Logic ; Vol. I ; The Judment, Concept, and Inference (1895)

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EDITED BY J.

H.

MUIRHEAD,

M.A.

THE LIBRARY OF PHILOSOPHY. THE LIBRARY OF

PHILOSOPHY

is

in

the

first

in

While a contribution to the History of Thought. much has been done in England in tracing the course of evolu tion in nature, history, religion, and morality, comparatively little has been done in tracing the development of Thought the evolution of these and kindred subjects, and yet stance

"

upon

is part of the whole evolution." This Library will deal mainly with Modern Philosophy, has already had a fair partly because Ancient Philosophy share of attention in this country through the labours of Grote, Ferrier, and others, and more recently through translations from Zeller partly because the Library does not profess to give a complete history of thought. By the co-operation of different writers in carrying out this

opinion

;

plan, it is hoped that a completeness and thoroughness of treat ment otherwise unattainable will be secured. It is believed, also, that from writers mainly English and American fuller

consideration of English Philosophy than it has hitherto re ceived from the great German Histories of Philosophy may be looked for. In the departments of Ethics, Economics, and for instance, the contributions of

English writers to stock of theoretic discussion have been especially valuable, and these subjects will accordingly have special pro minence in this undertaking. Another feature in the plan of the Library is its arrange ment according to subjects rather than authors and dates, enabling the writers to follow out and exhibit in a way hitherto unattempted the results of the logical development of particular lines of thought. Politics,

the

common

The

historical

portion of the Library is divided into two first contains works upon the develop ment of particular schools of Philosophy, while the second ex hibits the history of theory in particular departments. The bird series contains original contributions to Philosophy, and the fourth translations of valuable foreign works. To these has been added, by way of Introduction to the whole Library, an English translation of Erdmann s History sections, of

which the

sophy,"

long since recognised in J. ii

H.

Germany

as the

MUIRHEAD, General Editor.

ALREAD Y PUBLISHED. By DR. JOHANN EDUARD ERDMANN.

THE HISTORY OF PHILOSOPHY.

Edited by WlLLiSTON S. HOUGH, M.Ph., Professor of English Translation. Mental and Moral Philosophy and Logic in the University of Minnesota. In 3 vols., medium 8vo, cloth.

Vol.1. Ancient and Mediaeval Philosophy,

1

$s.

.

.

.

Third Edition.

Modern Philosophy, 15.? Third Edition. Modern Philosophy since Hegel, 12s. Third Edition. THE HISTORY OF ESTHETIC. By BERNARD BOSANQUET, M.A., LL.D., late Fellow of University College, Oxford. [SECOND SERIES. THE DEVELOPMENT OF RATIONAL THEOLOGY since Kant. By PROFESSOR OTTO PFLEIDERER, of Berlin. [SECOND SERIES. Second Edition. PHILOSOPHY AND POLITICAL ECONOMY IN SOME OF THEIR HISTORICAL RELATIONS. LL.D. M.A., BONAR, [SECOND SERIES. By JAMES APPEARANCE AND REALITY. By F. H. BRADLEY, M.A., Fellow of Merton College, Oxford. [THIRD SERIES. NATURAL RIGHTS. By DAVID G. RITCHIE, Professor of Logic and Metaphysics in the University of St. Andrews. [THIRD SERIES. Vol. II. Vol. III.

SIGWART

S

.

LOGIC.

Translated by

HELEN DENDY.

OF WORKS

LIST

IN

.

2 vols.

.

[FOURTH SERIES.

PREPARATION.

FIRST SERIES. EARLY IDEALISM

:

By W.

Descartes to Leibnitz.

COURTNEY, M.A., LL.D.

L.

(St.

Andrews), Fellow of New College, Oxford. GERMAN IDEALISTS Kant to Hegel. By WM. WALLACE, M.A., Whyte Professor of Moral Philosophy, University of Oxford. :

Leibnitz, Herbart, Lotze. By ANDREW SETH, M.A., Professor of Logic and English Literature, University of Edinburgh. SENSATIONALISTS: Locke to Mill. By W. S. HOUGH, M.Ph., Professor of Mental and Moral Philosophy, University of Minnesota, U.S.A. THE UTILITARIANS Hume to Contemporary Writers. By W. R. SORLEY, M.A., Fellow of Trinity College, Cambridge, and Professor of Philosophy in University College, Cardiff. PRINCIPLE OF EVOLUTION IN ITS SCIENTIFIC AND PHILOSOPHICAL ASPECTS. By JOHN

MODK.RN REALISTS:

:

WATSON, LL.D.,

Professor

of

Moral Philosophy, University of Queen

s

College,

Kingston, Canada.

SECOND SERIES. THE HISTORY OF PSYCHOLOGY

:

Empirical and Rational.

By ROBERT ADAMSON, M.A.,

LL.D., Professor of Logic, University of Aberdeen.

THE HISTORY OF POLITICAL PHILOSOPHY.

By D. G.

RITCHIE, M.A., Professor of

Logic and Metaphysics in the University of St. Andrews, and J. II. MUIRHEAD, M.A., Lecturer in Philosophy, Royal Holloway College, Egham, and Bedford College,

London.

THE HISTORY OF THE PHILOSOPHICAL TENDENCIES OF THE NINETEENTH CENTURY. ByJosiAH ROYCE,

Professor of Philosophy, Harvard University.

THIRD SERIES. FIRST PRINCIPLES OF PHILOSOPHY. By JOHN STUART MACKENZIE, M.A., Fellow of Trinity College. Cambridge. THE THEORY OF ETHICS. By EDWARD CAIRD, LL.D., Master of Balliol College, Oxford.

OR, THE THEORY OF KNOWLEDGE. By JAMES WARD, D.Sc., LL.D., Fellow and Lecturer of Trinity College, Cambridge. PRINCIPLES OF PSYCHOLOGY. By G. F. STOUT, M.A., Fellow of St. John s College, {Shortly. Cambridge. PRK-JCIPLES OF INSTRUMENTAL LOGIC. By JOHN DEWEY, Ph.D., Professor of Philo

EPISTEMOLOGY

;

sophy, University of Michigan.

SWAN SONNENSCHEIN & MACMILLAN &

Co.,

Co.,

NEW

LONDON.

YORK.

LOGIC BY

DR.

CHRISTOPH SIGWART

Professor of Philosophy at the University of Tubingen

VOL.

I

THE JUDGMENT, CONCEPT, AND INFERENCE SECOND EDITION, REVISED AND ENLARGED

TRANSLATED BY HELEN BENDY

SWAN SONNENSCHEIN NEW YORK: MACMILLAN 1895

& CO. & CO.

BUTLER & TANNER,

THE SELWOOD PRINTING WORKS, FROME, AND LONDON.

AUTHOR S PREFACE TO THE ENGLISH TRANSLATION WHEN

was requested to give

I I

Logic,

complied

willingly,

an essential part of Francis

my

Bacon down

to Jevons, Bradley,

find in

one

s

own language

this

work

to English logicians

from

and Venn

;

thus I

may hope

of the task

it is

;

simple and current expressions which might

culties

own language and

that Miss

and avoid

and the

translator

double

manuscript from beginning to proofs,

so that

completely free as

I

may

safely

danger.

end, assure

I

and

Miss Dendy

of

text, or

have carefully revised

and co-operated the

exactly as possible the original text.

really faithful

beset

best to overcome these

reader

from misunderstandings, and that

hearty thanks to

is

impairing easy understanding.

Dendy has done her

this

I

feel

for the trouble

that it

in correcting

the

diffi

her the

translation

obliged to express

my

she has taken to give

C.

1894.

is

represents everywhere

reliable translation.

TUBINGEN, November,

is

sometimes impossible to

by the danger of either missing the precise meaning of the

I think

that

to translate a philosophical treatise

exactly correspond to the terms of the original,

straining his

my

not appear entirely as a foreigner.

will

difficulties

and achieving

in preparing

had been devoted

Whoever has himself attempted acquainted with the

consent to an English translation of

because

studies

my book

to English readers

my

SIGWART.

a

AUTHOR S PREFACE TO FIRST GERMAN EDITION THE

following attempt to reconstruct logic from

methodology, thus bringing

it

the

point of view of

into active relations with the scientific prob

lems of the present day, must be justified by the success with which carried out

;

this first

parts of the doctrine,

and

in

them

I

the traditional form of the science. to

which

I

have adhered as closely as possible to I

would only ask that the small extent

have referred to previous and contemporary treatments of the

subject as a whole, or to particular views on special points,

that to

commend

or dispute even the

of investigation

discussed

may it

not be

seemed

to

most important previous doctrines

would be an undue extension of the work course

much

In a science which has been so

taken amiss.

me

it is

volume contains the preliminary and fundamental

;

and

further

I

feared lest the

and exposition prescribed by my view of the

subject would be confused

if

I

made

a rule of discussing at every point

opinions which are to a large extent based upon presuppositions quite different

from

my

own.

I

to

what was indispensable

of

my own

doctrine.

I

have therefore thought

need hardly say that

been most frequently before me, and to

I

whom

Trendelenburg, Ueberweg and Mill

was being planned and carried out

;

I

and

justification

have made extensive use of

I

hoped here

to express

my

have died while the book

must also make special mention of

the assistance I have received from Prantl

fuly, 1873.

right to confine myself

Three of the men whose works have

both ancient and modern authors.

obligation

it

for the correct representation

s

great work.

AUTHOR S PREFACE TO SECOND GERMAN EDITION IN the

which have passed since

fifteen years

literature of logic

book

this

first

appeared the

has been enriched by a remarkable series of valuable

Important works have appeared by Lotze, Schuppe, Wundt and Bradley to name only the most eminent ; and all start from the concep That is, logic is grounded by them, tion which has guided this attempt. books.

not upon an effete tradition, but upon a is

actually

and

its

in

its

new

investigation of thought as

psychological foundations, in its significance for

actual operation in scientific methods.

again, have received

s

welcome elucidations from more

treatment

of

relational-concepts,

most nearly akin to has thus become incumbent upon

original treatise are It

the conclusions arrived at by

my

my me

knowledge

Particular points of logic,

and amongst these Windelband s studies on

Meinong

it

the

and

special investigations,

negative

Volkelt

s

judgment, acute

and

views. to test

fellow-workers,

anew my own views by to find more accurate

expression where misunderstanding might arise, and elsewhere to amplify and extend, or to fortify against adverse opinions. But for the reasons already stated in

corporating

more

my

first

preface, I have

extensively in the

been obliged

to refrain

from

in

work the considerations which deter

mined me to adhere to my conclusions, or from mentioning in detail all the critical observations which have been so abundantly bestowed. Where these criticisms were really applicable to what I had said, I have gratefully use of them ; where they were due merely to misunderstandings, I was loth to weary the reader with unfruitful discussions. In the same

made way

I

have been forced

to

abstain from

enriching the work by intro

ducing more freely investigations not included in

its

original design, even

might agree with them the subject is so inexhaustible that com pleteness is not attainable, and I would rather sacrifice the appearance of

though

I

;

completeness in treatment than obscure the clearness of the design. TUBINGEN,

October, 1888.

CONTENTS. PAGE

I

/ INTRODUCTION i. The Problem 2. 3.

^/

4.

PARTI.

Limits to the Problem

The The

CHAPTER

I.

6. 7.

8.

CHAPTER

II.

The

9.

10. II. 12. X

3-

14.

i

.

10

.

l T

The

Nature of Judgment and its Presuppositions Proposition as the Expression of the Judgment. Subject and Predicate .

The General Idea and Necessity of the Word

the

2?

....

Word

.

29

.

29

40

....... -...... .......

as Predicate

Simple Judgments

Denominative Judgments. Judgments of Attributes and Activities Impersonal Judgments and Allied Forms

Validity of the

cj

e? c-j

r?

58

Relational Judgments. Existential Propositions Judgments about Abstract Nouns

The Objective

Words

Judgment,

....

59 65 77

and the Principle of

Identity 15.

II.

III.

1

79 to

Time

in Narrative

Judgments

6.

.

.

.

...

The Act

Judgments Immediate and Mediated, Analytical and Synthetical Judgments The Process of the Synthetical Judgment 19. CHAPTER IV. The Negation 20. The Negation as Denial of the Judgment 21. The Different Kinds of Negative Judgments 22. Privation and Opposition as Ground of the Negation 1

8.

...... .

23. ,

*

.89-

Explicative Judgments of Judgment as expressed in . Language III. How Judgments arise, and the Distinction between Analytical and \S Synthetical

17.

CHAPTER

The Reference

24. 25.

The The The

^ 6

23

.

..........

Ideas as Elements of Judgments and their Relation to The Highest Categories of the Objects of Thought

Narrative Judgments

I.

t

Postulate of Logic Divisions of Logic

Analytical. 5.

.......

of Logic

Principle of Contradiction Principle of Twofold Negation Principle of the Excluded Middle

.

.

yO 93 IO2 102 112

IIy no, 123 .

127 i ->9

^8 .

CONTENTS

x ji

PAGE

CHAPTER

V.

Plural Judgments Positive Plural Judgments

I.

Positive Copulative

26.

The

27.

and Plural Judgments

57

1

Universal Affirmative Judgment

60

166

29.

Negative Plural Judgments

1

II.

III.

30.

The Negation

I? 2

CHAPTER I.

VI.

Possibility

of Plural Judgments

and Necessity

32.

The Necessity

34.

Possibility

CHAPTER

VII.

I.

35.

II.

36.

189

III.

37.

RESULTS

PART

II.

Different

203

Ways

in

213

which Propositions may be Combined, and .

.

.

.

.214

.

220

The Hypothetical Judgment The Disjunctive Judgment

228 232

...... ....... ....

The Concept Nature of the Logical Concept

I.

43.

Analysis of the Concept into Simple Elements. Super- and Subordination, Content and Extension of Concepts Division of Concepts

44.

Definition

41.

42.

.

The Truth of Immediate Judgments The Truth of Judgments about Concepts The Truth of Statements about Ourselves The Truth of Judgments of Perception

II.

45. 46.

47.

301

The

49.

52

-

53. 5455. 56. 5.7.

58.

59-

APPENDIX A APPENDIX B APPENDIX C

Different Sources of Hypothetical Inferences according to Formal

Major Premises

Logical

The The The The

.

-315 .

.

.

330

.

.

336 338 343

.

.

.

Inference of Subsumption Inference from Divisive Judgments

Disjunctive Syllogism Relation between the Truth of the Conclusion and the Truth of the Premises

*"

326 326

Laws

Inferences from Relations between Concepts The meaning of the Aristotelian Figures and Moods. The Value of the Syllogism

254

265 277 286

306

50.

III.

245 245

295

51.

48.

CHAPTER

237

239

295

Axioms and Postulates The Rules of Inference as the Ground for Mediated Judgments The Hypothetical Syllogism The Introduction of a Subject in the Hypothetical Syllogism

s>r>

,

196

38

CHAPTER

196

.

Hypothetical and Disjunctive Judgments

The

40.

y

.

Regulative The Conditions of Perfect Judgments 39.

CHAPTER

\/

Judgments

of Reality

their Logical Significance

^

176

Possible and Necessary as Predicates of Actual 33.

1

I?6

The so-called Modal Distinctions The Law of Sufficient Reason

31.

II.

,

57

:

157

-The Particular Affirmative Judgment

28.

!

349 357 367

368 371

373 ,-oj

>_

o^3 O

.

GENERAL INTRODUCTION IF

we

consider the nature of our Thought,

part of

in the

it is

engaged are certain and universally

when

of ascertaining the

the rules to be followed in

problem would place us

in

in

To

i.

it

frequently

Hence

It

is

logy.

Such a science we

different varieties,

true there

which we can

enough to

refer,

is

fails

do

to

this

this

problem object can be

solution of this

possession of a technical science of

in

at certain call

is

and universally

Logic.

general

other psychical activities, in what relations its

which

arises the

The

attainment.

determine what Thinking

what are

an important

accordance with those conditions

its

Thought, directing us how to arrive valid propositions.

find that

under which

conditions

and of determining

attained,

but that

valid,

to its natural development.

left

we

attempt to arrive at propositions

it

is,

how

it

differs

from

stands to these, and

primarily the business of Psycho

no generally accepted

Psychology to it will be

but for our present investigation

refer to our ordinary use of language.

By Thinking

in

we always mean an Ideational Activity i.e. an which in itself does not include that inner subjective ex activity citement which we call Feeling, nor yet give rise to an immediate widest sense

its

effect it

upon ourselves or others

signifies

is

that something

;

as in willing is

present

and

to

acting.

All that

consciousness as

its

must however be further distinguished from Perception object. and Intuition these express immediate reference to an object It

;

which s.

L,

is

given to the subjective activity independently of B

itself,

GENERAL INTRODUCTION

2

while Thinking denotes a purely inner activity of ideation, thus to be a spontaneous action proceeding from the energy

seeming

of the subject alone.

Its

thoughts

products

are therefore dis

the objects tinguished, as merely subjective, ideal images, from which are looked upon as real in Perception and Intuition. In this sense

language gives the name of Thinking to Recollection

bethinking oneself of something, and

to

Imagination, picturing

and consideration. something But when Perception and Thought refer to the same object, as in in

Thought, as well as to reflection

knowledge of the external world, we distinguish between the spontaneous selection, combination and elaboration of the elements given to Perception, elements. to

and

the immediate

the former which

It is

we regard

of those

presentation

as the factor belonging

Thought. 2.

If for

the present

we take Thinking

to

mean

all

that

we mean

our ordinary use of language, then it is certain that with the development of conscious life Thought arises involuntarily and

by

it

in

As

of necessity.

soon as the individual begins to reflect upon his

inner activity he finds that he

of

Thought

;

ginning nor of activities.

is already engaged in various kinds he can have no immediate knowledge of its be

development out of simpler and more primitive

its

Only by means of a difficult psychological analysis of we find it at work, can we discover its

Thought, as factors

and the

particular

faculties

idea of the laws of

Moreover the

its

which give

rise to

it,

and thus form some

unconscious growth.

involuntary

throughout our whole

life.

production It

is

of

thoughts

continues

absolutely impossible,

when

conscious and awake, to

check the inner activity which is in cessantly excited by the most varied motives to form a constant succession of ideas which

combines in different ways, and thus, without any intention on our part, maintains an inner world of thoughts present before us. 3-

But besides

this

it

involuntary Thought, there

is

a voluntary

GENERAL INTRODUCTION which

action, a will to think,

to

endeavour to rule the

thoughts and

losing

led

by

arise

of

formerly involuntary

sight

involuntarily this

some

and aims

definite interests

them towards a given end.

to direct

the thoughts which selection,

is

3

course

the

From amongst makes

activity

altogether and

of

retaining

its

and

developing others by means of attention, thus seeking for thoughts and pursuing them. We need not enter here upon the question as to whether the production of thoughts in

a direct way, or whether

we can only

The

result is practically the

ever really voluntary

indirectly bring about the

conditions necessary to the involuntary desired.

is

production of

same

thoughts which satisfy a definite interest

in

both cases

;

are produced

what

is

that

is,

by the

influence of the will. 1

But

this interest

is

of

two

kinds.

From one

point of view the

voluntary activity which we direct towards our Thought falls under the general law that the pleasant is sought after, the un

Now we may

pleasant avoided.

a double sense.

Firstly, in so

far

regard Thought as pleasant in as every natural activity gives

a feeling of satisfaction within certain limits of intensity in so far as the

;

secondly,

manifold content of our Thought affects us plea

santly or unpleasantly.

Taking this question of pleasure alone, we find within us both a general tendency to excite Thought, or let it be excited, as an entertainment and escape from tedium and also a tendency to direct it in such a way that what we think may be pleasing to us. ;

When we

linger over pleasant

them, when we make strive to

chase

recollections

projects and build

away disagreeable

and anxiety, then

it

is

this

and seek to intensify

castles in the air,

when we

recollections or to dispel

fear

motive which determines the influence

of the will upon our Thought. 1

Cf.

Windelband,

treatment contains

not seem to

me

conscious willing.

to

iiber

much

His und Nachdenken (PrdluJien, p. 176 sq.). and valuable on certain points, although he docs determined the relation between "unconscious" and

Denken

that

is

have rightly

true

GENERAL INTRODUCTION

4

The

which

satisfaction

its

such cases

of a completely

is

the particular subject refers only to

individual character; to

arises in

itself,

own peculiar nature and circumstances. As a rule, therefore, of this kind varies with each individual, nor could we

Thought wish 4. is

it

otherwise.

But

immediate pleasure from Thought of the two. By far the most important

this desire of obtaining

the subordinate interest

and

both in extent part of our mental activity,

more

in value, follows

serious aims.

In the

Thought

first

place, our

into

their

wants and the necessities of

service

and

set

consciously grasped and pursued.

being depend upon

before

its

Our existence and our

well-

This action does not

purpose with the ease and certainty of instinct

calls for attentive

and of

take

conscious action and upon our influencing

things around us to serve our purposes.

accomplish

life

aims which are

it

and

;

it

careful observation of the nature of things

their relations to us, as well

as for manifold calculations

and considerations as to the way in which they may serve for a means to the satisfaction of our wants. Human Thought attains its end the preservation of our well-being only when its know ledge of things enables

it

to predict the future

;

when, therefore,

anticipation coincides with the actual course of events as partly

conditioned by our interference.

But the desire seeks a right

knowledge which makes itself felt everywhere understanding of things and their relations even for

beyond the sphere of our

knowing and thus

it

urges

Thought

practical needs,

Solely for the sake of

to penetrate into the nature of things,

to reproduce in the totality of our subjective

knowledge

a faithful and complete picture of the Satisfac objective world. tion of the desire for knowledge must then include this aim of

Thought also. The immediate purpose which excites and determines its direction is Thought knowledge of that which practical

is.

GENERAL INTRODUCTION

5

5. But the purposes towards which Thought is directed are far from being exhausted by this one interest the desire for know It is found to be just as active in a direction which cannot ledge.

be included

knowledge of that which

in the idea of

We

is.

find \

ourselves as a matter of fact under the dominion of certain laws

we

according to which

estimate the worth of

which we are willing to submit our

wills

and

human

deeds,

actions.

It

and to

matters

not for our present investigation whence these laws have their origin, for

nor by what motive that

Enough

us.

we

we

are led to recognise

are incessantly called upon to decide what

how we ought

to

act

if

we

are

to

which

unsullied.

No

avoid

its

end,

to

do and

with

by proving that our

accorded with the nature of

which

conflict

the

material result informs us whether or

not our Thought has attained culations

we ought

we acknowledge, and maintain honour and

principles,

conscience

at

as valid

of propriety, of morality, of justice and of duty, and

the rules

suit

them

are constantly endeavouring to observe

we aim

consists

things.

solely

in

Even

the

cal re-

thoughts, and the

thoughts which accuse or absolve or the us, recognition non-recognition by others and by our selves of the conformity of the particular action with the general

actual

results

also

are

the

rule. 6.

Let us consider more closely

this,

the most important part of

our practical Thought, as well as of our estimation of practical Before the Court of Conscience the only evidence we relations.

have as to whether the Thought which guides our action has

at

its purpose or not, is the inner consciousness of the neces our sity of Thought ; the certainty that the given mode of action the self-evidence which follows inevitably from the general rule

tained

;

was right and good to act so under the circum stances because the general principles of justice and morality

satisfies us that

it

demanded

Nor have we any

it.

external confirmation that

we

have attained our end except the assent of others, who, starting

/

GENERAL INTRODUCTION

6

from the same presuppositions, affirm the same consequences to be necessary.

Thought we must guard

In speaking of the necessity of our

against a confusion of meaning.

