administered, the destructive agency is instantly checked.
Now this peroxide is known to combine with the acid, and
form a compound, which, being insoluble, cannot act at all on
animal tissues. So, again, sugar is a well-known antidote to
poisoning by salts of copper; and sugar reduces those salts
either into metallic copper, or into the red suboxide, neither
of which enters into combination with animal matter. The
disease called painter's colic, so common in manufactories of
white lead, is unknown where the workmen are accustomed to
take, as a preservative, sulphuric acid lemonade (a solution of
sugar rendered acid by sulphuric acid). Now diluted sul-
phuric acid has the property of decomposing all compounds
of lead with organic matter, or of preventing them from being
formed.

There is another class of instances, of the nature required
by the Method of Difference, which seem at first sight to con-
flict with the theory. Soluble salts of silver, such for instance
as the nitrate, have the same stiffening antiseptic effect on
decomposing animal substances, as corrosive sublimate and
the most deadly metallic poisons ; and when applied to the
external parts of the body, the nitrate is a powerful caustic,
depriving those parts of all active vitality, and causing them
to be thrown off by the neighbouring living structures, in the

EXAMPLES OF THE FOUR METHODS. 475

form of an eschar. The nitrate and the other salts of silver
ought, then, it would seem, if the theory he correct, to be poi-
sonous ; yet they may be administered internally with perfect
impunity. From this apparent exception arises the strongest
confirmation which the theory has yet received. Nitrate of
silver, in spite of its chemical properties, does not poison when
introduced into the stomach ; but in the stomach, as in all
animal liquids, there is common salt; and in the stomach
there is also free muriatic acid. These substances operate as
natural antidotes, combining with the nitrate, and if its quan-
tity is not too great, immediately converting it into chloride
of silver ; a substance very slightly soluble, and therefore in-
capable of combining with the tissues, although to the extent
of its solubility it has a medicinal influence, though an entirely
different class of organic actions.

The preceding instances have afforded an induction of a
high order of collusiveness, illustrative of the two simplest of
our four methods ; though not rising to the maximum of cer-
tainty which the Method of Difference, in its most perfect
exemplification, is capable of affording. For (let us not for-
get) the positive instance and the negative one which the
rigour of that method requires, ought to differ only in the
presence or absence of one single circumstance. Now, in the
preceding argument, they differ in the presence or absence not
of a single circumstance, but of a single substance : and as
every substance has innumerable properties, there is no know-
ing what number of real differences are involved in what is
nominally and apparently only one difference. It is conceiv-
able that the antidote, the peroxide of iron for example, may
counteract the poison through some other of its properties than
that of forming an insoluble compound with it ; and if so, the
theory would fall to the ground, so far as it is supported by
that instance. This source of uncertainty, which is a serious
hindrance to all extensive generalizations in chemistry, is how-
ever reduced in the present case to almost the lowest degree
possible, when we find that not only one substance, but many
substances, possess the capacity of acting as antidotes to
metallic poisons, and that all these agree in the property of

476 INDUCTION.

forming insoluble compounds with the poisons, while they
cannot be ascertained to agree in any other property whatso-
ever. We have thus, in favour of the theory, all the evidence
which can be obtained by what we termed the Indirect Method
of Difference, or the Joint Method of Agreement and Diffe-
rence ; the evidence of which, though it never can amount to
that of the Method of Difference properly so called, may ap-
proach indefinitely near to it.

§ 2. Let the object be* to ascertain the law of what is
termed induced electricity; to find under what conditions any
electrified body, whether positively or negatively electrified,
gives rise to a contrary electric state in some other body adja-
cent to it.

The most familiar exemplification of the phenomenon to
be investigated is the following. Around the prime conductors
of an electrical machine, the atmosphere to some distance, or
any conducting surface suspended in that atmosphere, is found
to be in an electric condition opposite to that of the prime
conductor itself. Near and around the positive prime con-
ductor there is negative electricity, and near and around the
negative prime conductor there is positive electricity. When
pith balls are brought near to either of the conductors, they
become electrified with the opposite electricity to it ; either
receiving a share from the already electrified atmosphere by
conduction, or acted upon by the direct inductive influence of
the conductor itself: they are then attracted by the conductor
to which they are in opposition ; or, if withdrawn in their
electrified state, they will be attracted by any other oppositely
charged body. In like manner the hand, if brought near
enough to the conductor, receives or gives an electric dis-
charge ; now we have no evidence that a charged conductor
can be suddenly discharged unless by the approach of a body
oppositely electrified. In the case, therefore, of the electric
machine, it appears that the accumulation of electricity in an

* For this speculation, as for many other of my scientific illustrations, I
am indebted to Professor Bain, whose subsequent treatise on Logic abounds
\\ith apt illustrations of all the inductive methods.

EXAMPLES OF THE FOUR METHODS. 477

insulated conductor is always accompanied by the excitement
of the contrary electricity in the surrounding atmosphere, and
in every conductor placed near the former conductor. It does
not seem possible, in this case, to produce one electricity by
itself.

Let us now examine all the other instances which we can
obtain, resembling this instance in the given consequent,
namely, the evolution of an opposite electricity in the neigh-
bourhood of an electrified body. As one remarkable instance
we have the Leyden jar; and after the splendid experiments
of Faraday in complete and final establishment of the sub-
stantial identity of magnetism and electricity, we may cite the
magnet, both the natural and the electro-magnet, in neither of
which it is possible to produce one kind of electricity by itse'f,
or to charge one pole without charging an opposite pole with
the contrary electricity at the same time. We cannot have a
magnet with one pole : if we break a natural loadstone into a
thousand pieces, each piece will have its two oppositely elec-
trified poles complete within itself. In the voltaic circuit,
ngain, we cannot have one current without its opposite. In
the ordinary electric machine, the glass cylinder or plate, and
the rubber, acquire opposite electricities.

From all these instances, treated by the Method of Agree-
ment, a general law appears to result. The instances embrace
all the known modes in which a body can become charged
with electricity ; and in all of them there is found, as a con-
comitant or consequent, the excitement of the opposite electric
state in some other body or bodies. It seems to follow that
the two facts are invariably connected, and that the excitement
of electricity in any body has for one of its necessary condi-
tions the possibility of a simultaneous excitement of the oppo-
site electricity in some neighbouring body.

As the two contrary electricities can only be produced to-
gether, so they can only cease together. This may be shown
by an application of the Method of Difference to the example
of the Leyden jar. It needs scarcely be here remarked that in
the Leyden jar, electricity can be accumulated and retained in
considerable quantity, by the contrivance of having two con-

478 INDUCTION.

ducting surfaces of equal extent, and parallel to each other
through the whole of that extent, with a non-conducting sub-
stance such as glass between them. When one side of the jar
is charged positively, the other is charged negatively, and it
was by virtue of this fact that the Leyden jar served just now
as an instance in our employment of the Method of Agree-
ment. Now it is impossible to discharge one of the coatings
unless the o'ther can be discharged at the same time. A con-
ductor held to the positive side cannot convey away any elec-
tricity unless an equal quantity be allowed to pass from the
negative side : if one coating be perfectly insulated, the charge
is safe. The dissipation of one must proceed pari passu with
that of the other.

The law thus strongly indicated admits of corroboration
by the Method of Concomitant Variations. The Leyden jar
is capable of receiving a much higher charge than can ordi-
narily be given to the conductor of an electrical machine.
Now in the case of the Leyden jar, the metallic surface which
receives the induced electricity is a conductor exactly similar
to that which receives the primary charge, and is therefore as
susceptible of receiving and retaining the one electricity, as
the opposite surface of receiving and retaining the other; but
in the machine, the neighbouring body which is to be oppo-
sitely electrified is the surrounding atmosphere, or any body
casually brought near to the conductor; and as these are
generally much inferior in their capacity of becoming electri-
fied, to the conductor itself, their limited power imposes a
corresponding limit to the capacity of the conductor for being
charged. As the capacity of the neighbouring body for sup-
porting the opposition increases, a higher charge becomes pos-
sible : and to this appears to be owing the great superiority of
the Leyden jar.

A further and most decisive confirmation by the Method
of Difference, is to be found in one of Faraday's experiments
in the course of his researches on the subject of Induced
Electricity.

Since common or machine electricity, and voltaic electri-
city, may be considered for the present purpose to be identical,

EXAMPLES OF THE FOUR METHODS. 479

Faraday wished to know whether, as the prime conductor de-
velopes opposite electricity upon a conductor in its vicinity,
so a voltaic current running along a wire would induce an
opposite current upon another wire laid parallel to it at a
short distance. Now this case is similar to the cases previously
examined, in every circumstance except the one to which we
have ascribed the effect. We found in the former instances
that whenever electricity of one kind was excited in one body,
electricity of the opposite kind must be excited in a neigh-
bouring body. But in Faraday's experiment this indispensable
opposition exists within the wire itself. From the nature of a
voltaic charge, the two opposite currents necessary to the ex-
istence of each other are both accommodated in one wire ; and
there is no need of another wire placed beside it to contain one
of them, in the same way as the Leyden jar must have a posi-
tive and a negative surface. The exciting cause can and does
produce all the effect which its laws require, independently of
any electric excitement of a neighbouring body. Now the
result of the experiment with the second wire was, that
no opposite current was produced. There was an in-
stantaneous effect at the closing and breaking of the
voltaic circuit; electric inductions appeared when the
two wires were moved to and from one another; but
these are phenomena of a different class. There was
no induced electricity in the sense in which this is predicated
of the Leyden jar; there was no sustained current running
up the one wire while an opposite current ran down the
neighbouring wire ; and this alone would have been a true
parallel case to the other.

It thus appears by the combined evidence of the Method
of Agreement, the Method of Concomitant Variations, and the
most rigorous form of the Method of Difference, that neither
of the two kinds of electricity can be excited without an equal
excitement of the other and opposite kind : that both are
effects of the same cause ; that the possibility of the one is a
condition of the possibility of the other, and the quantity of
the one an impassable limit to the quantity of the other. A
scientific result of considerable interest in itself, and illus-

480 INDUCTION.

trating those three methods in a manner both characteristic
and easily intelligible.*

§ -3. Our third example shall be extracted from Sir John
Herschel's Discourse on the Study of Natural Philosophy, a
work replete with happily-selected exemplifications of induc-
tive processes from almost every department of physical science,
and in which alone, of all books which I have met with, the
four methods of induction are distinctly recognised, though
not so clearly characterized and defined, nor their correlation
so fully shown, as has appeared to me desirable. The present
example is described by Sir John Herschel as " one of the
most beautiful specimens" which can be cited "of inductive
experimental inquiry lying within a moderate compass ;" the
theory of dew, first promulgated by the late Dr. Wells, and
now universally adopted by scientific authorities. The pas-
sages in inverted commas are extracted verbatim from the
Discourse. f

" Suppose dew were the phenomenon proposed, whose cause
we would know. In the first place" we must determine pre-
cisely what we mean by dew : what the fact really is, whose
cause we desire to investigate. " We must separate dew from
rain, and the moisture of fogs, and limit the application of the
term to what is really meant, which is the spontaneous appear-
ance of moisture on substances exposed in the open air when
no rain or visible wet is falling." This answers to a prelimi-

* This view of the necessary coexistence of opposite excitements involves
a great extension of the original doctrine of two electricities. The early
theorists assumed that, when amber was rubbed, the amber was made positive
and the rubber negative to the same degree ; but it never occurred to them
to suppose tbat the existence of the amber charge was dependent on an opposite
charge in the bodies with which the amber was contiguous, while the existence
of the negative charge on the rubber was equally dependent on a contrary state
of the surfaces that might accidentally be confronted with it ; that, in fact, in
a case of electrical excitement by friction, four charges were the minimum that
could exist. But this double electrical action is essentially implied in the
explanation now universally adopted in regard to the phenomena of the common
electric machine.

+ Pp. 159- 162.

EXAMPLES OF THE FOUR METHODS. 481

nary operation which will be characterized in the ensuing book,
treating of operations subsidiary to induction.*

" Now, here we have analogous phenomena in the moisture
which bedews a cold metal or stone when we breathe upon it ;
that which appears on a glass of water fresh from the well in
hot weather ; that which appears on the inside of windows
when sudden rain or hail chills the external air; that which
runs down our walls when, after a long frost, a warm moist
thaw comes on." Comparing these cases, we find that they
all contain the phenomenon which was proposed as the subject
of investigation. Now " all these instances agree in one point,
the coldness of the object dewed, in comparison with the air
in contact with it." But there still remains the most impor-
tant case of all, that of nocturnal dew : does the same circum-
stance exist in this case ? " Is it a fact that the object dewed
is colder than the air ? Certainly not, one would at first be
inclined to say; for what is to make it so? But .... the
experiment is easy : we have only to lay a thermometer in
contact with the dewed substance, and hang one at a little dis-
tance above it, out of reach of its influence. The experiment
has been therefore made, the question has been asked, and the
answer has been invariably in the affirmative. Whenever an
object contracts dew, it is colder than the air."

Here then is a complete application of the Method of
Agreement, establishing the fact of an invariable connexion
between the deposition of dew on a surface, and the coldness
of that surface compared with the external air. But which of
these is cause, and which effect ? or are they both effects of
something else ? On this subject the Method of Agreement
can afford us no light : we must call in a more potent method.
" We must collect more facts, or, which comes to the same
thing, vary the circumstances ; since every instance in which
the circumstances differ is a fresh fact : and especially, we must
note the contrary or negative cases, i.e. where no dew is pro-
duced :" a comparison between instances of dew and instances
of no dew, being the condition necessary to bring the Method
of Difference into play.

* Infra, book iv. ch. ii. On Abstraction.
VOL. I. 31

INDUCTION.

"Now, first, no dew is produced on the surface of polished
metals, but it is very copiously on glass, both exposed with
their faces upwards, and in some cases the under side of a
horizontal plate of glass is also dewed." Here is an instance
in which the effect is produced, and another instance in which
it is not produced ; but we cannot yet pronounce, as the
canon of the Method of Difference requires, that the latter
instance agrees with the former in all its circumstances except
one ; for the differences between glass and polished metals are
manifold, and the only thing we can as yet be sure of is, that
the cause of dew will be found among the circumstances by
which the former substance is distinguished from the latter.
But if we could be sure that glass, and the various other sub-
stances on which dew is deposited, have only one quality in
common, and that polished metals and the other substances
on which dew is not deposited have also nothing in common
but the one circumstance, of not having the one quality which
the others have ; the requisitions of the Method of Difference
would be completely satisfied, and we should recognise, in that
quality of the substances, the cause of dew. This, accordingly,
is the path of inquiry which is next to be pursued.

" In the cases of polished metal and polished glass, the
contrast shows evidently that the substance has much to do
with the phenomenon ; therefore let the substance alone be
diversified as much as possible, by exposing polished surfaces
of various kinds. This done, a scale of intensity becomes
obvious. Those polished substances are found to be most
strongly dewed which conduct heat worst; while those which
conduct well, resist dew most effectually." The complication
increases; here is the Method of Concomitant Variations
called to our assistance ; and no other method was practicable
on this occasion ; for the quality of conducting heat could not
be excluded, since all substances conduct heat in some degree.
The conclusion obtained is, that c&teris parilus the deposition
of dew is in some proportion to the power which the body pos-
sesses of resisting the passage of heat ; and that this, there-
fore, (or something connected with this,) must be at least one
of the causes which assist in producing the deposition of dew
on the surface.

EXAMPLES OF THE FOUR METHODS. 483

" But if we expose rough surfaces instead of polished, we
sometimes find this law interfered with. Thus, roughened
iron, especially if painted over or blackened, becomes dewed
sooner than varnished paper ; the kind of surface, therefore,
has a great influence. Expose, then, the same material in very
diversified states as to surface," (that is, employ the Method
of Difference to ascertain concomitance of variations,) " and
another scale of intensity becomes at once apparent ; those
surfaces which part with their heat most readily by radiation,
are found to contract dew most copiously." Here, therefore,
are the requisites for a second employment of the Method of
Concomitant Variations ; which in this case also is the only
method available, since all substances radiate heat in some
degree or other. The conclusion obtained by this new appli-
cation of the method is, that cteteris paribus the deposition of
dew is also in some proportion to the power of radiating heat ;
and that the quality of doing this abundantly (or some cause
on which that quality depends) is another of the causes which
promote the deposition of dew on the substance.

" Again, the influence ascertained to exist of substance and
surface leads us to consider that of texture : and here, again,
we are presented on trial with remarkable differences, and with
a third scale of intensity, pointing out substances of a close
firm texture, such as stones, metals, &c., as unfavourable, but
those of a loose one, as cloth, velvet, wool, eider-down, cotton,
&c., as eminently favourable to the contraction of dew." The
Method of Concomitant Variations is here, for the third time,
had recourse to ; and, as before, from necessity, since the tex-
ture of no substance is absolutely firm or absolutely loose*
Looseness of texture, therefore, or something which is the cause
of that quality, is another circumstance which promotes the
deposition of dew ; but this third course resolves itself into the
first, viz. the quality of resisting the passage of heat: for sub-
stances of loose texture " are precisely those which are best
adapted for clothing, or for impeding the free passage of heat
from the skin into the air, so as to allow their outer surfaces
to be very cold, while they remain warm within ;" and this last
is, therefore, an induction (from fresh instances) simply corro-
borative of a former induction.

3J— *

484 INDUCTION.

It thus appears that the instances in which much dew is
deposited, which are very various, agree in this, and, so far as
we are able to observe, in this only, that they either radiate
heat rapidly or conduct it slowly : qualities between which
there is no other circumstance of agreement, than that by
virtue of either, the body tends to lose heat from the surface
more rapidly than it can be restored from within. The in-
stances, on the contrary, in which no dew, or but a small
quantity of it, is formed, and which are also extremely
various, agree (as far as we can observe) in nothing except
in not having this same property. We seem, therefore, to
have detected the characteristic difference between the sub-
stances on which dew is produced, and those on which it is not
produced. And thus have been realized the requisitions of
what we have termed the Indirect Method of Difference, or
the Joint Method of Agreement and Difference. The example
afforded of this indirect method, and of the manner in which
the data are prepared for it by the Methods of Agreement
and of Concomitant Variations, is the most important of all
the illustrations of induction afforded by this interesting
speculation.

We might now consider the question, on what the deposi-
tion of dew depends, to be completely solved, if we could be
quite sure that the substances on which dew is produced differ
from those on which it is not, in nothing but in the property
of losing heat from the surface faster than the loss can be
repaired from within. And though we never can have that
complete certainty, this is not of so much importance as might
at first be supposed ; for we have, at all events, ascertained
tbat even if there be any other quality hitherto unobserved
which is present in all the substances which contract dew, and
absent in those which do not, this other property must be
one which, in all that great number of substances, is present
or absent exactly where the property of being a better radiator
than conductor is present or absent ; an extent of coincidence
which affords a strong presumption of a community of cause,
and a consequent invariable coexistence between the two pro-
perties ; so that the property of being a better radiator than

EXAMPLES OF THE FO17R METHODS. 485

conductor, if not itself the cause, almost certainly always
accompanies the cause, and, for purposes of prediction, no
error is likely to be committed by treating it as if it were
really such.