From

a psychological point ot

view everything which the individual thinks

may

be looked upon

activity which results in accordance with That just general laws from whatever conditions may be present. this, and not something else, is thought, is the necessary consequence

as necessary,

as an

i.e.

of the particular individual

s

range of ideas, disposition and char

and the stimulus of the moment.

acter,

of psychological causality there

from the contents and

object of

is

But besides

this necessity

another which springs entirely itself

Thought

;

which

is,

therefore,

grounded, not upon the variable subjective states of the individual, but upon the nature of the object thought of, and which may so far

be called It

objective.

in

is

consciousness then of

this

its

objective necessity and

universal validity that our find

Thought finds satisfaction, and we shall upon examination that the same characteristics express the

aim of our Thought Here, again, tional

in its search for

we can only

knowledge of that which is. define the end towards which our inten

strives

Thought

consciousness of

its

by saying that it aims at satisfaction necessity and universal validity.

in

the

true that

any one unbiassed by critical reflexion is impelled by a psychological necessity to objectify his sensations and the thoughts relating to them, and to picture to himself a world to which he ascribes an existence independent of his subjective It is

When

activity.

his desire for

hesitate to attempt to

thoughts

in

such a

Nevertheless

be achieved.

it

is

We

mediately, and in

something

know

way

knowledge

bestirs itself

this objective world,

that they

may

he does not

and to frame

his

conform to that which

is.

a question of dispute whether this purpose can cannot refute the critical assertion that im

the

first

instance,

for us, consisting in

all

our knowledge

a system of ideas.

is

only

That there

is

GENERAL INTRODUCTION

1

an Existent corresponding to this thought of ours and ance with

is

it,

either a blind belief, or

in

accord

must be

the certainty

grounded upon a refutation of the doubt it dispels upon the That is, it depends, on the one proof that doubt is impossible. hand, upon our finding that the assumption of an Existent in volves us in no unthinkable contradiction on the other hand, ;

upon the nature of our ideas being such as to force us

Thought

to

assume

In both cases the proof rests upon a necessity

this Existent.

in

be counted amongst the surest results of the

may

It

analysis of our

knowledge that every assumption of an external mediated by Thought, and in some way or another derived by unconscious mental processes from the subjective facts of world

is

Thus, except by Thought, we have no means of as we have really achieved our purpose of knowing the Existent the possibility of comparing our knowledge with sensation.

certaining whether ;

things as they exist apart from our knowledge

At

we must be

is

for ever closed

agreement and amongst the thoughts which presuppose an Existent just as we are fully satisfied in the region of outward action when our ideas and movements, together with their con to us.

the best

satisfied

to find

Absence of contradiction ;

sequences, are in

harmony amongst themselves and with

the ideas

of others.

Granted that there of

it

is

is

a knowable Existent, then a knowledge

unless

impossible

there

is

some

relation

Existent and our subjective action which

between the

governed by laws, and by virtue of which the thoughts necessitated by what is given in consciousness

correspond to the Existent.

a knowable, external Existence, then

ing and thinking subjects, and

think alike in reference to the

knows the Existent If,

as

is

is

all

same

it

is

Further,

the

who know object.

same

if

we grant know

for all

the Existent must

Thus Thought which

of necessity a universally valid Thought.

on the contrary, we deny the possibility of knowing anything

it is

in itself

if

the Existent

is

only a thought of our production

GENERAL INTRODUCTION

3

it still

remains true that the ideas to which we attribute object

ivity are those

The

which we produce with a consciousness of necessity.

we regard anything

fact that

as existing implies that all other

when only with the same neces

thinking creatures of like nature with ourselves (even hypothetically assumed) would also be forced sity to

it

regard

as existing.

then unhesitatingly say that

may

if all

we can

attain to

is

but necessary and universally valid Thought, then knowledge of the Existent of

is

included therein, and

knowing our immediate aim

(We

is

and universally valid Thought. Truth consists.

the essence of actual, or call

"

"

moral truths, the

true

that

is

it

is

when we think with the

object

nothing more than this necessary It is in

this

conception also that

When we speak of mathematical, common characteristic of all which we

thought necessarily and with universal

validity.

This view of the task undertaken by the Thought of which treats avoids the difficulties which beset Logic every system of 7.

a theory of knowledge.

The

Logic calling

itself

a system

must begin by showing whether and how far possible at all ; and in doing this, it not only passes

is

knowledge

that is

difficulty of

such

it

into the disputed regions of metaphysics, but

proofs and refutations that

it

presupposes

in its

necessity and universal validity

of

Thought from which the conviction of its objectivity is to proceed. In the same way we avoid the one-sidedness into which the

Logic which professes to be a that of theory of knowledge is apt to fall treating only of the thought which aids us in our knowledge of the purely theoretical, and forgetting the which serves to

Thought

guide our action.

same

in

Nevertheless the psychical activities are the both cases, and the two aims must be classed together.

By thus including all Thought which pursues the common aim of certainty of its own necessity and universal validity we can also 8.

complete jinally

in

its

psychological limitations.

All such Thought results

judgments, which are expressed inwardly and outwardly

GENERAL INTRODUCTION as propositions.

Every

all

;

in

knowledge consists

judgments.

way

for the

judgment.

Again, the

;

judgments

of,

\

;

come

and preparing

I

/

judgment can be an object

of scientific investigation only in so far as position

in

All other functions

into consideration only as being the condition

the

and means \

practical consideration of ends

terminates in judgments

every conviction ends

9

it is

only through the proposition can

in

expressed

become an

it

general consideration, and only as a proposition can

it

a pro

object of aspire to

universal validity.

Now we know

9.

from the

fact that error

our Thought frequently misses

its

aim

in

and dispute exist

Sometimes these judgments

actually forms.

that^j

the judgments which are relinquished

it j

by

I

the individual thinker himself under the conviction that they are invalid,

that

i.e.

it

is

necessary to think otherwise.

again, other thinkers refuse to accept necessity, affirm possibility

them

to be

inasmuch as they

them

:

it

j

they dispute their

mere conjecture, or even deny find

\

Sometimes,

their

necessary to judge differently

I

concerning the same matter. Since then actual Thought can and does miss

its

aim,

we have

teach us to avoid error and dispute,

need of a discipline which shall to conduct Thought in such a manner that the judgments

and

may

be true

that

is,

necessary and certain

that

is,

accompanied

by a consciousness of their necessity, and therefore universally valid.

Reference to this aim distinguishes the logical from the psychoThe latter is concerned with the logical treatment of Thought.

knowledge of Thought as it actually is, hence it seeks the laws according to which, under certain conditions, a certain thought ap pears in just one actual

and

Thought

as arising

instance, thus

way and no

other.

Its

task

is

to explain all

according to the general laws of psychical activity,

from the particular conditions of the individual dealing with all Thought alike, whether erroneous

and disputable, or true and generally accepted. /The

antithesis

j

!

GENERAL INTRODUCTION

I0

of true and false thesis

no more a psychological one than

is

of good and bad

The

logical treatment,

to think the truth

it

;

human

in

in that region

Starting with this aim before

it.

the conditions of

its

how

the end

may

it,

who

are

Thought which is and investigating

Thought which are due

to the

and universal validity on the other hand, to conduct the mental operations in such a way that

for necessity

direct us

of

attainment, Logic proposes, on the one hand,

to set forth those Criteria of true

demand

the anti

on the contrary, presupposes the desire

has no meaning except for those

conscious of this desire and

governed by

is

action.

to

;

In one aspect then Logic

be attained.

is

a critical

Thought which has already taken a technical discipline. But as criticism is

discipline having reference to

place

;

in the other,

of value only as a

and that

in

which

it is

means it

to the end, the principal task of

properly consists,

is

Logic

to be a technical discipline

or Art.

Logic as the Art of Thought cannot undertake to instruct us how, beginning at any given time, we is

entirely

and

absolutely true.

It

may attain

must

to

Thought which

restrict itself to

showing what are the general Conditions which, from the nature of our Thought, every proposition must satisfy in order to be necessary and universally valid, and under what conditions and to according

we can

what

rules

shall

be necessary and universally valid.

judgment

pass from given premises in a

as to the necessity

from which we

start at

any

manner which

It declines to give any and universal validity of the premises

time.

Thus observance

of logical

ensures merely the formal correctness of the procedure and not the material truth of the results. In this sense our doctrine is of necessity formal rules

Logic.

Instruction in an art which claims to ensure success for the activity to which it gives rules presupposes that this activity is I.

GENERAL INTRODUCTION

n

completely free and voluntary. This implies, first, that I am able to bring about the conditions necessary to the activity whenever I choose

;

secondly, that

of the rules of

I

only need to be conscious of the aim and

attainment

its

in

order to

fulfil

every particular

operation in accordance with those rules, and so as to attain the

end

If there is to

in view.

be an Art ensuring the production of

necessary and universally valid Thought, by means of which we may know the Truth, we must assume that all the conditions lie within our grasp, and that at

This *

it

Methodus

It

to

any given time we are completely

our Thought accordance with its rules. was which Descartes had in view when he designed

free to control

in

recte

utendi ratione et veritatem in scientiis

his

investigandi"

was to put an end, once and for all, to all possibility of error, exclude all doubt, and to produce a series of thoughts which

one necessarily true and certain proposition and proceeding by infallible steps should contain none but absolutely His assumption was that, though we may not true propositions. starting from

be free to choose what ideas shall be present to is

and voluntary

a completely free

draw our assent with

full

act,

to every proposition

us, still judgment inasmuch as we can with

which we do not recognise

conviction to be true and certain.

by means of

Hence

presupposition involving danger of error, and to fresh start in the activity of

sumed

possible,

Thought.

In the

make an

are innate in us,

entirely

same way he

that the chief conditions of this activity

principles

it is

a thorough-going scepticism, to free oneself from every

as

concepts and

and that they are thus dependent

upon our self-consciousness alone.

Now .even

if

this latter

method would

assumption were as true as

it is

disputed,

complete application only in the of a and region only for those capable of making priori knowledge, and carrying out the resolution to free themselves from all presup the

positions.

But

it

at best find

is

absolutely impossible voluntarily to break the

continuity between past and present Thought, and to begin com-

GENERAL INTRODUCTION

I2

Voluntary Thought grows out of an involuntary it is continually fed, and we could

pletely ab ovo.

production of thoughts by which

make no

progress unless there were a supply of these thoughts

We need only forthcoming and a language representing them. see himself to in of the best inten turn to Descartes how, spite tions,

elements

of past

Thought will force their way into the Nor is it true that we can voluntarily refrain

newly started series.

from any judgment while we have no choice as to whether the it relates shall be present or not One reason for

ideas to which this

is

that a part of the presuppositions

we bring with

us are

judgments which inevitably involve others another, that our judg ments concerning the relations of ideas are predetermined by the ;

nature of those ideas, and

we

will affirm or

we

are not at liberty to choose whether

deny.

There can then be no method whatever by which we may begin Thought entirely anew. All that we can look for is a method of carrying it on from already existing data, which must always form the starting point for future Thought, even

when acknowledged

to

be uncertain. 2.

The

necessity

procedure of

of confining Logic to the

Thought makes

itself felt

regulation of the

more especially with

refer

ence to the Thought which aims at empirical knowledge of the

Such knowledge presupposes correct perceptions and in making observations which are to serve some end, we are depen dent not only upon the Thought which accompanies them, but also the conditions of upon sensation and the relation between our senses and the object. The art of correct observation is world.

;

only

partially included in

the art of right thinking it depends also the acuteness and training of the upon organs of sense, upon me chanical adroitness, and upon the art of bringing the object into the most favourable relations with our organs of sense and of ;

eliminating errors of observation. ent expedients

It must be guided in its differby the varying nature of the objects with which

GENERAL INTRODUCTION it

deals,

each class of these requiring

we were

its

13

particular

technology.

Thought and Judgment in the region of empirical knowledge until we could start from absolutely certain and necessary premises, empirical science would be altogether impos If

We

sible.

to suspend

should be forced to leave

in

suspense, together with the

and exactness of our perceptions, not merely the whole

validity

question as to the reality of the material world, but also the pos sibility of universally valid

laws of phenomena.

Moreover, the history of the development of our knowledge shows that the discovery of truth has often been indirectly attained by starting from erroneous and uncertain premises. In the course of scientific research dispute

is

frequently settled by pursuing false

propositions to their conclusions.

example of

Every apagogical proof

is

an

this procedure.

Finally, a large part

of the

Thought which aims

at universal

connected with premises which derive their validity validity from a Will, and which are so far purely arbitrary. To insist that Logic should establish the material truth of all propositions is

would be to exclude from

logical consideration all practical juris

prudence. 3.

Thus

all

that an Art of correct

Thought can

achieve, and

all

can propose to do, is to instruct us how we may proceed in Thought from given data in such a way that each step shall be

that

it

accompanied by the consciousness of necessity and universal/ to do us what we must think It does not teach validity. / that would be to comprehend if

we

think

this

the supply

data

we must

all

science.

of involuntary ideas

vations and general

It

teaches only that

think that, no matter

also

propositions

may

and

how

our

of particular obser

be constituted

in

other

respects. It

in

must be understood that by

any

direction

"

proceeding"

we mean

a progress

from grounds to consequences, as well as from

consequences to grounds, from general to particular, as well as the

GENERAL INTRODUCTION

14

Thus the

reverse.

art

must be applicable

to all

problems whatever

which present themselves to our Thought. is the sense in which we take Logic to be a formal 4. This then science

for the

;

sake of the generality and practical fulfilment of

I

Thought without

to construct

we cannot undertake

our task

we extend our

nor do volving any presuppositions,

the data from which gations to the validity of starts at any time, but only to the correctness of

logical investi

Thought actually

procedure from But by calling Logic formal, we do not mean that it

those data.

make

should

in

the vain attempt to regard

merely formal activity, which matter of Thought, and which

Nor do we mean

may is

its

Thought

in

general as a

be considered apart from

unaffected

by

all

differences of matter.

that logical investigation should entirely abstract

from and ignore the general nature of the matter and presupposi tions of actual Thought. itself in it

Of Thought developing entirely from we have no knowledge we know

the particular individual

;

only under the general relations and conditions, and with the

general

purposes of

human Thought.

neither from the particular

manner

Hence we can

abstract

which our Thought receives material and contents from sensations and forms them into ideas of things ,

;

nor yet from the

way

in

in

which

its

history has been

determined by the community of mankind. We abstract only from the particular nature of the occasions which at any given time give rise to a series of mental processes.

3-

The

possibility of determining the criteria

.and universally valid procedure in to distinguish objectively necessary

necessary, and this

we

find in the

and

rules of necessary

Logic depends upon our ability Thought from that which is not

immediate consciousness Q{ evident

which accompanies necessary Thought. J:ruth Experience of consciousness and belief in its trustworthiness form a

this~

Postulate,

beyond which we cannot

go.

GENERAL INTRODUCTION 1.

When we as

problem

we have

difficulty of finding

objectively

which

saw, misses

stated

an

it,

possible to solve the

is

it

the question resolves itself into the

infallible sign

by which we may distinguish

and universally valid Thought from that

necessary

differs

how

ask whether and

15

according to the person thinking, and thus, as

its

aim.

And

here there

is,

we

the last instance, no

in

answer but an appeal to our subjective experience of necessity, to the inwaird feeling of certainty by which some of our Thought is accompanied, to the consciousness that, starting from the given Belief in premises, we cannot think otherwise than we do think. the truth of this feeling and in

chorage of it

there 2.

is

all

certainty

for the

;

its

trustworthiness

man who

is

the last an

does not acknowledge

no knowledge

Certainty

nothing but accidental opinion. of the universal validity of our Thought

rests \

ultimately upon the consciousness of necessity, not the conscious

When we

ness of necessity upon certainty of universal validity.

assume a reason common

we think with

to

all

men we

are convinced that

what

a consciousness of inevitable necessity others will

same way. Our assumption that other people are bound by the same laws as ourselves, may indeed be strengthened by empirical confirmation when all agree but this also think in the

;

cannot supply the place of the immediate feeling of necessity, much less give rise to it. Habit, also, to which the empiricists appeal, and coincidence between experience and our calculations, affect

only the validity of the data from which

we

start

;

they can

neither produce nor modify the specific characteristic of mental

Here, then,

necessity.

we have

every logical system must to our

rest.

the fundamental fact upon which

Logic can do nothing but bring

knowledge the conditions under which this subjective feel

ing of necessity arises, and express

may be and

said that

this

matics

is

is

if

this

true in the

be

so,

then Logic

same sense

an empirical science.

them

in

which

in is it

a general form.

It

an empirical science, is

true that

Mathematics also

starts

mathe

from

facts

GENERAL INTRODUCTION

16

by which they are accompanied, from but both are distinguished merely empirical science in that they find in their facts the necessity which is wanting to accidental experience, and make this the basis of the certainty of their pro of consciousness and the necessity

positions.

4-

stating the problem in this

By

determined for

investigation

us.

way we find the course of our First we must consider the

nature of the function for which rules are to be found then

we

must lay down the conditions and laws of its normal action we must try to find rules for the process by which natural

;

finally,

Thought working with given presuppositions and expedients may pass from an imperfect into a perfect state. tion falls into three parts I.

Since

intentional

by a

it

;

has been shown

Thought

Thus our

analytical, normative and

fulfils its

i.

investiga

technical.

that the activity in which

8

purpose

is

all

Judgment we must begin >

right understanding of the nature of this function with the

we are concerned, and by recognising what elements and presuppositions are involved in it. This is all the correctness of which

more necessary because the judgment takes the same form whether Thought expressed by it be successful and universally valid or

the fail

to attain

its

purpose.

Only

in

judgments and finds, or seeks to can we have truth and error, in

so far as find, in

Thought takes shape them its final expression

certainty and doubt, agreement and

dispute.

carried

what

it

It is

out,

the

same function which

in the other

consists can

incorrectly

we give

;

is in

the one case correctly

and not

the rules for

its

until

we know

in

correct operation.

This knowledge can only be gained by an analysis of actual judgment, by considering what it is that we do when we judge,

and what other functions, if any, are presupposed in Judgment! We must also consider the process by which Judgment is formed from these other functions, and the general principles by which

GENERAL INTRODUCTION this process is naturally

for the present that

the

name

of

governed.

Meanwhile we must assume

we know what mental

Judgment language ;

17

acts are included under

will serve us here for a guide,

the immediate object of our investigation

may

and

be defined as

propositions which claim to be true and to be believed or

all

acknow

ledged as valid.

Of

the propositions enumerated by

put

present

aside

all

like

which,

Grammar, we

Imperatives

will for

the 1

or

Optatives,

1 No doubt the Imperative also includes the statement that the speaker wills the act which he commands ; while the Optative states that he wishes what he says. But the

statement

is

here contained in the fact of speech, not in what is said it is just as true A is the mere fact of speech involves the statement ;

that in every utterance of the form that the speaker thinks and believes

what he says. All speech alike is accompanied by such statements concerning the subjective state of the speaker, which are implied in the fact of his speech and are valid on condition of his veracity ; we cannot therefore found

The Imperative Silence is of course a the expression of the statement it is my will that you should be silent," but its purpose is not direct communication of this fact, but the determination of the will of the I have spoken of it as con person spoken to, it does not call for belief but obedience. any distinction amongst propositions on these.

way of varying

"

"

!

"

taining an intransferable element because the person addressed does not repeat the act of will of the person giving the command in the way in which he appropriates the thought

when he

of the speaker

No

believes a statement.

primary and usual meaning of the Imperative as

essential difference occurs in this

the expression of a particular individual will when it takes the form of a general law. When the legislator addresses an Imperative to the citizens of the State or members of

the religious community his relation to them is that of one individual to another. His purpose in speaking is not to communicate a truth which they are to believe, but to announce a command which they are to obey. It makes no difference whether the source of the command be an actual individual or a collective body, whether the assumed motive of obedience be submission to personal authority or an impersonal constitution the import of what is said is not the communication of a truth but the summons to do this, to leave that undone.

The form Thou shalt again, which appears in laws such as those of the Decalogue, has originally no other significance. Shall is the correlative of will. In delivering the command of master to servant we say "thou shalt do so and so ; it contained originally "

"

"

no more than the simple Imperative, the revelation of a law

to

one

whom

I

hold to be

subordinate to the will of another, either of a third person or myself. But this form does now contain a twofold meaning not to be found in the simple Shall (sollen = shall + ought) may also have the force of a proper Predi Imperative. "

"

meant to be true it signifies duty, obligation, and is thus a modal below 6. 3d) expressing the relation between the subjective individual

cate in a statement

;

Predicate (see will and an authoritative power, or an objective law. The original Imperative here passes over into the significance of a Predicate expressing the obligatory relation of a

command

to the will to

the statement that I also find

S. L.

am

which it applies and if we assume a legal or moral constitution, under an obligation may be true or false. In may again we

two meanings.

;

"

"You

may

"is

originally the expression of

"

momentary

C

per-

GENERAL INTRODUCTION.

8

X

contain an element peculiar to the individual and intransferable

All those again which while they refer to an assertion,

to others.

do not present

it

as true,

may

the time be disregarded

for

;

such

are questions, or propositions which express merely an opinion or

How

a subjective view.

far the latter

come

into consideration as

preliminary to the judgment, further investigation alone can show.

But

all

of

propositions

matter to what they

refer,

statement or declaration,

actual

must be investigated by

us.

In this

no

we

follow Aristotle, 1 and reject the distinction of the so-called logical

judgment from other statements, according

to

which Logic would

deal only with the subsumption of the particular under the general,

and exclude the mere communication of munications also aim at truth, and error

and dispute

well as

arise in reference

But such com

facts.

make claim to

to be believed

them and hence

;

they, as

judgments of subsumption, must have the conditions of

their validity investigated. 2 mission by which

I

The

desire to limit

Logic to judg-

liberate the will of another, disclaiming the determination of his

and declining to be a check upon his will. It expresses merely the The real import of the proposition subjective fact that I have no wish to prohibit. is On the other practical, and to this extent "you may" is akin to an Imperative. hand may may also be the Predicate of an actual statement expressing the fact that no authoritative prohibition is opposed to an action, that the existing order of things action or inaction,

"

"

permits

it.

Finally the same ambiguity extends to propositions which bear the grammatical form of a simple statement. That portion of the penal code which says that whoever acts in a certain way will incur a certain penalty, is not meant, like the formuloe of a natural law, as a

communication of what actually happens,

it conveys a command. But when the depicted as taking effect the same proposition contains an actual statement ; it states what regularly happens within a given state. Cf. here Zitelmann, Irrthum und Kechtsgeschaft, p. 222, sq. Bierling, zur Kritik der juristischen Grundbegriffe, ii.,

law

is

259, sq.

Thus the mere grammatical form statement.

A

statement

and of which we

/^^

is

no

infallible indication that

we have

nothing more than a proposition which can ask whether it be true or false. is

is

to

meant

do with a be true,

to

1

Aristotle constantly mentions as the characteristic which distinguishes the judgment, the dTrd^cwo-is, from other forms of speech, the fact that we can attribute truth or false

hood

to

inra.pxfi. 2

Cf.

it.

De

interpr. 4 (\6yos) diro0cu TiKds ov

Again,

De anima,

on the other hand

iii.

TTO.S,

dXX

iv

$

rb

dX^eiW

rj

ifsevSeaGai

6.

Ulrici, Comp. der Logik, ed. 2, 72, p. 266, 267. Hegel, judgment the determination of the concept by itself, says first {Logik, Werke, iv. 69) "A proposition has indeed Subject and Predicate in the grammatical sense, but is not therefore a judgment. For this it is necessary that the Predicate should

who

calls the

:

GENERAL INTRODUCTION,

19

ments of subsumption could have arisen only under the scholastic view of the nature of science, the view that Definition alone has

any

Where

scientific value.

are the basis

and

is

it

recognised that particular facts

of a great part of our knowledge, Logic

test

must also deal with those judgments which express particular facts. It also

forms a part of our plan of investigation to take up the

analysis of the

judgment

natural course of

at the point

Thought without

where

skill

it

takes shape in the

or reflection on the part of

the thinker. 2.

Our

investigation of

what takes place

in

Judgment completed,

we may then proceed

to enquire as to

judgment must

order to be perfect and answer fully to

In this

purpose.

in

fulfil

way we may

the conditions which a

set before

us an ideal, agreement

with which will be the end and object of our

we begin by asking and apply all

its

that

Thought

shall

this test to the function of

conditions and factors

;

its

Thought

That

is,

be necessary and universal,

judgment

after discovering

there then result certain laws to

which judgment must be submitted, and hence certain criteria by which we may distinguish between perfect and imperfect judg ment.

These

laws, so far as they fall within the scope of a logical

treatment in our view, First, the i.e.

may

be

summed up

two principal

in

points.

elements of the judgment must be completely determined,

fixed in concepts

proceed from

its

;

secondly, the act of judgment itself must

data in such a

way

as to be necessary.

Thus

stand to the Subject in the relation of conceptual determinations, that is, as general to Aristotle died in the 73rd year of his age, in the 4th year of the special or particular. But he adds decisively, H5th Olympiad, is a mere proposition, not a judgment." It would have something of the nature of the judgment only if one of the circumstances, the time of death or the age of the philosopher had been called in question and there Thus the communication, had been some ground for affirming the given number. "

.

N

.

.

a proposition, and would be a judgment only supposing it to be questioned whether he were really or merely apparently dead." So that Hegel also it is true agrees in calling every proposition a judgment, in so far as we can ask whether and -what are its grounds. Cf. also Franz Kern (die deutsche Satzlehre, 1883, p. 189), who errs only in directing his remarks against Logic instead of against a one-sided logical

my

friend

theory.

has died

is

j

;

;

GENERAL INTRODUCTION,

20 this part of

our treatment will contain the doctrine of concepts

and inferences as subject matter of the normal laws

for the

forma

tion of perfect judgments.

But knowledge of the nature of ideally perfect Thought does enable us to attain to this ideal state, nor even

3.

not necessarily

show us the way which leads at our disposal

upon human

by Nature,

thought,

Hence we have

to the goal.

consider how, starting from a given

state,

arid subject to the

we may reach

concerned here, therefore,

also to

with the means placed conditions imposed

logical perfection.

We

with the methods of obtaining

are

right

conceptions and hypotheses which will serve towards the formation This is the domain of the Art in of judgments and inferences. its

narrower sense, of the properly technical instruction to which

the two preceding parts form a necessary preliminary.

important

place in this technical instruction is

The most

taken by the Theory

method by which concepts be obtained from particular percep

of Induction as the doctrine of the

and general propositions

may

tions. 4.

our

We

believe that

by thus apprehending our task and arranging

investigation, the

different

views which have

made

their

appearance as Logic has been elaborated, are combined and justice done to each. One view has assigned to Logic the task of ex

pounding the natural forms of Thought and the natural laws which it necessarily follows, and we also recognise the necessity of stating the natural laws to which

all

Judgment

ing the principles applicable to .particular kind.

it

is

subject,

and of discover

as a conscious function of a

But we deny that

this completes the task of which aims at Logic, being not the Physics but the Ethics of Thought. Others, again, have defined Logic as the doctrine of

the normal laws of

we

human Thought

or

recognise this regulative character as

we deny

that

Knowing, and here again an essential feature. But

any knowledge of these laws can be attained that

is

not founded upon the study of the natural forces and functions to

GENERAL INTRODUCTION.

21

be regulated by them, and we deny also that a mere code of normal laws can by itself be productive or fulfil the purpose for the sake of which alone it is worth while to construct a logic.

Much

rather do

generally

made

we hold

it

necessary that Methodology, which

the special, final and chief aim of our science.

Methodology must have

for

its

principal

some extent those who endeavour

And

object

science from the natural data of knowledge, also to

is

to take a subordinate place, should be regarded as

since this

the growth of

we hope

to satisfy

to avoid the barrenness

and abstract character of the formal scholastic Logic by making it

include a Theory of

Knowledge

;

nevertheless

we exclude

all

questions relating to the metaphysical significance of the processes of Thought, and keep strictly to the prescribed limits within which

we regard Thought our claims upon limit

them

which,

it

as a subjective function.

so far as to

demand

We

do not extend

a knowledge of Being, but

and universal validity always and everywhere

to the sphere of that necessity

even

in

ordinary language, are

regarded as the distinguishing and essential characteristics of what is

logical.

PART

I

THE NATURE OF JUDGMENT AND PRESUPPOSITIONS

ITS

LOGIC PART

I

INTRODUCTION THE

Proposition in which something is stated about something, is the This originates as an active move

verbal expression of the Judgment.

ment of Thought, and always presupposes that there are present to the person forming and uttering the judgment, two ideas the Subject and Predicate ideas, which can at saying that the Subject that i.

which

is

is

first

is

stated, the Predicate

stated.

The judgment which we

appears in the tal activity.

be only superficially distinguished by

that of which something

find

in the

form of a spoken assertion

instance as a completed whole, a finished product of

first

As such

new combinations,

it is

men

capable of entering into

reproducible in

memory, by communication with others, and such But this objectivity and writing to all time.

transferable

it can be perpetuated in independent existence, which leads us to speak of

that

it

as stating, connecting

apparent only, and the expressions merely figurative ; rightly speaking, the judgment as such has real existence only in active or disconnecting,

is

judging, in that mental act of a thinking individual which takes place at a

given moment, and the only possible way in which

we can perpetuate

the

an active process in thought is by consciously repeating The judgment itself never attains to objective existence, but only

judgment

as

it.

its

material sign, the spoken or written proposition, which, by being externally present for others

and recognisable, announces

that a certain mental act has

taken place in active Thought.

Now

the proposition, as this outward sign, presents two aspects for our

consideration, which

must be

carefully distinguished

from the beginning.

INTRODUCTION

26

\

\\

On

the one hand

who

other hand

he

it

refers to

gives utterance to

is

called

addresses

it

it,

its

itself

source, the mental processes of the person

On the doing reveals his thoughts. to the hearer by whom it is to be understood ;

and

in so

to interpret the

upon

outward

and out of them

signs,

to re

But the functions of the

construct the thought expressed by the speaker.

person understanding the spoken words are not the same as those of the speaker; although if we assume complete understanding, the final result in the

mind of the hearer must coincide with

When

started.

my

I

recognise the familiar

what

I describe

from which the speaker "the castle is on

fire,"

In

the image of the burning castle.

is

starting point

and

that

express a perception in the words

I

this

image I form of the building, and the flames rising from it, saw by first separating these two elements, and then

The person who hears my proposition uniting them in the proposition. must begin by uniting the ideas which are excited in him by the two words, and which are

at first separate

;

only

when

this

is

done does he obtain the

idea from which the speaker set out.

Grammar and Hermeneutics, which

start

from the spoken or written

word, naturally tend mainly to the standpoint of the hearer ; they direct their attention to those functions which are active in understanding, and treat of them in the order in which occur in the hearer. But in they psychological analysis, where our aim in judging, the other side

portance

;

and

this the

necessarily the object of

to investigate the nature of thought

is

the action of the speaker

Thought which clothes

all

itself in

For us, then, the investigation of the nature of the a consideration of the mental act which takes place engaged

And

in judging,

and

is

more so because communication

to

of primary to others

is

im not

words.

judgment consists

when we

in

are actively

which we proceed to give expression in words~ judgment (whether mental or spoken) pre

since every repetition of a

supposes its original production, the cases with which we must deal are those in which our Thought produces a new judgment and provides it with its verbal expression (as, e.g., whenever we give utterance to a new observation).

The

2.

process which goes on

be described 1

thing.

for the present

when

/

*

\6yos

form and utter a judgment may something about some

There are always two elements present, the one is that which is the other one is that about which

stated, rl Karrjyopo^vov, the Predicate \

I

by saying that I state

Kara^ar^

shall consider later

on

1) (

d7ro0cm^ ? 12) the

;

6s /caret riris.

Aristotle s

view that judgments do not

all

Anal,

pr.

I.

I

have two elements.

We

INTR OD UCTION the statement

But

this

description

Statement

what

is

made, or

is

an

is

which

to

it

27

TO VTTOK^^VOV, the Subject.

refers,

merely superficial, and derived from language. of the organs of speech, and the question arises

is

activity

:

Thought when we

the mental process of

"

state

something about

"

something If

3.

?

we

from the spoken proposition we must begin by making There are some propositions in which we mean only the such to be Subject or Predicate, the words as these particular start

a distinction.

words

as

combinations of sounds.

a

is

Hebrew word, Contra

position refers to the

made about them which

Possibly remarks are

and have no reference

are purely grammatical

a preposition)

is

or

it

meaning (Samiel

may be

word or name, (Oxide

of a

meaning

;

to their

is

that the pro

a

compound

of

oxygen ; Alexandras is another name for Paris Jagsthausen is a village and castle on the Jagst *). We may for the present put aside these merely etymological and hermeneutic statements, and there then remain for our ;

which the words appear as signs of understood by both speaker and hearer, i.e.,

investigation only those propositions in ideas,

and are assumed

to be

be connected with the same definite ideas, so that the statement

to

not

is

concerned with the words themselves, but with the ideas connected with the words. 4.

Here

then,

if

the statement

is

Subject as well as Predicate, must be

At

consciousness.

first

sight,

appears to be that one which

which by

I

itself

consciousness

in

the subject of a judgment

it

;

may be

already

received

into

other ideas.

I

consciousness,

cannot say

familiar with the ideas blue 1

"

this

and

To

an object or an event.

are understood.

enabling us to retain and reproduce

object whatever

qualified to

It

is

should be taken from those of our ideas which are already

named by words which

it,

is

It

become

it is

added

essential that this

known

to us

and

must be an idea which has been

which

is

and which

blue, this

red,

Subject-idea/

the immediate intuition of a

the Predicate- idea.

in consciousness,

Any is

my

present to

generally, the

present to me.

is first

can retain independently

second

have any meaning, each element,

and speaking

particular thing, or an abstract idea,

as

to

some idea immediately

is

connected with a word is

distinguished from

red,"

unless

1

am

all

already

and can reproduce them with the

has been objected that the real meaning of this phrase is That which is called is a village, etc., hence that the proposition does not refer to a mere name. But for anyone as yet ignorant of the significance of the word, the only possible import of It

:

Jagsthausen

the proposition is to give him the meaning of a hitherto nect any idea with the subject.

unknown word

;

he cannot con

INTRODUCTION

28

Judgment is possible only where a number of such distinct ideas are and easily called into consciousness. Hence conscious judgment

word.

retained

presupposes that these ideas are already formed.

Now,

it

is

some Thought is already involved in the process by Whatever we may think of the functions by ideas of definite objects, or at any ideas which can serve

true that

which these ideas are formed. which we arrive for Predicates,

at

it

cannot be denied that

different sensations, to

it is

comprehend a

necessary to distinguish between

plurality as a

whole, to refer this

whole as a unity to its manifold content, and to retain in memory the pro duct so gained ; and these are all of them acts which we can only think of as analogous to conscious mental acts of the nature of judgment.

But

this

and independent ideas, precedes our con scious and intentional Thought, and is governed by laws of which we are unconscious. If we begin to reflect upon it we are conscious only of the activity

which

results in distinct

results of these processes in the

The

form of ideas already possessed of names.

processes themselves must have been originally guided

logical necessity,

human

beings

;

by a psycho same in all

since their course has been essentially the

or else they have

attained to such mechanical

become

facility,

certainty even within the conscious

so

much

a matter of habit, and

that they take place with unconscious life.

We

must further presuppose the

beginnings and appropriation of language, since conscious and volun tary Thought takes place almost entirely through its aid. Properly speaking, then, that Thought by which ideas are first produced does not first

come

within the scope of our enquiry, nor yet the investigation of the origin of language, and the appropriation of it by the individual, although we may

be obliged to touch upon these questions as our analysis proceeds.

Still it

is

necessary to take a survey of those ideas which are capable of entering as elements either as Subject or Predicate into our judgments, and to

determine the relation between the mental fact and

its

verbal expression.

CHAPTER

I

IDEAS AS ELEMENTS OF THE JUDGMENT, AND THEIR RELA TION TO WORDS

we examine

IF

the contents of our Thought, that which can enter into our

judgments

as Subject or Predicate, or as part of Subject or Predicate,

find that

consists of:

it

THINGS, their Attributes and Activities, and Modifications of RELATIONS OF THINGS and of their Attributes and Activities.

I.

II.

These may be 1.

Language

Spatial

and Temporal, Logical, Causal or Modal. its classification of words, seems to give us the

it

clue which was certainly

Thought a ;

use of by Aristotle in his enumeration of the Categories as the highest

classes of that

an

these.

itself in

clue to the different kinds of objects of

made

we

which

infallible one.

develops

its

is

It is

thought and that which

different forms vary in their functions.

not coined for every

new kind

morphologically equivalent

of idea

organs

essentially different physiologically, so

as Substantives, Verbs, Adjectives. sarily

;

but as

in

is

not

A

special form

the organic

is

kingdom

can discharge functions which are it is also with classes of words, such

Different kinds of words

do not neces

correspond to differences of meaning in such a way that we can be

guided entirely by these external characteristics, of the indications given by language,

nature

But the clue

is.

the peculiarity of the structure of language that as

of the

objects

we must take

of Thought, which alone

While

still

keeping sight

a general survey of the will

show us how

far

differences in forms of speech correspond to differences of mental content.

The most

universal possession of humanity consists in that series of ideas which constitutes the world of the Existent, and though as a matter 2.

of fact this series

think of

it

language.

is

generally accompanied by language,

To

this series

we

are forced to

even without the co-operation of besides the idea of self, the idea of our belongs,

as possible to every individual,

IDEAS AS ELEMENTS OF THE JUDGMENT

3

whole empirically known surroundings, as well as the idea of everything

which we think of as existing in the same way as ourselves and the objects of immediate perception.

Ideas of particular Things form the material from which this world is and the words by which they are denoted are concrete Substan built up,

These Things we think of as supporting Attributes which find their and as developing with the course of time expression in Adjectives,

tives.

Activities

and

falling into conditions

which are expressed by Verbs. 1

This distinction between the ideas of Things

and the ideas of Attributes

which they are engaged, must be which inhere in them, and of fact Thought. That part of our judgment regarded as a fundamental can and be which is conscious guided by reflection and here alone can Activities in

there be any logic

presupposes both this distinction and the necessity

which obliges us to refer the different kinds of ideas to each other,

and

to

regard every thinkable and independent object as the unity of a Thing with No doubt the impressions from which we its Attributes and Activities.

The

1

generality of the process by which the affections of sense are referred to Things, no way prejudiced by the fact that such reference may be uncertain in particular cases, and that a thing perceived in a certain phenomenon may be apprehended in various is

in

Night, shadow, rainbow, wind, ways. the word concrete and particular. It

etc., is

are originally things in the fullest sense of which first deprives them of

scientific reflexion

and causes us

to look upon them as merely the results of certain relations in this con substance Hence, also, we avoid using the expression for it is an expression which implies that a scientific reflexion, and a criticism of nection those ideas which arise immediately and naturally, have already taken place. Not every thing which the ordinary consciousness led by the analogy of its own mental processes apprehends as a thing, is for that reason substance in the strict sense, or will permit of

this solidity,

"

amongst things.

"

;

the conscious application of this category. need not enter here upon the difficult question as to whether the present verbal form, in all its applications, is founded upon one definite common conception, nor what

We

that conception

may

be.

To me

it

appears certain that according to the original dis

between noun and verb, the expressing of temporal action (in its widest sense) be longs to the latter ; and the thought of movement and change which proceeds from, and arises in, the Thing, and which can, moreover, extend its influence to other things, forms tinction

the nucleus of that group of ideas which the verb serves to denote. In proportion as our imagination looks upon things as alive, even persisting states, such as lying, standing, the result of a resistance to change which etc., seem to be reflective actions and almost volitional. Or at least it is looked upon, as is evident in the Greek 0T77Ka, Kd8rifj.ai, as the result of an activity. It seems to me, then, more correct to regard the concept of action as original, and to subordinate to it the concept of state, than to reverse the relation, as Wundt does. That according to our present treatment many verbs seem to have the value of Adjectival Predicates, in no way alters the original dis tinction. The same state of a Thing may be regarded either as its inactive Attribute, or

remaining, is

as

active

its

continuous Activity

holding one

s

peace, etc.

as, for

example, at

rest

and

resting, ruber

and rubeo,

silent

and

IDEAS AS ELEMENTS OF THE JUDGMENT gain the idea of light

and

31

that of the light-giving object, or the ideas of

hardness and coldness, and those of hard and cold Things, are the same in

each case

but we cannot in conscious Thought force ourselves back to a any more than we can talk in the roots from

:

point prior to the distinction,

which the forms of Verb and

Noun have

What

developed.

forms of Substantive, Verb and Adjective imply

is

the linguistic

just this unity in differ

Every Verb implies a Subject, every Adjective a Substantive, and are thus supplemented can Thought come to rest in a

ence.

only when they

complete

relatively

act,

having attained a whole which

thinkable inde

is

In this process the part of the Substantive is to pendently and by itself. denote more especially the unity, a unity, however, which tends constantly to develop itself into

its

the Adjective and

elements

Verb

exhibit these

elements as abstracted from, but always striving back to unity. Thus wher ever we find our ideas denoted by various forms of speech such as Substan tives,

Adjectives and Verbs, there Thought has been busy, distinguishing to the categories of Thing, Attribute and Activity

and unifying according

;

governed by our habit of bringing everything under Only in a few onomatopoetic words at the most such as

our way of speaking these categories.

is

can we reproduce an impression which has not yet been seized

pop, splash

upon by categorizing Thought. The antithesis between Verb and etymologically.

actually

and Substantive claims

Even

original signification are of the nature of verbs,

that quick

excite the

movement and

activity

accompanying sound more

upon which

all

that

names were

first

this

easily,

not that the idea of activity in

Movement, the fundamental

general preceded the idea of the agent. tuition

and

in their

would prove no more than exercise the strongest stimulus, and

changes and movements,

given to events,

both

priority,

were true that roots

if it

in

ideas of external activity are grounded, cannot be

perceived without a localization of the moving object and

its

background,

and a comparison which presupposes that stationary images have been seen and retained by memory. 1 It is just in movement that the identity ot the agent in its activity, as the distinction of the permanent Thing from the in beginning temporary event, is most easily grasped it is more difficult ;

and ceasing adjective distinct

1

in

when

it

change of

attributes.

For the

attribute expressed

has a purely sensuous signification

from the idea of the Subject,

it is

permanent

e.g.

like

This agrees with what Steinthal says, Abriss der Sprachwiss.

colour

it,

,

by the is

not

and what we

1,396 sq.

IDEAS AS ELEMENTS OF THE

32

perceive of the thing their different

just its Attribute.

is

JUDGMENT

It is the plurality

of Attributes,

combinations in different Things, and their changeableness

in one continuously intuited object, which first impels us to disengage them from one another, and makes us able to think of each independently ; and it is the repetition of action which first impels us to express its permanent

ground by an Adjective. Thus there arise the two classes of Adjectives ; those which partake more of the nature of Nouns, and those which approach more nearly to Verbs. While the ideas of Thing and Activity are so bound together that an action or attribute must always be the action or attribute of some Thing,

and a Thing must always be thought of as having a

we

Activity,

Attribute or Activity by

In

Thing.

this

itself,

way they

isolation

artificial

they are also raised to universality to

and

by the distinction to think of an and disengage it from reference to any par

are thought of as abstract, i.e., withheld in from the unity towards which they naturally tend. In abstraction not only are they cut off from unity with definite Things,

ticular

this

definite Attribute

are nevertheless enabled

and find them

cesses

;

i.e.,

it

becomes possible to refer them J These two pro

any number of particular instances.

in

that of resolving a given

complex idea into the

different elements

of Attributes and Activities, and that of forming from these elements ab stract

and general ideas are mutually dependent, or rather we should say one and the same process, and that their result presents

that they are

different aspects.

In

my

intuition of a stone as a round, white Thing, the

ideas of round shape and white colour disengage themselves from this par ticular combination, and thus it becomes possible for them to enter into or

be recognised

By

in

any other combination.

the distinction of Attributes and Activities

from Things we are

enabled to think of the same Attributes and the same Activity as belong ing to different Things ; and a basis is also given for the comparison of similar Activities

differences

mode.

and Attributes

in different Things,

and the recognition of

between them, which we think of as variations in degree or

And

just as

in

Things are distinguished by their Activities and

Attributes, so the similar Activities

distinguished by degrees

name

of Modifications.

and Attributes of particular Things are and modes which we may comprehend under the Here we have a new distinction and a new unity

which finds expression in language in the relation in which Adverbs stand to Adjectives and Verbs. The etymological form of the Adverb also

announces

it

to be a

dependent element which must be united

to the idea

IDEAS AS ELEMENTS OF THE JUDGMENT of an Attribute or Activity with such an idea as

So

its

as Abstract

far

;

incomprehensible except in connection

more accurate determination. ideas can be retained independently,

centre to which other ideas

form

is

it

33

may

attach, language gives

and form a

them a

substantival

they are Abstract Substantives, and their meaning consists in ideas of Attributes and Activities. This form implies that they are comparable ;

with Things, in so far as their relations to Adjectives to those of

Concrete Substantives.

and the unity between them and Adjectives or Verbs,

is

and Verbs

But they are not therefore their determinations,

are similar

really

Things,

as expressed in

not that unity of inherence or action through which

they themselves, as abstract, indicate a something which supports them.

Except where Relations are involved, only the differentiation of a

common

element, the modification of the Attribute or Activity, can be thought of in connection with that Attribute and referred to it in a manner analogous to that in

which

itself referred

it is

two relations have in

common is

to a Thing.

where we have a substantival

in the sense that

the distinguishing characteristics which

an independent position their unity with

it

ball

is

round

chief point which the

is

contained a unification

idea, its determinations

offers for

in consciousness,

(The

it.

The

that in both there

and

and

comparison both occupy

at the

same time maintain

the ball moves

movement

the

is

the rapidity increases).

rapid

The one

common to the ideas of Things and their which we have been considering is, that in all there is an immediately intuitable element, which is determined by the function of one or more of our senses, or by inner perception. This characteristic

and

Attributes

Activities

intuitable content never constitutes

upon by Thought which gives

by

itself

the whole of the idea

;

it is

form, and it is then retained as the idea of the Attribute or Activity of a Thing to which it is referred as to a seized

permanent

unity.

of sense intuition

;

it

This unity is as much a part of our idea as the element but while the categories of Thing, Attribute and Activity

are always the same, the product of sense-intuition, or of imitative imagin constitutes the real essence of the idea,

ation,

and

gives to

it its

distin

guishing content. It

3.

their

is

this

Attributes

RELATION. the other

element which distinguishes the ideas of Things and Activities from the second main class IDEAS OF

and

In these the ideas of Things are always presupposed ; while on their content is the result of a relating Activity, and indues

hand

them from the

first

with a generality which

the idea of the particular by s.

L.

means

makes

it

impossible to excite

of the corresponding words.

D

LOGIC

34

The relations which are first and most easily comprehended, (a) of Things and their because already implicitly contained in our intuition SPACE. Right and left, above and below, and TIME of those are Activities, are ideas which, as consciously distinguished elements of before and after,

our ideal world, are due entirely to a subjective Activity, passing to and fro which are already intuited in spatial and temporal exten between

Things

sion

;

their content consists in the

this Activity as

it

consciousness of the determination of

and Time, and

passes through Space

is

therefore inde

It is true that these relations are all pendent of any particular reference. ideas of Things as spatially extended and implicitly contained in our before us in spatial and enduring in time in the manifold which extends

temporal order, but they do not as yet come into consciousness independ We have an idea of a spatial object in which there is right and left, ently.

above and below, and our intuition moves through space in these various directions in order to grasp the spatial image as a unity ; but this does not

we

necessarily imply that

At

directions. figure

and

meaning

its

we

first

are conscious of the

movement and

of

its

different

are conscious of the result only, of the definite

situation with reference to others.

for us until this Activity of

movement

Relational words have no to

and

fro itself

comes

into

we

distinguish one direction from another, the further movement of they presuppose reaching sight or hand from the shorter

consciousness, until

:

a spontaneous

movement

given material,

of Thought supervening

upon the immediately and being thus disengaged from any particular sensuous

affection they possess a generality peculiar to themselves.

"Movement"

must always be thought of in the last instance as movement of something, however faint the sensuous image of that something may be but direction "

"

:

presupposes only that scious of

its

we

ourselves describe a line in space

determinations.

Space and Time, and

these,

These

and are con

by Adverbs of denote relations thought of as

relations are expressed

when used

to

connected with the objects to which they refer, become prepositions or case-suffixes, or blend as prefixes with Adjectives and Verbs; in other words, again, such as

a spatial or temporal relation is "follow," blended with the meaning of the word, and finds no separate expression. The relation of Whole and Part is also derived from spatial relations. "fall,"

Intuition begins by a process of limitation and distinction which disengages what we perceive as a single Thing from the surroundings by which it is

accompanied images of

in

immediate sensation.

men and

animals,

their

way that we obtain movement compelling us to

It is in this

power of

IDEAS AS ELEMENTS OF THE JUDGMENT them from

distinguish their

shape

their

facilitates

background, and for

complete limitation

But within

and

35

reason also, because

this

distinction,

we regard

and stones

as

differences,

and we can describe new boundaries, and thus there

unities.

this original unity there

subordinate spatial unities within the circumference of the relatively

or animal

appear new arise

Their

first.

independent power of movement causes the limbs of the human body to appear as such unities, and when we break a stone the

separate pieces are perceived as distinct by the

present in

is still

trees

what we have

its

merely a

at first is

The

limitations to.

same

intuition to

which

it

Now, when we thus break up a whole, plurality of new unities, new things to fix

original shape.

fact that

we have an

idea of the head as well as of the

whole body, of the finger as well as of the hand, does not necessarily make us think of the head as part of the body, or of the finger as part of the

Immediate

hand.

intuition or reproduction

that of the

hand

to

com

finger

by

but not until we are conscious of the relation between

;

and the

the subordinate unity

and

may even proceed

head by that of the body, the idea of the

plete the idea of the

higher, not until

two processes

we

reunite what

we have

each other, does the head appear as part of the body, the finger as part of the hand. No doubt the idea of the separated,

relation,

refer the

of belonging to a whole,

to

more intimately connected with the we always perceive as

is

idea of such things as the limbs of the body, which parts,

and never

objects which

wholes

(e.g.

as isolated wholes (hand, arm, limb, etc.) than

may be

indifferently presented as parts or as

it is

with

independent

flower as a whole, blossom as a part).

This relational idea

is

thus presupposed in every idea of magnitude.