Reverting now to an earlier stage of the inquiry, let us
remember that we had ascertained that, in every instance
where dew is formed, there is actual coldness of the surface
below the temperature of the surrounding air ; but we were
not sure whether this coldness was the cause of dew, or its
effect. This doubt we are now able to resolve. We have
found that, in every such instance, the substance is one which,
by its own properties or laws, would, if exposed in the night,
become colder than the surrounding air. The coldness there-
fore being accounted for independently of the dew, while it
is proved that there is a connexion between the two, it must
be the dew which depends on the coldness ; or in other words,
the coldness is the cause of the dew.

This law of causation, already so amply established, ad-
mits, however, of efficient additional corroboration in no less
than three ways. First, by deduction from the known laws of
aqueous vapour when diffused through air or any other gas;
and though we have not yet come to the Deductive Method,
we will not omit what is necessary to render this speculation
complete. It is known by direct experiment that only a
limited quantity of water can remain suspended in the state
of vapour at each degree of temperature, and that this maxi-
mum grows less and less as the temperature diminishes. From
this it follows, deductively, that if there is already as much
vapour suspended as the air will contain at its existing tem-
perature, any lowering of that temperature will cause a portion
of the vapour to be condensed, and become water. But, again,
we know deductively, from the Jaws of heat, that the contact
of the air with a body colder than itself, will necessarily lower
the temperature of the stratum of air immediately applied to
its surface ; and will therefore cause it to part with a portion
of its water, which accordingly will, by the ordinary laws of
gravitation or cohesion, attach itself to the surface of the
body, thereby constituting dew. This deductive proof, it will

486 INDUCTION.

have been seen, has the advantage of at once proving causa-
tion as well as coexistence ; and it has the additional advan-
tage that it also accounts for the exceptions to the occurrence
of the phenomenon, the cases in which, although the body is
colder than the air, yet no dew is deposited ; by showing that
this will necessarily be the case when the air is so under-sup-
plied with aqueous vapour, comparatively to its temperature,
that even when somewhat cooled by the contact of the colder
body, it can still continue to hold in suspension all the vapour
which was previously suspended in it : thus in a very dry
summer there are no dews, in a very dry winter no hoar frost.
Here, therefore, is an additional condition of the production
of dew, which the methods we previously made use of failed
to detect, and which might have remained still undetected, if
recourse had not been had to the plan of deducing the effect
from the ascertained properties of the agents known to be
present.

The second corroboration of the theory is by direct experi-
ment, according to the canon of the Method of Difference. We
can, by cooling the surface of any body, find in all cases some
temperature, (more or less inferior to that of the surrounding
air, according to its hygrometric condition,) at which dew will
begin to be deposited. Here, too, therefore, the causation is
directly proved. We can, it is true, accomplish this only on
a small scale ; but we have ample reason to conclude that the
same operation, if conducted in Nature's great laboratory,
would equally produce the effect.

And, finally, even on that great scale we are able to verify
the result. The case is one of those rare cases, as we have
shown them to be, in which nature works the experiment for
us in the same manner in which we ourselves perform it ; in-
troducing into the previous state of things a single and per-
fectly definite new circumstance, and manifesting the effect so
rapidly that there is not time for any other material change
in the pre-existing circumstances. " It is observed that dew
is never copiously deposited in situations much screened from
the open sky, and not at all in a cloudy' night ; but if the
clouds withdraw even for a few minutes, and leave a clear

EXAMPLES OF THE FOUR METHODS. 487

opening, a deposition of deiv presently begins, and goes on in-
creasing Dew formed in clear intervals will often even

evaporate again when the sky becomes thickly overcast." The
proof, therefore, is complete, that the presence or absence of
an uninterrupted communication with the sky causes the de-
position or non-deposition of dew. Now, since a clear sky is
nothing but the absence of clouds, and it is a known property
of clouds, as of all other bodies between which and any given
object nothing intervenes but an elastic fluid, that they tend
to raise or keep up the superficial temperature of the object
by radiating heat to it, we see at once that the disappearance
of clouds will cause the surface to cool ; so that Nature, in
this case, produces a change in the antecedent by definite and
known means, and the consequent follows accordingly : a
natural experiment which satisfies the requisitions of the
Method of Difference.*

The accumulated proof of which the Theory of Dew has
been found susceptible, is a striking instance of the fulness of
assurance which the inductive evidence of laws of causation
may attain, in cases in which the invariable sequence is by no
means obvious to a superficial view.

* I must, however, remark, that this example, which seems to militate
against the assertion we made of the comparative inapplicability of the Method
of Difference to cases of pure observation, is really one of those exceptiona
which, according to a proverbial expression, prove the general rule. For in
this case, in which Nature, in her experiment, seems to have imitated viio type
of the experiments made by man, she has only succeeded in producing the like-
ness of man's most imperfect experiments ; namely, those in which, though
he succeeds in producing the phenomenon, he does so by employing complex
means, which he is unable perfectly to analyse, and can form therefore no
sufficient judgment what portion of the effects may be due, not to the supposed
cause, but to some unknown agency of the means by which that cause was
produced. In the natural experiment which we are speaking of, the means
used was the clearing off a canopy of clouds ; and we certainly do not know
sufficiently in what this process consists, or on what it depends, to be certain
a priori that it might not operate upon the deposition of dew independently of
any thermometric effect at the earth's surface. Even, therefore, in a case so
favourable as this to Nature's experimental talents, her experiment is of little
value except in corroboration of a conclusion already attained through other

INDUCTION.

§ 4. The admirable physiological investigations of Dr.
Brown-Sequard afford brilliant examples of the application of
the Inductive Methods to a class of inquiries in which, for
reasons which will presently be given, direct induction takes
place under peculiar difficulties and disadvantages. As one of
the most apt instances, I select his speculation (in the pro-
ceedings of the Royal Society for May 16, 1861) on the rela-
tions between muscular irritability, cadaveric rigidity, and
putrefaction.

The law which Dr. Brown-Sequard's investigation tends
to establish, is the following : — " The greater the degree of
muscular irritability at the time of death, the later the cada-
veric rigidity sets in, and the longer it lasts, and the later also
putrefaction appears, and the slower it progresses." One
would say at first sight that the method here required must
be that of Concomitant Variations. But this is a delusive
appearance, arising from the circumstance that the conclusion
to be tested is itself a fact of concomitant variations. For the
establishment of that fact any of the Methods may be put in
requisition, and it will be found that the fourth Method,
though really employed, has only a subordinate place in this
particular investigation.

The evidences by which Dr. Brown-Sequard establishes
the law may be enumerated as follows : —

1st. Paralysed muscles have greater irritability than
healthy muscles. Now, paralysed muscles are later in assu-
ming the cadaveric rigidity than healthy muscles, the rigidity
lasts longer, and putrefaction sets in later, and proceeds more
slowly.

Both these propositions had to be proved by experiment;
and for the experiments which prove them, science is also in-
debted to Dr. Brown-Sequard. The former of the two — that
paralysed muscles have greater irritability than healthy mus-
eles — he ascertained in various ways, but most decisively by
" comparing the duration of irritability in a paralysed muscle
and in the corresponding healthy one of the opposite side,
while they are both submitted to the same excitation." He
" often found in experimenting in thai way, that the paralysed

EXAMPLES OF THE FOUR METHODS. 489

muscle remained irritable twice, three times, or even four times
as long as the healthy one." This is a case of induction by
the Method of Difference. The two limbs, being those of the
same animal, were presumed to differ in no circumstance
material to the case except the paralysis, to the presence and
absence of which, therefore, the difference in the muscular
irritability was to be attributed. This assumption of complete
resemblance in all material circumstances save one, evidently
could not be safely made in any one pair of experiments, be-
cause the two legs of any given animal might be accidentally
in very different pathological conditions ; but if, besides taking
pains to avoid any such difference, the experiment was re-
peated sufficiently often in different animals to exclude the
supposition that any abnormal circumstance could be present
in them all, the conditions of the Method of Difference were
adequately secured.

In the same manner in which Dr. Brown-Sequard proved
that paralysed muscles have greater irritability, he also proved
the correlative proposition respecting cadaveric rigidity and
putrefaction. Having, by section of the roots of the sciatic
nerve, and again of a lateral half of the spinal cord, produced
paralysis in one hind leg of an animal while the other re-
mained healthy, he found that not only did muscular irritability
last much longer in the paralysed limb, but rigidity set in
later and ended later, and putrefaction began later and was
less rapid than on the healthy side. This is a common case
of the Method of Difference, requiring no comment. A further
and very important corroboration was obtained by the same
method. When the animal was killed, not shortly after the
section of the nerve, but a month later, the effect was reversed ;
rigidity set in sooner, and lasted a shorter time, than in the
healthy muscles. But after this lapse of time, the paralysed
muscles, having been kept by the paralysis in a state of rest,
had lost a great part of their irritability, and instead of more,
had become less irritable than those on the healthy side. This
gives the A B C, a b c, and B C, b c, of the Method of Dif-
ference. One antecedent, increased irritability, being changed,
and the other circumstances being the same, the consequence

490 INDUCTION.

did not follow ; and moreover, when a new antecedent, con-
trary to the first, was supplied, it was followed by a contrary
consequent. This instance is attended with the special advan-
tage, of proving that the retardation and prolongation of the
rigidity do not depend directly on the paralysis, since that was
the same in both the instances ; but specifically on one effect
of the paralysis, namely, the increased irritability ; since they
ceased when it ceased, and were reversed when it was reversed.

2ndly. Diminution of the temperature of muscles before
death increases their irritability. But diminution of their tem-
perature also retards cadaveric rigidity and putrefaction.

Both these truths were first made known by Dr. Brown-
Sequard himself, through experiments which conclude accord-
ing to the Method of Difference. There is nothing in the
nature of the process requiring specific analysis.

3rdly. Muscular exercise, prolonged to exhaustion, dimi-
nishes the muscular irritability. This is a well-known truth,
dependent on the most general laws of muscular action, and
proved by experiments under the Method of Difference, con-
stantly repeated. Now it has been shown by observation that
overdriven cattle, if killed before recovery from their fatigue,
become rigid and putrefy in a surprisingly short time. A
similar fact has been observed in the case of animals hunted
to death ; cocks killed during or shortly after a fight ; and
soldiers slain in the field of battle. These various cases agree
in no circumstance, directly connected with the muscles, except
that these have just been subjected to exhausting exercise.
Under the canon, therefore, of the Method of Agreement, it
may be inferred that there is a connexion between the two
facts. The Method of Agreement, indeed, as has been shown,
is not competent to prove causation. The present case, how-
ever, is already known to be a case of causation, it being cer-
tain that the state of the body after death must somehow
depend upon its state at the time of death. We are therefore
warranted in concluding that the single circumstance in which
all the instances agree, is the part of the antecedent which is
the cause of that particular consequent.

4thly. In proportion as the nutrition of muscles is in a

EXAMPLES OF THE FOUR METHODS.

good state, their irritability is high. This fact also rests on
the general evidence of the laws of physiology, grounded on
many familiar applications of the Method of Difference. Now,
in the case of those who die from accident or violence, with
their muscles in a good state of nutrition, the muscular irri-
tability continues long after death, rigidity sets in late, and
persists long without the putrefactive change. On the contrary,
in cases of disease in which nutrition has been diminished for
a long time before death, all these effects are reversed. These
are the conditions of the Joint Method of Agreement and
Difference. The cases of retarded and long continued rigidity
here in question, agree only in being preceded by a high state
of nutrition of the muscles ; the cases of rapid and brief
rigidity agree only in being preceded by a low state of mus-
cular nutrition ; a connexion is therefore inductively proved
between the degree of the nutrition, and the slowness and pro-
longation of the rigidity.

5thly. Convulsions, like exhausting exercise, but in a
still greater degree, diminish the muscular irritability. Now,
when death follows violent and prolonged convulsions, as in
tetanus, hydrophobia, some cases of cholera, and certain
poisons, rigidity sets in very rapidly, and after a very brief
duration, gives place to putrefaction. This is another ex-
ample of the Method of Agreement, of the same character
with No. 3.

Gthly. The series of instances which we shall take last, is
of a more complex character, and requires a more minute
analysis.

It has long been observed that in some cases of death by
lightning, cadaveric rigidity either does not take place at all,
or is of such extremely brief duration as to escape notice, and
that in these cases putrefaction is very rapid. In other cases,
however, the usual cadaveric rigidity appears. There must be
some difference in the cause, to account for this difference in
the effect. Now " death by lightning may be the result of,
1st, a syncope by fright, or in consequence of a direct or reflex
influence of lightning on the par vagum ; 2ndly, hemorrhage
in or around the brain, or in the lungs, the pericardium, &c. ;

492 INDUCTION.

3rdly, concussion, or some other alteration in the brain ;" none
of which phenomena have any known property capable of
accounting for the suppression, or almost suppression, of the
cadaveric rigidity. But the cause of death may also be that
the lightning produces " a violent convulsion of every muscle
in the body," of which, if of sufficient intensity, the known
effect would be that " muscular irritability ceases almost at
once." If Dr. Brown- Sequard's generalization is a true law,
these will be the very cases in which rigidity is so much
abridged as to escape notice ; and the cases in which, on the
contrary, rigidity takes place as usual, will be those in which
the stroke of lightning operates in some of the other modes
which have been enumerated. How, then, is this brought to
the test? By experiments not on lightning, which cannot be
commanded at pleasure, but on the same natural agency in a
manageable form, that of artificial galvanism. Dr. Brown-
Sequard galvanized the entire bodies of animals immediately
after death. Galvanism cannot operate in any of the modes in
which the stroke of lightning may have operated, except the
single one of producing muscular convulsions. If, therefore,
after the bodies have been galvanized, the duration of rigidity
is much shortened and putrefaction much accelerated, it is
reasonable to ascribe the same effects when produced by light-
ning, to the property which galvanism shares with lightning,
and not to those which it does not. Now this Dr. Brown-
Sequard found to be the fact. The galvanic experiment was
tried with charges of very various degrees of strength ; and the
more powerful the charge, the shorter was found to be the dura-
tion of rigidity, and the more speedy and rapid the putrefaction.
In the experiment in which the charge was strongest, and the
muscular irritability most promptly destroyed, the rigidity only
lasted fifteen minutes. On the principle, therefore, of the
Method of Concomitant Variations, it maybe inferred that the
duration of the rigidity depends on the degree of the irrita-
bility ; and that if the charge had been as much stronger than
Dr. Brown- Sequard's strongest, as a stroke of lightning must
be stronger than any electric shock which we can produce
artificially, the rigidity would have been shortened in a corre-

EXAMPLES OF THE FOUR METHODS. 493

spending ratio, and might have disappeared altogether. This
conclusion having heen arrived at, the case of an electric shock,
whether natural or artificial, becomes an instance in addition
to all those already ascertained, of correspondence between the
irritability of the muscle and the duration of rigidity.

All these instances are summed up in the following state-
ment : — " That when the degree of muscular irritability at the
time of death is considerable, either in consequence of a good
state of nutrition, as in persons who die in full health from
an accidental cause, or in consequence of rest, as in cases of
paralysis, or on account of the influence of cold, cadaveric
rigidity in all these cases sets in late and lasts long, and putre-
faction appears late, and progresses slowly :" but " that when
the degree of muscular irritability at the time of death is slight,
either in consequence of a bad state of nutrition, or of exhaus-
tion from over-exertion, or from convulsions caused by disease
or poison, • cadaveric rigidity sets in and ceases soon, and
putrefaction appears and progresses quickly." These facts
present, in all their completeness, the conditions of the Joint
Method of Agreement and Difference. Early and brief rigidity
takes place in cases which agree only in the circumstance of a
low state of muscular irritability. Rigidity begins late and
lasts long in cases which agree only in the contrary circum-
stance, of a muscular irritability high and unusually prolonged.
It follows that there is a connexion through causation between
the degree of muscular irritability after death, and the tardiness
and prolongation of the cadaveric rigidity.

This investigation places in a strong light the value and
efficacy of the Joint Method. For, as we have already seen, the
defect of that Method is, that like the Method of Agreement,
of which it is only an improved form, it cannot prove causation.
But in the present case (as in one of the steps in the argument
which led up to it) causation is already proved; since there
could never be any doubt that the rigidity altogether, and the
putrefaction which follows it, are caused by the fact of death :
the observations and experiments on which this rests are too
familiar to need analysis, and fall under the Method of Dif-
ference. It being, therefore, beyond doubt that the aggregate

494 INDUCTION.

antecedent, the death, is the actual cause of the whole train of
consequents, whatever of the circumstances attending the death
can be shown to he followed in all its variations by variations,
in the effect under investigation, must be the particular feature
of the fact of death on which that effect depends. The degree
of muscular irritability at the time of death fulfils this con-
dition. The only point that could be brought into question,
would be whether the effect depended on the irritability itself,
or on something which always accompanied the irritability :
and this doubt is set at rest by establishing, as the instances
do, that by whatever cause the high or low irritability is pro-
duced, the effect equally follows ; and cannot, therefore, depend
upon the causes of irritability, nor upon the other effects of
those causes, which are as various as the causes themselves ;
but upon the irritability, solely.

§ 5. The last two examples will have conveyed to any
one by whom they have been duly followed, so clear a concep-
tion of the use and practical management of three of the four
methods of experimental inquiry, as to supersede the necessity
of any further exemplification of them. The remaining method,
that of Eesidues, not having found a place in any of the pre-
ceding investigations, I shall quote from Sir John Herschel
some examples of that method, with the remarks by which they
are introduced.

" It is by this process, in fact, that science, in its present
advanced state, is chiefly promoted. Most of the phenomena
which Nature presents are very complicated; and when the
effects of all known causes are estimated with exactness, and
subducted, the residual facts are constantly appearing in the
form of phenomena altogether new, and leading to the most
important conclusions.

" For example : the return of the comet predicted by Pro-
fessor Encke, a great many times in succession, and the
general good agreement of its calculated with its observed
place during any one of its periods of visibility, would lead us
to say that its gravitation towards the sun and planets is the
sole and sufficient cause of all the phenomena of its orbitual

EXAMPLES OF THE FOUR METHODS. 495

motion ; but when the effect of this cause is strictly calculated
and subducted from the observed motion, there is found to
remain behind a residual phenomenon, which would never have
been otherwise ascertained to exist, which is a small anticipa-
tion of the time of its reappearance, or a diminution of its
periodic time, which cannot be accounted for by gravity, and
whose cause is therefore to be inquired into. Such an antici-
pation would be caused by the resistance of a medium dis-
seminated through the celestial regions ; and as there are other
good reasons for believing this to be a vera causa," (an actually
existing antecedent,) "it has therefore been ascribed to such a
resistance.*

" M. Arago, having suspended a magnetic needle by a silk
thread, and set it in vibration, observed, that it came much
sooner to a state of rest when suspended over a plate of copper,
than when no such plate was beneath it. Now, in both
cases there were two verce causa" (antecedents known to
exist) " why it should come at length to rest, viz. the resis-
tance of the air, which opposes, and at length destroys, all
motions performed in it ; and the want of perfect mobility in
the silk thread. But the effect of these causes being exactly
known by the observation made in the absence of the copper,
and being thus allowed for and subducted, a residual pheno-
menon appeared, in the fact that a retarding influence was
exerted by the copper itself; and this fact, once ascertained,
speedily led to the knowledge of an entirely new and unex-
pected class of relations." This example belongs, however,
not to the Method of Residues but to the Method of Diffe-
rence, the law being ascertained by a direct comparison of
the results of two experiments, which differed in nothing but
the presence or absence of the plate of copper. To have made
it exemplify the Method of Residues, the effect of the resistance
of the air and that of the rigidity of the silk should have been
calculated a priori, from the laws obtained by separate and
foregone experiments.

* In his subsequent work, Outlines of Astronomy (§ 570), Sir John Hersche'
suggests another possible explanation of the acceleration of the revolution of a
comet.

496 INDUCTION.

" Unexpected and peculiarly striking confirmations of
inductive laws frequently occur in the form of residual phe-
nomena, in the course of investigations of a widely different
nature from those which gave rise to the inductions them-
selves. A very elegant example may be cited in the unex-
pected confirmation of the law of the development of heat in
elastic fluids by compression, which is afforded by the phe-
nomena of sound. The inquiry into the cause of sound had
led to conclusions respecting its mode of propagation, from
which its velocity in the air could be precisely calculated.
The calculations were performed ; but, when compared with
fact, though the agreement was quite sufficient to show the
general correctness of the cause and mode of propagation
assigned, yet the whole velocity could not be shown to arise
from this theory. There was still a residual velocity to be
accounted for, which placed dynamical philosophers for a
long time in great dilemma. At length Laplace struck on
the happy idea, that this might arise from the heat developed
in the act of that condensation which necessarily takes place
at every vibration by which sound is conveyed. The matter
was subjected to exact calculation, and the result was at once
the complete explanation of the residual phenomenon, and a
striking confirmation of the general law of the development
of heat by compression, under circumstances beyond artificial
imitation."

" Many of the new elements of chemistry have been
detected in the investigation of residual phenomena. Thus
Arfwedson discovered lithia by perceiving an excess of weight
in the sulphate produced from a small portion of what he
considered as magnesia present in a mineral he had analysed.
It is on this principle, too, that the small concentrated
residues of great operations in the arts are almost sure to be
the lurking places of new chemical ingredients : witness
iodine, brome, selenium, and the new metals accompanying
platina in the experiments of Wollaston and Tennant. It was
a happy thought of Glauber to examine what everybody else
threw away."*

* Discourse, pp. 156-8, and 171.

EXAMPLES OF THE FOUR METHODS. 497

"Almost all the greatest discoveries in Astronomy," says
the same author,* " have resulted from the consideration of
residual phenomena of a quantitative or numerical kind. . . .
It was thus that the grand discovery of the precession of
the equinoxes resulted as a residual phenomenon, from the
iraperi'ect explanation of the return of the seasons by the
return of the sun to the same apparent place among the
fixed stars. Thus, also, aberration and nutation resulted as
residual phenomena from that portion of the changes of the
apparent places of the fixed stars which was left unac-
counted for by precession. And thus again the apparent
proper motions of the stars are the observed residues of
their apparent movements outstanding and unaccounted for
by strict calculation of the effects of precession, nutation, and
aberratioa. The nearest approach which human theories
can make to perfection is to diminish this residue, this caput
mortuum of observation, as it may be considered, as much as
practicable, and, if possible, to reduce it to nothing, either by
showing that something has been neglected in our estimation
of known causes, or by reasoning upon it as a new fact, and
on the principle of the inductive philosophy ascending from
the effect to its cause or causes."

The disturbing effects mutually produced by the earth
and planets upon each other's motions were first brought to
light as residual phenomena, by the difference which appeared
between the observed places of those bodies, and the places
calculated on a consideration solely of their gravitation
towards the sun. It was this which determined astronomers
to consider the law of gravitation as obtaining between
all bodies whatever, and therefore between all particles of
matter; their first tendency having been to regard it as a
force acting only between each planet or satellite and the
central body to whose system it belonged. Again, the
catastrophists, in geology, be their opinion right or wrong,
support it on the plea, that after the effect of all causes
now in operation has been allowed for, there remains in the

* Outlines of Astronomy, § 856.

VOL. i. 32

498 INDUCTION.

existing constitution of the earth a large residue of facts,
proving the existence at former periods either of other forces,
or of the same forces in a much greater degree of intensity.
To add one more example : those who assert, what no one
has shown any real ground for believing, that there is in
one human individual, one sex, or one race of mankind
over another, an inherent and inexplicable superiority in
mental faculties, could only substantiate their proposition by
subtracting from the differences of intellect which we in fact
see, all that can be traced by known laws either to the ascer-
tained differences of physical organization, or to the dif-
ferences which have existed in the outward circumstances in
which the subjects of the comparison have hitherto been
placed. What these causes might fail to account for, would
constitute a residual phenomenon, which and which alone
would be evidence of an ulterior original distinction, and the
measure of its amount. But the assertors of such supposed
differences have not provided themselves with these necessary
logical conditions of the establishment of their doctrine.

The spirit of the Method of Kesidues being, it is hoped,
sufficiently intelligible from these examples, and the other
three methods having already been so fully exemplified, we
may here close our exposition of the four methods, considered
as employed in the investigation of the simpler and more
elementary order of the combinations of phenomena.

§ 6. Dr. Whewell has expressed a very unfavourable
opinion of the utility of the Four Methods, as well as of the
aptness of the examples by which I have attempted to illus-
trate them. His words are these :* —

" Upon these methods, the obvious thing to remark is,
that they take for granted the very thing which is most
difficult to discover, the reduction of the phenomena to
formulae such as are here presented to us. When we have
any set of complex facts offered to us ; for instance, those
which were offered in the cases of discovery which I have

* Philosophy of Discovery, pp. 263, 264.

EXAMPLES OP THE FOUR METHODS. 499

mentioned, — the facts of the planetary paths, of falling
bodies, of refracted rays, of cosinical motions, of chemical
analysis ; and when, in any of these cases, we would discover
the law of nature which governs them, or, if any one chooses
so to term it, the feature in which all the cases agree, where
are we to look for our A, B, C, and a, b, c? Nature does
not present to us the cases in this form ; and how are we to
reduce them to this form ? You say, ivhen we find the com-
bination of A B C with a b c and A B D with a b d, then
we may draw our inference. Granted ; but when and where
are we to find such combinations ? Even now that the dis-
coveries are made, who will point out to us what are the
A, B, 0, and a, b, c elements of the cases which have just
been enumerated ? Who will tell us which of the methods
of inquiry those historically real and successful inquiries
exemplify ? Who will carry these formulae through the
history of the sciences, as they have really grown up ; and
show us that these four methods have been operative in their
formation ; or that any light is thrown upon the steps of
their progress by reference to these formulae ?"

He adds that, in this work, the methods have not been
applied " to a large body of conspicuous and undoubted ex-
amples of discovery, extending along the whole history of sci-
ence ;" which ought to have been done in order that the methods
might be shown to possess the " advantage " (which he claims
as belonging to his own) of being those " by which all great
discoveries in science have really been made." — (p. 277.)

There is a striking similarity between the objections here
made against Canons of Induction, and what was alleged, in
the last century, by as able men as Dr. Whewell, against the
acknowledged Canon of Ratiocination. Those who protested
against the Aristotelian Logic said of the Syllogism, what
Dr. Whewell says of the Inductive Methods, that it " takes
for granted the very thing which is most difficult to discover,
the reduction of the argument to formulae such as are here
presented to us." The grand difficulty, they said, is to obtain
your syllogism, not to judge of its correctness when obtained.
On the matter of fact, both they and Dr. Whewell are right.

32—2

INDUCTION.

The greatest difficulty in both cases is first that of obtaining
the evidence, and next, of reducing it to the form which tests
its conclusiveness. But if we try to reduce it without know-
ing what it is to be reduced to, we are not likely to make
much progress. It is a more difficult thing to solve a geome-
trical problem, than to judge whether a proposed solution is
correct: but if people were not able to judge of the solution
when found, they would have little chance of finding it
And it cannot be pretended that to judge of an induction
when found, is perfectly easy, is a thing for which aids and
instruments are superfluous; for erroneous inductions, false
inferences from experience, are quite as common, on some
subjects much commoner, than true ones. The business of
Inductive Logic is to provide rules and models (such as the
Syllogism and its rules are for ratiocination) to which if in-
ductive arguments conform, those arguments are conclusive,
and not otherwise. This is what the Four Methods profess
to be, and what I believe they are universally considered to be
by experimental philosophers, who had practised all of them
Jong before any one sought to reduce the practice to theory.

The assailants of the Syllogism had also anticipated Dr.
Whewell in the other branch of his argument. They said
that no discoveries were ever made by syllogism ; and Dr.
Whewell says, or seems to say, that none were ever made by
the four Methods of Induction. To the former objectors,
'Archbishop Whately very pertinently answered, that their
argument, if good at all, was good against the reasoning pro-
cess altogether ; for whatever cannot be reduced to syllogism,
is not reasoning. And Dr. Whewell's argument, if good at
all, is good against all inferences from experience. In saying
that no discoveries were ever made by the four Methods, he
affirms that none were ever made by observation and experi-
ment ; for assuredly if any were, it was by processes reducible
to one or other of those methods.

This difference between us accounts for the dissatisfaction
which my examples give him ; for I did not select them with
a view to satisfy any one who required to be convinced that
observation and experiment are modes of acquiring knowledge :

EXAMPLES OF THE FOUR METHODS. 501

I confess that in the choice of them I thought only of illus-
tration, and of facilitating the conception of the Methods by
concrete instances. If it had been my object to justify the
processes themselves as means of investigation, there would
have been no need to look far off, or make use of recondite or
complicated instances. As a specimen of a truth ascertained
by the Method of Agreement, I might have chosen the pro-
position "Dogs bark." This dog, and that dog, and the
other dog, answer to A B C, A D E, A F G. The circum-
stance of being a dog, answers to A. Barking answers to a.
As a truth made known by the Method of Difference, " Fire
burns" might have sufficed. Before I touch the fire I am not
burnt; this is B C ; I touch it, and am burnt; this is A B C,
«B C.

Such familiar experimental processes are not regarded as
inductions by Dr. Whewell ; but they are perfectly homo-
geneous with those by which, even on his own showing, the
pyramid of science is supplied with its base. In vain he
attempts to escape from this conclusion by laying the most
arbitrary restrictions on the choice of examples admissible as
instances of Induction: they must neither be such as are still
matter of discussion (p. 265), nor must any of them be drawn
from mental and social subjects (p. 269), nor from ordinary
observation and practical life (pp. 241 — 247). They must be
taken exclusively from the generalizations by which scientific
thinkers have ascended to great and comprehensive laws of
natural phenomena. Now it is seldom possible, in these com-
plicated inquiries, to go much beyond the initial steps, without
calling in the instrument of Deduction, and the temporary
aid of hypotheses ; as I myself, in common with Dr. Whewell,
have maintained against the purely empirical school. Since
therefore such cases could not conveniently be selected to
illustrate the principles of mere observation and experiment,
Dr. Whewell is misled by their absence into representing the
Experimental Methods as serving no purpose in scientific
investigation ; forgetting that if those methods had not sup-
plied the first generalizations, there would have been no mate-
rials for his own conception of Induction to work upon.

502 INDUCTION.

His challenge, however, to point out which of the four
methods are exemplified in certain important cases of scientific
inquiry, is easily answered. " The planetary paths," as far as
they are a case of induction at all,* fall under the Method of
Agreement. The law of "falling bodies," namely that they
describe spaces proportional to the squares of the times, was
historically a deduction from the first law of motion ; but the
experiments by which it was verified, and by which it might
have been discovered, were examples of the Method of Agree-
ment; and the apparent variation from the true law, caused
by the resistance of the air, was cleared up by experiments
in vacua, constituting an application of the Method of Dif-
ference. The law of " refracted rays" (the constancy of the
ratio between the sines of incidence and of refraction for each
refracting substance) was ascertained by direct measurement,
and therefore by the Method of Agreement. The " cosmical
motions" were determined by highly complex processes of
thought, in which Deduction was predominant, but the
Methods of Agreement and of Concomitant Variations had
a large part in establishing the empirical laws. Every case
without exception of "chemical analysis" constitutes a well-
marked example of the Method of Difference. To any one
acquainted with the subjects — to Dr. Whewell himself, there
would not be the smallest difficulty in setting out " the ABC
and a b c elements" of these cases.

If discoveries are ever made by observation and experiment
without Deduction, the four methods are methods of discovery :
but even if they were not methods of discovery, it would not
be the less true that they are the sole methods of Proof; and
in that character, even the results of deduction are amenable
to them. The great generalizations which begin as Hypo-
theses, must end by being proved, and are in reality (as will
be shown hereafter) proved, by the Four Methods. Now it is
with Proof, as such, that Logic is principally concerned. This
distinction has indeed no chance of finding favour with
Dr. Whewell ; for it is the peculiarity of his system, not to
recognise, in cases of Induction, any necessity for proof. If,

* See, on this point, the second chapter of the present Book.

EXAMPLES OF THE FOUR METHODS. 503

after assuming an hypothesis and carefully collating it with
facts, nothing is brought to light inconsistent with it, that is,
if experience does not disprove it, he is content: at least
until a simpler hypothesis, equally consistent with experience,
presents itself. If this be Induction, doubtless there is no
necessity for the four methods. But to suppose that it is so,
appears to me a radical misconception of the nature of the
evidence of physical truths.

So real and practical is the need of a test for induction,
similar to the syllogistic test of ratiocination, that inferences
which bid defiance to the most elementary notions of inductive
logic are put forth without misgiving by persons eminent in
physical science, as soon as they are off the ground on which
they are conversant with the facts, and not reduced to judge
only by the arguments ; and as for educated persons in gene-
ral, it may be doubted if they are better judges of a good or
a bad induction than they were before Bacon wrote. The
improvement in the results of thinking has seldom extended
to the processes ; or has reached, if any process, that of inves-
tigation only, not that of proof. A knowledge of many laws
of nature has doubtless been arrived at, by framing hypotheses
and finding that the facts corresponded to them ; and many
errors have been got rid of by coming to a knowledge of facts
which were inconsistent with them, but not by discovering
that the mode of thought which led to the errors was itself
faulty, and might have been known to be such independently
of the facts which disproved the specific conclusion. Hence
it is, that while the thoughts of mankind have on many sub-
jects worked themselves practically right, the thinking power
remains as weak as ever: and on all subjects on which the
facts which would check the result are not accessible, as in
what relates to the invisible world, and even, as has been seen
lately, to the visible world of the planetary regions, men of
the greatest scientific acquirements argue as pitiably as the
merest ignoramus. For though they have made many sound
inductions, they have not learnt from them (and Dr. Whewell
thinks there is no necessity that they should learn) the prin-
ciples of inductive evidence.

CHAPTER X.

OF PLURALITY OF CAUSES; AND OF THE INTERMIXTURE
OF EFFECTS.

§ 1. IN the preceding exposition of the four methods of
observation and experiment, by which we contrive to distin-
guish among a mass of coexistent phenomena the particular
effect due to a given cause, or the particular cause which gave
birth to a given effect ; it has been necessary to suppose, in
the first instance, for the sake of simplification, that this ana-
lytical operation is encumbered by no other difficulties than
what are essentially inherent in its nature ; and to represent
to ourselves, therefore, every effect, on the one hand as con-
nected exclusively with a single cause, and on the other hand
as incapable of being mixed and confounded with any other
coexistent effect. We have regarded a b c d e, the aggregate
of the phenomena existing at any moment, as consisting of
dissimilar facts, a, b, c, d, and e, for each of which one, and
only one, cause needs be sought ; the difficulty being only
that of singling out this one cause from the multitude of
antecedent circumstances, A, B, C, D, and E. The cause
indeed may not be simple ; it may consist of an assemblage of
conditions; but we have supposed that there was only one
possible assemblage of conditions, from which the given effect
could result.

If such were the fact, it would be comparatively an easy
task to investigate the laws of nature. But the supposition
does not hold, in either of its parts. In the first place, it is
not true that the same phenomenon is always produced by
the same cause : the effect a may sometimes arise from A,
sometimes from B. And, secondly, the effects of different
causes are often not dissimilar, but homogeneous, and marked

PLURALITY OF CAUSES. 505

out by no assignable boundaries from one another: A and B
may produce not a and 6, but different portions of an effect a.
The obscurity and difficulty of the investigation of the laws of
phenomena is singularly increased by the necessity of ad-
verting to these two circumstances; Intermixture of Effects,
and Plurality of Causes. To the latter, being the simpler of
the two considerations, we shall first direct our attention.

It is not true, then, that one effect must be connected with
only one cause, or assemblage of conditions ; that each phe-
nomenon can be produced only in one way. There are often
several independent modes in which the same phenomenon
could have originated. One fact may be the consequent in
several invariable sequences ; it may follow, with equal uni-
formity, any one of several antecedents, or collections of ante-
cedents. Many causes may produce mechanical motion :
many causes may produce some kinds of sensation : many
causes may produce death. A given effect may really be pro-
duced by a certain cause, and yet be perfectly capable of being
produced without it.

§ 2. One of the principal consequences of this fact of
Plurality of Causes is, to render the first of the inductive
methods, that of Agreement, uncertain. To illustrate that
method, we supposed two instances, ABC followed by a b c,
and A D E followed by a d e. From these instances it might
apparently be concluded that A is an invariable antecedent of
a, and even that it is the unconditional invariable antecedent,
or cause, if we could be sure that there is no other antecedent
common to the two cases. That this difficulty may not stand
in the way, let us suppose the two cases positively ascertained
to have no antecedent in common except A. The moment,
however, that we let in the possibility of a plurality of causes,
the conclusion fails. For it involves a tacit supposition, that
a must have been produced in both instances by the same
cause. If there can possibly have been two causes, those two
may, for example, be C and E : the one may have been the
cause of a in the former of the instances, the other in the
latter, A having no influence in either case.

506 [NDUCTION.

Suppose, for example, that two great artists, or great phi-
losophers, that two extremely selfish, or extremely generous
characters, were compared together as to the circumstances of
their education and history, and the two cases were found to
agree only in one circumstance : would it follow that this one
circumstance was the cause of the quality which characterized
both those individuals ? Not at all ; for the causes which
may produce any type of character are very numerous ; and the
two persons might equally have agreed in their character,
though there had heen no manner of resemblance in their pre-
vious history.