B

B

A

a part of A, or can be regarded (by means of contact, superposition, etc.) as a part of A. All comparison of

is

large in comparison with

magnitudes and

all

true

if

is

measurement

is

grounded upon the observation or

establishment of the relation of parts to a whole, and the "

the whole

u great."

is

greater than the

part,"

is

(Such words as great and high

or Attributes after

we

really first

first

principle,

an interpretation of the idea

appear as absolute predicates

are familiar with a definite standard of measurement.)

Again, the idea of the whole as a Thing with Attributes and Activities is not without influence upon the idea of the parts. The parts do not stand in external juxtaposition, the whole does not side side merely by

merely surround them as a frame

;

a causal relation

embraces the parts, holds them together and has them. after.

is

implied, the whole

More

of this here

-

LOGIC

36

The same differentiation takes place in the region of Time. The word breaks up into syllables, the melody into single phrases ; and here also the ideas of temporal magnitudes, of longer and shorter, are developed in proportion as the temporal relations obtain

an independent position

in

consciousness. their origin in the relating Activity

These ideas have

(b}

in

Space and Time, and

their content consists in the intuitive

movement through Space and Time.

of the

also the co-operation of functions of relating

other ideas of relation resulting from idea of Difference

is

of several distinct objects

them

but at

;

first

consciousness, that

it

is

is

it

But their completion requires Thought, which gives rise to

is

In our consciousness

given.

certainly presupposed that

is

we

the result only of the function which

distinguish

comes

into

the co-existence of several objects, each of which

The

independently perceived.

The

is

idea of Difference, of likeness or unlikeness,

does not develop until distinction takes place consciously, and panied by reflection.

The

and comparison.

distinction

not something which

which moves consciousness

is

accom

idea of Identity does not presuppose merely

same object was present for some time, or repeatedly ; it arises through negation of difference in the contents of two or more ideas

that the first

which succeed each other

in time,

and

it

this

is

Activity which forms

its

Only in so far as it presents conditions and ground for this Activity can identity be ascribed to an object. Difference, Identity and Similarity are never to be regarded as mere abstractions from the intuited content.

content, which can give nothing

of which

we have become

Number

content.

when

beyond itself; they are mental processes and it is this that gives them their

conscious,

also has

its

origin in such mental processes,

similar contents are spatially or temporally differentiated,

tinguishable repetition of the

same

intuition

such, while each step of the repetition

hended

is

comes

retained in

and

arises

and the

dis

into consciousness as

memory and compre

new

in a

The fact that I see three unity with the preceding series. things, and that the impression made by them differs from the impression made by two and difference

is

one,

is

not sufficient to give

not perceived by

me

as

sciously perform the act of proceeding from (c)

The

third

main

me

one of number

class consists of the

the idea three.

until I

one unity

count

:

i.e.

The con

to another.

CAUSAL RELATIONS.

These

all

contain, in infinitely varied modifications, the idea of Efficient Action, that of action which is directed is, upon some other thing (transitive verbs). Any explanation of the origin of the causal and even the

conception,

IDEAS AS ELEMENTS OF THE JUDGMENT question of

we must This

is

exact meaning,

its

reserved for later enquiry

is

indicate the position occupied by

;

nevertheless

in the totality of

it

37

our ideas.

not easy inasmuch as the close connection between efficiency and

action impels us to regard the latter as a relation because the former

and

is

one,

doing we are in danger of representing the position of the agent

in so

towards his action as mere relation, and the action of the Subject as other

than himself, an independent something of his creation.

more

liable to regard the position of a

Thing towards

its

We

are all the

varying actions as

a relation, inasmuch as the identity of a Thing throughout

its changes cannot be thought except by a unifying synthesis, so that as a matter of

fact

we

are forced to distinguish between the changes

The

and the Thing.

impossibility of drawing any fixed line of distinction seems to find confirm

When

ation in two ways.

a

man

walks he moves his legs

;

that which from

one point of view is mere action, appears from another as an effect upon his limbs, which are relatively independent things ; and it is the same in all cases where there is room for doubt as to what is a single thing, and what must be regarded as a complex of different things. Even the inactive relation of the whole to its parts appears as an influence exerted by the whole upon the holds

parts, or

the parts, binds

The whole

by the parts upon the whole.

them

into unity

by

has

influence, the parts

its

"

i.e.

form

"

Again, in view of the fact that what we ordinarily look upon as such as colour, smell, etc., has been resolved by the progress of Attribute, into an effect upon our sense-organs, much can be said for the knowledge

the whole.

proposition that efficacy

Substance

is

causal

in

and Attribute pass over into each other, and that Thus Inherence and Causality Attributes.

its

different ways of regarding one and the same relation. But these considerations merely show the difficulty of deciding where the determinations of Attribute, Action and Efficiency can be applied with

become merely

they do not obliterate the distinction between the concepts of Attribute, Action and Efficiency as distinct elements in our ideas. We may come to think that what we used to regard as an Attribute objective validity;

inhering in a Thing, such as colour, does not really inhere in the Thing, but is its effect upon our sensibility ; nevertheless it takes effect because

of

some

which we must conclude

attribute,

to

the effect, that

not directly cognizable through the senses the structure of

And

before

it

its

surface

can take

upon a change of

and

effect

state, or

its it

some

power of

reflecting

must, before sort of

be there, even though

all,

movement.

be

is,

is

it

due

is

to

and absorbing light. active, it must enter

The

fact

still

remains

LOGIC

38 that

if

we

think of a definite Thing

Attributes which inhere in

it,

we must

and constitute

its

think of

it

as possessing

particular nature,

and can

It is the same with be predicated of it without reference to anything else. Action. Our world would be a chaos, presenting no clear distinctions for

we

our recognition, unless ;

,

Things, each having this

think of

it

as a plurality of particular individual

definite nature,

and

nature in Time, or changes and alters

affects

active in so far as

moves or grows.

it

asserts

Of

course

is

it

Efficiency cannot even be expressed without distinguishing The antithesis is that between causa immanent and causa

question here.

from Action.

That which proceeds from the former

transient.

idea of the Subject, a latter

it,

both determined by other Things which affect it, and other Things and determines their action, but that is not the

in this action

[t

its

mode

of

its

being

;

is

inseparable from the

which proceeds from the something else. We cannot

that

cannot be thought except in relation to

therefore obliterate the distinction that the idea of Efficiency belongs to the ideas of Relations between different Things, while that of Action

an inherent portion of the idea of the particular Thing by and involves itself, only the Relations of space and time without which no particular Thing can ever be thought. It is for this reason also that the constitutes

idea of efficiency

is

never intuitable, since the passing over of Causality is an addition of the which connects

from one thing to another only the Action

itself,

Thought

;

the change in the Things which are entering into

Relation with each other, can be intuited.

The many forms briefly

indicated.

in It

which is

this Relation finds expression can only be most accurately and appropriately denoted by

transitive verbs ; but when these are regarded as proceeding from a perma nent ground, adjectives are developed which indicate that a Thing is capable of producing an effect, is constantly doing so, and always prepared to clo so. And when the idea of efficiency is joined in Thought to the

Thing

itself,

and the Thing takes its name from the effect which numerous substantives which denote

duces, then there arise the

according to their results

Causal Relation alone.

From

an

this

there

it

pro

Things

naturally

incongruity between the substantival form, which indicates permanence and independent existence, and the fortuitousness and change the Relation, and the possibility arises of confusing between what is true only of the Relation, and what is true of the This to the thing.

expression effect,

and

"cause"

at the

itself.

moment

A in

applies

Thing is a Cause only in so far as it takes which it takes effect but on the other hand ;

IDEAS AS ELEMENTS OF THE JUDGMENT we

name

give the

of Cause to a

Thing having a permanent

Now

with reference to the Relation

there

is

no

no Cause

effect there is

is

it

existence.

quite correct to say that where

but

;

39

incorrect to extend the

is

it

proposition to Things which might become causes under certain circum This is true again stances, or are causes from some other point of view.

and object

in reference to the Relation of subject

object without a

"no

subject."

Relation by virtue of which the

when

only

name

But

myself, or,

indeed, everything which

I

under certain circumstances all

is

famous proposition

conferred upon a Thing

when

and the Relation

ceases.

We

I fall asleep.

my Thought, because me and then it is

be presented to

may

it

everything existing externally to other than

is

the things ever presented to

subject withdraws

vanish myself

in the

the word Object merely the

of object

may mean by Object

a truism.

not true that

mean by

actually presented, then the proposition becomes merely

is

it

If I

do not

me If

it

;

vanish so soon as the

were so

must needs

I

hesitate to say

"

I

have been

denotes a subject which is conscious of itself, conscious asleep," I is meant the cannot sleep if by ness disappears in sleep, hence no the to it is conscious of itself. in far as so theory According subject but

"

"I

"

"

"

/"

"

object without a

but

is

if I

I

subject"

must cease

an absurd contradiction,

"

foot

mean men who

if

is

subject

walk

true in the

be during sleep.

same sense

"Cavalry

on

cavalry means only men on horseback

serve in a cavalry regiment, then

course that they sometimes walk. "

to

;

a matter of

no object without a

The

proposition

that

the proposition

"

is

it

"

a rider cannot

"

is

true.

The relation between ourselves as the subjects of psychical activity, (d) and the objects of our subjective action of our intuition and thought as cannot be compared with any other. An well as of our desire and will Thought or Will, contains in itself as such all we have been considering it is Thing, Attribute, Activity But under which category shall we class seeing, hearing,

object or definite content of the categories or Efficacy.

;

these functions in thinking, willing, etc., when we consider reference to their objects, and not merely as manifestations of activity on Do seeing, hearing, and thinking, belong to the the part of the subject ? intuiting,

Causal Relations

?

are not

They

other than the subject

;

mere

action, for they refer to

but neither are they

efficient,

for

something

they neither

Only that which never exists but in Thought comes under the Causal Relation of and fancies) imaginations (such in so far as we may be justified this and and creation, only production

produce nor as

alter a

Thing.

LOGIC

40

or a dream as a Thing." regarding a thought think of as in any way existing is not produced by our

But what we can

"

in

to the real

no difference

Thought

Thing when we think about

it

;

it

makes

nevertheless

;

an object of Thought, and as standing in relation to we may call this class it. By an extension of the Kantian phraseology which exist between relations all the it will contain of Relations MODAL of and desire, wish for, and them, and ourselves when we think

we regard

as

it

;

objects

Thus

estimate them according to their value for us.

include not

will

it

an ideational activity with reference to an only all the verbs which express and adverbs, such as true" and false," which object, but also adjectives "

"

express the relation between

my

and the Thing

idea

to

which

it

refers, or

and "good," which express the reference of a thing to a "beautiful" standard of value, and therefore express an attribute belonging to the Thing as such only indirectly and when this standard is absolutely fixed. Finally

it

includes such substantives as

"

sign,"

or

"

purpose."

7.

Every object of which we form an idea

We may

think

of

is

thought of

as having particular existence

it

in

one

of

two ways.

existing as a

(i.e.,

particular Thing, or as an Attribute, activity or relation of particular things)

or as subject to the conditions of particular existence (as with the images

produced by imagination). its

particular existence,

sented

it

may

Or we may think of

and as general

it

without attending to

in the sense that as

enter into the thought of any

number of

mentally repre

things or instances.

This mental representation finds its expression in the Word as such. But when words are appropriated from existing language and employed to express the natural thought of the individual, their

the individual

The

and are

meanings

differ

with

liable to great transformations.

ideas which have preceded the act of

judgment in a judging by means of the words that denote them. Now there is no doubt that what language aims at is that a word should have the same meaning for every one but in actual life this is far from i.

subject are generally indicated

;

being the case.

It is

words have different meanings same person at different times. 1 Hence of actual judgment we must never start by assuming that

for different people,

in the analysis

a

more

and

true to say that

for the

word has a generally accepted meaning without further investigation; 1

Cf.

Paul, Principien

tier

Sprachgeschichte, ed. 2, p. 83.

1DEAS AS ELEMENTS OF THE JUDGMENT we must always regard the word as being merely the present to the individual who is making the judgment.

The

2.

denotes

is

41

sign of the idea

between the verbal expression and the idea which it Some words (such as nouns and verbs)

relation

not always the same.

are connected with a definite ideal content, which constitutes their

mean

understood by the individual. Others such as pronouns and demonstratives denote nothing definite by themselves or by the mere sound of the word all they serve for is to express a reference to the ing as

;

thinking and speaking Subject (or to that of which he speaks), and they do

not therefore become the sign of a definite idea until this reference

is

understood by means of actual intuition. I and you, this and that, here and there, do not express by their sound the idea of a definite person, thing or place, although they are used to denote definite things or places.

As the circumstances differ,

in which,

and the people by

whom

they are used

they denote different objects, and these objects must be supplied

from some other source. 3.

But words which are

significant in themselves are all of them, so far

and

primary and immediate meaning, no more than

as understood,

in their

and can be reproduced by Whether a word be a proper name or quite general in meaning it can never be of use until it has become capable of calling into con sciousness a definite ideal-content, by the mere sound alone, and without signs of ideas which are present to the mind,

memory.

help from present intuition.

and

On

the other

firm possession of an idea, or use

it

hand we cannot have

by which to denote it when the word is wanting to as a want, and have a difficulty in grasping the idea ;

it

and difference from guarding

it

others, in reproducing

from confusion.

As

certain

we have a word an idea we always feel

in thought, unless

it

in its individuality

with any certainty, and in

a matter of fact the process of psychical

aided by language and greatly influenced by it, and it becomes a new mental possession, seeks a word to every ideal-content, as This is why we are always so anxious to know names, and are denote it.

development always

is

content to be answered by a to the question

"what

is

name we have never heard Here we easily lend

that?"

before, in answer

ourselves to the

knowledge of this plant that from knowing really gain nothing directly things, Still we have gained a is called Aristolochia and that one Clematis.

names adds

to our

means of recurring more easily to these things, of memory, and of afterwards extending our knowledge.

fixing

delusion of thinking that the learning of

though we

them

Hence

all

in

our

progress

Wv -

*^

42 in

accompanied by a change and extension of

is

knowledge

scientific

terminology.

Let us

4.

now

consider the nature of the ideas which

accompany our

most important here to remember that the thought we are in the particular individual in the dealing with is that which takes place natural course of his mental development and the idea as it is connected words.

It is

;

by the individual with one and the same word passes through stages of development which cannot be explained either by philology,, which aims merely at determining the generally accepted meaning of the word, or by the ordinary logical treatment of the word.

Words

5.

Concept

are generally held to be the signs of

the logical sense

in

is

a work of

elaboration of our ideas in which definition fixed,

and

it is

the

its

work of

CONCEPTS.

But a

produced by a conscious characteristics are analysed and its art,

logic to help us to attain to the ideal

which words represent such Concepts. As a matter of fact most of our words only approximate to this state, and when we are treating of state in

the beginning of judgment in the first appropriation of the simplest elements of language, it can only lead to confusion if we call every mental If we counterpart to a word a Concept, without further discrimination.

we should have to follow Herbart s example, and give a much wider meaning than the ordinary one to the expression Concept." 6. We seem able here to distinguish a twofold relation J?t ween the idea did this

"

and the

Some

word.

immediate intuition help of language

;

of our ideas

those,

that

is,

which

rest

upon

form themselves up to a certain point without the

and these

ideas,

developing independently in

every

individual, are the conditions under

Here speech

is

added

amongst our ideas,

to

e.g.,

which speech first becomes possible. an image which is already formed. But others all those belonging to the region ot the non-

sensuous, are aroused in us by tradition, and the formation of these

is

occasioned and determined by the range of the Thought of the Com munity as expressed in the language we hear. The word comes first, and

becomes only gradually

richer

and more

as the individual enters into the

between the two cases

definite in

Thought

of the

meaning

in proportion

Community.

The con

merely apparent. We never understand a word except by connecting it with our own ideas, and its contents consist in just those elements which the individual has really trast

is,

however,

consciously grasped and retained.

the child

is

guided

at

Even the immediate sense-intuition of an early stage by language and on the other hand, ;

IDEAS AS ELEMENTS OF THE JUDGMENT the most abstract terms are no

more than empty sounds

43

Con

until their

Thought. independently reproduced always a discovery when a thought of our own is found to agree with the meaning of a word as accepted in common language, and all our explanation of words aims tent

in

is

at bringing

must

them

difference

It

is

about the conditions under which the ideas corresponding to be produced according to psychological laws. The real

merely that

is

in

the natural development the sensuous ideas

come first and are all formed number of elements involved

in

more or the

in

less

same way, while the

the

higher and more abstract

increases the variety of ways in which they are formed, differences of the

products become more

general process by which idea and word individual

is

essentially the

ideas

and the individual

difficult to

But the

expound.

become wedded

together for the

same throughout. We connect the word with at one time or another have been self-

an ideal-content which must produced, and

it

then passes through a series of developments becomes enriched and modified.

the

in

process of which this content

Look how

7.

the child obtains the almost exclusively sensuous ideas,

which belong to its first words, and enable it to make its first judgments. It always starts from the particular intuition of a thing or an event which is

named But

in

to

it

words are

;

proportion as

it

first

is little

understood in reference to particular cases. practised in apprehension

and

scantily pre

pared by a previous store of ideas, the intuitive image which enters into memory, and is afterwards reproduced with the word, falls short of being a faithful taining

the

man

object,

and exhaustive copy of the thing presented which might have been perceived in the

all

unless a practised observer

what he receives

and

in intuition

actually

to sense,

in

sees

stores in his

and of con

Even what

object.

the

memory,

Hence when we

presented

is

generally

begin to speak the traces which remain of the particular object seen can be no more than a quite inadequate to the object

itself.

rough and faded copy of the thing, in which, as

first

in a hasty sketch,

only

more prominent features appear. Generally speaking then, we can have no idea of what image the child really connects at any time with the words which it hears. When an intuition occurs similar to those already retained in memory none of the conditions are present which would enable the

it

to perceive

a difference between the present

fusion takes place immediately

object

name

is

called

and

is

and former

objects

;

expressed by the fact that the

by the name already learned.

Children

the

new

will give the

same

or

some

to things only remotely similar so long as they agree in

all

LOGIC

44

of those characteristics which have been securely apprehended, and this

Here we may find it possible for them to get on with few words. the explanation, both of the wit which so often surprises us in childlanguage, and of the numerous confusions into which, as we think, they makes

does not consist in subsuming something new

Progress, for them,

fall.

ideas, but

under familiar distinguish

more

to

in learning

apprehend more completely and

1

exactly.

We may

8.

say, then, that in the earlier stages of the Thought of the meaning of every word is connected with a particular in and there is here no difference whatever between particular and

individual the tuition,

The memory image which remains from our first imperfect is not retained by the mind as a fixed im reproduction is always the result of a new activity, and

general ideas.

apprehension of an object Its

pression.

instead of speaking of images

and ideas

we ought

as in a store-house,

as of solid

things lying in the

speak of having gained habits and capabilities of reproducing ideas, such as do not exclude

memory

really to

changes of more or hence in the product

less

a house, or landscape

an absence of some time, we find that its This quite different from our recollection of it.

actual appearance

of

uncertainty

is

the

importance in every act of reproduction, and

How

itself.

it

when

seeing a familiar object

and the general

memory-image,

expressed by Beneke as the

needed to unify

often

after

"attraction

of the

new images, and

with a series of

The process of continually ourselves for the present to substantives

function of a general idea. to confine

hand

to fix the

prominent features

keep the image fluid

and

common

shifting, so that

to

now

all,

one,

can come to the fore and determine new associations. th-at in

the natural course of

their sphere

;

their

law appropriately are

similar,"

is

the

and on the other

now

to

another, feature

It is for this

all

and admit new ideas of the same kind.

it

naming new things serves on the one

words have a tendency boundaries are indefinite, and always ready

Thought

that

all

so to give

This extension

is

reason

to

widen

to

open

continually

favoured by the fact that in

new objects we always notice and apprehend those characteristics which coincide with an outline already easily familiar to us ; we cover things, as it were, with our ready made images, and so conceal any new and distinctive features they may possess. But side by side with this As we gain process there runs another. most

1

p.

Cf. the very appropriate remarks of Steinthal, Abriss der Sprachwissenschaft, 148 sq., 401 sq., and Paul, Princ. d. Sprachgeschichte, ed. 2, p. 75 sq.

i.,

IDEAS AS ELEMENTS OF THE JUDGMENT we observe not only

practice in apprehension

but also those which are less prominent.

more defined and

new

to

and

richer in content,

objects diminishes, their

more

the

this

striking features,

way our images become

in proportion as their application

number and our power of

But

between them increases.

In

45

in distinction

of

this

distinguishing

kind wholes are

compared with wholes we do not begin by taking account of the differ ences in detail, and consciously sorting out the characteristics which agree :

and

We

differ.

constantly and unhesitatingly distinguish between persons

whom we know and do

not know, without being conscious exactly how an unanalysed total impression, as immediate in its they nature as feeling itself, which makes us recognise the familiar as such, and judge that the unfamiliar is not known. differ.

It is

It is

much

not so

the individual

frequency of observation as interest, which determines

and the accuracy of

attention

s

The

his apprehension.

images of objects which rejoice or terrify him, or which are connected with his needs and inclinations, impress themselves upon his all

their details

;

memory

in

but where objects are indifferent to him, he does not

and hence they leave only

trouble himself with accurate apprehension,

only the more striking

faded impressions which contain

characteristics

and can fuse with similar impressions over a wide range. In this way in his

we may

explain

how

mind and connected with

rich in content, others less defined

He may which all

give special

troublesome

is

other varieties are

Nor

kinds.

finiteness "

names

that

is

all

is

to the

in his

it

happens that of the images stored some are well defined and

his words,

and more

hen which

it is

a

in

and he cares nothing about the

he conscious that the idea

the specific kinds

not a bird,

change

meaning.

garden, the stork which builds upon his roof

"birds,"

ing things the less defined

liable to

lays eggs for him, the sparrow

hen."

;

"bird"

includes in

;

different its

inde-

we may hear others than children say Where there is no interest in distinguish

and poorer image, which is derived only from and flight, is sufficient, and this

the two principal characteristics of form

extends to flying beetles and butterflies. The history of language shows a similar development.

Its roots_are were fixed very general in meaning, not because the most general features upon from the first by a comprehensive process of abstraction, but because few distinctions were made, and only those phenomena retained and

apprehended and especially prominent. Particu the things are generally named after some one of these phenomena

named which were lar

easily

;

-

LOGIC

46 from

river

its

movement, the cock from

different aspects are arise the

and there

in different series

its

crowing, and so on. receive

apprehended in the things they numerous synonyms which cause them

to

Then

as

new names, be

classified

Further specialization does not

of similar phenomena.

and words originally take place until, as language develops, derivates arise, to different specific classes of things and events synonymous are applied with the special. Contrary the more general meaning continuing side by side to the common doctrine of the formation of general ideas, general precedes ;

individual as in language, as certainly as the incomplete and special in the the complete idea in which careful distinction is indefinite idea

precedes

presupposed.

A

and place with regard to ideas of qualities most of the general kind, Here, again, apprehension is at first

similar process takes

activities.

and deals only with considerable and easily distinguished characteristics. With the child as with language the first ideas of colours are few and uncertain in their differentiation,

together

movement

in

;

it

stage are the manifold differences observed

movement

this

are denoted by such a

Assuming

9.

word

intuition

going

or

word

"

running."

arises originally in

first

meaning of the word,

and

we can

see in what sense Generality attaches to such an idea.

That any idea may be general, lar ideas, is

upon

its

soon as

involved in

*>.,

applicable to any

number of

particu

nature as reproducible, and in no way depends

its

As having been formed from a number of such particular ideas. has disengaged itself from the original intuition with its spatial

it

and temporal connections, and reproduced,

it

is

is

a mental image which can be freely

capable also of fusing with a

and of appearing

number

of fresh intuitions

judgment. If we con our attention to the contents of the idea this kind of generality belongs

or ideas, fine

"

"

of a particular object, the incomplete

shifting image of which constitutes the

now

How many kinds

and denoted. as

that the idea connected with a

way from the

practised

to all similar forms, only at a later

hended and unconditionally extended of

is

which were formerly indiscriminately classed is the most familiar forms which are appre

differences

to distinguish

only gradually that sight

it is

as their Predicate in a

not only to images such as those of the sun or the moon, but also to the As often as the sun rises in the sky, or the images of particular persons.

moon becomes with the idea

visible

left

we have a new

particular intuition,

by a previous intuition.

identity of all these suns

and moons

The

which

is

unified

recognition of the material

follows later, and,

where continuity

IDEAS AS ELEMENTS OF THE JUDGMENT intuition

-of

is

reflection of a

no means of

absent, by

person

with the memory-image,

In a similar way the

necessity.

in a mirror, or his portrait,

is

47

immediately identified

and here again our knowledge

that these are

merely images, and that the name belongs properly to one individual, comes later, and checks our attempt to treat the idea as general, in the widest sense

chance that

Thus

so

;

far,

indeed, as concerns the idea

not the special content of the idea, nor yet

it is

determines whether or not that the idea

assumed

is

it

a matter of

its

origin,

which

general in the ordinary sense, but the fact

is

actually applied

to

a plurality of particular intuitions

to be copies of a real plurality of things,

this plurality as

we being conscious

of

the Singular must extend to a Plural.

such

This plurality

10.

itself, it is

not really general.

it is

is

at first

merely numerical.