This, therefore, is a characteristic imperfection of the
Method of Agreement ; from which imperfection the Method
of Difference is free. For if we have two instances, ABC
and B C, of which B C gives b c, and A being added converts
it into a b c, it is certain that in this instance at least, A was
either the cause of a, or an indispensable portion of its cause,
even though the cause which produces it in other instances
may be altogether different. Plurality of Causes, therefore,
not only does not diminish the reliance due to the Method of
Difference, but does not even render a greater number of ob-
servations or experiments necessary : two instances, the one
positive and the other negative, are still sufficient for the most
complete and rigorous induction. Not so, however, with the
Method of Agreement. The conclusions which that yields,
when the number of instances compared is small, are of no
real value, except as, in the character of suggestions, they may
lead either to experiments bringing them to the test of the
Method of Difference, or to reasonings which may explain and
verify them deductively.

It is only when the instances, being indefinitely multiplied
and varied, continue to suggest the same result, that this re-
sult acquires any high degree of independent value. If there
are but two instances, ABC and A D E, though these in-
stances have no antecedent in common except A, yet as the
effect may possibly have been produced in the two cases by
different causes, the result is at most only a slight probability
in favour of A; there may be causation, but it is almost

PLURALITY OF CAUSES. 507

equally probable that tbere was only a coincidence. But the
oftener we repeat the observation, varying the circumstances,
the more we advance towards a solution of this doubt. For
if we try A F G, A H K, &c., all unlike one another except
in containing the circumstance A, and if we find the effect a
entering into the result in all these cases, we must suppose
one of two things, either that it is caused by A, or that it has
as many different causes as there are instances. With each
addition, therefore, to the number of instances, the presump-
tion is strengthened in favour of A. The inquirer, of course,
will not neglect, if an opportunity present itself, to exclude A
from some one of these combinations, from A H K for instance,
and by trying H K separately, appeal to the Method of Dif-
ference in aid of the Method of Agreement. By the Method
of Difference alone can it be ascertained that A is the cause
of a \ but that it is either the cause, or another effect of the
same cause, may be placed beyond any reasonable doubt by
the Method of Agreement, provided the instances are very
numerous as well as sufficiently various.

After how great a multiplication, then, of varied instances,
all agreeing in no other antecedent except A, is the supposition
of a plurality of causes sufficiently rebutted, and the conclu-
sion that a is connected with A divested of the characteristic
imperfection, and reduced to a virtual certainty ? This is a
question which we cannot be exempted from answering : but
the consideration of it belongs to what is called the Theory of
Probability, which, will form the subject of a chapter hereafter.
It is seen, however, at once, that the conclusion does amount
to a practical certainty after a sufficient number of instances,
and that the method, therefore, is not radically vitiated by the
characteristic imperfection. The result of these considerations
is only, in the first place, to point out a new source of infe-
riority in the Method of Agreement as compared with other
modes of investigation, and new reasons for never resting con-
tented with the results obtained by it, without attempting to
confirm them either by the Method of Difference, or by con-
necting them deductively with some law or laws already ascer-
tained by that superior method. And, in the second place,

508 INDUCTION*

we learn from this the true theory of the value of mere number
of instances in inductive inquiry. The Plurality of Causes is
the only reason why mere number is of any importance. The
tendency of unscientific inquirers is to rely too much on
number, without analysing the instances; without looking
closely enough into their nature, to ascertain what circum-
stances are or are not eliminated by means of them. Most
people hold their conclusions with a degree of assurance pro-
portioned to the mere mass of the experience on which they
appear to rest ; not considering that by the addition of in-
stances to instances, all of the same kind, that is, differing
from one another only in points already recognised as imma-
terial, nothing whatever is added to the evidence of the con-
clusion. A single instance eliminating some antecedent which
existed in all the other cases, is of more value than the greatest
multitude of instances which are reckoned by their number
alone. It is necessary, no doubt, to assure ourselves, by
repetition of the observation or experiment, that no error has
been committed concerning the individual facts observed ; and
until we have assured ourselves of this, instead of varying the
circumstances, we cannot too scrupulously repeat the same
experiment or observation without any change. But when
once this assurance has been obtained, the multiplication of
instances which do not exclude any more circumstances is
entirely useless, provided there have been already enough to
exclude the supposition of Plurality of Causes.

It is of importance to remark, that the peculiar modifica-
tion of the Method of Agreement, which, as partaking in some
degree of the nature of the Method of Difference, I have called
the Joint Method of Agreement and Difference, is not affected
by the characteristic imperfection now pointed out. For, in
the joint method, it is supposed not only that the instances in
which a is, agree only in containing A, but also that the
instances in which a is not, agree only in not containing A.
Now, if this be so, A must be not only the cause of a, but the
only possible cause : for if there were another, as for example
B, then in the instances in which a is not, B must have been
absent as well as A, and it would not be true that these

PLURALITY OF CAUSES. 509

instances agree only in not containing A. This, therefore,
constitutes an immense advantage of the joint method over
the simple Method of Agreement. It may seem, indeed, that
the advantage does not belong so much to the joint method,
as to one of its two premises, (if they may be so called,) the
negative premise. The Method of Agreement, when applied
to negative instances, or those in which a phenomenon does
not take place, is certainly free from the characteristic imper-
fection which affects it in the affirmative case. The negative
premise, it might therefore be supposed, could be worked as
a simple case of the Method of Agreement, without requiring
an affirmative premise to be joined with it. But though this
is true in principle, it is generally altogether impossible to
work the Method of Agreement by negative instances without
positive ones : it is so much more difficult to exhaust the field
of negation than that of affirmation. For instance, let the
question be, what is the cause of the transparency of bodies ;
with what prospect of success could we set ourselves to inquire
directly in what the multifarious substances which are not
transparent, agree ? But we might hope much sooner to
seize some point of resemblance among the comparatively few
and definite species of objects which are transparent; and this
being attained, we should quite naturally be put upon exa-
mining whether the absence of this one circumstance be not
precisely the point in which all opaque substances will be
found to resemble.

The Joint Method of Agreement and Difference, therefore,
or, as I have otherwise called it, the Indirect Method of Diffe-
rence (because, like the Method of Difference properly so called,
it proceeds by ascertaining how and in what the cases where
the phenomenon is present, differ from those in which it is
absent) is, after the Direct Method of Difference, the most
powerful of the remaining instruments of inductive investiga-
tion ; and in the sciences which depend on pure observation,
with little or no aid from experiment, this method, so well ex-
emplified in the speculation on the cause of dew, is the primary
resource, so far as direct appeals to experience are con-
cerned.

510 INDUCTION.

§ 3. We have thus far treated Plurality of Causes only as
a possible supposition, which, until removed, renders our in-
ductions uncertain ; and have only considered hy what means,
where the plurality does not really exist, we may he enabled to
disprove it. But we must also consider it as a case actually
occurring in nature, and which, as often as it does occur, our
methods of induction ought to be capable of ascertaining and
establishing. For this, however, there is required no peculiar
method. When an effect is really producible by two or more
causes, the process for detecting them is in no way different
from that by which we discover single causes. They may
(first) be discovered as separate sequences, by separate sets of
instances. One set of observations or experiments shows that
the sun is a cause of heat, another that friction is a source of
it, another that percussion, another that electricity, another
that chemical action is such a source. Or (secondly) the
plurality may come to light in the course of collating a
number of instances, when we attempt to find some circum-
stance in which they all agree, and fail in doing so. We find
it impossible to trace, in all the cases in which the effect is
met with, any common circumstance. We find that we can
eliminate all the antecedents ; that no one of them is present
in all the instances, no one of them indispensable to the effect.
On closer scrutiny, however, it appears that though no one is
always present, one or other of several always is. If, on fur-
ther analysis, we can detect in these any common element, we
may be able to ascend from them to some one cause which is
the really operative circumstance in them all. Thus it is now
thought that in the production of heat by friction, percussion,
chemical action, &c., the ultimate source is one and the same.
But if (as continually happens) we cannot take this ulterior
step, the different antecedents must be set down provisionally
as distinct causes, each sufficient of itself to produce the
effect.

We here close our remarks on the Plurality of Causes, and
proceed to the still more peculiar and more complex case of
the Intermixture of Effects, and the interference of causes
with one another : a case constituting the principal part of

INTERMIXTURE OF EFFECTS. 511

the complication and difficulty of the study of nature ; and
with which the four only possible methods of directly induc-
tive investigation by observation and experiment, are for the
most part, as will appear presently, quite unequal to cope.
The instrument of Deduction alone is adequate to unravel the
complexities proceeding from this source ; and the four
methods have little more in their power than to supply pre-
mises for, and a verification of, our deductions.

§ 4. A concurrence of two or more causes, not separately
producing each its own effect, but interfering with or modify-
ing the effects of one another, takes place, as has already
been explained, in two different ways. In the one, which is
exemplified by the joint operation of different forces in
mechanics, the separate effects of all the causes continue to
be produced, but are compounded with one another, and dis-
appear in one total. In the other, illustrated by the case of
chemical action, the separate effects cease entirely, and are
succeeded by phenomena altogether different, and governed by
different laws.

Of these cases the former is by far the more frequent, and
this case it is which, for the most part, eludes the grasp of
our experimental methods. The other and exceptional case is
essentially amenable to them. When the laws of the original
agents cease entirely, and a phenomenon makes its appearance,
which, with reference to those laws, is quite heterogeneous ;
when, for example, two gaseous substances, hydrogen and
oxygen, on being brought together, throw off their peculiar
properties, and produce the substance called water ; in such
cases the new fact may be subjected to experimental inquiry,
like any other phenomenon ; and the elements which are said
to compose it may be considered as the mere agents of its
production ; the conditions on which it depends, the facts
which make up its cause.

The effects of the new phenomenon, the properties of water,
for instance, are as easily found by experiment as the effects
of any other cause. But to discover the cause of it, that is,
the particular conjunction of agents from which it results, is

512 INDUCTION.

often difficult enough. In the first place, the origin and
actual production of the phenomenon are most frequently in-
accessible to our observation. If we could not have learned
the composition of water until we found instances in which it
was actually produced from oxygen and hydrogen, we should
have been forced to wait until the casual thought struck some
one of passing an electric spark through a mixture of the two
gases, or inserting a lighted taper into it, merely to try what
would happen. Besides, many substances, though they can
be analysed, cannot by any known artificial means be recom-
pounded. Further, even if we could have ascertained, by the
Method of Agreement, that oxygen and hydrogen were both
present when water is produced, no experimentation on oxygen
and hydrogen separately, no knowledge of their laws, could
have enabled us deductively to infer that they would produce
water. We require a specific experiment on the two com-
bined.

Under these difficulties, we should generally have been
indebted for our knowledge of the causes of this class of effects,
not to any inquiry directed specifically towards that end, but
either to accident, or to the gradual progress of experimenta-
tion on the different combinations of which the producing
agents are susceptible ; if it were not for a peculiarity belong-
ing to effects of this description, that they often, under some
particular combination of circumstances, reproduce their
causes. If water results from the juxtaposition of hydrogen
and oxygen whenever this can be made sufficiently close and
intimate, so, on the other hand, if water itself be placed in
certain situations, hydrogen and oxygen are reproduced from
it : an abrupt termination is put to the new laws, and the
agents reappear separately with their own properties as at
first. What is called chemical analysis is the process of
searching for the causes of a phenomenon among its effects,
or rather among the effects produced by the action of some
other causes upon it.

Lavoisier, by heating mercury to a high temperature in a
close vessel containing air, found that the mercury increased
in weight, and became what was then called red precipitate,

INTERMIXTURE OF EFFECTS. 513

while the air, on being examined after the experiment, proved
to have lost weight, and to have become incapable of sup-
porting life or combustion. When red precipitate was exposed
to a still greater heat, it became mercury again, and gave off
a gas which did support life and flame. Thus the agents
which by their combination produced red precipitate, namely
the mercury and the gas, reappear as effects resulting from
that precipitate when acted upon by heat. So, if we decom-
pose water by means of iron filings, we produce two effects,
rust and hydrogen : now rust is already known by experiments
upon the component substances, to be an effect of the union
of iron and oxygen : the iron we ourselves supplied, but the
oxygen must have been produced from the water. The result
therefore is that water has disappeared, and hydrogen and
oxygen have appeared in its stead : or in other words, the
original laws of these gaseous agents, which had been sus-
pended by the superiuduction of the new laws called the pro-
perties of water, have again started into existence, and the
causes of water are found among its effects.

Where two phenomena, between the laws or properties of
which considered in themselves no connexion can be traced,
are thus reciprocally cause and effect, each capable in its turn
of being produced from the other, and each, when it produces
the other, ceasing itself to exist (as water is produced from
oxygen and hydrogen, and oxygen and hydrogen are repro-
duced from water) ; this causation of the two phenomena by
one another, each being generated by the other's destruction,
is properly transformation. The idea of chemical composition
is an idea of transformation, but of a transformation which is
incomplete ; since we consider the oxygen and hydrogen to be
present in the water as oxygen and hydrogen, and capable of
being discovered in it if our senses were sufficiently keen : a
supposition (for it is no more) grounded solely on the fact,
that the weight of the water is the sum of the separate
weights of the two ingredients. If there had not been this
exception to the entire disappearance, in the compound, of the
Jaws of the separate ingredients; if the combined agents had
not, in this one particular of weight, preserved their own laws,
VOL. i, 33

514

INDUCTION.

and produced a joint result equal to the sum of their separate
results ; we should never, probably, have had the notion now
implied by the words chemical composition : and, in the facts
of water produced from hydrogen and oxygen, and hydrogen
and oxygen produced from water, as the transformation would
have been complete, we should have seen only a transforma-
tion.

In these cases, where the heteropathic effect (as we called
it in a former chapter)* is but a transformation of its cause, or
in other words, where the effect and its cause are reciprocally
such, and mutually convertible into each other ; the problem
of finding the cause resolves itself into the far easier one of
finding an effect, which is the kind of inquiry that admits of
being prosecuted by direct experiment. But there are other
cases of heteropathic effects to which this mode of investiga-
tion is not applicable. Take, for instance, the heteropathic
laws of mind ; that portion of the phenomena of our mental
nature which are analogous to chemical rather than to dyna-
mical phenomena ; as when a complex passion is formed by the
coalition of several elementary impulses, or a complex emotion
by several simple pleasures or pains, of which it is the result
without being the aggregate, or in any respect homogeneous
with them. The product, in these cases, is generated by its
various factors ; but the factors cannot be reproduced from the
product; just as a youth can grow into an old man, but an old
man cannot grow into a youth. We cannot ascertain from
what simple feelings any of our complex states of mind are
generated, as we ascertain the ingredients of a chemical com-
pound, by making it, in its turn, generate them. We can only,
therefore, discover these laws by the slow process of studying
the simple feelings themselves, and ascertaining synthetically,
by experimenting on the various combinations of which they
are susceptible, what they, by their mutual action upon one
another, are capable of generating.

§ 5. It might have been supposed that the other, and
* Ante, ch. vii. § 1.

INTERMIXTURE OF EFFECTS. 515

apparently simpler variety of the mutual interference of causes,
where each cause continues to produce its own proper effect
according to the same laws to which it conforms in its separate
state, would have presented fewer difficulties to the inductive
inquirer than that of which we have just finished the con-
sideration. It presents, however, so far as direct induction
apart from deduction is concerned, infinitely greater diffi-
culties. When a concurrence of causes gives rise to a new
effect, hearing no relation to the separate effects of those
causes, the resulting phenomenon stands forth undisguised,
inviting attention to its peculiarity, and presenting no obstacle
to our recognising its presence or absence among any number
of surrounding phenomena. It admits therefore of being easily
brought under the canons of Induction, provided instances
can be obtained such as those canons require : and the non-
occurrence of such instances, or the want of means to produce
them artificially, is the real and only difficulty in such inves-
tigations; a difficulty not logical, but in some sort physical.
It is otherwise with cases of what, in a preceding chapter, has
been denominated the Composition of Causes. There, the
effects of the separate causes do not terminate and give place
to others, thereby ceasing to form any part of the phenomenon
to be investigated ; on the contrary, they still take place, but
are intermingled with, and disguised by, the homogeneous
and closely allied effects of other causes. They are no longer
a, b, c, d, e, existing side by side, and continuing to be sepa-
rately discernible ; they are + a, — a, | b, — b, 2 b, &c. ; some
of which cancel one another, while many others do not appear
distinguishably, but merge in one sum : forming altogether
a result, between which and the causes whereby it was pro-
duced there is often an insurmountable difficulty in tracing by
observation any fixed relation whatever.

The general idea of the Composition of Causes has been
seen to be, that though two or more laws interfere with one
another, and apparently frustrate or modify one another's
operation, yet in reality all are fulfilled, the collective effect
being the exact sum of the effects of the causes taken sepa-
rately. A familiar instance is that of a body kept in equili-

33—2

516 INDUCTION.

brium by two equal and contrary forces. One of the forces
if acting alone would carry the body in a given time a certain
distance to the west, the other if acting alone would carry it
exactly as far towards the east ; and the result is the same as
if it had been first carried to the west as far as the one force
would carry it, and then back towards the east as far as the
other would carry it, that is, precisely the same distance ;
being ultimately left where it was found at first.

All laws of causation are liable to be in this manner
counteracted, and seemingly frustrated, by coming into con-
flict wiih other laws, the separate result of which is opposite
to theirs, or more or less inconsistent with it. And hence,
with almost every law, many instances in which it really is
entirely fulfilled, do not, at first sight, appear to be cases of
its operation at all. It is so in the example just adduced: a
force, in mechanics, means neither more nor less than a cause
of motion, yet the sum of the effects of two causes of motion
may be rest. Again, a body solicited by two forces in direc-
tions making an angle with one another, moves in the diago-
nal ; and it seems a paradox to say that motion in the diagonal
is the sum of two motions in two other lines. Motion, how-
ever, is but change of place, and at every instant the body is
iu the exact place it would have been in if the forces had
acted during alternate instants instead of acting in the same
instant ; (saving that if we suppose two forces to act succes-
sively which are in truth simultaneous, we must of course
allow them double the time.) It is evident, therefore, that
each force has had, during each instant, all the eifect which
belonged to it ; and that the modifying influence which one of
two concurrent causes is said to exercise with respect to the
other, may be considered as exerted not over the action of the
cause itself, but over the effect after it is completed. For all
purposes of predicting, calculating, or explaining their joint
result, causes which compound their effects may be treated as
if they produced simultaneously each of them its own effect,
and all these effects coexisted visibly.

Since the laws of causes are as really fulfilled when the
causes are said to be counteracted by opposing causes, as
when they are left to their own undisturbed action, we must

INTERMIXTURE OF EFFECTS. 517

be cautious not to express the laws in such terms as would
render the assertion of their being fulfilled in those cases
a contradiction. If, for instance, it were stated as a law
of nature that a body to which a force is applied moves
in the direction of the force, with a velocity proportioned
to the force directly, and to its own mass inversely ; when
in point of fact some bodies to which a force is applied
do not move at all, and those which do move (at least
in the region of our earth) are, from the very first,
retarded by the action of gravity and other resisting forces,
and at last stopped altogether ; it is clear that the general
proposition, though it would be true under a certain hypo-
thesis, would not express the facts as they actually occur. To
accommodate the expression of the law to the real pheno-
mena, we must say, not that the object moves, but that it
tends to move, in the direction and with the velocity specified.
We might, indeed, guard our expression in a different mode,
by saying that the body moves in that manner unless pre-
vented, or except in so far as prevented, by some counteracting
cause. But the body does not only move in that manner
unless counteracted ; it tends to move in that manner even
when counteracted; it still exerts, in the original direction,
the same energy of movement as if its first impulse had been
undisturbed, and produces, by that energy, an exactly equi-
valent quantity of effect. This is true even when the force
leaves the body as it found it, in a state of absolute rest ; as
when we attempt to raise a body of three tons weight with
a, force equal to one ton. For if, while we are applying this
force, wind or water or any other agent supplies an additional
force just exceeding two tons, the body will be raised ; thus
proving that the force we applied exerted its full effect, by
neutralizing an equivalent portion of the weight which it
was insufficient altogether to overcome. And if while we are
exerting this force of one ton upon the object in a direction
contrary to that of gravity, it be put into a scale and weighed,
it will be found to have lost a ton of its weight, or in other
words, to press downwards with a force only equal to the
difference of the two forces.

These facts are correctly indicated by the expression

518 INDUCTION.

tendency. All laws of causation, in consequence of their
liability to be counteracted, require to be stated in words
affirmative of tendencies only, and not of actual results. In
those sciences of causation which have an accurate nomen-
clature, there are special words which signify a tendency to
the particular effect with which the science is conversant ;
thus pressure, in mechanics, is synonymous with tendency to
motion, and forces are not reasoned on as causing actual
motion, but as exerting pressure. A similar improvement
in terminology would be very salutary in many other branches
of science.

The habit of neglecting this necessary element in the
precise expression of the laws of nature, has given birth to
the popular prejudice that all general truths have exceptions ;
and much unmerited distrust has thence accrued to the con-
clusions of science, when they have been submitted to the
judgment of minds insufficiently disciplined and cultivated.
The rough generalizations suggested by common observation
usually have exceptions ; but principles of science, or in
other words, laws of causation, have not. " What is thought
to be an exception to a principle," (to quote words used on
a different occasion,) " is always some other and distinct
principle cutting into the former ; some other force which
impinges* against the first force, and deflects it from its
direction. There are not a law and an exception to that law,
the law acting in ninety-nine cases, and the exception in one.
There are two laws, each possibly acting in the whole hundred
cases, and bringing about a common effect by their conjunct
operation. If the force which, being the less conspicuous of
the two, is called the disturbing force, prevails sufficiently
over the other force in some one case, to constitute that case
what is commonly called an exception, the same disturbing
force probably acts as a modifying cause in many other cases
which no one will call exceptions.

" Thus if it were stated to be a law of nature that all

* It seems hardly necessary to say that the word impinge, as a general term
to express collision of forces, is here used by a figure of speech, and not as ex-
preasive of any theory respecting the nature of force.

INTERMIXTURE OF EFFECTS. 519

heavy bodies fall to the ground, it would probably be said
that the resistance of the atmosphere, which prevents a balloon
from falling, constitutes the balloon an exception to that
pretended law of nature. But the real law is, that all heavy
bodies tend to fall ; and to this there is no exception, not even
the sun and moon ; for even they, as every astronomer knows,
tend towards the earth, with a force exactly equal to that
with which the earth tends towards them. The resistance of
the atmosphere might, in the particular case of the balloon,
from a misapprehension of what the law of gravitation is, be
said to prevail over the law; but its disturbing effect is quite
as real in every other case, since though it does not prevent,
it retards the fall of all bodies whatever. The rule, and the
so-called exception, do not divide the cases between them ;
each of them is a comprehensive rule extending to all cases.
To call one of these concurrent principles an exception to
the other, is superficial, and contrary to the correct principles
of nomenclature and arrangement. An effect of precisely the
same kind, and arising from the same cause, ought not to be
placed in two different categories, merely as there does or does
not exist another cause preponderating over it."*

§ 6. We have now to consider according to what method
these . complex effects, compounded of the effects of many
causes, are to be studied ; how we are enabled to trace each
effect to the concurrence of causes in which it originated, and
ascertain the conditions of its recurrence — the circumstances
in which it may be expected again to occur. The conditions
of a phenomenon which arises from a composition of causes,
may be investigated either deductively or experimentally.

The case, it is evident, is naturally susceptible of the
deductive mode of investigation. The law of an effect of this
description is a result of the laws of the separate causes on
the combination of which it depends, and is therefore in
itself capable of being deduced from these laws. This is
called the method ct priori. The other, or a posteriori method,

* Essays on some Unsettled Questions oj Political Economy, Essay V.

520 INDUCTION.

professes to proceed according to the canons of experimental
inquiry. Considering the whole assemblage of concurrent
causes which produced the phenomenon, as one single cause,
it attempts to ascertain the cause in the ordinary manner, by a
comparison of instances. This second method subdivides
itself into two different varieties. If it merely collates
instances of the effect, it is a method of pure observation. If
it operates upon the causes, and tries different combinations
of them, in hopes of ultimately hitting the precise combina-
tion which will produce the given total effect, it is a method
of experiment.

In order more completely to clear up the nature of each of
these three methods, and determine which of them deserves the
preference, it will be expedient (conformably to a favourite
maxim of Lord Chancellor Eldon, to which, though it has
often incurred philosophical ridicule, a deeper philosophy will
not refuse its sanction) to " clothe them in circumstances."
We shall select for this purpose a case which as yet furnishes
no very brilliant example of the success of any of the three
methods, but which is all the more suited to illustrate the
difficulties inherent in them. Let the subject of inquiry be,
the conditions of health and disease in the human body ; or
(for greater simplicity) the conditions of recovery from a given
disease ; and in order to narrow the question still more, let it
be limited, in the first instance, to this one inquiry : Is, or is
not some particular medicament (mercury, for instance) a
remedy for the given disease.

Now, the deductive method would set out from known
properties of mercury, and known laws of the human body,
and by reasoning from these, would attempt to discover
whether mercury will act upon the body when in the morbid
condition supposed, in such a manner as would tend to restore
health. The experimental method would simply administer
mercury in as many cases as possible, noting the age, sex,
temperament, and other peculiarities of bodily constitution,
the particular form or variety of the disease, the particular
stage of its progress, &c., remarking in which of these cases it
was attended with a salutary effect, and with what circum-

INTERMIXTURE OF EFFECTS. 521

stances it was on those occasions combined. The method of
simple observation would compare instances of recovery, to
find whether they agreed in having been preceded by the ad-
ministration of mercury ; or would compare instances of
recovery with instances of failure, to find cases which, agree-
ing in all other respects, differed only in the fact that mercury
had been administered, or that it had not.

§ 7. That the last of these three modes of investigation
is applicable to the case, no one has ever seriously contended.
No conclusions of value on a subject of such intricacy, ever
were obtained in that way. The utmost that could result
would be a vague general impression for or against the efficacy
of mercury, of no avail for guidance unless confirmed by one
of the other two methods. Not that the results, which this
method strives to obtain, would not be of the utmost possible
value if they could be obtained. If all the cases of recovery
which presented themselves, in an examination extending to a
great number of instances, were cases in which mercury had
been administered, we might generalize with confidence from
this experience, and should have obtained a conclusion of real
value. But no such basis for generalization can we, in a case
of this description, hope to obtain. The reason is that which
we have spoken of as constituting the characteristic imperfec-
tion of the Method of Agreement ; Plurality of Causes. Sup-
posing even that mercury does tend to cure the disease, so
many other causes, both natural and artificial, also tend to
cure it, that there are sure to be abundant instances of
recovery in which mercury has not been administered : unless,
indeed, the practice be to administer it in all cases ; on which
supposition it will equally be found in the cases of failure.

When an effect results from the union of many causes, the
share which each has in the determination of the effect cannot
in general be great : and the effect is not likely, even in its
presence or absence, still less in its variations, to follow, even
approximately, any one of the causes. Recovery from a
disease is an event to which, in every case, many influences
must concur. Mercury may be one such influence ; but from

522 INDUCTION.

the very fact that there are many other such, it will necessarily
happen that although mercury is administered, the patient,
for want of other concurring influences, will often not recover,
and that he often will recover when it is not administered, the
other favourable influences being sufficiently powerful without
it. Neither, therefore, will the instances of recovery agree in
the administration of mercury, nor will the instances of failure
agree in its non-administration. It is much if, by multiplied
and accurate returns from hospitals and the like, we can
collect that there are rather more recoveries and rather fewer
failures when mercury is administered than when it is not ; a
result of very secondary value even as a guide to practice,
and almost worthless as a contribution to the theory of the
subject.*

§ 8. The inapplicability of the method of simple obser-
vation to ascertain the conditions of effects dependent on
many concurring causes, being thus recognised; we shall next
inquire whether any greater benefit can be expected from the

* It is justly remarked by Professor Bain, that though the Methods of Agree-
ment and Difference are not applicable to these cases, they are not wholly
inaccessible to the Method of Concomitant Variations. " If a cause happens
to vary alone, the effect will also vary alone : a cause and effect may be thus
singled out under the greatest complications. Thus, when the appetite for
food increases with the cold, we have a strong evidence of connexion between
these two facts, although other circumstances may operate in the same direc-
tion. The assigning of the respective parts of the sun and moon in the action
of the tides, may be effected, to a certain degree of exactness, by the variations
of the amount according to the positions of the two attractive bodies. By a
series of experiments of Concomitant Variations, directed to ascertain the
elimination of nitrogen from the human body under varieties of muscular exer-
cise, Dr. Parkes obtained the remarkable conclusion, that a muscle grows
during exercise, and loses bulk during the subsequent rest." (Logic, ii. 83.)

It is, no doubt, often possible to single out the influencing causes from,
among a great number of mere concomitants, by noting what are the ante-
cedents, a variation in which is followed by a variation in the effect. But
when there are many influencing causes, no one of them greatly predominating
over the rest, and especially when some of these are continually changing, it is
scarcely ever possible to trace such a relation between the variations of the
effect and those of any one cause, as would enable us to assign to that cause its
real share in the production of the effect.

INTERMIXTURE OF EFFECTS. 523

other branch of the d, posteriori method, that which proceeds
by directly trying different combinations of causes, either
artificially produced or found in nature, and taking notice what
is their effect : as, for example, by actually trying the effect of
mercury, in as many different circumstances as possible. This
method differs from the one which we have just examined, in
turning our attention directly to the causes or agents, instead
of turning it to the effect, recovery from the disease. And
since, as a general rule, the effects of causes are far more
accessible to our study than the causes of effects, it is natural
to think that this method has a much better chance of proving
successful than the former.

The method now under consideration is called the Empi-
rical Method; and in order to estimate it fairly, we must
suppose it to be completely, not incompletely, empirical. We-
must exclude from it everything which partakes of the nature
not of an experimental but of a deductive operation. If for
instance we try experiments with mercury upon a person in
health, in order to ascertain the general laws of its action upon
the human body, and then reason from these laws to determine
how it will act upon persons affected with a particular disease,
this may be a really effectual method, but this is deduction.
The experimental method does not derive the law of a com-
plex case from the simpler laws which conspire to produce it,
but makes its experiments directly upon the complex case.
We must make entire abstraction of all knowledge of the
simpler tendencies, the modi operandi of mercury in detail.
Our experimentation must aim at obtaining a direct answer to
the specific question, Does or does not mercury tend to cure
the particular disease ?

Let us see, therefore, how far the case admits of the
observance of those rules of experimentation, which it is found
necessary to observe in other cases. When we devise an ex-
periment to ascertain the effect of a given agent, there are
certain precautions which we never, if we can help it, omit.
In the first place, we introduce the agent into the midst of a
set of circumstances which we have exactly ascertained. It
needs hardly be remarked how far this condition is from being

INDUCTION.

realized in any case connected with the phenomena of life ;
how far we are from knowing what are all the circumstances
which pre-exist in any instance in which mercury is admi-
nistered to a living being. This difficulty, however, though
insuperable in most cases, may not be so in all; there are
sometimes concurrences of many causes, in which we yet know
accurately what the causes are. Moreover, the difficulty may
be attenuated by sufficient multiplication of experiments, in
circumstances rendering it improbable that any of the un-
known causes should exist in them all. But when we have got
clear of this obstacle, we encounter another still more serious.
In other cases, when we intend to try an experiment, we do
not reckon it enough that there be no circumstance in the
case the presence of which is unknown to us. We require
also that none of the circumstances which we do know, shall
have effects susceptible of being confounded with those of
the agents whose properties we wish to study. We take the
utmost pains to exclude all causes capable of composition with
the given cause ; or if forced to let in any such causes, we take
care to make them such that we can compute and allow for
their influence, so that the effect of the given cause may, after
the subduction of those other effects, be apparent as a residual
phenomenon.

These precautions are inapplicable to such cases as we are
now considering. The mercury of our experiment being tried
with an unknown multitude (or even let it be a known multi-
tude) of other influencing circumstances, the mere fact of their
being influencing circumstances implies that they disguise the
effect of the mercury, and preclude us from knowing whether
it has any effect or not. Unless we already knew what and
how much is owing to every other circumstance, (that is,
unless we suppose the very problem solved which we are con-
sidering the means of solving,) we cannot tell that those other
circumstances may not have produced the whole of the effect,
independently or even in spite of the mercury. The Method
of Difference, in the ordinary mode of its use, namely, by
comparing the state of things following the experiment with
the state which preceded it, is thus, in the case of intermixture

INTERMIXTURE OF EFFECTS. 525

of effects, entirely unavailing ; because other causes than that
whose effect we are seeking to determine, have been operating
during the transition. As for the other mode of employing
the Method of Difference, namely by comparing, not the same
case at two different periods, but different cases, this in the
present instance is quite chimerical. In phenomena so com-
plicated it is questionable if two cases, similar in all respects
but one, ever occurred ; and were they to occur, we could not
possibly know that they were so exactly similar.

Anything like a scientific use of the method of experiment,
in these complicated cases, is therefore out of the question.
We can generally, even in the most favourable cases, only
discover by a succession of trials, that a certain cause is very
often followed by a certain effect. For, in one of these con-
junct effects, the portion which is determined by any one of the
influencing agents, is usually, as we before remarked, but
small ; and it must be a more potent cause than most, if even
the tendency which it really exerts is not thwarted by other
tendencies in nearly as many cases as it is fulfilled. Some
causes indeed there are which are more potent than any
counteracting causes to which they are commonly exposed ;
and accordingly there are some truths in medicine which are
sufficiently proved by direct experiment. Of these the most
familiar are those that relate to the efficacy of the substances
known as Specifics for particular diseases ; " quinine, col-
chicum, lime juice, cod liver oil,"* and a few others. Even
these are not invariably followed by success ; but they succeed
in so large a proportion of cases, and against such powerful
obstacles, that their tendency to restore health in the disorders
for which they are prescribed may be regarded as an experi-
mental truth, f

* Bain's Logic, ii. 360.

t What is said in the text on the inapplicability of the experimental
methods to resolve particular questions of medical treatment, does not detract
from their efficacy in ascertaining the general laws of the animal or human
system. The functions, for example, of the different classes of nerves have
been discovered, and probably could only have been discovered, by experi-
ments on living animals. Observation and experiment are the ultimate basis
of all knowledge : from them we obtain the elementary laws of life, as we

526 INDUCTION.

If so little can be done by the experimental method to
determine the conditions of an effect of many combined causes,
in the case of medical science ; still less is this method appli-
cable to a class of phenomena more complicated than even
those of physiology, the phenomena of politics and history.
There, Plurality of Causes exists in almost boundless excess,
and effects are, for the most part, inextricably interwoven
with one another. To add to the embarrassment, most of the
inquiries in political science relate to the production of effects
of a most comprehensive description, such as the public
wealth, public security, public morality, and the like : results
liable to be affected directly or indirectly either in plus or in
minus by nearly every fact which exists, or event which occurs,
in human society. The vulgar notion, that the safe methods
on political subjects are those of Baconian induction — that the
true guide is not general reasoning, but specific experience —
will one day be quoted as among the most unequivocal marks
of a low state of the speculative faculties in any age in which
it is accredited. Nothing can be more ludicrous than the sort
of parodies on experimental reasoning which one is accus-
tomed to meet with, not in popular discussion only, but in
grave treatises, when the affairs of nations are the theme.
"How," it is asked, "can an institution be bad, when the
country has prospered under it ?" " How can such or such
causes have contributed to the prosperity of one country,
when another has prospered without them ?" Whoever makes
use of an argument of this kind, not intending to deceive,
should be sent back to learn the elements of some one of the
more easy physical sciences. Such reasoners ignore the fact
of Plurality of Causes in the very case which affords the most
signal example of it. So little could be concluded, in such
a case, from any possible collation of individual instances, that
even the impossibility, in social phenomena, of making arti-
ficial experiments, a circumstance otherwise so prejudicial to

obtain all other elementary truths. It is in dealing with the complex combi-
nations that the experimental methods are for the most part illusory, and the
deductive mode of investigation must be invoked to disentangle the com-
plexity.

INTERMIXTURE OF EFFECTS. 527

directly inductive inquiry, hardly affords, in this case, addi-
tional reason of regret. For even if we could try experiments
upon a nation or upon the human race, with as little scruple as
M. Magendie tried them on dogs and rabbits, we should never
succeed in making two instances identical in every respect
except the presence or absence of some one definite circum-
stance. The nearest approach to an experiment in the philo-
sophical sense, which takes place in politics, is the introduction
of a new operative element into national affairs by some
special and assignable measure of government, such as the
enactment or repeal of a particular law. But where there are
so many influences at work, it requires some time for the in-
fluence of any new cause upon national phenomena to become
apparent ; and as the causes operating in so extensive a sphere
are not only infinitely numerous, but in a state of perpetual
alteration, it is always certain that before the effect of the new
cause becomes conspicuous enough to be a subject of induc-
tion, so many of the other influencing circumstances will have
changed as to vitiate the experiment.*

Two, therefore, of the three possible methods for the study
of phenomena resulting from the composition of many causes,

* Professor Bain, though concurring generally in the views expressed in this
chapter, seems to estimate more highly than I do the scope for specific experi-
mental evidence in politics. (Logic, ii. 333 — 337.) There are, it is true, as he
remarks (p. 336) some cases "when an agent suddenly introduced is almost
instantaneously followed by some other changes, as when the announcement of
a diplomatic rupture between two nations is followed the same day by a
derangement of the money-market." But this experiment would be quite in-
conclusive merely as an experiment. It can only serve, as any experiment may,
to verify the conclusion of a deduction. Unless we already knew by our know-
ledge of the motives which act on business men, that the prospect of war tends
to derange the money-market, we should never have been able to prove a con-
nexion between the two facts, unless after having ascertained historically that
the one followed the other in too great a number of instances to be consistent
with their having been recorded with due precautions. Whoever has carefully
examined any of the attempts continually made to prove economic doctrines
by such a recital of instances, knows well how futile they are. It always turns
out that the circumstances of scarcely any of the cases have been fully stated ;
and that cases, in equal or greater numbers, have been omitted, which would
have tended to an opposite conclusion.