When

a

number of

like

or indistinguishably similar things present themselves contemporaneously

or successively in intuition, not only

memory-image, but the time makes

it

each one identified with the

is

fact that the content of the idea

or temporal difference with the sameness of the image. antithesis

between singularity and plurality

As a

11.

rule,

when we

refer

mean

the

however,

it

is

first

same each

It is

here that the

appears.

is

we What we

not this numerical generality to which

say that words are general in their signification.

that their generality

is

is

necessary to count in order to reconcile the external spatial

such that they include different objects,

which are distinguishable and are actually distinguished by their contents. In this sense the idea tree is said to be general with respect to oak, beech, fir,

etc.,

the idea colour with respect to red, blue, and green.

Here we must be idea

careful to distinguish

and the generality of the word.

So

far

between the generality of the as the actual meaning of words

for the individual is

derived from particular images, the very indefiniteness

of an idea renders

applicable to things which

it

and temporally, but

also in their

content.

A

differ,

not merely spatially

visible thing

may be

repre

sented by copies of every degree of resemblance, from the few lines with

which schoolboys draw horses and

men

in their books,

to the perfect

photograph, and in the same way we may have a series of ideas, represent ing the same object with a gradually increasing definiteness, all continuing to exist side

application.

by side. The more indefinite the idea, the easier it is of But until we become conscious of the difference between

the various objects to which an idea once formed that idea

is

of the

same kind

is

constantly being applied,

as the idea of the sun, or an idea having

LOGIC

48

When

merely numerical generality.

the

word grass brings

mind only

to

a group of green, narrow, pointed leaves, and we disregard the differences between particular kinds of grass, then we merely see grass and all is grass

each apprehension becomes more definite and we notice between things which at first sight all coincided with a given idea, then, while the common name still remains, new ones are formed In course of time these crowd out for the more fully determined ideas. alike; but as

distinctions

the

more

which becomes too vague

indefinite idea,

botanist has

him there would be

no

arises set

down

To such

two eyes. is

things,

made

vivid.

The ;

as alike

by a

like that in the field of vision

word

be

to

image corresponding to the word grass or tree for a rivalry between differently determined forms which

ideal

general in

ideas there its

less

when is

a rivalry

practised apprehension

different in

nothing

images are presented to the common but the word. The

so far as

signification in

it comprehends different and denotes a number of distinguishable images by elements which

are alike in

common

It

all.

element

is

we

here that

in difference

;

are

to

i.e.

first

called

upon

to

realize the

form by abstraction the concept in

the ordinary sense of the word.

The same also, as

more

process goes on with the

more

fully

apprehension becomes more acute and

faithful,

determined

memory for

Here

ideas.

small differences

the originally single image resolves itself into many.

But

language cannot keep pace in its derivatives, combinations and qualitative determinations with this process of specialization also fails to ;

be equally retentive of vividness to

all

all

So that

images.

group of distinguishable not, however, all

particulars for

ideas, all of

memory

and imagination every word there

which

it

is

specially

finally

an equal remains a

serves to denote.

bear the same relation to the word

definite than the others,

to lend

connected with

it,

;

They do

one image, more

as the centre of the

group round which the others gather. In a neighbourhood where fir grow the image of the fir is that which a man primarily connects with the word tree ; any other varieties he know are trees

may

and

fall

into

the background.

The word

"red"

less distinct

is

most immediately distinguished from

connected with an especially striking impression, easily others as it becomes extended in application to further modifications Df the colour it ceases to denote anything definite, and calls to mind now

all

;

this shade,

possible.

now that, amongst a number which occur The word has become general its

and reproducing a

series

to us as

definite

equally

by losing meaning of shades which is not at first distinctly limited.

IDEAS AS ELEMENTS OF THE JUDGMENT Each of these shades

a general idea, in so far as

is

it is

itself

49

applicable

a plurality of particular intuitions, but their names (blood-red, rose-red, etc.) serve to remind us of the original process by which words derive to

meanings from particular intuitions. Essentially different from this natural development of the relations between word and idea is another process which is conditioned by the fact their

12.

naming we are always under the influence of a language which is The language in use hinders combinations which would already there. take To naturally place, and forces upon us others which would not. that in

declare the

common

one word

a very different matter from declaring what things any given

is

element in

all

the things which language denotes by

individual subsumes under the idea which he considers they resemble.

Many words

are for the individual

of the ideas which

and

first

mere homonyms, the

essential similarity

caused them to be named alike escapes his notice is language which first makes us conscious of many ;

same way it similarities which would never have been discovered by one man carrying on his comparisons independently. On the other hand the language in in the

use prohibits and destroys

many

similarities,

and

forces

upon us

distinc

tions which might never have occurred to the individual thinker. latter case the idea is forced into fuller determination,

In the

but in the former

how many

really disconnected ideas may correspond In Etymology we aim rightly at tracing the most remote connections, but our task then is quite different from what it

it is

to

is

impossible to say

one and the same word.

when we endeavour

to realise the actual process of thought in the indi

vidual.

For the individual the meaning of a word is determined, not by its etymology, but by the thought of those objects to which it is applied in ordinary language.

We

never think, until we have been taught, that there to the cock on the barrel, the cocking of the

may be something common trigger,

and the cock

in

same name

called by the

the poultry yard, which led to their ;

for us the three

connected, the words have become mere homonyms. the

original

dis

In the same way

;

metaphorical force of words such as concept, judgment, conclusion. If the

13. tent,

being

meaning of the words by which we denote most of the is completely lost to us no one feels now the figura

psychical activities tive,

all

meanings are completely

which

words which we use are only signs of a definite ideal con detachment from present intuition has gained an in

in its

dependent existence in that s. L.

it

is

capable of mental reproduction at E

will,

5o

then it follows that by themselves, by their mere sound, they can never In order denote the particular as such, and as it is presented to intuition. that a word may be understood to apply to a definite particular object we

have to make use of special expedients, such as possessive or demonstra or else we must be able to assume that though tive adjectives or gestures ;

is unspoken, it will be correctly by the hearer. But when a particular thing is denoted by means of a word it is always because it is recognised as agreeing with the

the reference to a definite particular thing

carried out

general idea expressed by the word; I can denote

me

as this book, or

word book

is

It is true

This

is

my

the thing lying before book, only because the general meaning of the

applicable to that

one

it.

class

1

of words denotes particular things as such.

either because the thing corresponding to the idea

is

be

actually to

found only once in the world, as in the case of sun and moon, sky and earth, or because a name has been given by express agreement to the particular thing as such,

on purpose

objects, as with the proper

the meaning of these

to distinguish

it

from other similar

names of people, towns, mountains,

is still

recognisable

it

may be

etc.

Where

traced back to general

Mont Blanc, Neustadt, Erlenbach but this meaning, words, which explains the giving of the name, is in most cases forgotten, and the idea aroused by the now meaningless name is only that of a definite as

in

;

Nor can they fulfil the function of comprehensible way unless the object has been intuited and remem The import of the name is related to the momentary intuition of

particular

object.

words even in bered.

this

the person or mountain, as the general

word

to the particular thing

;

it

cannot be applied to anything present to sense unless the identity of the present intuition with the mental image is recognised. The proper name is

distinguished from the general

word only by the consciousness which is a particular thing and

that the corresponding reality the same in fact. always

accompanies

it

Finally, there are also certain relational

words of general content, which apply only to a single thing; reference to a single object forms part of their meaning, as with all true In so far superlatives, or ordinal numbers. as only their context can tell us like 1

demonstrative

adjectives,

what is compared or counted they are which also can express their particular

In reference to this Mill s analysis is superficial (Logic, bk. L, ch. 2), when he classi the adjectives, white, heavy, and even the demonstrative adjective "this," as names of things. Cf. also Paul, Princ. d. Sprachg., ed. 2, p. 66 sq fies

IDEAS AS ELEMENTS OF THE JUDGMENT object only by day, but

it is

means

The first of January 1871 is a single we assume a definite system of enumeration

of a Relation.

only

definite

51

if

;

Russian calendar and for ours, and the meaning of the expression depends further upon the idea of a series of days and years which is nothing more than an object of Thought. it

differs for the

The peculiar function of words makes it indispensable to the completion of the judgment that the predicate should be expressed in them; the subject, if not general, can dispense with the verbal expression. i

It follows

.

from what has been said of the nature of words that we must

be careful to distinguish whether a word signifies merely the ideal content immediately denoted, or whether it is being used to denote a definite par ticular thing

which

not indicated as such by the meaning, but which

is

represents that meaning and can therefore be

named by the word. depends the essential difference of the way in which words are related to the subject and predicate of a judgment. When,

Upon

that

a statement does not refer to the content of the subject term as

is,

such

this distinction

as in definition

sary that

a significant word. "this

tive a

is

but to a definite particular thing, it is quite unneces or even be able to denote, the subject idea by

we should denote,

red,"

mere

"that

We may is

falling

";

merely use a demonstrative

and we may

is

ice,"

demonstra

gesture, or even give utterance to the predicate without anything

the mental process will

further,

"this

substitute for this

still

be a judgment

which a statement

in

made about something.

is

We

see this most clearly in the judgments in which

all

human judgment

begins, those in which definite objects of sense-intuition are recognised

The

and named. its

child

makes a judgment when

it

names the animals

the exclamations elicited by a startling sight (father

!

fire

!

the cranes of

judgments ; it is only the verbal expression which not the mental process. 1 incomplete, Ibycus

1

in

picture-book by pointing to them and pronouncing their names, and

!)

are proper

is

The first step is the sight of the Herbart, Psychologic (sammtliche Werke), iv. 169. the idea immediately given by this arouses the previous idea, which fuses with it. ; immediate perception gives the subject, it is the fusion which would be denoted

thing

The

by the copula

;

the place of the predicate

is

taken by the previous idea, which

is

aroused

and fuses with the perception. Paul (I.e., p. 104) takes sentences in which what is said and hearer, the situation being the predicate kt Some one :

is

the subject for both speaker example, that a child

sees, for

LOGIC

52

On

2.

the other

hand

it is

essential to the

(e.g.]

an object

completion of the judgment there may be cases where

It is true

that the predicate should be spoken.

recognised for which the approximate word

is

is

wanting,

mental process can find no expression ; but for as an immature this very reason we regard the process as incomplete to be complete in which alone that consider and judgment production,

and where,

therefore, the

the predicate appears, denoted by a word. predicate that the idea belonging to

It

is

indeed essential to the

should be none other than the

it

meaning of the word, the ideal content which is connected with the word and has thus become ours. It is no matter whether this idea is

as such

general in the ordinary sense, or whether "This

Socrates

is

"

the

is

to-day

"

is

as

much

of January

first

neither Socrates nor the

first

is

in

danger

the idea of a particular thing.

as

much

as

"Socrates

"

to-day

ideas which can

at all

then he merely calls to the person in charge of

;

is

a

is

cold

man";

"

;

although

of January are general ideas in content. 1

enough that they are ideas and with the spoken word. is

"

it is

a judgment as

it

It

be reproduced by

the child.

This only

indicates the object to which attention is to be directed, that is the logical subject ; that which the person addressed sees when she obeys this direction of her attention gives her

But here, I think, we must distinguish between two things. The ex an imperative, not a statement ; and it can only be understood as an imperative. For the judgment really passed by the person speaking "the child is the

predicate."

clamation in

is,

in intention,

"

danger

finds no place in the words of the exclamation ; at the most it makes the anxious tone of voice. The object is to direct attention to the thing With this view it is simply named ; thus the full expression of the thought

itself felt in

named. would run

"

thus,

take care of the

child."

and the word of cry of alarm, "Fire of which fire is the predicate ; the latter

It is

a distinction similar to that between the

Fire." The former is a judgment, an imperative. Fire is the object, not the of the incomplete imperative and the case is the same with "child" in the preceding example. By merely exclaiming "the child" all that I can communicate to (subject, any one as the object of his and my belief and assent, is that what I see or think of is tlie child. But then the word is predicate. In like manner the exclamation, "the "

!

command,

"

"

"

is

;

or Daniel, a second Daniel," contains the judgment that the person thought a rascal, or a second Daniel ; and on this is based the indignation or joy which is manifest in the tone of the exclamation. 1 Volkelt holds (Erfahning und Denken, 319) that in This is propositions such as my father, this is the moon," the predicate indicates the common characteristics of that which I denote as my father, etc., hence not the individual as such. It is true rascal,"

of

"a

is

"

certainly

that the relation between a proper name which is used as a predicate (according to p. 42) is similar to the relation between a general idea and

and its subject an idea compre

hended under

it. It is similar, that is, in so far as the proper name (particularly in the case of changeable things) does not indicate a momentary state, but that which is identical through all states, or that which might with less be called the common element.

It

does not, however, follow from this that

meant.

it

accuracy is not the individual as such which

is

CHAPTER

II.

SIMPLE JUDGMENTS BY

JUDGMENT we mean one

in which the subject may be regarded does not include a plurality of independent objects, therefore be represented as singular the statement made con

a SIMPLE

as a single idea

and may cerning

;

it

;

must be distinguished of these simple judgments subject

is

Two

subject takes place in one act of judgment.

this

thought of as having a particular existence

NARRATIVE JUDGMENTS

;

classes

those in which the

:

is

(this

and those of which the subject idea

meaning of a word, nothing being stated about any these are EXPLICATIVE JUDGMENTS.

is

white)

the general

definite particular

thing

i.

NARRATIVE JUDGMENTS. 9-

The simplest and most elementary form of judgment is that in which we name particular objects of intuition. The subject-idea is given im mediately to intuition as a unity, the predicate-idea with

its

appropriate word, and the

by which the two ideas are consciously unified iv OVTCOI/, Aristot., de i.

anima^ III.

It is easy to explain the

a sentence as

"

this

is

6.

mentally reproduced

vo^^dr^v oxnrep

(o-vvOccns

4303, 27).

inward process which corresponds to such

Socrates,"

the abbreviated exclamations

is

act of judging consists in the thought

is

"this "

"

fire,"

the

stork,"

The

the expression of immediate recognition.

"this

snow,"

when

is

blood";

or to

these appear as

object before us awakens

by some former impression, and connected with the word, and the two are. unified. That which I am looking at is, according to an idea

its

left

content, one with that which I have in

this unity,

and

proposition. processes.

it

is

By In the

this

this first

my

idea

consciousness to which

the judgment

place

it is

is

I

;

I

am

conscious of

give utterance in the

distinguished

from the kindred

distinguished from what has been called

LOGIC

54

we

unconscious fusion

I

not here discuss whether the expression

will

Here the of an actual process. appropriate and descriptive in ideas such a with once at to unite previous

is

new image is way that the

supposed of the previous idea at the product of the union is merely a repetition nor of new is no and there most more vivid ; holding apart distinguishing old, of that

ference

to

which this

conscious act

is

is

present and that which

Herbart

right in pointing

is

possible only

ideas are held in suspense,

when such

and

that

it

is

remembered.

With

re

out that a judgment as a

fusion

is

therefore has

delayed and the two its

most characteristic

form when a question or a doubt has intervened. As a rule, however, it is true that attention is chiefly claimed by the present, and only its utter

ance reveals that the idea already in our possession has become active, particularly in the case of the mere exclamation which accompanies re 1

cognition.

In the second place, the judgment

is

from the merely involun

distinct

tary reproduction of a previous image which might co-exist with the

without

being unified with

seeing a

fire

I

for instance,

It

might happen, should remember other occasions of it.

fire,

that

first

on

but that each

image being accompanied by its distinguishing circumstances, they should be prevented from combining into one, and being thus retained in their From the Denominative Judgments described above, in which the object presented is (according to his view) compared with others previously known and called by their name, 1

Stumpf (Tonpsychologie, vol. i., p. 5) distinguishes yet another kind of judgment the Judgment of Habit. It often happens entirely as a matter of habit that a phenomenon when seen or rieard reproduces in consciousness both the appropriate name and the which case the previously perceived object judgment x is red, x is the note "

A"

;

"in

does not enter into consciousness at all, much less is compared with the present object." I cannot however find sufficient reason for this distinction. On the one hand it is

not, generally speaking, the case that in denominative judgments as I understand them a present object is compared with previous objects in the sense that the latter are present to thought as differentiated particulars and their name transferred to the new object.

That which is reproduced by the present object is only the general idea connected with the word, and there is no need of any express comparison in order to be aware of its coincidence with what is present. On the other hand it is clearly too much to say that what was previously perceived "does not enter into consciousness at all "how else should a recognition take place differentiated that

it

? Only so much is true that it is not necessarily as conies into consciousness. The process goes on so rapidly that I am :

not aware of each particular step which is necessary before I can

;

when I meet an acquaintance the memory-image him pales in contrast with my present percep in consciousness. Thus it becomes impossible to

recognise

but

must have taken effect between judgments of habit and those which are not of habit all that we ; can allow is that when we are dealing with familiar ideas which are well known and often applied, the process, which is always essentially the same, takes more tion,

draw a

it

line

place

rapidly.

SIMPLE JUDGMENTS

55

number of similar images. The union can when no such hindrance occurs either because all the

individuality present merely a

only take place

accompanying circumstances are the same, or because the content of the idea is already isolated and raised into generality.

When

2.

this simplest

know

and most immediate form of judgment

ing in its original sense of recognising

presupposed that both ideas are undivided wholes, not consciously resolved into their Immediate unification is thus distinguished from the particular elements. takes place,

it is

other case in which a series of intermediate acts of thought

and predicate

in order that subject "

"

blood

maybe

When

unified.

is

necessary

"snow

"or

denotes a scientific concept, the distinguishing characteristics of

which are present in memory, we do not form a judgment at first sight, but investigate the object in order to ascertain whether all the charac of the concept are appropriate to

teristics

we place

of a process of inference that that

we

attribute to

it

It is

it.

only upon the ground

the object under the concept

;

i.e.,

the whole complex of qualities universally accepted

snow or blood. This judgment, then, is mani mediated in it is foldly repeated several times the process which takes at in once the coincidence of two images through the unanalysable place act by which they are brought together. Between these two extremes as contained in the term ;

may be connected with the predi and corresponding to it a graduated series of mediation of the judgment. But what the judgment always states is, that the idea of the there lies a whole series of ideas which

cate terms,

predicate agrees with that of the subject in such a

way

that the predicate,

one with the subject. It might also be held that there is a process of inference in the numerous cases where the predicate contains more than can be offered by the first in as a whole,

which gives rise to the judgment. When a child sees an apple and then the predicate-idea includes also its taste and its quality as

tuition

names edible

is

it,

;

and

in the

"

judgment

this

an apple

is

"

we might suspect an

ference from the visible image to the presence of the other attributes.

previous experiences have

made

the association of the other attributes with

the visible image so firm that there

them

;

in

But

is

no conscious

distinction

between

the visible image at once awakens recollection of the other attributes,

with this enriched intuition that the predicate-idea is connected. this looks like an apple, there make the inference

and

it is

The

child does not

fore

we can

eat

"

"

it

reproduce the idea

;

but the sight of "

"

apple

it

and lead

gives rise to desire, to

its

and both together

being named.

In such cases

LOGIC

56

also, then,

we

still

have the simple coincidence between the present intui from idea, and they are to be distinguished

and the remembered

tion

cases in which further attributes only occur to us in

consequence of the

name.

and a reproduced image Complete coincidence between a present 3. does not take place only when we recognise one and the same object as which identifies the ideas, such; when, that is, we may add to the judgment a consciousness of the material identity of the things which is not itself in It

cluded in the judgment.

occurs also whenever there

is

no conscious

ness of difference between subject- and predicate-ideas, so that what is ap and consciously noticed in the object exactly coincides with the

prehended

This

predicate-idea.

same

of the

snow

this

is

of an object

comes

a sheep

is

always be the case where particular phenomena is only distinguishable by special attention (this this is a poplar) ; or, again, when the apprehension

will

sort are

determined by a preconceived idea, and that part of it which is exhausted by the predicate-idea; here the

into consciousness

predicate-idea itself

is

not absolutely fixed, but

is

often

unconsciously

by the subject which happens to be present. To these must be added other cases, in which we are conscious of

affected 4.

but are not led by it to an express judgment. Such are the judgments which merely make a comparison or note a similarity, and which difference,

as in fanciful or

frequently

humorous comparisons take exactly the same judgments most of the metaphors of lan

external form as denominative

:

guage also depend upon this process. Such, again, are the judgments in which the subject-idea is richer and more fully determined than the predi cate-idea, but only that part of it is noticeable which coincides with the predicate-idea

judgments, that

;

and more general idea than the by

This

it.

is

particularly evident

of the idea coinciding with

the special

to

it

which the predicate is a less definite which we know is not exhausted

my

when

object,

I

for

in

fully

determined.

Not

thought, which

is

image

until

there any interest in subsuming under the

its

special

name be

to

the natural course of thought the predicate-idea

easily connects itself with every

and most

ideas at

do not know the

and am therefore obliged

its

name;

which most

in

more general name (this is a bird, a tree, a fluid); or when name is not so familiar to me as the more frequently used

content with

general

is,

subject,

is

that

scientific

which

is

most

like

thought begins

is

most general ideas ordinary concerned with the particular, clings to the most concrete

command.

;

(For logical purposes ideas which are expressed in

SIMPLE JUDGMENTS

57

language by the more exact attributival determinations of a substantive, such as black horse," round leaf" are just as much one as those which "

"

can be expressed by one word.

Their comprehension into one whole has

when they appear as predicate.) In naming we naturally think first of the ideal content as a 5. unity, but in the process of thought the predicate-idea becomes connected with the idea of plurality wherever we have the numerical generality of many already taken place

vaguely remembered individuals, or wherever the meaning of a word con a number of slightly different ideas. When a word denotes a sharply defined individual image, this is accompanied by a number of individual

sists in

images amongst which the new object ranks itself as another (this finds this is a tree when the meaning of the word has expression in the form ; "

")

not this individual determination the generality of the predicate appears in our consciousness of other ideas which are nearly akin to the one which

happens

to

be before us

Herbart

this is ("

paper and wine stand is

for a

paper,"

number

"this

is

wine

";

here the words

of slightly different ideas).

right in saying (Introduction to Philosophy,

i.

So

far

92) that the con

cept which serves as predicate always loses part of its meaning in that cap acity, only so much of it enters into thought as can be connected with the

Of all the many ideas comprehended by the which coincides with the subject. pre-eminent These denominative judgments 1 have always ^preceded, when the

subject which word,, that 6.

one

it

determines.

is

concerning which the judgment is being made is denoted, not merely by a demonstrative, but by a significant word. This flower definite object

"

is

a rose

"

includes a twofold denominative judgment

by the less definite

word

;

first,

there

is

the

which has taken place previously,

naming flower, and of which only the result appears in the verbal expression of the subject then the more exact naming in which the judgment itself consists.

\

1 I choose this expression in order that I may have one denotation to cover statements which elsewhere are sometimes treated as judgments of subsumption (when the predicate is a more general idea), sometimes as judgments of identity (when the predicate completely coincides with the subject). In the simplest cases there is no clear line between the two in both the process is essentially the same, i.e. we are conscious that what is presented is in its totality one with a previously known idea. Schuppe (Erk. Logik, p. 375 sq.), in his thorough and appropriate treatment of the subject, calls this process pure identifica tion ; but since it is seldom a question of absolute identity between the ideas of subject and predicate, I should prefer to avoid the expression. In the same way I avoid using ;

the expression subsumption ; for this, when applied in its strict sense, does not represent the general idea which is connected with the term in its popular use, but a logically deter mined generic concept under which we place a particular thing or a specific concept.

!/,*

LOGIC

58

The

7.

and processes to things is so strong, which denominative judg

habit of referring attributes

that there are comparatively few instances in

ments about them do not also include a judgment of attribute or

activity.

our power of abstraction enables us by means of "that" and "This to denote even the mere attribute or activity as such. Still

"

walking, but running which are spoken of

There

is

"this

is

dark-blue, not

but colours and activities apart from things.

here,,

however always the tendency

to the thing.

black,"

not

is

not things

is

it

"this"

from the attribute or activity

to pass

u.

Cf.

10.

When is i.

judgment concerning a specified particular thing

the predicate of a

a verb or an adjective, then the judgment contains a twofold synthesis.

The

synthesis which unifies the thing

and

its activity,

attributes, in the subject-idea itself; 2. the synthesis

vity or attribute contained in the

the thing

which

and

its

unifies the acti

thought of the subject with the activity

or attribute denoted by the predicate-word, that

is,

names

by the predi

it

cate word.