528 INDUCTION.

being, from the very nature of the case, inefficient and illu-
sory, there remains only the third, — that which considers the
causes separately, and infers the effect from the balance
of the different tendencies which produce it : in short, the
deductive, or a priori method. The more particular con-
sideration of this intellectual process requires a chapter to
itself.

CHAPTER XI.

OF THE DEDUCTIVE METHOD.

§ 1. THE mode of investigation which, from the proved
inapplicability of direct methods of observation and experiment,
remains to us as the main source of the knowledge we possess
or can acquire respecting the conditions, and laws of recur-
rence, of the more complex phenomena, is called, in its most
general expression, the Deductive Method ; and consists of
tlirep operations : the first, one of dkect induction ; the second,
of ratiocination ; the third, of verification.

I call the first step in the process an inductive operation,
because there must be a direct induction as the basis of the
whole ; though in many particular investigations the place
of the induction may be supplied by a prior deduction; but
the premises of this prior deduction must have been derived t
from induction.

The problem of the Deductive Method is, to find the law
of an effect, from the laws of the different tendencies of which
it is the joint result. The first requisite, therefore, is to know
the laws of those tendencies ; the law of each of the concurrent
causes : and this supposes a previous process of observation or
experiment upon each cause separately ; or else a previous
deduction, which also must depend for its ultimate premises
on observation or experiment. Thus, if the subject be social
or historical phenomena, the premises of the Deductive Method
must be the laws of the causes which determine that class of
phenomena ; and those causes are human actions, together
with the general outward circumstances under the influence of
which mankind are placed, and which constitute man's posi-
tion on the earth. The Deductive Method, applied to social
phenomena, must begin, therefore, by investigating, or must
suppose to have been already investigated, the laws of human
VOL. i. 34

530 INDUCTION.

action, and those properties of outward things by which the
actions of human beings in society are determined. Some of
these general truths will naturally be obtained by observation
and experiment, others by deduction : the more complex laws
of human action, for example, may be deduced from the
simpler ones ; but the simple or elementary laws will always,
and necessarily, have been obtained by a directly inductive
process.

To ascertain, then, the laws of each separate cause which
takes a share in producing the effect, is the first desideratum
of the Deductive Method. To know what the causes are,
which must be subjected to this process of study, may or may
not be difficult. In the case last mentioned, this first condi-
tion is of easy fulfilment. That social phenomena depend on
the acts and mental impressions of human beings, never could
have been a matter of any doubt, however imperfectly it may
have been known either by what laws those impressions
and actions are governed, or to what social consequences their
laws naturally lead. Neither, again, after physical science
had attained a certain development, could there be any real
doubt where to look for the laws on which the phenomena of
life depend, since they must be the mechanical and chemical
laws of the solid and fluid substances composing the organized
body and the medium in which it subsists, together with the
peculiar vital laws of the different tissues constituting the
organic structure. In other cases, really far more simple than
these, it was much less obvious in what quarter the causes
were to be looked for : as in the case of the celestial pheno-
mena. Until, by combining the laws of certain causes, it was
found that those laws explained all the facts which experience
had proved concerning the heavenly motions, and led to pre-
dictions which it always verified, mankind never knew that
those were the causes. But whether we are able to put the
question before, or not until after, we have become capable of
answering it, in either case it must be answered ; the laws of
the different causes must be ascertained, before we can proceed
to deduce from them the conditions of the effect.

The mode of ascertaining those laws neither is, nor can be,

THE DEDUCTIVE METHOD. 531

any other than the fourfold method of experimental inquiry,
already discussed. A few remarks on the application of that
method to cases of the Composition of Causes, are all that is
requisite.

It is obvious that we cannot expect to find the law of a
tendency, by an induction from cases in which the tendency
is counteracted. The laws of motion could never have been
brought to light from the observation of bodies kept at rest
by the equilibrium of opposing forces. Even where the ten-
dency is not, in the ordinary sense of the word, counteracted,
but only modified, by having its effects compounded with the
effects arising from some other tendency or tendencies, we are
still in an unfavourable position for tracing, by means of such
cases, the law of the tendency itself. It would have been
scarcely possible to discover the law that every body in motion
tends to continue moving in a straight line, by an induction
from instances in which the motion is deflected into a curve,
by being compounded with the effect of an accelerating force.
Notwithstanding the resources afforded in this description of
cases by the Method of Concomitant Variations, the principles
of a judicious experimentation prescribe that the law of each
of the tendencies should be studied, if possible, in cases in
which that tendency operates alone, or in combination with
no agencies but those of which the effect can, from previous
knowledge, be calculated and allowed for.

Accordingly, in the cases, unfortunately very numerous and
important, in which the causes do not suffer themselves to be
separated and observed apart, there is much difficulty in laying
down with due certainty the inductive foundation necessary to
support the deductive method. This difficulty is most of all
conspicuous in the case of physiological phenomena; it being
seldom possible to separate the different agencies which col-
lectively compose an organized body, without destroying the
very phenomena which it is our object to investigate:

— following life, in creatures we dissect,
We lose it, in the moment we detect.

And for this reason I am inclined to the opinion, that phy-

34-2

532 INDUCTION.

siology (greatly and rapidly progressive as it now is) is embar-
rassed by greater natural difficulties, and is probably susceptible
of a less degree of ultimate perfection, tban even tbe social
science ; inasmuch as it is possible to study tbe laws and
operations of one buman mind apart from other minds, much
less imperfectly than we can study the laws of one organ or
tissue of the human body apart from the other organs or
tissues.

It has been judiciously remarked that pathological facts,
or, to speak in common language, diseases in their different
forms and degrees, afford in the case of physiological investi-
gation the most valuable equivalent to experimentation pro-
perly so called ; inasmuch as they often exhibit to us a definite
disturbance in some one organ or organic function, the remain-
ing organs and functions being, in the first instance at least,
unaffected. It is true that from the perpetual actions and re-
actions which are going on among all parts of the organic
economy, there can be no prolonged disturbance in any one
function without ultimately involving many of the others ;
and when once it has done so, the experiment for the most
part loses its scientific value. All depends on observing the
early stages of the derangement; which, unfortunately, are of
necessity the least marked. If, however, the organs and func-
tions not disturbed in tbe first instance, become affected in a
fixed order of succession, some light is thereby thrown upon
the action which one organ exercises over another : and we
occasionally obtain a series of effects which we can refer with
some confidence to the original local derangement ; but for
this it is necessary that we should know that the original
derangement was local. If it was what is termed constitu-
tional, that is, if we do not know in what part of the animal
economy it took its rise, or the precise nature of the distur-
bance which took place in that part, we are unable to deter-
mine which of the various derangements was cause and which
effect; which of them were produced by one another, and
which by the direct, though perhaps tardy, action of the
original cause.

Besides natural pathological facts, we can produce patho-

THE DEDUCTIVE METHOD. 533

logical facts artificially ; we can try experiments, even in the
popular sense of the term, by subjecting the living being to
some external agent, such as the mercury of our former ex-
ample, or the section of a nerve to ascertain the functions of
different parts of the nervous system. As this experimenta-
tion is not intended to obtain a direct solution of any prac-
tical question, but to discover general laws, from which
afterwards the conditions of any particular effect may be ob-
tained by deduction ; the best cases to select are those of which
the circumstances can be best ascertained : and such are gene-
rally not those in which there is any practical object in view.
The experiments are best tried, not in a state of disease, which
is essentially a changeable state, but in the condition of
health, comparatively a fixed state. In the one, unusual
agencies are at work, the results of which we have no means of
predicting ; in the other, the course of the accustomed physio-
logical phenoinena would, it may generally be presumed,
remain undisturbed, were it not for the disturbing cause which
we introduce.

Such, with the occasional aid of the Method of Concomi-
tant Variations, (the latter not less incumbered than the more
elementary methods by the peculiar difficulties of the subject,)
are our inductive resources for ascertaining the laws of the
causes considered separately, when we have it not in our power
to make trial of them in a state of actual separation. The
insufficiency of these resources is so glaring, that no one can
be surprised at the backward state of the science of physio •
logy ; in which indeed our knowledge of causes is so imperfect,
that we can neither explain, nor could without specific expe-
rience have predicted, many of the facts which are certified to
us by the most ordinary observation. Fortunately, we are
much better informed as to the empirical laws of the pheno-
mena, that is, the uniformities respecting which we cannot
yet decide whether they are cases of causation, or mere results
of it. Not only has the order in which the facts of organiza-
tion and life successively manifest themselves, from the first
germ of existence to death, been found to be uniform, and
very accurately ascertainable; but, by a great application of

534 INDUCTION.

the Method of Concomitant Variations to the entire facts of
comparative anatomy and physiology, the characteristic organic
structure corresponding to each class of functions has been
determined -with considerable precision. Whether these organic
conditions are the whole of the conditions, and in many cases
whether they are conditions at all, or mere collateral effects of
some common cause, we are quite ignorant ; nor are we ever
likely to know, unless we could construct an organized body,
and try whether it would live.

Under such disadvantages do we, in cases of this descrip-
tion, attempt the initial, or inductive step, in the application
of the Deductive Method to complex phenomena. But such,
fortunately, is not the common case. In general, the laws of
the causes on which the effect depends may be obtained by an
induction from comparatively simple instances, or, at the
worst, by deduction from the laws of simpler causes, so
obtained. By simple instances are meant, of course, those
in which the action of each cause was not intermixed or inter-
fered with, or not to any great extent, by other causes whose
laws were unknown. And only when the induction which fur-
nished the premises to the Deductive method rested on such
instances, has the application of such a method to the ascer-
tainment of the laws of a complex effect, been attended with
brilliant results.

§ 2. When the laws of the causes have been ascertained,
and the first stage of the great logical operation now under
discussion satisfactorily accomplished, the second part follows;
that of determining from the laws of the causes, what effect
any given combination of those causes will produce. This is a
process of calculation, in the wider sense of the term ; and very
often involves processes of calculation in the narrowest sense.
It is a ratiocination ; and when our knowledge of the causes
is so perfect, as to extend to the exact numerical laws which
they observe in producing their effects, the ratiocination may
reckon among its premises the theorems of the science of
number, in the whole immense extent of that science. Not
only are the most advanced truths of mathematics often

THE DEDUCTIVE METHOD. 535

required to enable us to compute an effect, the numerical law
of which we already know; but, even by the aid of those most
advanced truths, we can go but a little way. In so simple a
case as the common problem of three bodies gravitating
towards one another, with a force directly as their mass and
inversely as the square of the distance, all the resources of the
calculus have not hitherto sufficed to obtain any general solu-
tion but an approximate one. In a case a little more complex,
but still one of the simplest which arise in practice, that of the
motion of a projectile, the causes which affect the velocity and
range (for example) of a cannon-ball may be all known and
estimated; the force of the gunpowder, the angle of elevation,
the density of the air, the strength and direction of the wind ;
but it is one of the most difficult of mathematical problems to
combine all these, so as to determine the effect resulting from
their collective action.

Besides the theorems of number, those of geometry also
come in as premises, where the effects take place in space, and
involve motion and extension, as in mechanics, optics, acous-
tics, astronomy. But when the complication increases, and
the effects are under the influence of so many and such shift-
ing causes as to give no room either for fixed numbers, or for
straight lines and regular curves, (as in the case of physio-
logical, to say nothing of mental and social phenomena,)
the laws of number and extension are applicable, if at all,
only on that large scale on which precision of details becomes
unimportant. Although these laws play a conspicuous part
in the most striking examples of the investigation of nature
by the Deductive Method, as for example in the Newtonian
theory of the celestial motions, they are by no means an indis-
pensable part of every such process. All that is essential in
it is reasoning from a general law to a particular case, that
is, determining by means of the particular circumstances of
that case, what result is required in that instance to fulfil the
law. Thus in the Torricellian experiment, if the fact that air
has weight had been previously known, it would have been
easy, without any numerical data, to deduce from the general
law of equilibrium, that the mercury would stand in the tube

536 INDUCTION.

at such a height that the column of mercury would exactly
balance a column of the atmosphere of equal diameter;
because, otherwise, equilibrium would not exist.

By such ratiocinations from the separate laws of the
causes, we may, to a certain extent, succeed in answering
either of the following questions : Given a certain combina-
tion of causes, what effect will follow ? and, What combi-
nation of causes, if it existed, would produce a given effect ?
In the one case, we determine the effect to be expected in any
complex circumstances of which the different elements are
known : in the other case we learn, according to what law —
under what antecedent conditions — a given complex effect
will occur.

§ 3. But (it may here be asked) are not the same argu-
ments by which the methods of direct observation and expe-
riment were set aside as illusory when applied to the laws of
complex phenomena, applicable with equal force against the
Method of Deduction ? When in every single instance a
multitude, often an unknown multitude, of agencies, are
clashing and combining, what security have we that in our
computation a priori we have taken all these into our reckon-
ing ? How many must we not generally be ignorant of?
Among those which we know, how probable that some have
been overlooked ; and, even were all included, how vain the
pretence of summing up the effects of many causes, unless we
know accurately the numerical law of each, —a condition in
most cases not to be fulfilled ; and even when it is fulfilled, to
make the calculation transcends, in any but very simple cases,
the utmost power of mathematical science with all its most
modern improvements.

These objections have real weight, and would be altogether
unanswerable, if there were no test by which, when we employ
the Deductive Method, we might judge whether an error
of any of the above descriptions had been committed or not.
Such a test however there is : and its application forms, under
the name of Verification, the third essential component part of
the Deductive Method; without which all the results it can

THE DEDUCTIVE METHOD. 537

give have little other value than that of conjecture. To
warrant reliance on the general conclusions arrived at by
deduction, these conclusions must be found, on careful com-
parison, to accord with the results of direct observation
wherever it can be had. If, when we have experience to com-
pare with them, this experience confirms them, we may safely
trust to them in other cases of which our specific experience
is yet to come. But if our deductions have led to the conclu-
sion that from a particular combination of causes a given effect
would result, then in all known cases where that combination
can be shown to have existed, and where the effect has not
followed, we must be able to show (or at least to make a pro-
bable surmise) what frustrated it : if we cannot, the theory is
imperfect, and not yet to be relied upon. Nor is the verifi-
cation complete, unless some of the cases in which the theory
is borne out by the observed result, are of at least equal com-
plexity with any other cases in which its application could be
called for.

If direct observation and collation of instances have fur-
nished us with any empirical laws of the effect (whether true
in all observed cases, or only true for the most part), the most
effectual verification of which the theory could be susceptible
would be, that it led deductively to those empirical laws;
that the uniformities, whether complete or incomplete, which
were observed to exist among the phenomena, were accounted
for by the laws of the causes — were such as could not but exist
if those be really the causes by which the phenomena are pro-
duced. Thus it was very reasonably deemed an essential
requisite of any true theory of the causes of the celestial
motions, that it should lead by deduction to Kepler's laws:
which, accordingly, the Newtonian theory did.

In order, therefore, to facilitate the verification of theories
obtained by deduction, it is important that as many as pos-
sible of the empirical laws of the phenomena should be as-
certained, by a comparison of instances, conformably to the
Method of Agreement: as well as (it must be added) that
the phenomena themselves should be described, in the most
comprehensive as well as accurate manner possible; by col-

538 INDUCTION.

lecting from the observation of parts, the simplest possible
correct expressions for the corresponding wholes : as when
the series of the observed places of a planet was first expressd
by a circle, then by a system of epicycles, and subsequently by
an ellipse.

It is worth remarking, that complex instances which
would have been of no use for the discovery of the simple
laws into which we ultimately analyse their phenomena,
nevertheless, when they have served to verify the analysis,
become additional evidence of the laws themselves. Although
we could not have got at the law from complex cases, still
when the law, got at otherwise, is found to be in accordance
with the result of a complex case, that case becomes a new
experiment on the law, and helps to confirm what it did
not assist to discover. It is a new trial of the principle in
a different set of circumstances; and occasionally serves to
eliminate some circumstance not previously excluded, and the
exclusion of which might require an experiment impossible to
be executed. This was strikingly conspicuous in the example
formerly quoted, in which the difference between the observed
and the calculated velocity of sound was ascertained to result
from the heat extricated by the condensation which takes
place in each sonorous vibration. This was a trial, in new
circumstances, of the law of the development of heat by com-
pression; and it added materially to the proof of the univer-
sality of that law. Accordingly any law of nature is deemed
to have gained in point of certainty, by being found to explain
some complex case which had not previously been thought of
in connexion with it; and this indeed is q, consideration to
which it is the habit of scientific inquirers to attach rather too
much value than too little.

To the Deductive Method, thus characterized in its three
constituent parts, Induction, Ratiocination, and Verification,
the human mind is indebted for its most conspicuous triumphs
in the investigation of nature. To it we owe all the theories
by which vast and complicated phenomena are embraced under
a few simple laws, which, considered as the laws of those
great phenomena, could never have been detected by their

THE DEDUCTIVE METHOD. 539

direct study. We may form some conception of what the
method has done for us, from the case of the celestial motions ;
one of the simplest among the greater instances of the Com-
position of Causes, since (except in a few cases not of primary
importance) each of the heavenly bodies may be considered,
without material inaccuracy, to be never at one time influenced
by the attraction of more than two bodies, the sun and one
other planet or satellite ; making, with the reaction of the body
itself, and the force generated by the body's own motion and
acting in the direction of the tangent, only four different
agents on the concurrence of which the motions of that body
depend ; a much smaller number, no doubt, than that by which
any other of the great phenomena of nature is determined or
modified. Yet how could we ever have ascertained the com-
bination of forces on which the motions of the earth and planets
are dependent, by merely comparing the orbits or velocities
of different planets, or the different velocities or positions of
the same planet ? Notwithstanding the regularity which mani-
fests itself in those motions, in a degree so rare among the
effects of concurrence of causes ; and although the periodical
recurrence of exactly the same effect, affords positive proof
that all the combinations of causes which occur at all, recur
periodically ; we should not have known what the causes were,
if the existence of agencies precisely similar on our own earth
had not, fortunately, brought the causes themselves within the
reach of experimentation under simple circumstances. As we
shall have occasion to analyse, further on, this great example
of the Method of Deduction, we shall not occupy any time
with it here, but shall proceed to that secondary application of
the Deductive Method, the result of which is not to prove laws
of phenomena, but to explain them.

CHAPTER XII.

OF THE EXPLANATION OF LAWS OF NATURE.

§ 1. THE deductive operation by which we derive the
law of an effect from the laws of the causes, the concurrence
of which gives rise to it, may be undertaken either for the
purpose of discovering the law, or of explaining a law already
discovered. The word explanation occurs so continually and
holds so important a place in philosophy, that a little time
spent in fixing the meaning of it will be profitably employed.

An individual fact is said to be explained, by pointing out
its cause, that is, by stating the law or laws of causation, of
which its production is an instance. Thus a conflagration
is explained, when it is proved to have arisen from a spark
falling into the midst of a heap of combustibles. And in a
similar manner, a law or uniformity in nature is said to be
explained, when another law or laws are pointed out, of
which that law itself is but a case, and from which it could be
deduced.

§ 2. There are three distinguishable sets of circumstances
in which a law of causation may be explained from, or, as it
also is often expressed, resolved into, other laws.

The first is the case already so fully considered ; an
intermixture of laws, producing a joint effect equal to the
sum of the effects of the causes taken separately. The law
of the complex effect is explained, by being resolved into the
separate laws of the causes which contribute to it. Thus,
the law of the motion of a planet is resolved into the law of
the acquired force, which tends to produce an uniform motion
in the tangent, and the law of the centripetal force which tends
to produce an accelerating motion towards the sun ; the real
motion being a compound of the two.

It is necessary here to remark, that in this resolution of

EXPLANATION OF LAWS. 541

the law of a complex effect, the laws of which it is compounded
are not the only elements. It is resolved into the laws of the
separate causes, together with the fact of their coexistence.
The one is as essential an ingredient as the other; whether the
object be to discover the law of the effect, or only to explain
it. To deduce the laws of the heavenly motions, we require
not only to know the law of a rectilineal and that of a gravita-
tive force, but the existence of both these forces in the celestial
regions, and even their relative amount. The complex laws of
causation are thus resolved into two distinct kinds of elements :
the one, simpler laws of causation, the other (in the aptly
selected expression of Dr. Chalmers) collocations ; the collo-
cations consisting in the existence of certain agents or powers,
in certain circumstances of place and time. We shall hereafter
have occasion to return to this distinction, and to dwell on it
at such length as dispenses with the necessity of further in-
sisting on it here. The first mode, then, of the explanation
of Laws of Causation, is when the law of an effect is resolved
into the various tendencies of which it is the result, together
with the laws of those tendencies.

§ 3. A second case is when, between what seemed the
cause and what was supposed to be its effect, further observa-
tion detects an intermediate link ; a fact caused by the ante-
cedent, and in its turn causing the consequent ; so that the
cause at first assigned is but the remote cause, operating
through the intermediate phenomenon. A seemed the cause
of C, but it subsequently appeared that A was only the cause
of B, and that it is B which was the cause of C. For example:
mankind were aware that the act of touching an outward object
caused a sensation. It was subsequently discovered, that after
we have touched the object, and before we experience the sen-
sation, some change takes place in a kind of thread called a
nerve, which extends from our outward organs to the brain.
Touching the object, therefore, is only the remote cause of our
sensation ; that is, not the cause, properly speaking, but the
cause of the cause ; — the real cause of the sensation is the
change in the state of the nerve. Future experience may not

542 INDUCTION.

only give us more knowledge than we now have of the parti-
cular nature of this change, but may also interpolate another
link : between the contact (for example) of the object with our
outward organs, and the production of the change of state in
the nerve, there may take place some electric phenomenon ;
or some phenomenon of a nature not resembling the effects of
any known agency. Hitherto, however, no such intermediate
link has been discovered ; and the touch of the object must be
considered, provisionally, as the proximate cause of the affec-
tion of the nerve. The sequence, therefore, of a sensation of
touch on contact with an object, is ascertained not to be an
ultimate law ; it is resolved, as the phrase is, into two other
laws, — the law that contact with an object produces an affec-
tion of the nerve ; and the law, that an affection of the nerve
produces sensation.

To take another example : the more powerful acids corrode
or blacken organic compounds. This is a case of causation,
but of remote causation ; and is said to be explained when it is
shown that there is an intermediate link, namely, the separa-
tion of some of the chemical elements of the organic structure
from the rest, and their entering into combination with the
acid. The acid causes this separation of the elements, and
the separation of the elements causes the disorganization, and
often the charring of the structure. So, again, chlorine
extracts colouring matters (whence its efficacy in bleaching)
and purifies the air from infection. This law is resolved into
the two following laws. Chlorine has a powerful affinity for
bases of all kinds, particularly metallic bases and hydrogen.
Such bases are essential elements of colouring matters and
contagious compounds : which substances, therefore, are de-
composed and destroyed by chlorine.

§ 4. It is of importance to remark, that when a sequence
of phenomena is thus resolved into other laws, they are always
laws more general than itself. The law that A is followed by
C, is less general than either of the laws which connect B
with C and A with B. This will appear from very simple
considerations.

EXPLANATION OF LAWS. 543

All laws of causation are liable to be counteracted or frus-
trated, by the non-fulfilment of some negative condition : tbe
tendency, therefore, of B to produce C may be defeated. Now
the law that A produces B, is equally fulfilled whether B is
followed by C or not; but the law that A produces C by
means of B, is of course only fulfilled when B is really fol-
lowed by C, and is therefore less general than the law that A
produces B. It is also less general than the law that B pro-
duces C. For B may have other causes besides A; and as A
produces C only by means of B, while B produces C whether
it has itself been produced by A or by anything else, the
second law embraces a greater number of instances, covers as
it were a greater space of ground, than the first.

Thus, in our former example, the law that the contact of
an object causes a change in the state of the nerve, is more
general than the law that contact with an object causes sensa-
tion, since, for aught we know, the change in the nerve may
equally take place when, from a counteracting cause, as, for
instance, strong mental excitement, the sensation does not
follow ; as in a battle, where wounds are sometimes received
without any consciousness of receiving them. And again, the
law that change in the state of a nerve produces sensation, is
more general than the law that contact with an object pro-
duces sensation ; since the sensation equally follows the
change in the nerve when not produced by contact with an
object, but by some other cause; as in the well-known case,
when a person who has lost a limb, feels the same sensation
which he has been accustomed to call a pain in the limb.

Not only are the laws of more immediate sequence into
which the law of a remote sequence is resolved, laws of greater
generality than that law is, but (as a consequence of, or rather
as implied in, their greater generality) they are more to be
relied on ; there are fewer chances of their being ultimately
found not to be universally true. From the moment when
the sequence of A and C is shown not to be immediate, but to
depend on an intervening phenomenon, then, however con-
stant and invariable the sequence of A and C has hitherto
been found, possibilities arise of its failure, exceeding those

544 INDUCTION.

which can effect either of the more immediate sequences, A, B,
and B, C. The tendency of A to produce C may be defeated
by whatever is capable of defeating either the tendency of A
to produce B, or the tendency of B to produce C ; it is there-
fore twice as liable to failure as either of those more elemen-
tary tendencies ; and the generalization that A is always fol-
lowed by C, is twice as likely to be found erroneous. And so
of the converse generalization, that C is always preceded and
caused by A ; which will be erroneous not only if there should
bappen to be a second immediate mode of production of C
itself, but moreover if there be a second mode of production of
B, the immediate antecedent of C in the sequence.

The resolution of the one generalization into the other
two, not only shows that there are possible limitations of the
former, from which its two elements are exempt, but shows
also where these are to be looked for. As soon as we know
that B intervenes between A and C, we also know that if there
be cases in which the sequence of A and C does not hold,
these are most likely to be found by studying the effects or
the conditions of the phenomenon B.

It appears, then, that in the second of the three modes in
which a law may be resolved into other laws, the latter are
more general, that is, extend to more cases, and are also less
likely to require limitation from subsequent experience, than
the law which they serve to explain. They are more nearly
unconditional; they are defeated by fewer contingencies; they
are a nearer approach to the universal truth of nature. The
same observations are still more evidently true with regard to
the first of the three modes of resolution. When the law of
an effect of combined forces is resolved into the separate laws
of the causes, the nature of the case implies that the law of the
effect is less general than the law of any of the causes, since it
only holds when they are combined ; while the law of any one
of the causes holds good both then, and also when that cause
acts apart from the rest. It is also manifest that the complex
law is liable to be oftener unfulfilled than any one of the
simpler laws of which it is the result, since every contingency
which defeats any of the laws prevents so much of the effect

EXPLANATION' OF LAWS. 545

as depends on it, and thereby defeats the complex law. The
mere- rusting, for example, of some small part of a great
machine, often suffices entirely to prevent the effect which
ought to result from the joint action of all the parts. The
law of the effect of a combination of causes is always subject
to the whole of the negative conditions which attach to the
action of all the causes severally.

There is another and an equally strong reason why the law
of a complex effect must be less general than the laws of the
causes which conspire to produce it The same causes, acting
according to the same laws, and differing only in the propor-
tions in which they are combined, often produce effects which
differ not merely in quantity, but in kind. The combination
of a centripetal with a projectile force, in the proportions
which obtain in all the planets and satellites of our solar
system, gives rise to an elliptical motion ; but if the ratio of
the two forces to each other were slightly altered, it is demon-
strated that the motion produced would be in a circle, or a
parabola, or an hyperbola : and it is thought that in the case
of some comets one of these is probably the fact. Yet the
law of the parabolic motion would be resolvable into the very
same simple lows into which that of the elliptical motion
is resolved, namely, the law of the permanence of rectilineal
motion, and the law of gravitation. If, therefore, in the
course of ages, some circumstance were to manifest itself
which, without defeating the law of either of those forces,
should merely alter their proportion to one another, (such as
the shock of some solid body, or even the accumulating effect
of the resistance of the medium in which astronomers have
been led to surmise that the motions of the heavenly bodies
take place,) the elliptical motion might be changed into a
motion in some other conic section ; and the complex law,
that the planetary motions take place in ellipses, would be de-
prived of its universality, though the discovery would not at
all detract from the universality of the simpler laws into which
that complex law is resolved. The law, in short, of each of
the concurrent causes remains the same, however their collo-
cations may vary ; but the law of their joint effect varies with

VOL. i. 35

546

INDUCTION.

every difference in the collocations. There needs no more
to show how much more general the elementary laws must
be, than any of the complex laws which are derived from
them.

§ 5. Besides the two modes which have been treated of,
there is a third mode in which laws are resolved into one
another ; and in this it is self-evident that they are resolved
into laws more general than themselves. This third mode is
the subsumption (as it has been called) of one law under
another : or (what comes to the same thing) the gathering up
of several laws into one more general Taw which includes
them all. The most splendid example of this operation was
when terrestrial gravity and the central force of the solar
system were brought together under the general law of gravi-
tation. It had been proved antecedently that the earth and
the other planets tend to the sun; and it had been known
from the earliest times that terrestrial bodies tend towards the
earth. These were similar phenomena; and to enable them
both to be subsumed under one law, it was only necessary to
prove that, as the effects were similar in quality, so also they,
as to quantity, conform to the same rules. This was first
shown to be true of the moon, which agreed with terrestrial
objects not only in tending to a centre, but in the fact that
this centre was the earth. The tendency of the moon towards
the earth being ascertained to vary as the inverse square of
the distance, it was deduced from this, by direct calculation,
that if the moon were as near to the earth as terrestrial objects
are, and the acquired force in the direction of the tangent were
suspended, the moon would fall towards the earth through ex-
actly as many feet in a second as those objects do by virtue of
their weight. Hence the inference was irresistible, that the
moon also tends to the earth by virtue of its weight: and that
the two phenomena, the tendency of the moon to the earth
and the tendency of terrestrial objects to the earth, being not
only similar in quality, but, when in the same circumstances,
identical in quantity, are cases of one and the same law of
causation. But the tendency of the moon to the earth, and

EXPLANATION OF LAWS. 547

the tendency of the earth and planets to the sun, were already
known to be cases of the same law of causation : and thus the
law of all these tendencies, and the law of terrestrial gravity,
were recognised as identical, and were subsumed under one
general law, that of gravitation.

In a similar manner, the laws of magnetic phenomena have
more recently been subsumed under known laws of electricity.
It is thus that the most general laws of nature are usually
arrived at : we mount to them by successive steps. For, to
arrive by correct induction at laws which hold under such an
immense variety of circumstances, laws so general as to be
independent of any varieties of space or time which we are
able to observe, requires for the most part many distinct sets of
experiments or observations, conducted at different times and
by different people. One part of the law is first ascertained.,
afterwards another part : one set of observations teaches us
that the law holds good under some conditions, another
that it holds good under other conditions, by combining which
observations we find that it holds good under conditions much
more general, or even universally. The general law, in this
case, is literally the sum of all the partial ones ; it is a
recognition of the same sequence in different sets of instances ;
and may, in fact, be regarded as merely one step in the pro-
cess of elimination. The tendency of bodies towards one
another, which we now call gravity, had at first been observed
ouly on the earth's surface, where it manifested itself only as a
tendency of all bodies towards the earth, and might, therefore,
be ascribed to a peculiar property of the earth itself: one of
the circumstances, namely, the proximity of the earth, had
not been eliminated. To eliminate this circumstance required
a fresh set of instances in other parts of the universe : these
we could not ourselves create ; and though nature had created
them for us, we were placed in very unfavourable circum-
stances for observing them. To make these observations, fell
naturally to the lot of a different set of persons from those
who studied terrestrial phenomena ; and had, indeed, been a
matter of great interest at a time when the idea of explaining
celestial facts by terrestrial laws was looked upon as the con-

35—2

548 INDUCTION.

founding of an indefeasible distinction. When, however, the
celestial motions were accurately ascertained, and the deduc-
tive processes performed, from which it appeared that their
laws and those of terrestrial gravity corresponded, those celes-
tial observations became a set of instances which exactly
eliminated the circumstance of proximity to the earth; and
proved that in the original case, that of terrestrial objects, it
was not the earth, as such, that caused the motion or the
pressure, but the circumstance common to that case with the
celestial instances, namely, the presence of some great body
within certain limits of distance.

§ 6. There are, then, three modes of explaining laws of
causation, or, which is the same thing, resolving them into
other laws. First, when the law of an effect of combined
causes is resolved into the separate laws of the causes, together
with the fact of their combination. Secondly, when the law
which connects any two links, not proximate, in a chain of
causation, is resolved into the laws which connect each with
the intermediate links. Both of these are cases of resolving
one law into two or more ; in the third, two or more are
resolved into one: when, after the law has been shown to hold
good in several different classes of cases, we decide that what
is true in each of these classes of cases, is true under some
more general supposition, consisting of what all those classes
of cases have in common. We may here remark that this last
operation involves none of the uncertainties attendant on
induction by the Method of Agreement, since we need not
suppose the result to be extended by way of inference to any
new class of cases, different from those by the comparison of
which it was engendered.

In all these three processes, laws are, as we have seen,
resolved into laws more general than themselves ; laws ex-
tending to all the cases which the former extended to, and
others besides. In the first two modes they are also resolved
into laws more certain, in other words, more universally true
than themselves; they are, in fact, proved not to be themselves
laws of nature, the character of which is to be universally true,
but results of laws of nature, which may be only true condi-

EXPLANATION OF LAWS. 549

tionally, and for the most part. No difference of this sort
exists in the third case ; since here the partial laws are, in
fact, the very same law as the general one, and any exception
to them would be an exception to it too.

By all the three processes, the range of deductive science is
extended ; since the laws, thus resolved, may be thenceforth
deduced demonstratively from the laws into which they are
resolved. As already remarked, the same deductive process
which proves a law or fact of causation if unknown, serves to
explain it when known.

The word explanation is here used in its philosophical
sense. What is called explaining one law of nature by another,
is but substituting one mystery for another; and does nothing
to render the general course of nature other than mysterious :
we can no more assign a why for the more extensive laws
than for the partial ones. The explanation may substitute a
mystery which has become familiar, and has grown to seem
not mysterious, for one which is still strange. And this is the
meaning of explanation, in common parlance. But the process
with which we are here concerned often does the very contrary:
it resolves a phenomenon with which we are familiar, into one
of which we previously knew little or nothing; as when the
common fact of the fall of heavy bodies was resolved into the
tendency of all particles of matter towards one another. It
must be kept constantly in view, therefore, that in science,
those who speak of explaining any phenomenon mean (or
should mean) pointing out not some more familiar, but merely
some more general, phenomenon, of which it is a partial exem-
plification ; or some laws of causation which produce it by
their joint or successive action,. and from which, therefore, its
conditions may be determined deductively. Every such opera-
tion brings us a step nearer towards answering the question
which was stated in a previous chapter as comprehending the
whole problem of the investigation of nature, viz. What
are the fewest assumptions, which being granted, the order of
nature as it exists would be the result ? What are the fewest
general propositions from which all the uniformities existing
in nature could be deduced ?

The laws, thus explained or resolved, are sometimes said

550 INDUCTION.

to be accounted for ; but tbe expression is incorrect, if taken
to mean anything more than what has been already stated. In
minds not habituated to accurate thinking, there is often a
confused notion that the general laws are the causes of the
partial ones; that the law of general gravitation, for example,
causes the phenomenon of the fall of bodies to the earth. But
to assert this, would be a misuse of the word cause : terrestrial
gravity is not an effect of general gravitation, but a case of it ;
that is, one kind of the particular instances in which that
general law obtains. To account for a law of nature means,
and can mean, nothing more than to assign other laws more
general, together with collocations, which laws and collocations
being supposed, the partial law follows without any additional
supposition.

CHAPTER XIII.

MISCELLANEOUS EXAMPLES OF THE EXPLANATION OF
LAWS OF NATURE.

§ 1. THE most striking example which the history of
science presents, of the explanation of laws of causation and
other uniformities of sequence among special phenomena, by
resolving them into laws of greater simplicity and generality,
is the great Newtonian generalization : respecting which
typical instance so much having already been said, it is suf-
ficient to call attention to the great number and variety of the
special observed uniformities which are in this case accounted
for, either as particular cases, or as consequences, of one very
simple law of universal nature. The simple fact of a tendency
of every particle of matter towards every other particle, varying
inversely as the square of the distance, explains the fall of
bodies to the earth, the revolutions of the planets and satel-
lites, the motions (so far as known) of comets, and all the
various regularities which have been observed in these special
phenomena; such as the elliptical orbits, and the variations
from exact ellipses ; the relation between the solar distances
of the planets and the duration of their revolutions; the pre-
cession of the equinoxes ; the tides, and a vast number of
minor astronomical truths.

Mention has also been made in the preceding chapter of
the explanation of the phenomena of magnetism from laws of
electricity ; the special laws of magnetic agency having been
affiliated by deduction to observed laws of electric action, in
which they have ever since been considered to be included as
special cases. An example not so complete in itself, but even
more fertile in consequences, having been the starting point
of the really scientific study of physiology, is the affiliation,
commenced by Bichat, and carried on by subsequent biologists,

552 INDUCTION.

of the properties of the bodily organs, to the elementary
properties of the tissues into which they are anatomically
decomposed.