In uttering a judgment, such as

i. hot"

iron

"the

a subject with

of the words

;

glows"

"

:

horse

cloud

this

runs,"

we

is

first

red

"

"

the stove

is

express the unity of

being indicated by the form we then name the attribute or activity which we have per its

ceived by unifying "run."

"the

activity or attribute, this

it

That which

with the general idea

is

given to perception

is

"red,"

"hot"

"glow"

or

the red cloud, the hot stove,

the glowing iron, the running horse ; but we analyse the originally undivided whole of perception by distinguishing and separating the attribute and from the idea of the We have and activity subject. by its

shape

recognised

position that what

we

see

is

a cloud,

and

this recognition

expressed in

is

it by the definite subject-word cloud we are struck by its colour, and hence this is easily disengaged from the whole. It is this colour which

calling

we

;

call red,

thing which

ment,

it is

and ascribe is

to the cloud as its attribute.

running to

running, but

we

under other circumstances ticular

be a horse

;

We

as presented to us

recognise the it

is

in

move

distinguish this incident from the subject which is

known

kind of movement which

we

to us as standing

still.

express as running.

It is this

We

par

have thus

distinguished two constituent parts in the total-image, the thing and its in each of them we find ; again an idea already familiar to us, and by uniting these two elements in our statement we express just what we

activity

SIMPLE JUDGMENTS

59

have seen as a unity of a thing with its attribute or judgment presupposes an analysis, whilst its own work different elements.

By

Thus the

to synthesize the

twofold synthesis the judgments which state attributes and acti

this

it

is

1

from the simple denominative judgments

vities are distinguished

latter

activity.

the subject of an undivided whole which

is

is

in the

;

unified with the

predicate.

We

have spoken of the generality of substantives when treating of the and what we then said applies also to the relation between ;

ideas of things

the generality of the predicate-idea and that element in the subject-idea

which corresponds

we

to

Such a

it.

relation

may

vary from the case in which

are conscious of a complete coincidence (as, "

this lichen is

colours,

cate-word activity

denote the

too indefinite to

is

down

"),

of the subject, and can only be

means of

e.g.,

with sharply denned

to cases in

fully

which the predi

determined attribute or

made

to agree with the idea by and other distinguishing words. opposed to that which would force even

further determination with adverbs

The view we

2.

sulphur-yellow

here take

is

such judgments as these into the conception of a simple subsumption of the subject under the more general predicate. But the predicate which expresses an attribute

general only with reference to the attribute of the

is

The predicate which expresses an subject, never to the subject itself. is with reference to its activity. We must distinguish activity general only attributes

and

activities in the

verbal predicates to them. "

What

is

this ?

But

"

question must be,

"

adjectival or

the answer to the question,

we

"

is

a judgment presupposes, therefore, that action or attribute

we can apply

Simple naming are to answer with an adjective or verb, the Such the quality of this ? What does it do ? is

if

What

subject before

and the

we have

distinguished between the

thing. ii.

In judgments which express the attribute or action of a thing, the move ment of thought is not always the same that which first comes into con ;

sometimes the thing (the grammatical subject), sometimes the In the former case the attribute or activity (the grammatical predicate). sciousness

is

attribute or activity

then

named;

is

first

in the latter

distinguished as a part of the total idea, and

it is

perceived

first

by

itself

and named, and then

referred to a thing. :

Cf.

Wundt, Logik,

i.

136

schr.fiir iviss. Philos., 1880,

sq. iv.

Also

458

sq.

my

treatment of the question in the Vierteljahrs-

LOGIC

6o This

(

1 and

last act

reference to a thing

is,

under certain conditions, omitted,

omission we find the explanation of the so-called impersonals. impersonal propositions are those only from which all

in this

Strictly speaking,

those in which a subject-thing is thought of a subject-thing is excluded, not 1 and indicated but expressed. only vaguely implied, i. When the statement which ascribes an attribute or activity to a thing starts

from immediate perception, two things

from the

first

this total

the thing with

idea,

and form

is

action, state

;

or I

may

I

may happen.

and

may

perceive

attribute, so that I analyse

out of

my judgment

iron glows, the balloon rises

which

its

it

:

perceive at

the leaf

is

faded, the

only that element

first

expressed by the adjective or verb, a colour, a flash of light, a it is not until afterwards, by a second act, that I

movement; and then

recognise the definite subject of the attribute or activity, "there

runs

Rhine,"

a

"

hare";

there

a dead

flies

leaf";

and can name

"there

sparkles

it

:

the

etc

In the latter case the synthesis which

first

takes place

is

that

which

names the given phenomenon of shining, sparkling, movement ; the refer ence of the attribute or action to its thing is not added until afterwards. In such cases language will also naturally begin with that which

is

first

The Hebrew custom immediate expression of a mode of

present in consciousness, with the adjective or verb.

of putting the predicate

first

the

is

thought which moves pre-eminently in sense-perception as particular languages continue to

pression of the active

movement

;

and

be the immediate and

is

furthest

ex

of ideas, they have retained their freedom

of beginning either with the predicate or with the subject. determines the position of the word entirely according to character,

in proportion

unartificial

removed from

French, which its

grammatical

this original flexibility. 2

1

Cf. with this F. Miklosich, Subject lose Satze, 2nd ed., Vienna, 1883 ; Schuppe in the Zeitschrift fur Volkerpsychologie und Sprachwissensch. , vol. xvi. 3, 1886; essay, die Impersonalien, Freiburg, 1888, and Steinthal s review, Zeitsch. filr Vblkerps., xviii.

W.

my

170. It might be maintained that we must always regard that which sciousness as the logical subject, because it is the given point with

ment

is

connected.

But

first

enters into con

which a further

ele

would be a doubtful proceeding to ground the distinction between subject and predicate only upon the chance priority of the elements of the judgment as they might happen to succeed each other in the individual, instead of upon the contents of the ideas themselves. The relation between the ideas which we denote by verbs and adjectives on the one hand, and by substantives on the other, necessarily involves the thought that the objective foundation and presupposition of that which is expressed in the verbal form is that which the substantive denotes. When we apprehend motion,

etc.,

we

it

are led by

its

similarity to other cases to think of

it

as something depen-

SIMPLE JUDGMENTS These two

2.

the reference of

acts, the its

naming of a perceived

thing, are sometimes

and more widely and ob

attribute or activity,

still

All that

viously distinct. is

to

it

61

denoted from

is immediately perceived is an impression, which resemblance to previous cases, by an adjective or verb

its

;

being added in thought only through association and on the ground of former experience. This takes place especially with sen the thing belonging to

it

That

and smelling.

sations of hearing

of a visible and tangible object

due

I

can predicate a sound or a smell

an act of combination by means of which the sensation of the ear or the nose is referred to the object which

makes

is

to

known at the same time to the eye and the hand. We cannot how this combination comes about but in all ordinary so much a matter of habit, the visible signs of the origin of the

itself

here investigate cases

it is

;

sound are so familiar

and

(as with crying

mer and the stamping of the

foot) that

talking, the

we

knocking of a

think the sound

is

perceived by us as the activity of a definite visible thing.

ham

immediately

But when a

noise strikes the ear without our being able to see the thing which pro

duces it, this thing must be added in thought our judgment does not the appear as the result of the analysis of a given complex, as when I say, leaf is yellow," but as the result of a synthesis by which the thought of a ;

"

thing belonging to

very

many

is

it

scarcely conscious of familiar idea of the it

represents

ing,"

added

to the

cases this association

it

in

it.

dog

is

is

When

I

hear

my dog

there as soon as the

the act of barking,

may be regarded

sound which was given alone. In and certain, and we are

perfectly easy

and

my

barking at the door, the is heard ; my idea of

sound

"

judgment,

the

dog

as the analysis of the idea of the barking

is

bark

dog which

has thus been put together by association. But it is different if the associa tion is not certain, if I hear unusual or imperfectly defined noises, such Now there intervenes the as the cry of an unknown animal in the wood.

and I am unable to put together any from the analogy of my former experience, definite image. I certain, a from that the sound proceeds thing, but I cannot get any definite idea "

question,

What

is

that crying ?

"

am

;

the synthesis referring the sound to a thing remains uncompleted, and the dent, something which presupposes and demands a reference to a thing. By^pur .choice of the adjective or verbal form, we indicate that there is a subject, of which the verb and

Grammar is right, therefore, in retaining adjective are to be regarded as determinations. the substantive as subject, even when the concept of the verb is the first in the psycho fundamental presup logical series of which we are clearly conscious ; it contradicts the positions of our thought, to predicate a thing of an attribute or activity. is subject to apparent exceptions will be discussed hereafter.

How

far this rule

LOGIC

62

"

can only be denoted by a

thing

"

something

which

is

quite indefi

nite.

It

we

accords with this that

are apt to look

upon the sounds which we

hear as independent objects, and to abstract from the things producing them. Having a longer or shorter duration in time, and definite limits, they are apprehended as distinct

phenomena

and substantives

;

like

thun

point to a thing,

waver between being abstract nouns, which and concrete subjects which denote independent objects,

and of which, in where there

is

der, shot, whistle, call,

etc.,

their turn, verbs

may be

predicated

a call resounds,

:

person who calls. The same thing Coldness and warmth are on the occurs in the region of the other senses.

e.g.,

no reference

to the

one hand names of the attributes of a thing on the other they appear as independent existences, the question of the subject to which they belong remaining in the background. Here, again, the synthesis by which thought adds a thing to every sensation (which can at first be expressed only by an adjective or a verb)

not complete

is

or, at

least

does not find complete

expression. 3.

By

recognising the twofold synthesis in

actions or attributes to a subject-thing,

all

propositions which ascribe

we obtain

the key to the solution of

the difficult and much-discussed question as to the logical nature of the ]

so-called Impersonals

more

;

correctly speaking, of impersonal proposi

tions.

Amongst

the statements which contain a predicate

verb or the verb

"to

be"

without any expressed

which are

ojnly

denoted subject,

or definitely

distinguish two classes;

whether a simple

combined with an adjective or substantive, it

is

important to

apparently

those which are really impersonals, and so.

ReaMm personals

those

are those in which the

thought of the thing to which

the predicate would apply is entirely we cannot even ask what the thing is. The others are propositions in which a subject, though not named, is nevertheless implied, although the idea may be indefinite and denoted only by the neuter

wanting, in which

pronoun or the terminal hungert,"

"hungert

mich

"pudet,"

goes/

"it

diirstet

there

is

no room

German

say in for

the

question

"

mich what

any more than a substantive can be added as subject to or "pcenitet." But when I say is beginning," "there it "

;

"it

is

"

over,"

series of events either

battle;

When we

inflection. "

"mich

and

I

it is

finished,"

I

always

expected or going on

:

mean something

definite, a

a play, a piece of music, or a

assume that the person who hears

me

has his attention

SIMPLE JUDGMENTS same

directed toward the necessary. brevity,

Here

thing, so that

any more accurate denotation is un is only chosen for the sake of

a real pronoun, which

would be

I say,

difficult to

is

mean

is

"

is

it

name a

indefinite extension of that

the subject

I

superfluous, or

to the nature of the thing meant, too circumstantial.

same way when

the

is

because the express denotation of what

perhaps owing

it

"

"it

63

slippery, dusty,

is

I

mean

In

the roads

;

subject in words, because of the

definite

which

wet,"

slippery or wet;

on the other hand,

already indicated definitely enough by the nature of the

When we

predicates belonging to them.

we

"

it is

say

shady,

it is

full,"

can only mean a certain space when we say it thaws snow and ice. It is true that an imperceptible transition from one class to the other "

"

;

often takes place

;

and we cannot

whether or not the pronoun still

why

"

"

it

tell

from the mere grammatical form

or the personal ending of old languages

indicates a subject-thing to which the predicate applies.

This explains the two classes of so-called impersonals are often confused, although

extreme cases they are definitely distinguished. It explains also why it all impersonal forms we must be able to find a

in

has been thought that for

subject in the sense of a thing to which the attribute or activity,

though

all

that could

be

predicate

finally

belongs as

its )

found to serve as such

a subject was an indefinite idea of the totality cf being, an idea which no

one

really thinks of in

When

speaking of a particular perception.

real impersonal propositions serve to express

accessible to immediate outer perception,

we nor

start

from a simple sense-impression

memory

supplies a subject.

hear a carriage

rattle

When,

it

something which is it lightens, then

thunders,

which neither perception

to

for instance, I see

a rocket

itself

rise or

over the pavement, the action immediately added to

the sound or sight which was given alone

naming, the unification of the This naming may take place by means of uninflected, onomatopoetic words, which merely reiterate the is

present impression with a familiar idea.

special

thunder, that leave

it

of the

or by substantives (that is concrete and abstract, between lightning) which, wavering undetermined in what direction thought will proceed to follow out characteristics

the event.

impression

;

is

But language, guided by experience of

similar cases, offers

verbs for the temporal event, and the present perception

means of the customary

inflections, the justification

is

expressed by

of this being

that

the personal ending of the third person was without doubt originally a If a substantive were added, it would interpret what was thus indicated, and would determine it more exactly as the

demonstrative adjective.

\

LOGIC

64

But

thundering thing.

if this

reference which the verb implies cannot be

the impression itself remains as the subject actually carried out, then only

and the termination can indicate nothing but the present The reference to a subject-thing which is contained in the

of the statement, impression.

is then an empty customary form ; we pronoun of modern languages in it the ? and answer sense of a what lightens cannot ask thing, "

however the

All that the impersonal proposition can

indefinite.

phenomenon

"

"

"

present at the

the particular flash of light

moment

;

the subject

is

do

to

is

name

nothing more than

itself.

This limitation becomes very clear in cases where we know quite well what the thing is which flashes or makes a noise, but omit any expression of it in language as a matter of course, because we are interested merely in

what

is

seen or heard.

German, when we What we sound.

meaning "

way

there

;

es brennt

is

which

is

stress

lays is

something burning, is

Es

"

lautet,"

are interested in

no object

"

course something

Nor

"

"

es

pfeift,"

es

klopft,"

we

say in

are quite certain as to the nature of the cause of the is

the signal

who makes

in saying

upon the

fact that

we have heard and the signal.

a

fire

has broken out

burning, but the tacit subject of the verb it is

merely the

fire itself

its

In the same ;

of

not this

is

as perceived by us.

there any doubt that this limitation of the statement to the state

perceived or

felt,

applies also to the

express subjective states of feeling

mir schwindelt, ekelt,

graut,"

etc.

"

Mich

numerous impersonals which

hungert, diirstet, mir

ist heiss,

permit of absolutely no reference of

these verbs to a subject of which they are the activity. Nothing is given but the present feeling itself, and this contains no reference to a thing giving rise to

Again, we

it.

which express in the passive form, and without any reference to an agent, an activity which has been perceived es wird gespielt," etc. Here again, all that we do is to name the event find also statements

:

"

perceived without proceeding further to the denotation of the subject in

which

it

takes place.

mentioned

For further examples

I

may

refer to

my

above-

treatise.

The way is already prepared for this separation of the synthesis of naming from the synthesis which refers the named phenomenon to a subject-thing, by the distinction between the verbal forms of substantive, adjective and From verbs and adjectives we can abstract substantives which enable that which generally appears as dependent upon a thing to be thought of by itself; we can make use of infinitives (I hear

verb.

talking, ringing,

SIMPLE JUDGMENTS

65

which are quite impersonal; and in the same \vaya statement is possible of which the logical subject is nothing more than the event or state

etc.),

perceived at the moment.

These propositions are that a subject-thing

"without

a

only in the narrower sense

subject"

wanting; they are no exception to the general nature

is

of the proposition which expresses a judgment.

known

of a

general idea with a present

phenomenon which ending with

is

They contain

phenomenon

the subject, and which

is

;

the synthesis

and

this

is

it

indicated by the personal

originally demonstrative significance.

its

just because they name something which is present, such proposi tions also contain an implicit statement of the actuality of the event named

But

for is

;

always immediately assumed that the particular object of perception This does not, however, make them existential something actual. it is

judgments

jmean

when we say

in the ordinary sense;

lightens

"it

!"

we do

not

to predicate actuality of the lightning, but to predicate lightening of

something actual. The naming of the present impression is the funda mental act, without which the proposition, as the expression of present When we say it lightens, it perception, could never come about. "

we must have seen a flash in the sky and recognised it as light but must have had a sensation of sound and called it thunder we ning, all that we directly say is that what we have seen is lightning, and what thunders,"

;

we have

heard, thunder.

It is true that

the hearer goes through the same

He

process as with an existential judgment. of lightning from the word, and by the flash of lightning as particular

must add those

who

its

receives the general idea

first

inflexion

and present

is

;

called

upon

to think of

to this general

word he So

thought the corresponding particular phenomenon.

in

with the completed proposition and explain

start

cally are justified in

emphasizing

declares the actuality of the

this view,

lightning.

it

far

grammati

according to which the judgment In some cases of propositions

derived from the original form this declaration of existence comes to the fore for the person speaking as well

based upon

memory

propositions.

occurs

it

"It

is

application of

when,

for instance, his information

is

often

rains

in

the

Alps"

means

"raining

often

the two-sidedness of the original form which makes this

"

;

;

or hearsay, and also in the future tense and in general

it

possible. 12-

Those judgments which predicate a contain a manifold synthesis. s.

L.

relation of a definite particular thing

The connection which

is

brought about by F

LOGIC

66

the relational idea itself takes the place of the unity of the thing

and

its

10 are upon which the judgments treated of in Every relational idea presupposes at least two points of

attribute or activity

grounded.

reference which are thought of as independent

;

these

it

connects by an act

Thus

of mental reference, though not coalescing with either.

a

judgment

between given things, names the given relation

stating a definite relation

by a general relational idea, and

same time

at the

unifies the necessary

points of reference with definite objects.

Logically considered Existential of view as Relational

Judgments

;

Judgments come under the same point what they express in the first instance is

the relation in which an object of thought stands to me, the subject think ing and intuiting this

mere

it,

but the meaning of their predicate extends beyond

relation.

Judgments which

i.

state relations

greater than B, to the right of etc.)

,

(A

is

J3, different

from B,

earlier, later

than B,

equal to

to the left of

B,

contain a synthesis of another kind from that contained by statements

which ascribe attributes and

activities

to a

These predicates

subject.

remain distinct from the subject-idea no inward unification can take place between them. Their predicates never belong to the subject when thought ;

of alone as

particular definite thing

this

denied of the subject nothing

For my thought the sun the left of me, whether

do not "

is

just

it

is

affect the idea of the

the sun

"

is blood-red,"

or attributes

and

activities,

first

place

of relation that

The

itself,

as

moves,"

when "the

I say,

"

the sun

sun stands

is

pale,"

The

pre

must pass beyond the idea of the subject, and something else, and then realize what kind

in relation to

it is.

peculiarity of relational ideas consists just in this at least

still."

whether predicates of denominative judgments, form a part of the subject-idea. But in order to

state a relational predicate I

must

whether they are affirmed or

visible or invisible; the different predicates

sun

the sun

dicates considered hitherto,

;

changed in the idea of the subject itself. the same sun whether it is to the right or

is

two

which are

that they pre

in the first place

thought of as sepa rate and independent of each other our ideas of these must be already ; there before a relation can be stated of them. Thus the unity which binds

suppose

objects,

together the elements of relational judgments is of quite another kind from the unity of the constituent parts of a particular object which can be

thought of alone this therefore lies

it is contained only in the relational idea itself, and in the ground of the peculiar synthesis now before us.

;

SIMPLE JUDGMENTS follows further from the nature of

It

relational ideas

every relation

the connection between these and the points of reference presupposed by them, that between two objects A and B can be apprehended and

expressed in two ways, according as

The

A.

kinds

reference

they

;

A

may be

A

or

,

B

A

we

to B, or from to pass from always mutual, but the relations are of different

is

the same, whatever the direction, or they may be the A beside B, beside A, equal to B, equal below A, B, smaller than A. greater than B,

B

opposite of each other to

67

B

upon

B

A

A

B

B

depends upon the movement of thought in connecting A and relation how a given reference shall be apprehended or expressed. It

every relational judgment implies in

its

by the

Thus, nature a second equivalent one,

every relational concept has its correlative concept. 2. If we look for the psychological ground of the synthesis brought

about by relations, we shall find are

immediately intuitable.

we can never and from these we have to

spatial things ings,

intuition

itself,

that

most

it

It

belongs to the nature

that

all

is

We

whole.

house

and attend

cular things are

we combine

to us as

comprehended

are able to isolate a particular object to

it

alone,

movable favours

and the

fact that a great

this isolation

the ;

in a larger

this tree, this

number

of parti

by enabling us to think of

from any given surroundings.

as disengaged

our idea of

perceptible around us into a spatial image

and thus every particular thing appears spatial

of

perceive them apart from their surround In separate them as particular things.

before any conscious reflection takes place,

particular parts of

them

easily in spatial relations, as these

But wherever we may

perceive them they always stand amongst others in one continuous space. As soon as we pass beyond the intuition of the particular thing, we find

occupying a definite position. We distinguish and the directions in which we thus pass beyond one

others already there

become conscious of Thing

combine

to

reference to our

it

own

above and below

with

others

directions which

standpoint, such as right

and

and

left,

originally

all

have

before and behind,

we analyse the complex picture pre by means of general relational concepts which represent the particular kind of unity in which the spatial whole contains sented to

its

us,

;

so doing

in

and express

it

parts.

When ment first

is

I

"

say

the house

is

on the

road,"

the starting-point of

a complex image of the house with

the building, and call

bourhood, and

call

what

it

I

a house

;

I

its

surroundings.

look further and notice

see here a road.

The

my

judg

I

notice

its

neigh

position in which the

LOGIC

68

my image

two parts of

stand to each other "

denote

by the preposition

it

its

nest,"

which

is is

immediate contiguity, and I used to name this kind of

In the same way the propositions,

spatial co-existence. "

on,"

The dog

under the

is

whole, and which

to

it

what

is

way the

may be

expressed,

stork

it

does the relational

a given, which expresses unification into

needed by the hearer to enable him to unify

is

we must have

in

is

presuppose the same analysis of and their particular kind of spatial

parts presented to him.

definite

The

table,"

a given complex image into its parts, It is the preposition, containing as co-existence. idea and applying

"

In order then that the

a threefold

naming of the

in a

judgment

particular parts,

besides the unity contained in the thought expressed by the relational word. One of these namings preceded the judgment and appears in the

word by which we denote the subject; the other syntheses are expressed by the judgment itself. Now these various syntheses may be combined in various ways, and 3. This

take place in different orders.

When

possibly stand.

is

mainly because

we

are accustomed

every object the thought of relations in which

to connect with

two objects,

A

A

and B, are presented

to

may

it

me

side by

but since every object stands in spatial proximity to others, the idea of something next to it presents itself, and I On the other hand proceed to make this second point of reference clear. I

may

look at

may

I

side,

first;

from B, connect the relation

start

with

first

it,

and then

attribute

second point A as subject. Finally, I may look at These different both together and determine their relation to each other. to the

this relation

ways of proceeding are expressed as A next to This is most obvious next to each other.

B

B

which "

start

;

next to B,

A A

and

;

in those spatial relations

A judgment such as from myself as point of reference. which comprehends an intuition here proceeds from "

Socrates

is

Socrates and myself in one and the

same

space.

Now

in every intuitable

idea of a space, the place which I occupy and a space surrounding posited,

and

this

idea,

"

pressed by it.

here,"

is

which always accompanies

added

me

Socrates.

is

Thus our

natural

first

predicate

first.

Socrates occupies the vacant position of the

way of describing such

my own

conscious of

(To the

relations as these, in

position as point of reference, right

is

is

ex

now

general possibility of something else, and in the present instance this

thing else

it

is

given and unified with must have something in it ; it is the

to the intuition

But the space surrounding

me and which

A, to the

left

is

some

"here."

which

I

am

to place the local

B, before C, behind

Z>.)

SIMPLE JUDGMENTS On

the other hand,

the objects

it is

it

may happen

that

recognised as Socrates.

69

what we

first

But with

this idea, as

observe

is

one of

with that

of every other spatial thing, we can at once connect the idea of a sur rounding, of the proximity of other things. Socrates is somewhere ; and this indefinite reference is now unified with the definite one ; the space here." surrounding him is unified with my space, with In this case also, "

Socrates is here then, a judgment such as on the one hand, in answer to the question, "

"

may "

take place in two ways

Who

:

on the other,

is here?"

answer to the question, Where is Socrates ? There are many predicates, primarily expressive of states and move ments, with which relational ideas may be connected to determine them in

"

more

"

The dog

exactly.

ent positions of

stands, sits, lies, denotes, in the first place, differ But the verbs body, which have reference to it alone.

its

themselves contain a further reference to that upon which or its definite place, and the relational idea connects as

predicate "

follow

hence

and

"

is

What

more exact determination.