Another striking instance is afforded by Dalton's gene-
ralization, commonly known as the atomic theory. It had
been known from the very commencement of accurate chemical
observation, that any two bodies combine chemically with one
another in only a certain number of proportions ; but those
proportions were in each case expressed by a percentage — so
many parts (by weight) of each ingredient, in 100 of the
compound ; (say 35 and a fraction of one element, 64 and a
fraction of the other) : in which mode of statement no relation
was perceived between the proportion in which a given element
combines with one substance, and that in which it combines
with others. The great step made by Dalton consisted in per-
ceiving, that a unit of weight might be established for each
substance, such that by supposing the substance to enter into
all its combinations in the ratio either of that unit, or of some
low multiple of that unit, all the different proportions, pre-
viously expressed by percentages, were found to result. Thus
1 being assumed as the unit of hydrogen, if 8 were then taken
as that of oxygen, the combination of one unit of hydrogen
with one unit of oxygen would produce the exact proportion
of weight between the two substances which is known to exist
in water ; the combination of one unit of hydrogen with two
units of oxygen would produce the proportion which exists in
the other compound of the same two elements, called peroxide
of hydrogen ; and the combinations of hydrogen and of oxygen
with all other substances, would correspond with the suppo-
sition that those elements enter into combination by single
units, or twos, or threes, of the numbers assigned to them,
1 and 8, and the other substances by ones or twos or threes
of other determinate numbers proper to each. The result is
that a table of the equivalent numbers, or, as they are called,
atomic weights, of all the elementary substances, comprises in
itself, and scientifically explains, all the proportions in which
any substance, elementary or compound, is found capable of
entering into chemical combination with any other substance
whatever.

EXAMPLES OF THE EXPLANATION OF LAWS. 553

§ 2. Some interesting cases of the explanation of old
uniformities by newly ascertained laws are afforded by the
researches of Professor Graham. That eminent chemist was
the first who drew attention to the distinction which may be
made of all substances into two classes, termed by him crystal-
loids and colloids ; or rather, of all states of matter into the
crystalloid and the colloidal states, for many substances are
capable of existing in either. When in the colloidal state,
their sensible properties are very different from those of the
same substance when crystallized, or when in a state easily
susceptible of crystallization. Colloid substances pass with
extreme difficulty and slowness into the crystalline state, and
are extremely inert in all the ordinary chemical relations. Sub-
stances in the colloid state are almost always, when combined
with water, more or less viscous or gelatinous. The most
prominent examples of the state are certain animal and vege-
table substances, particularly gelatine, albumen, starch, the
gums, caramel, tannin, and some others. Among substances
not of organic origin, the most notable instances are hydrated
silicic acid, and hydrated alumina, with other metallic per-
oxides of the aluminous class.

Now it is found, that while colloidal substances are easily
penetrated by water, and by the solutions of crystalloid sub-
stances, they are very little penetrable by one another : which
enabled Professor Graham to introduce a highly effective pro-
cess (termed dialysis) for separating the crystalloid substances
contained in any liquid mixture, by passing them through a
thin septum of colloidal matter, which does not suffer any-
thing colloidal to pass, or suffers it only in very minute quan-
tity. This property of colloids enabled Mr. Graham to account
for a number of special results of observation, not previously
explained.

For instance, " while soluble crystalloids are always highly
sapid, soluble colloids are singularly insipid," as might be ex-
pected ; for, as the sentient extremities of the nerves of the
palate " are probably protected by a colloidal membrane," im-
permeable to other colloids, a colloid, when tasted, probably
never reaches those nerves. Again, " it has been observed
that vegetable gum is not digested in the stomach; the coats

554 INDUCTION*.

of that organ dialyse the soluble food, absorbing crystalloids,
and rejecting all colloids." One of the mysterious processes
accompanying digestion, the secretion of free muriatic acid by
the coats of the stomach, obtains a probable hypothetical
explanation through the same law. Finally, much light is
thrown upon the observed phenomena of osmose (the passage of
fluids outward and inward through animal membranes) by the
fact that the membranes are colloidal. In consequence, the
water and saline solutions contained in the animal body pass
easily and rapidly through the membranes, while the sub-
stances directly applicable to nutrition, which are mostly col-
loidal, are detained by them.*

The property which salt possesses of preserving animal
substances from putrefaction is resolved by Liebig into two
more general laws, the strong attraction of salt for water, and
the necessity of the presence of water as a condition of putre-
faction. The intermediate phenomenon which is interpolated
between the remote cause and the effect, can here be not
merely inferred but seen ; for it is a familiar fact, that flesh
upon which salt has been thrown is speedily found swimming
in brine.

The second of the two factors (as they may be termed)
into which the preceding law has been resolved, the necessity
of water to putrefaction, itself affords an additional example
of the Eesolution of Laws. The law itself is proved by the
Method of Difference, since flesh completely dried and kept
in a dry atmosphere does not putrefy ; as we see in the case of
dried provisions, and human bodies in very dry climates. A
deductive explanation of this same law results from Liebig's
speculations. The putrefaction of animal and other azotised
bodies is a chemical process, by which they are gradually dis-
sipated in a gaseous form, chiefly in that of carbonic acid and
ammonia ; now to convert the carbon of the animal substance
into carbonic acid requires oxygen, and to convert the azote

* Vide Memoir by Thomas Graham, F.R.S., Master of the Mint, "On
Liquid Diffusion Applied to Analysis," in the Philosophical Transactions for
1862, reprinted in the Journal of the Chemical Society, and also separately aa
a pamphlet.

EXAMPLES OF THE EXPLANATION OF LAWS. 555

into ammonia requires hydrogen, which are the elements of
water. The extreme rapidity of the putrefaction of azotised
substances, compared with the gradual decay of non-azotised
hodies (such as wood and the like) by the action of oxygen
alone, he explains from the general law that substances are
much more easily decomposed by the action of two different
affinities upon two of their elements, than by the action of
only one.

§ 3. Among the many important properties of the nervous
system which have either been first discovered or strikingly
illustrated by Dr. Brown-Sequard, I select the reflex influence
of the nervous system on nutrition and secretion. By reflex
nervous action is meant, action which one part of the nervous
system exerts over another part, without any intermediate
action on the brain, and consequently without consciousness ;
or which, if it does pass through the brain, at least produces
its effects independently of the will. There are many experi-
ments which prove that irritation of a nerve in one part of
the body may in this manner excite powerful action in another
part; for example, food injected into the stomach through a
divided oesophagus, nevertheless produces secretion of saliva;
warm water injected into the bowels, and various other irrita-
tions of the lower intestines, have been found to excite secre-
tion of the gastric juice, and so forth. The reality of the
power being thus proved, its agency explains a great variety
of apparently anomalous phenomena; of which I select the
following from Dr. Brown-Sequard's Lectures on the Nervous
System :

The production of tears by irritation of the eye, or of the
mucous membrane of the nose :

The secretions of the eye and nose increased by exposure
of other parts of the body to cold :

Inflammation of the eye, especially when of traumatic
origin, very frequently excites a similar affection in the other
eye, which may be cured by section of the intervening
nerve :

Loss of sight sometimes produced by neuralgia; and has

556 INDUCTION.

been known to be at once cured by the extirpation (for in-
stance) of a carious tooth :

Even cataract has been produced in a healthy eye by
cataract in the other eye, or by neuralgia, or by a wound of
the frontal nerve :

The well-known phenomenon of a sudden stoppage of the
heart's action, and consequent death, produced by irritation
of some of the nervous extremities : e.g., by drinking very
cold water ; or by a blow on the abdomen, or other sudden
excitation of the abdominal sympathetic nerve ; though this
nerve may be irritated to any extent without stopping the heart's
action, if a section be made of the communicating nerves :

The extraordinary effects produced on the internal organs
by an extensive burn on the surface of the body ; consisting
in violent inflammation of the tissues of the abdomen, chest,
or head: which, when death ensues from this kind of injury,
is one of the most frequent causes of it :

Paralysis and anesthesia of one part of the body from
neuralgia in another part; and muscular atrophy from neu-
ralgia, even when there is no paralysis :

Tetanus produced by the lesion of a nerve ; Dr. Brown-
Sequard thinks it highly probable that hydrophobia is a phe-
uomenon of a similar nature :

Morbid changes in the nutrition of the brain and spinal
cord, manifesting themselves by epilepsy, chorea, hysteria, and
other diseases, occasioned by lesion of some of the nervous
extremities in remote places, as by worms, calculi, tumours,
carious bones, and in some cases even by very slight irrita-
tions of the skin.

§ 4. From the foregoing and similar instances, we may
see the importance, when a law of nature previously unknown
has been brought to light, or when new light has been thrown
upon a known law by experiment, of examining all cases
which present the conditions necessary for bringing that law
into action; a process fertile in demonstrations of special laws
previously unsuspected, and explanations of others already
empirically known.

EXAMPLES OF THE EXPLANATION OP LAWS. 557

For instance, Faraday discovered by experiment, that
voltaic electricity could be evolved from a natural magnet,
provided a conducting body were set in motion at right angles
to the direction of the magnet : and this he found to hold
not only of small magnets, but of that great magnet,the earth.
The law being thus established experimentally, that electricity
is evolved, by a magnet, and a conductor moving at right
angles to the direction of its poles, we may now look out for
fresh instances in which these conditions meet. Wherever a
conductor moves or revolves at right angles to the direction
of the earth's magnetic poles, there we may expect an evolu-
tion of electricity. In the northern regions, where the polar
direction is nearly perpendicular to the horizon, all horizontal
motions of conductors will produce electricity ; horizontal
wheels, for example, made of metal ; likewise all running
streams will evolve a current of electricity, which will circulate
round them ; and the air thus charged with electricity may be
one of the causes of the Aurora Borealis. In the equatorial
regions, on the contrary, upright wheels placed parallel to the
equator will originate a voltaic circuit, and waterfalls will
naturally become electric.

For a second example ; it has been proved, chiefly by
the researches of Professor Graham, that gases have a
strong tendency to permeate animal membranes, and diffuse
themselves through the spaces which such membranes in-
close, notwithstanding the presence of other gases in those
spaces. Proceeding from this general law, and reviewing a
variety of cases in which gases lie contiguous to membranes,
we are enabled to demonstrate or to explain the following
more special laws: 1st. The human or animal body, when
surrounded with any gas not already contained within the
body, absorbs it rapidly ; such, for instance, as the gases of
putrefying matters : which helps to explain malaria. 2nd. The
carbonic acid gas of effervescing drinks, evolved in the stomach,
permeates its membranes, and rapidly spreads through the
system. 3rd. Alcohol taken into the stomach passes into
vapour and spreads through the system with great rapidity;
(which, combined with the high combustibility of alcohol, or in

558 INDUCTION^

other words its ready combination with oxygen, may perhaps
help to explain the hodily warmth immediately consequent on
drinking spirituous liquors.) 4th. In any state of the hody in
which peculiar gases are formed within it, these will rapidly
exhale through all parts of the body ; and hence the rapidity
with which, in certain states of disease, the surrounding atmo-
sphere becomes tainted. 5th. The putrefaction of the interior
parts of a carcase will proceed as rapidly as that of the
exterior, from the ready passage outwards of the gaseous pro-
ducts. 6th. The exchange of oxygen and carbonic acid in
the lungs is not prevented, but rather promoted, by the inter-
vention of the membrane of the lungs and the coats of the
blood-vessels between the blood and the air. It is necessary,
however, that there should be a substance in the blood with
which the oxygen of the air may immediately combine ;
otherwise instead of passing into the blood, it would permeate
the whole organism : and it is necessary that the carbonic
acid, as it is formed in the capillaries, should also find a sub-
stance in the blood with which it can combine ; otherwise it
would leave the body at all points, instead of being discharged
through the lungs.

§ 5. The following is a deduction which confirms, by ex-
plaining, the empirical generalization, that soda powders
weaken the human system. These powders, consisting of a
mixture of tartaric acid with bicarbonate of soda, from which
the carbonic acid is set free, must pass into the stomach as
tartrate of soda. Now, neutral tartrates, citrates, and acetates
of the alkalis are found, in their passage through the system,
to be changed into carbonates ; and to convert a tartrate into
a carbonate requires an additional quantity of oxygen, the
abstraction of which must lessen the oxygen destined for
assimilation with the blood, on the quantity of which the
vigorous action of the human system partly depends.

The instances of new theories agreeing with and explaining
old empiricisms, are innumerable. All the just remarks made
by experienced persons on human character and conduct, are
so many special laws, which the general laws of the human

EXAMPLES OF THE EXPLANATION OF LAWS. 559

mind explain and resolve. The empirical generalizations ou
which the operations of the arts have usually been founded,
are continually justified and confirmed on the one hand, or
corrected and improved on the other, by the discovery of the
simpler scientific laws on which the efficacy of those operations
depends. The effects of the rotation of crops, of the various
manures, and other processes of improved agriculture, have
been for the first time resolved in our own day into known laws
of chemical and organic action, by Davy, Liebig, and others.
The processes of the medical art are even now mostly empirical :
their efficacy is concluded, in each instance, from a special and
most precarious experimental generalization : but as science
advances in discovering the simple laws of chemistry and
physiology, progress is made in ascertaining the intermediate
links in the series of phenomena, and the more general laws
on which they depend ; and thus, while the old processes are
either exploded, or their efficacy, in so far as real, explained,
better processes, founded on the knowledge of proximate
causes, are continually suggested and brought into use.*
Many even of the truths of geometry were generalizations
from experience before they were deduced from first prin-
ciples. The quadrature of the cycloid is said to have been
first effected by measurement, or rather by weighing a
cycloidal card, and comparing its weight with that of a piece
of similar card of known dimensions.

§ 6. To the foregoing examples from physical science,
let us add another from mental. The following is one of the

* It was an old generalization in surgery, that tight bandaging had a ten-
dency to prevent or di>sipate local inflammation. This sequence, being, in the
progress of physiological knowledge, resolved into more general laws, led to
the important surgical invention made by Dr. Arnott, the treatment of local
inflammation and tumours by means of an equable pressure, produced by a
bladder partially fillei with air. The pressure, by keeping back the blood
from the part, prevents the inflammation, or the tumour, from being nourished :
iu the case of inflammation, it removes the stimulus, which the organ is unfit
to receive ; in the case of tumours, by keeping back the nutritive fluid, it
causes the absorption of matier to exceed the supply, and the diseased mass is
gradually absorbed aud disappears.

560 INDUCTION.

simple laws of mind : Ideas of a pleasurable or painful cha-
racter form associations more easily and strongly than other
ideas, that is, they become associated after fewer repetitions,
and the association is more durable. This is an experimental
law, grounded on the Method of Difference. By deduction
from this law, many of the more special laws which expe-
rience shows to exist among particular mental phenomena
may be demonstrated and explained : — the ease and rapidity,
for instance, with which thoughts connected with our passions
or our more cherished interests are excited, and the firm hold
which the facts relating to them have on our memory ; the
vivid recollection we retain of minute circumstances which
accompanied any object or event that deeply interested us,
and of the times and places in which we have been very happy
or very miserable ; the horror with which we view the acci-
dental instrument of any occurrence which shocked us, or the
locality where it took place, and the pleasure we derive from
any memorial of past enjoyment ; all these effects being pro-
portional to the sensibility of the individual mind, and to the
consequent intensity of the pain or pleasure from which the
association originated. It has been suggested by the able
writer of a biographical sketch of Dr. Priestley in a monthly
periodical,* that the same elementary law of our mental con-
stitution, suitably followed out, would explain a variety of
mental phenomena previously inexplicable, and in particular
some of the fundamental diversities of human character and
genius. Associations being of two sorts, either between
synchronous, or between successive impressions; and the
influence of the law. which renders associations stronger in
proportion to the pleasurable or painful character of the im-
pressions, being felt with peculiar force in the synchronous
class of associations; it is remarked by the writer referred
to, that in minds of strong organic sensibility synchronous
associations will be likely to predominate, producing a ten-
dency to conceive things in pictures and in the concrete,
richly clothed in attributes and circumstances, a mental habit

* Since acknowledged and reprinted in Mr. Martineau's Miscellanies.

KXAMPLES OF THE EXPLANATION OF LAWS. 561

which is commonly called Imagination, and is one of the
peculiarities of the painter and the poet; while persons of more
moderate susceptibility to pleasure and pain will have a ten-
dency to associate facts chiefly in the order of their succes-
sion, and such persons, if they possess mental superiority, will
addict themselves to history or science rather than to creative
art. This interesting speculation the author of the present
work has endeavoured, on another occasion, to pursue farther,
and to examine how far it will avail towards explaining the
peculiarities of the poetical temperament.* It is at least an
example which may serve, instead of many others, to show
the extensive scope which exists for deductive investigation
in the important and hitherto so imperfect Science of
Mind.

§ 7. The copiousness with which the discovery and ex-
planation of special laws of phenomena by deduction from
simpler and more general ones has here been exemplified, was
prompted by a desire to characterize clearly, and place in its
due position of importance, the Deductive Method; which, in
the present state of knowledge, is destined henceforth irrevo-
cably to predominate in the course of scientific investigation.
A revolution is peaceably and progressively effecting itself in
philosophy, the reverse of that to which Bacon has attached
his name. That great man changed the method of the sciences
from deductive to experimental, and it is now rapidly reverting
from experimental to deductive. But the deductions which
Bacon abolished were from premises hastily snatched up, or
arbitrarily assumed. The principles were neither established
by legitimate canons of experimental inquiry, nor the results
tested by that indispensable element of a rational Deductive
Method, verification by specific experience. Between the pri-
mitive method of Deduction and that which I have attempted
to characterize, there is all the difference which exists between
the Aristotelian physics and the Newtonian theory of the
heavens.

* Dissertations and Discussions, vol. i., fourth paper.

VOL. i. 36

562 INDUCTION.

It would, however, be a mistake to expect that those great
general] Ziitions, from which the subordinate truths of the
more backward sciences will probably at some future period be
deduced by reasoning (as the truths of astronomy are deduced
from the generalities of the Newtonian theory), will be found,
in all, or even in most cases, among truths now known and
admitted. We may rest assured, that many of the most
general laws of nature are as yet entirely unthought of; and
that many others, destined hereafter to assume the same cha-
racter, are known, if at all, only as laws or properties of some
limited class of phenomena; just as electricity, now recognised
as one of the most universal of natural agencies, was once
known only as a curious property which certain substances
acquired by friction, of first attracting and then repelling light
bodies. If the theories of heat, cohesion, crystallization, and
chemical action, are destined, as there can be little doubt that
they are, to become deductive, the truths which will then be
regarded as the principia of those sciences would probably, if
now announced, appear quite as novel* as the law of gravita-
tion appeared to the cotemporaries of Newton ; possibly even
more so, since Newton's law, after all, was but an extension of
the law of weight — that is, of a generalization familiar from of
old, and which already comprehended a not inconsiderable
body of natural phenomena. The general laws of a similarly
commanding character, which we still look forward to the dis-
covery of, may not always find so much of their foundations
already laid.

These general truths will doubtless make their first ap-
pearance in the character of hypotheses ; not proved, nor even
admitting of proof, in the first instance, but assumed as pre-
mises for the purpose of deducing from them the known laws
of concrete phenomena. But this, though their initial, cannot
be their final state. To entitle an hypothesis to be received as
one of the truths of nature, and not as a mere technical help
to the human faculties, it must be capable of being tested by

* Written before the rise of the new views respecting the relation of heat to
mechanical force ; but confirmed rather than contradicted by them.

EXAMPLES OF THE EXPLANATION OF LAWS. 563

the canons of legitimate induction, and must actually have
been submitted to that test. When tbis sball have been done,
and done successfully, premises will have been obtained from
which all the other propositions of the science will thence-
forth be presented as conclusions, and the science will, by
means of a new and unexpected Induction, be rendered
Deductive.

END OF VOL, I.

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