"

fall,"

also

is

the

sits,

with

the

part of their

is

synthesis of the

combined with the

stands or

itself

In other verbs, such as

a relation to something else

such statements

in

activity

its

it

thing with

meaning

its

state

;

of

relation.

true of space-relations applies equally to time-relations.

Here

again, from the nature of our apprehension, every particular object appears to us in temporal connection with others, and as a member of a temporal series 4.

running parallel to other temporal series. The relational ideas denoted by like, different,

intuitable.

intuition

Here

itself,

the reference to something else

but

added by our thought, which

is

gether the most remote objects for

similar, etc., are less

is

not given with the

can, at

will,

bring to

purposes of comparison. Two things which are alike or different do not, apart from my reflection, form a the unity single whole, which can be resolved into its constituent parts its

;

which they are placed by the relational judgment arises from my con sciousness of mental activities having reference to the content of the objects in

of thought.

The immediate and

hend and recognise is

apt to

make

us look

thing sense-given, and

we become conscious

and

of

them

as if they

were some

the particular functions through which

functions which always presuppose that

and compared

when taken

we appre

similarity in the simplest cases,

upon these determinations to overlook

several objects are presented

the relational ideas,

evident certainty with which

likeness, difference

as to their nature.

Here

also

alone, are quite without significance

;

it

7

LOGIC

o

would be meaningless to say ent are really predicates

A

only

is

like,

A

Like and

is different.

when combined with a

differ

definite point of

reference.

reason also that mathematical equations, of the form

It is for this

B are i

j

A and

"

cannot be looked upon as judgments which state the same equal," and are ten feet long"; for they of two subjects, such as

B

"A

predicate

cannot be resolved into the two judgments, "A is equal," and If we start from both subjects then the full expression is,

"

B

A

"

is

and

equal."

B are equal to each is equal B?

other,"

to

\

"

"B

equal to

A

to

A

and here we have the two judgments, "

;

thus the real predicates are

"

"A

is

equal

equal to

E"

A."

mathematical object again naturally

calls forth

the question,

"

What

is

and has a reference beyond itself to something else. In the same way comparisons between larger and smaller things are always forcing B or A according as one or the other then themselves upon us equal to

"

it

?

5.

The

is first

B<

A>

;

magnitude

noted.

causal relations, which are expressed by propositions containing

transitive verbs

and

close connection

their objects, are

between

"

"action

with a definite intuition, which

is

difficult to

and

to

analyse because of the

Let us

"

efficiency."

start

be narrated by the judgment,

Then

intuition of a bull butting against a tree.

at

again

e.g.

the

any moment that which

immediately given together with the idea of the subject is its action, which we can think of by itself as a definite form of movement. Butting,

is

hurling, grasping, etc., all contain

striking,

the idea of definite forms of

movement, which can be thought of without any reference to a particular object, and can therefore be referred to the subject simply as its action. But the judgment,

bull

"the

does not completely exhaust the

butts,"

accompanied by the tree that which happens must somehow be expressed as a relation between the two. This may be done by merely determining the general form of the movement by its image, in which the bull

is

;

by adverbs of direction (the bull butts against local significance of the case and the preposition). So far the

direction, as, for instance,

the tree

"

"

only relation contained in the judgment

nature of the

movement

in

is

that necessitated

which the action consists,

as determined in the particular case.

By

if it is

spatial

specifying a definite object

merely determine the predicate-idea more exactly ; the idea purely relational predicate, it only includes an action which

complete by a relational idea.

by the

to be expressed

itself is is

we

not a

made more

SIMPLE JUDGMENTS But

if

we look

to the result

71

upon the object of the

activity of the subject,

the shaking and bruising of the tree, then to this extent the causal relation

This result

appears.

no longer confined

is

to the action of the subject in

extends to that which takes place in the object ; the effect,, as The general idea denoted by such, lies outside of the efficient agent. it

itself,

"

"

butting

no longer contains merely a form of movement which needs a movement which has the effect of shaking or crushing some When we look upon what takes place as conforming to the

subject, but a

thing else.

idea of butting in this sense,

we must determine and

reference to a definite object, reference to the subject

annihilation, destruction, etc.,

upon various

itself;

"

produced or destroyed.

activity expressed

;

it is

the

;

to signify an effect, production,

the causal relation it

particular objects,

equivalent expressions

two syntheses

the third.

is

In the case of verbs, whose nature

meaning of the word

more exactly by

the idea

this gives us the first

To

is

and

it

necessitates a something

and

cause,"

"

cause

to

the idea of an object, which

in the verb,

be found in the

to

the generalization of definite effects

is

which

something,"

is

is

are

affected by the

and with which the given object

is

partially

The definitely connected with the verb itself. unified, is more of the second of idea also the reference, includes point meaning of the word or less

the source of the

meaning food

;

is

just

and with

effect,

the same whether

this the

subject

say, I eat, I

I

identified.

is

something, or

eat

The I

eat

whether named or not, the two points of reference are given with the the idea of point to notice is that now the process is reversed included in that of causation, and the syntheses brought about

The

verb.

action

is

in the category of action. by the relation are accompanied by the syntheses We may see how these syntheses may succeed each other from the ques tions,

"Who

The

6.

of the active

When

causes

What does

"

The

i.e.

cause

?

itself

What in the

A

is

doing?"

interchangeableness

stone

is thrown,"

idea of which this

the event

is

not expressed as

it first

as action of the stone (the stone

flies).

Instead of this

substituted the

more

distant relation,

immediate statement there

which denotes

whence of

A

and passive forms by which the same event can be expressed.

I say,

appears to us, first

B?

nature of this relation shows

is

this action as the effect of

something

else,

and with the

connected definitely or indefinitely the thought of the Thus predicate-ideas which are denoted by passive effect. is

verbs cannot be subsumed under that form of unification which has for less than its ground the category of action ; they are neither more nor

LOGIC

?2

relational predicates, although they include

an action having reference to

the subject alone. It is true that

these simple

and

different

fundamental relations are

fre

forms and disguises of

varied

verbal quently concealed by infinitely as are far from The forms of language ordinarily understood, expression. coinciding exactly with the distinctions of the idea.

"To

suffer"

is itself

an active verb, and we generally forget that as such it represents the subject as a rule we think of it in the activity of endurance or of feeling pain ;

only in opposition to efficacy, as the relation to some efficient agent. The predicate u to be," in the so-called Existential Propositions, must 7. also be regarded as a relation

that

a

is

modal

relation

though

it

occupies

a unique position. In the

first

place, there can

be no doubt that in their external form

these propositions exhibit exactly the tions,

same structure as any other proposi

Being is stated of that which is denoted by and thought of under the subject-term, and a definite brought about between the subject and the general concept of

whatever their verb.

"

"

the subject-term, is

unity

In these judgments, therefore, as

Being.

of distinguishable thoughts takes place.

much

as in any others, a synthesis

Nor can

the question,

"

does

A

be understood except as expressing the doubt whether actual ex istence can be declared of the we are thinking of, whether it is in accordance with truth to connect the thought of existence with it. 1 "

exist

?

A

1

Brentano (Psychologic vom empirischen Standpunkte, vol. I, 1874, p. 266 sq.) disputes the ordinary doctrine that a connection or separation of two elements takes _place in every judgment.

According

to

him, the essential characteristic of judgment

is

acknowledgment

or rejection, which refers to the object of an idea ; in acknowledgment and rejection con sciousness is related to an object quite otherwise than when But framing an idea of it. in acknowledging and rejecting we are concerned sometimes with connections between ideas,

sometimes with isolated objects. In the the object of our proposition "A is not the connection between a characteristic "existence" and A but is,"

acknowledgment

A

itself.

It is

undoubtedly true that judgment does not consist merely in a subjective connecting we shall deal more fully with this below ( 14). But that there is a kind of judgment which contains no connection of ideas at all, that in addition to judgments having two terms there are to be found judgments having one only, and that these judg ments of one term are none other than existential this I cannot of ideas, and

When I form the idea

of an

"

"object

allow. propositions conscious of it as an idea, as something that of being the object of which I form an idea.

A,

thought ; its primary relation to me is In so far as I actually have an idea of acknowledge it, then all I could

I

am

first

I cannot reject it and should I wish to it, acknowledge would be that I actually have an idea of it. This "acknowledgment," however, would not be the statement of its existence. The very point in question is whether, in addition to my having an idea of it, it is further implied that the object forms a part of the actual world surrounding me, can be perceived ;

SIMPLE JUDGMENTS About the meaning from

start

its

it

"

is

"JBeing

but

is

to

"

"

is

it,

no doubt,

if

we

appears before critical and philo

I think of

it,

is not merely produced by my mental activity and remains the same whether I am thinking of it

to

Being belongs

me, as

it

;

independent of

or not.

as

though indeed we cannot define the concept of Being, from other concepts, but can only contrast it with its opposite. opposed to that which is merely an idea, a thought, animagina-

That which

jion.

of the predicate also there can be

popular meaning

sophical reflection

nor derive

73

it

in the

same sense

as to myself;

as something independent of

my

it

is

opposed

thought, something

not made by me, but only recognised in its independent exist But although the chief meaning is this independence of the existent,

which

is

ence.

the judgment also includes an open or concealed reference to myself, as the subject which is thinking the existent and which can be actually affected by it.

The attempt

to derive the thought

of being from anything else

is

as

vain as the attempt to find an explanation of self-consciousness in the

unconscious. often as

we

It is "

say

I

included in self-consciousness from the beginning "

it is

present in thought, although not expressly

;

as

empha

In the same way it is from the first inseparable from the objects of our intuition and thought, for we never find ourselves conscious without being surrounded by a world of objects which are, in just the same way sized.

that

we

and

is,

No fr6m

are.

as

We know

opposed

occasion presents this original

ourselves only together with something else which

to other things

which are not ourselves.

for disengaging the idea of Being connection with the consciousness of ourselves and of itself at

first

the objects before us, or for expressly declaring Being of ourselves

the external world.

This

is

and of

because the thought never arises that

it

is

by me, and can take

If I wish to maintain the effect upon myself and other things. existence of the object, I must connect this last thought with the mere idea. When I the tower of Babel these words are in the first place a sign that begin a proposition "

"

have the idea of the tower of Babel as it is aroused by the story in Genesis, and this same idea is excited within any one who hears me. So far the idea is simply there, and as such it can neither be But now the rejected nor does it call for any acknowledgment. I

"What is the meaning of this idea?" If I complete the proposition by tower of Babel exists," then I pass beyond the mere idea and state that the If I say it does not exist, thing denoted by the words may be perceived in some place. then what I have rejected is not the idea of the tower of Babel, but the thought that

question arises,

saying

"the

the idea of a visible and tangible thing. Thus what is acknowledged or rejected by not the idea of the tower of Babel, but the thought that the given idea corre On this whole question cf. my die sponds to an actual thing that is, a connection.

it is

me

is

Impersonalien, p. 50 sq.

LOGIC

74

me

possible for

not to be, or that the whole external world might not be to assert that I am, when neither I myself nor any

it is

quite superfluous

one

else

doubts

Only

it.

in

;

an advanced state of reflection can we attain

to an express consciousness of our own being ; at first my being is indisimmediate consciousness of myself; the only tinguishably included in the

question

is,

in

what

do

state or activity

I

find myself.

Immediate sense-perception does for external things what this immediate If we reflect, and consider what it is self-consciousness does for myself. that induces us to

find that

we

acknowledge the being of particular external things, we That which we touch and see is there, and when

sensation.

it is

what we mean by Being, we find that we connect with

try to realize

the idea of being perceived, capability of taking effect is

and of the

upon the sense-organs of a

not Being

it

possibility of being perceived, the

feeling subject.

But

and consequence

its

it is

; itself, only sign Being does not begin with being perceived, nor does it cease when being That which is perceptible must be in order that it may perceived ceases.

being perceived

be perceived, and the perception of a thing irrefutable proof that

When we

attribute

it

is

only the most direct and

exists.

Being to insensible or supersensible things, as in the

ontological proof of the existence of

God, or

in

the conception of things

per se, we have always a difficulty in freeing ourselves entirely from the spatial ideas which accompany the thought of being in the world of sense. We say that there is a God," and when we try to impart greater reality to the thought, we can only do so by including in it an effect upon a per "

ceptible world, in

and through which there is an effect upon us by means But this itself and may be known.

of which the non-sensuous reveals is

efficacy

quence of agent

not the origin of the thought it,

"

Being,"

it

is

merely a conse

and hence the ground of our knowledge that the

Here we brings with

see clearly the peculiar difficulty which this concept of Being it.

On

the one hand,

it

cannot be spoken of

at

presupposing a relation to me, the person who thinks of it. idea of the object because it has entered into some relation to is, is

efficient

is.

my

thought.

and declare

But by

this very

that the existent

thinking creature

is,

thought

apart from

I set

its

aside this

reference to

I

me

mere

me

without

all

have an ;

that

it

relativity

or any other

that its being does not ; wholly consist in the relation of being thought as an object of my consciousness. The Herbartian formula of absolute position in its double meaning combines these two aspects, with-

SIMPLE JUDGMENTS out however solving the difficulty

made of

clear what it

difficulties,

If

we wish

it is

but

;

75

has at least the merit of having

it

that our natural thought really

means when,

careless

predicates Being.

to analyse

and understand

we must

existential propositions,

meaning which they have in common use, before they have been critically approached ; and then the question arises what do we think when we say A exists, and in what sense do we declare the unity of start

from

this

:

the subject

and predicate

?

we must

In order to answer this question, presupposition which gives

rise to the

see what

first

A

"

judgment

exists,"

is

the general

as a

judgment

concerning a particular thing in the ordinary course of our thought. Evidently this presupposition is, that some doubt has been or may be

and

raised as to the existence of the subject;

which the subject-word originally which appears in consciousness either that

given by the

cannot ask whether

I

which

it

only possible

when

merely an

idea, something form of memory or as occa Concerning that which is immedi

signifies in the

sioned by communication from others. ately present,

this is is

exists

certainty of

;

But

its

existence

is

learn from

my experience have previously seen in definite places, and from my experience of being deceived by others, that not everything of which I form an idea is also to be found in actual per in

intuited.

way and vanishing of it is

of the passing

ception.

which

Thus

I

am

I

things which

I

driven to distinguish between

the intuition of that

present and the mere idea, to which there is no corresponding intuition present. When I have lost anything, when I fail to find what I formerly possessed or knew, then, though I have the image of the thing in is

my memory,

the present intuition

coming, not to be found. in

my

It is

is

wanting

;

consciousness as subject idea, and to this

Only

perception.

question as to that of

which

Thus

its

I

such an idea

in reference to

existence,

have an idea

in every existential

is

it

not there, not forth

only the idea of the thing which I is

it

present

possible to raise the

and the meaning of the question still

is

seek the corresponding

is

whether

forms a part of the perceptible world.

judgment the

subject- word

becomes a

sign of

something which is merely an idea, from the very fact that the thought of its existence is withdrawn from it in order that it may for the first time be expressly attributed to

wanting,

i.e.

as soon as

it.

I

This happens as soon as I have found what was have experienced the corresponding perception,

or have convinced myself through

information from other people that

some process

it is still

of inference or through

perceptible somewhere.

Thus

\

LOGIC

?6

of the empirical world rest upon judgments within the sphere idea (of memory or of fancy) and the distinction between the merely inner is the what they assert identity of that which is perception and existential

all

present

;

mere idea which perceived and the

named

especially clear

is

to

me

from other people.

the idea of a Hercules or a Theseus, of the

me

create in

as subject.

idea of the object whose existence

when my been communicated question has only

This in

is

or of the magnetic mountain

is

They

Tower of

Babel,

thus the question arises whether these have

;

connected with the words are ideas of existed, whether therefore the ideas real beings or are mere imaginations, whether the information is based

upon perception or

fiction.

This throws light again upon the proposition so strongly emphasized by Kant that the predicate to be adds nothing whatever to the content of "

"

:

Whether

the idea as such. just the

same

more nor by me. dicate,"

;

I

"

say

A

"

is

Kant says;

as

my

faculty

to the fact that I

my

not,"

"

is

being

of

knowledge.

may be

The

A

is

that neither

synthesis, then,

A

thought

"real

A

pre

which

which

is

is

judgment referring to the empirical, idea and an object as intuited it is ;

conscious of the same contents in two forms,

The thought

of

immediately connected with the intuited object.

far existential

ments.

thought of

demands

form of the mere idea and in the form of intuition.

"

So

is

merely expresses the relation of the

it

the identity between an object as

in the

A

be present in the actual world than just the Thus "being" forms no part of the subject-idea, no

primarily contained in the existential

due

"

less shall

thought to

is

or

the meaning of the statement itself

judgments reverse the process of denominative judg is given as intuited, and is therefore thought

In the latter the object

of from the

first

as actual

;

to

and the agreement of the two

it is

is

added an idea which was known

before,

declared in the denominative judgment.

In the existential judgment it is the mere idea which precedes, and it is then said to agree with a particular object of intuition. But while this relation the agreement of the idea of a thing with a possible perception "

to exist

relation

"

to

is its

chief significance, the

extends further.

me

That which

exists

meaning of the predicate does not stand

alone, but to everything else which

is

;

it

in

this_

occupies space

between other objects, it exists at a definite time before and after other and it stands in causal relations to the rest of the world hence even ;

things,

of the perceptible

we may assert an existence which is merely inferred. Herbart finds in the concept of Being complete unconditionedness and

SIMPLE JUDGMENTS

77

absence of relations, and against

this

think of in the concept of Being

just this fact of standing in relations.

From around

is

Lotze rightly shows that what we

of view the ever-present thought of an actual world

this point

me

is

presupposed

in every existential

judgment

merely supplies a definite subject for some place in It is

existent.

the question

which

This

is

train

last

such a judgment of the

always assumed that there is something external to me ; whether the object of my thought is to be found in that

given, or whether something actual falls

is

;

this totality

under a certain concept.

of our thought leads to those statements in which the

expression of being stands

first,

and which are thus akin to the impersonals.

extent also they assume the outer form of impersonal propositions these phrases first indicate something which there is, es gibt

To some

_

o- T i 5

exists,

which

is, is

order to denote

it

proposition, then, is

is

which

when the question we are dealing with we think of as definite and par

present which

is

because we knew

it

before) but whether a thing exists

under a given concept and can only be denoted as

falls

Those

definitely afterwards.

the natural one,

not whether a thing

ticular (perhaps

by the world which is presented, in This form of the existential

there, is offered to us

more

"

an

1 A."

judgments concerning particulars in which the subjects are and the predicates, adjectival or verbal, cannot be brought

abstract nouns

The first synthesis under the categories of thing, attribute and activity. in the unity of the found either be is to which are upon they grounded attribute or activity with its modification, or in that view of a thing which it

merely because of some given attribute, activity

and, to

an undeveloped thought, the natural way of

attributes a predicate to

or relation. i.

The

first,

regarding perceived events, express everything which

of particular things

;

is

is

to refer

and happens

them

there are few propositions in

subjects are not particular persons or things.

comes

to distinguish

we have any occasion particular

done

concrete things, and to

to

as attribute, activity

It

Homer is

only

and

relation

of which the

when thought

more accurately and compare more extensively to

employ the

things as independent subjects of a statement.

either with the intention of distinguishing 1

Cf.

my

that

attributes, activities or relations of

Impersonalien, p. 65 sq.

This

may be

and determining more

LOGIC

3

7

or in order to refer a causal relation to exactly an event or attribute,

element of a thing.

definite

In judgments such as

2. is

a

one

hop,"

there

is

"

this

red

"

is

bright,"

the gait of this animal

presupposed the judgment of attribute or activity which

The breaks up the presentation into a thing and its determinations. in consists the of attribute the the of partly synthesis judgment synthesis or activity with P- 3 2

3.

its

modification, partly in the

naming of the

latter (cf.

6, 2,

sq.)-

Before an attribute or activity can be the subject of a causal relation

the general idea of an efficient agent which

is

originally

connected with a

must have been more exactly determined by a process of

thing as cause

comparison so that a thing is regarded as taking effect only by virtue of one of its attributes, or only in so far as it is engaged in a certain activity. ;

When we

say that friction

warms, and weight

subjects belonging to the verbs are the

is

the true

oppressive,

body by which the

friction

is

pro

duced and the heavy thing these alone are capable of causing an effect. But by comparison our thought distinguishes that element in the body in ;

virtue of

which

noun, because

gives rise to the effect,

it

in this

way

and expresses

it

by an abstract

the event can be presented as the expression of

a general law. 4.

Relational ideas also

same way appear

When

effect.

such as distance, difference,

the attraction of two bodies

the words in which the change relation

as

that this

is

if it

in the

is

is

stated attribute an efficacy to a spatial

were a substantial cause.

But there

is

no need

to

prove

a mere abbreviation.

We know

from general laws, which include both the

and the conditions of follow

can

etc.

which express an diminished by their distance

as the subjects of adjectives or verbs

its

upon the change

of the change

fact of the efficacy

modifications, that a certain result will necessarily in

distance,

and

this

result

is

stated as the effect

The higher

the abstractions in which our thought and unsuited to them do the original meanings of

itself.

knowledge move the more words and constructions become.

Without our perceiving

it,

language,

by the aid of abstract nouns, abbreviates and leaves unexpressed that which mental habits lead us to understand as a matter of course. chiefly

The complex

relations of scientific

cular event depends

of

expression in

insignificant in

upon many

such

a

laws,

according to which the parti

conditions, are forced into simple forms

way

that

the

efficient

cause

itself

appears

comparison with the varying circumstances under which

it

SIMPLE JUDGMENTS The

takes effect.

idea of efficacy

original

is

79

attenuated into the uniform

interdependence of different movements, and this

is adequately expressed a can mathematical but be formula, only represented in words by the by

aid of figures of speech

and metaphors which we have ceased

to feel

as such.

Tlie unification of different ideas does not exhaust the nature of judg

ment

every complete judgment as such includes also the consciousness

;

of the objective validity of this unification.

But objective

validity

does not, as might be supposed,

rest

immediately

the fact that the subjective connection corresponds to the relations of

upon

the corresponding existent

This necessity has

its

;

it

rests

upon

the necessity of the unification.

|

/

/

and this again but these logical principles can,give)not

root in the principle of agreement,,

presupposes stability in our ideas

;

assurance of the real identity of things.

Those

1.

definitions of the

judgment which

limit

it

to the merely sub-

^

jective connection of ideas or concepts, overlook the fact that the import

of a statement mo.men1: 2

form

is

never merely to assert the subjective fact that I, at the On the contrary, the judgment, by the a connection.

make such

assumes, claims that the connection

it

and

is

true of the objects them-

S

must be acknowledged by every one. It is this which distinguishes the judgment from the merely subjective combinations of ingenious and witty comparisons which assume the outward selves,

that just for this reason

it

form of the proposition, but do not aim, objectively valid statement.

like the

In the same

way

judgment, at making an

the judgment differs from /

mere conjecture, opinions and probabilities. 1 2. But objective validity has more than one meaning. In the first place we must distinguish a verbal, nominal validity, from a material, real validity.

When

I

"

say

this is

red

"

the

first

question which

may be raised

is,

whether

what every one else calls red. Then the objective validity, which may be denied of my judgment, refers to the general use of language, which is opposed as an objective rule, or general law, to sub

what

I

call

red

jective caprice.

is

All verbal disputes turn

upon the question of

this validity

;

such disputes are possible partly because the subjective meaning of words for the individual differs from that which is generally recognised, partly 1 Ueberweg, for instance, 67, gives a correct definition from this point of view, whenV he says the judgment is our consciousness concerning the objective validity of a subjec- j :

tive

connection of ideas.

LOGIC

So because language

is

not absolutely fixed even in

its

general use, and be

are fluctuating. cause the boundaries of particular words l But when the nominal correctness which is implied in every judg 3. be to meant and understood, is present, inasmuch as it is spoken

ment,

when

the speaker connects the

same ideas with

his

words which every one

else connects with them, then the point to observe

of ideas

is

stated as

so that every one

is

way about the same

is

that the connection

the spoken proposition as true, objectively valid, and it and to judge in the same believe to called upon subject.

determine the meaning of this material validity is not so simple as that the same connection must exist between might appear when it is said the corresponding objective elements as between the elements of the

To

judgment;

or,

that

what

is

thought must actually happen.

when

peculiarity of our thought,

with the existent to which they

judgments

so far

considered

:

judging, that refer.

its

For

it

is

the

processes are incongruent

Let us confine ourselves to the

those which ascribe attributes and activities

by a name. In the first place we which agrees with the predicate-idea in

to particular things, or denote things (

find that there

is

nothing existent

something which agrees with the subject-idea is from its nature general and does not refer directly to any particular thing which is thought of as having a All words (with the exception of proper names) are_ particular existence.

the same sense as there I

for the

is

;

predicate-idea, as such,

the immediate signs of ideas which, though formed from intuitions of the

Marty has made the following objections to the view that every judgment contains the implicit statement that its terms are correctly used ( Vierteljahrsschr. fur wiss. Phil. This is snow, it "When, in good faith, I state the proposition, 1884, VIII., I p. 85). 1

,

no doubt, presupposed that I believe what I call snow to be called snow by every one But we cannot say that this judgment concerning language is implicitly contained in the statement." But suppose I say to some one, That is crimson," and he replies, No, it is scarlet," does he mean to say that I am wrong as to the colour itself, and see a different colour from that which the object really has ? or does he not rather mean that I am mistaken in my denotation, that I am calling crimson what, in the ordinary use of

is,

else.

"

"

language,

is

called scarlet

?

Thus the judgment,

ment

"

That

is crimson,"

contains the state

that I not only see the colour rightly, but also give it its right name latter part only did the apply. Marty goes on to say that there is "

No

;

for to this

"

no need

for

the judgment as to language (the agreement of my use of language with the ordinary use) to be present to consciousness in any form when I utter the proposition in question. "It is enough that it has previously been there, and that a habit of speech, which can now act by itself, has been formed on the ground of ozir confident assumption of Thus, it."

according to Marty himself, my judgment includes a confident assumption ; all that he main tains is that it need not But what does this always come into express consciousness. mean, if not that it is implicitly contained in the statement ?

SIMPLE JUDGMENTS existent^

do not represent

_given_ cases.

particular,

nor as

exists

it

in particular

Again, the judgment presupposes the mental separation of

and predicate

subject

as

it

Si

;

it

takes place in the recognition of the unity of

two ideal elements which, for our consciousness, had formerly a divided existence. There is no such separation in the existent to which our refers. The thing exists only with its attribute, the attribute with the In the same way only thing ; the two form an undivided unity. a body exists only as at rest or as moved, its state is not separable from it

judgment

L-

Thus the general and the particular, predicate and subject, with their preliminary separation and act of unification, find no counter

in reality.

part whatever in

the

the existent

we cannot

;

say that the connection between

elements of the judgment corresponds to a connection between

analogous objective elements. Only when, by the act of judging itself,]. we do away with the subjective separation between subject and predicated

and thus think of the two

do we

as united,

the existent, which

revert to

remains an undivided unity and never undergoes an actual separation There has been no distinctio corresponding to our mere distinction.

itself

"

corresponding to

realis"

essential characteristic of

kind,

its

the

"distinctio

judgment

to

objective validity must have

rationis"

then,

If,

it

the

is

be a function of a merely subjective

some other meaning than

that of the

agreement between the connection in the judgment and an objective connection ; a meaning which can only be understood when we take into consideration the peculiar nature of our predicate-ideas.

The simplest judgments are those which are merely denominative4. judgments, declaring the immediate coincidence of images, unmediated by subsumptive inferences.

Presupposing

nominal

it

correctness,

is

necessary to the validity of such a judgment, as ordinarily understood, that intuition It is

and idea should coincide

also necessary that the

a relation which

is

purely mental.

subjective intuition, which claims to be the

copy of an objective thing, should really correspond to this; i.e., that the subjective image which is present should be that which, according to the general laws of our sensual intuition, would necessarily be aroused in

everybody by the same object. objectively valid when that which "

is

"

This

is

snow,"

is

seen coincides with the idea called

by every one, and when, moreover, it is seen distinctly by an eye normal condition. Objective validity then reduces itself to this that

snow

in a

The judgment,

"

:

both the process of forming the intuition and the act of judgment take When there is agreement as to place in a way which is universally valid. s.

L.

G

-

LOGIC

82

now meaning of the predicate, any dispute which may

the

arise

can only

refer to the question as to whether the person giving utterance to the is snow," sees correctly; i.e., sees in the same way as "This

judgment, every one

and under the conditions of correct knowledge. In par is purely a qucestio facti which differs with the individual,

else,

ticular cases this

and cannot be determined according to any general rule. But the general we have for referring our ideas to real question as to what authority objects,

we

and

an existence independent of ourselves

for attributing

perceive, does not belong to

all

is

ordinary thought

logic.

grounded, that

affirmed in the realistic sense

;

or

it

may have

its

what

meaning so changed

the idealistic sense that Being merely denotes something which

of necessarily and by every one in the

to

The presupposition, upon which we know an existent, may be

same way.

But

is

in

thought

in either case the

subjective functions, which are active in judgment, remain the same.

Concerning the metaphysical validity which we attribute to ideas, our Logic need come to no conclusion at present ; it investigates thought as a subjective function, and can therefore decide nothing as to the signifi cance of

that

differ,

But when an

intuitions.

we cannot allow

man

one

ideas as like

;

that

for

we

it

is

intuition

possible for

and a predicate-idea are

there,

the inward act of unification to

should posit like ideas as unlike, another different immediate certainty of the necessity of

find within us

our unification and the impossibility of the contrary, and should thus be forced to exclude from the arrive at a different result. validity for us because 1

It

it is

community of thought any one who should In other words, the judgment has objective

1 necessary to unify ideas which coincide.

might be argued by one conversant with objective logic that after all the judg This is snow," is intended to state something concerning the nature and constitu

"

ment,

and that the question as to its objective validity depends upon whether or not. This would remind us of the question of the clever critic, How do the astronomers know that the star which they call Uranus is really Uranus ? It is a necessary condition of all use of words that at any given stage of our knowledge

tion of a thing, this is really

snow

"

"

snow shall, by general agreement, denote some definite idea, and that when we give names we shall be guarded from confusion by the fact that the distinctions in that which is presented are not more numerous than those of the ideas named. This being presupposed, then, however we may turn and twist the statement, that this is really snow, the question as to its objective validity still demands the answer given above. Instead of an idea like the above, which was sufficiently characterised by sense-intuition, "

"

I

might take as the ground of

attributes.

Then

characteristics of

60;

it

the

snow

becomes water

my

statement ;

at

it

is

statement an exact concept with accurately determined This is snow," would mean, "This has all the "

white,

it

whose angles of contact are But this brings me no further beyond the statements (i) That at the moment consists of crystals

a temperature of o

with the question of objective validity

degrees."

:

SIMPLE JUDGMENTS

83

We might be tempted to recognise the fundamental principle just 5. found as that known in the traditional Logic as the PRINCIPLE OF IDENTITY; for this principle of identity

is

there regarded as the ground of validity in

judgments attributing a predicate mental law of our thought.

all

to a subject,

and hence as a funda

1

Unfortunately, the word identity has in the course

many meanings, and

of time received

made

the so-called law of identity has been

use of

in very different senses.

my

perception is correct, my senses do not deceive me and convey impressions to me from those which the same object at other times gives to me and to other

different

That the elements which

I distinguish in this image exactly correspond in with which I am thoroughly con white, crystals, melt, etc. are denoted by me as by every one else by these words the total

people

;

detail

with the ideas

(2)

versant, and which idea thus corresponding perfectly to what I Further, I am certain, in the first place, that

means

am I

accustomed to think of as "snow." have not forgotten what white," etc., "

and, secondly, that I do not identify blue or red when seen with my idea of white, that, on the contrary, it is necessary that I should unify my perception with the idea. There is no other objective truth and subjective certainty for this ;

proposition,

nor can there be so long as the universal as such has its existence only in my mind, and only the particular in reality. Again, it might be said that the proposition, "This is snow," means that the thing present

is

and that

like or similar to other particular things which I have previously perceived, it is this material likeness of existing things which forms the contents of

my

But though

contained in the judgment, it is so only in so far as these particular things are also stated to be snow ; the judgment would only be multiplied by this explanation. But then, it may be asked, does all error in this department consist in verbal mistakes

judgment.

and

in denotation

false

this is indirectly

perception

?

May

there not also be false subsumption of the

particular under the universal in such a way that in the synthesis of two ideas unlike things may be held to be like ? This certainly happens, inasmuch as in no stage of our judgment have we a sufficiency of ideas which are fixed in meaning, clearly distinguished

and named, TrewtpavTai

to the manifoldness of the particular. To, yap ovb^ara. rb rwv \6ywv TrA^os, ret be irpdy/J-aTa rbv api.6fj.bv iLireipd. tanv (Arist., de It is the difficult task of science to establish a complete system of predicate-

to correspond

fj,fi>

/cat

Soph., el. i). ideas which shall be clearly distinguished and unambiguously named, and which shall make any error of subsumption impossible. So long as this ideal is not attained both in general and by each individual, there will always be particular ideas which cannot find

amongst those which are known and familiar to us and an immediate unification is not possible, will seek their names by inferences. If these inferences are hasty, and are guided merely by analogy in extending the use of but it will in the first instance be a nominal error, antici names, there will be errors pating the formation of concepts in a direction in which it will not follow, and it does not refute the principle given above, which is valid only where the general idea which their corresponding general idea

;

these, as

;

corresponds to the particular is already formed. Only so far, again, is perfect certainty When we reach the predicate by means of mere inferences of the ordinary possible. sort, we may indeed state it in words, but we cannot attain to the certainty of the necessity of the act of judgment. 1 Cf. with what follows my article in the Vierteljahrsschr.fiir wiss. Philos.,

iv., p.

482

sq.

LOGIC

84 In the

first

under the formula

place,

ing that every object of thought

thought as just

this

and no

is

A

is

A,

it

was interpreted as affirm itself, that it must be

identical with

other.

Then, as the principle of

affirmative judgments,

all

that subject and predicate must stand

in

it

was said to

the relation of identity

state if

the

judgment were to be possible or valid; possible, when the principle was to which we always do think ; valid, presented as a natural law according when it was presented as a normal law according to which we ought to In the latter case it was the criterion of valid judgments. think. Finally

received a metaphysical significance,

it

stating that everything

that

which

exists

is

and was interpreted as itself, and

absolutely identical with

Being can therefore be attributed only to that which is absolutely itself, hence only to the unchangeable which contains no

identical with

sort of plurality.

We may begin which

its

etymology

determine that meaning of the term identity,

to

by trying

points to as the

connection with this logical question,

what

most is

means

different

names, or in different connections,

one and the same object

thought of

is

at

different

in

Here, then,

times,

or under

nevertheless not two,j3iit of twice. The term cannot merely thought

it is

;

be applied to an idea which

and which, except

generally accepted.

identity

that

original,

is

is

quite simple

and occurs only once

;

like

I cannot requires two points of reference. even recognise the identity of something which remains absolutely the same unless I am aware that I have thought of it at different times and compare

every relational concept,

it

the recurring ideas.

Now when we say that something which is thought of twice is the same, we may mean one of two things we may mean either a real or a logical A real identity is stated when two ideas, two perceptions, two identity. accounts, two names or other denominations are referred to the same ;

person, thing or event.

Seneca in

is

Olympia

sanias

It is in this

sense that

identical with the philosopher is

identical with the

who met me

such a place.

by Thales, is on May

;

the

is

the

same

whom

I

25, 585; that the saw years ago in such and

This real identity does not exclude difference in the object the tree, which I have formerly seen in foliage, is now

at different times leafless

to-day

Hermes found

mentioned by Pauthe same which took

place, according to astronomical reckoning,

person

;

that the tragedian

that the

statue of Praxiteles,

that the solar eclipse, predicted

;

I state

Seneca

man

;

is

now

grey

whom

I

knew

in his youth.

But where we

SIMPLE JUDGMENTS

85

are not concerned with the reference of our ideas to particular things or events in space or time, the identity must be logical, i.e, it must refer to the contents of the idea as such. We saylhat ideas which we have at different times

and on

different occasions

the same as to their contents

;

;

only according to their contents,

different things

we can even

and compare them

say the colour of one material

same

the

is

but are absolutely

differ,

words or expressions denote formulae the same number. In so far,

same concept different then, as we abstract the attributes of the

do not

thus, different

second

;

as that of another, the length of one rod the same as that of a but the materials and rods are not therefore identical ; they are

In the same way, we speak in diplomatic for, when the contents of the notes are the

only alike in the given respect.

language of identical notes

;

same, we disregard the plurality of the documents. This is the extent to which we can apply the word identity, and, indeed, any definite meaning

meaning

this, it follows that identity is

either

is

to

if its

original

be preserved.

From

complete or not at

all

;

that identity

has no degrees, and that the expressions relative partial identity," if meant to denote kinds or degrees of contain a contraidentity," identity, "

dictio in adjecto.

Europe and

To

A

We

can speak of an identitas partium

(e.g.,

of parts of

parts of the Russian Empire), but not of an identitas partialis.

return to our Principle of Identity.

A

"

In

its first

meaning, the formula

all thought and thought nor judgment is possible, except when particular ideal-objects can be retained, and reproduced and recognised as the same; is

certainly expresses a necessary presupposition of

judgment.

for

no

No

definite relation could

be established between ideas which were

always wavering and shifting. Thus, all thought depends upon the stability of our particular ideal-contents as its condition. In so far as the stability is always realized to a certain extent, in the sense that

it

we may speak

expresses a fundamental fact

;

of a principle of stability so far as

as the condition of all true judgment, the formula

precept, which

But

it is

recognised

contains also a

must always be satisfied if our thought is to be perfect. which refers only to the stability of each idea in itself,

this principle,

cannot serve also as a ground in the

A =A

judgment.

for the

union of the subject and predicate

For judgments which are meant only

to state the identity

No

of an object of thought with itself are quite barren. stating that a circle

is

a circle, and that this

hand

is

this

propositions which apparently correspond to the formula subject

and

predicate-terms

really

refer

to

different

one thinks of

hand

A

things.

is

;

and

in

A, the In

the

,

LOGIC

86 children are

"

proposition

children,"

characteristic of childhood

age

which are connected with to say that

when once a

it.

the

subject-term

By

connected with

other qualities war,"

we mean

we need not -be

surprised

the proposition

state of warfare has arisen,

means only the

the

the predicate-term

;

"

war

is

appear also thus, the to the meaning in which the subject new determinations adds predicate was first taken. that all the consequences usually

But

in the case of

it

;

simple denominative judgments,

we cannot speak of

represented by the subject and predicate terms. In a judgment concerning a particular thing the predicateidea is generally the more indefinite, and does not exhaust all the speciality the strictly logical identity of that which

of the subject-idea find again in

my

particular thing

more

we can only speak of the agreement

of the two.

subject-idea the thought denoted

I

by the predicate the idea. Thus, it would be ;

image of my ground of these judgments the Principle of the necessity that there should be agreement of

like the general

to call the

correct

Agreement;

is

;

is

it

states

between what we connect as subject and predicate ; that the consciousness of this agreement should be expressed in the judgment. It implies, moreover, that no thinker can be mistaken as to whether there is ideal content

agreement between the ideas present to him as subject and predicate, in so far as

they are present.

Thus, the principle states the immediate and

infallible certainty of the

consciousness of agreement, both as a fundamental psychological fact and as a necessary presupposition of judgment.

When

the predicate of a denominative

any verbal expression which by

its

judgment is a proper name, or sound gives rise to the idea of a single

existing thing as such,

and

watch

the judgment

is

mine), and

if

is

used as a sign of the thing (this is Socrates, this is based upon immediate knowledge,

then, in this case also, the agreement of the two ideas

the intuition

and the

memory- image is presupposed. But here again it is not necessary that there should be absolute I recognise an identity of the ideal contents. acquaintance even in a new dress, or when he looks paler than usual. this

agreement

But

accompanied by the consciousness of the real identity of the subject with the particular This real thing denoted by the predicate. is

identity of the thing corresponding to the two ideas which different times, and which are both ideas of the same thing,

have arisen is

at

again funda

mentally different from the agreement and stability of ideas ; it refers to a determination of being as opposed to being thought. We can, however, formulate a principle from this point of view also, viz. that in the concept

SIMPLE JUDGMENTS of the particular thing itself there identity with

is

included both

which alone gives a meaning

itself,

and permanency of the thing

;

its

singularity

that

so that the very concept of a thing includes

far as to state the Eleatic or

But

and immutability thing is what it is."

"every

in saying this,

we

Herbartian principle of absolute

indistinguishability, or of the identity

(for instance) the formula

and

to the idea of the duration

the assumption of things identical with themselves.

do not go so

87

of the

On

what

in

the contrary,

our conviction of the real identity of particular things with themselves

permanence during change of action, their duration under we constantly refer ideas having a partially different

refers to their

different appearances

;

content to one and the same thing.

In the judgment

"

this is

we

Socrates"

really identical with the definite individual

say that the person present

known

as Socrates.

is

Here again

the statement refers to the objective validity of this identity, for in making it

are conscious of the necessity of referring the two ideas to one and

we

To

the same thing.

its

question

objective validity would be to say that

subject and the thing referred to as predicate

the

thing referred to as

may

be, or are, two different things,

The law

them.

of agreement

and

among

it

is

not necessary to unify

our ideas

is

not sufficient to prove

that

the necessity of referring two ideas to a single real thing, for this law only

guarantees the agreement of their contents ; it is here that assumptions con cerning the nature of the existent and the distinguishing characteristics of real identity

not

itself

become important, and Such

give us.

is

these the function of judgment does

the assumption that

kinds, can be confidently distinguished,

be mistaken

alike that they can It is

on

known

for

and

one another

if

no two objects so

we examine them

closely.

example, that our conviction rests of the identity of persons

to us.

When

our recollection of the outward form

we have recourse

knowledge of the arrangement of

ward things

it

is

penetrability that

their marriage

is

bed

;

its

as

but with out

and the principle of im

finally establish their identity.

lieving in real identity

to give

when she examined Odysseus

their spatial determinations

by

we

fails

to the identity of consciousness with

individual peculiarities, as Penelope did

arise

individuals, of certain

this, for

us certainty,

to his

all

that there are

The

necessity of be

the result of presuppositions such as these, which

from our knowledge of the nature of things.

To

these statements con

cerning real identity, which are supported by considerations obtained from

another source, we

may add

the judgments which express the coincidence

of a certain subject with a given

member

of a series, or with any other

LOGIC

88 particular thing is

the 6.

first

which

is

of the Caesars

determined by a relational predicate Aristotle is the teacher of Alexander.

Augustus

;

With regard to the objective validity of the judgments which pre and activities, everything which has been said with refer

dicate attributes

ence to naming is, from one point of view, true of these also, because of The attribute or activity the twofold synthesis which takes place in them. which is thought of in the subject must agree with the general predicateidea.

On

the other hand, their objective validity can be maintained only

upon the assumption activity,

is

attributes,

that the unity of thing

a real relation, hence that

and

to look

we

upon a change

and

are able to

in

and

attribute, of thing

know

a thing by

our idea as an alteration in

This relation of the thing to its attributes and under the concept of identity, though here again an ascribed to the term which does not really belong to it.

activities has also

it.

been brought has been

elasticity

The

its

thing

is

only

permanent support of its attributes, as the subject remains one with itself; it is not identical with its attri

identical with itself as the

which in activity butes, nor with its identical with

its

it is

activities,

not the same as these.

redness, nor the sun with

its

Cinnabar is red," by which the judgments, justified, cannot be the principle of identity. "

thought which fact

is,

which

and

that

exists

that the

we can we

lay

down,

and

it

shining "

;

Cinnabar

not

are to be

the sun shines/

The

is

and the principle

only general law of

expresses also a fundamental

and recognise anything by means of these categories of inherence and action alone ; are able to distinguish, retain,

Being of a thing

is

also the

Being of

its

attributes

and

activi

ties.

But even when we is

the existent,

all

start

from

we can mean

this is

law and hold that what we judge about which we

that the existent concerning

of thought by which we distin and then unify them again. The general ideas of things which we use as predicates of denomi 7. native judgments, are, to some extent, accompanied at every further de

judge

necessitates this particular

guish between

it

and

its

movement

attribute,

velopment of thought by those judgments of attributes and activities, of which they have been the subjects. Snow, for example, may signify not an unanalysed image, but a white, loose, cold thing ; the general name has become a summary of attributes. To this extent the relations of

thus

inherence

and action are

implicitly

contained even

in

judgments, as belonging to that meaning of the word which consciousness.

When

there

is

added the

denominative is

real identity of things

present to

which

fall

SIMPLE JUDGMENTS under

steam

different ideas (water, ice,

serve merely to denote a

may

89

boy, man, old man), a substantive

complex of

different temporal states of a particular

attributes

which express the

kind of subject.

Everything which exists as a particular thing is given to us in time, it occupies a definite position in time, and is intuited as lasting during a period of time, as developing varying activities in time, and possibly as changing its attributes. Thus a REFERENCE TO TIME is necessarily con nected with all our judgments "concerning the existence, attributes, activities, and relations of particular things, and all such judgments can claim to be valid for a definite time only. 1

While

.

this proposition is self-evident for activities the reference to

time seems wanting in some of the attributive-predicates, inasmuch as they are regarded as invariable

But while there

is

and given with the existence of the subject

always the general possibility that attributes

found only

in

judgment by

exceptional cases

changeable,

exclude

all

at the

itself;

attaching to the

meaning

etc.).

it

;

most

it

to

be

not contained in the form of the

is

found in the secondary relations

of the predicate, or in the predicate itself (un

Only when we call a thing by a proper name do we and by the nature of our predicate refer to

reference to time,

judgments admit of far as in

is

is

the subject, irrespective of temporal relations.

minent

may change

of the identity of the subject, this relation of permanence

in spite

itself.

All other denominative

this limitation of their validity to a certain time, in so

naming the predication of attributes and activities becomes pro end of 14), and the same thing may thus be called first by

(v.

one name, then by another.

Thus

2.

the narrative-judgment

is

never completely expressed unless

it

contains a statement of the time for which the unity of predicate and sub is

ject

objectively valid

The

future tense.

;

it

must be expressed

temporal relations in predications It

is

only

absorbed it is

ness

to the

;

becomes

the

present,

is

one measure of their

past

or

logical perfection.

disconnected thought of the child,

in the interest of the

present

in

extent to which languages are capable of expressing

moment,

that everything

the power of distinguishing times clearer

and more methodical.

which

is

quite

which occurs to

grows as self-conscious

LOGIC

90

EXPLICATIVE JUDGMENTS.

II.

1

The judgments we have so

far

6.

make

considered

statements about par

from these are judgments of which ticular things. Essentially the subject-word, which do not refer of in the the subject consists meaning different

named by

to the definite existence of particular things

the subject-word,

nature of the idea, frequently presupposed by the though this existence Their objec is it derived. which from source the of or, as a consequence, is

tive

validity

general idea,

which

independent of time. As explaining the contents of a_ of a rule they may be regarded as the indirect expression is

refers to the existent. "

1.

Blood

is

red and snow

is white,"

such judgments do not speak

of this or that particular thing, nor give

present at the is

express

that

expression to any perception

Since the subject- word

moment.

which constitutes

its

meaning

;

is

and

absolute, all that this

meaning

is

it

can

an ideal

content of indefinite generality which has been disengaged from the idea of

any particular existing thing, and which in its indefiniteness cannot be said to exist. Hence all that the statement blood is red can tell us must refer "

"

to this ideal content, is

and

it

nothing more than that the predicate

signifies

thought of in connection with the subject.

What

sort of unity there is

between subject and predicate depends upon the nature of the ideas con If both belong to the same category, then the simple coincidence nected. of the ideas

is

attributes

and

the thing

itself.

It is in

stated

is

We

which

predicated of

a similar sense that

where the subject-idea

dog

that

;

activities

is

is it

thought as a concrete thing has which are contained in the idea of

we make use of

the article, particularly

the idea of a thing having an individual form (the

a quadruped).

must also include

in the class of explicative

seem, by means of the so-called indefinite

judgments those which

article,

to

make

a statement

concerning a particular individual, a particular state, etc. ; such propositions as a fir-tree is a conifer, an ague is accompanied by high fever," do not "

any definite particular thing what they mean is, that that which a conifer, and this statement can only be based upon the relation between the general ideas fir-tree and conifer, not upon knowledge

refer to is

a

;

fir-tree is

of the particular. 2.

The

objective validity of these judgments has immediate reference

SIMPLE JUDGMENTS

91

onlyjo the sphere of ideas ; all that they tell us is, that when the subject (presupposing nominal correctness) is thought, it will be thought together with the predicate

that

;

thought of as red.

what

I

and every one

else think of as

"

blood

"

when we

only secondarily, pass from the of the word to the actual contained under generality things it, that the is

It

is

judgment refers to the Being of these things also; and states concerning them the rule that when there is a thing which is denoted by the subject the predicate belongs to

it.

According to one view, such judgments are from the first general judg-j ments gained from experience by induction, having for subjects particular; things thought of as indefinite in number. But here it is forgotten that the first

essential for such an induction

according to which so

we may name

naming

this

;

in

we should have some standard same word and

judgment common to all. Such a standard we the meaning of the words we bring to our process of

comprehend them

can find only

that

is

particular things by the

in a

meaning must be already

to

some

extent fixed before there

can be any question of judgments of induction. It is perfectly true that under the influence of progressive experience, which is always adding something to our ideas, these ideas remodel themselves, and that it is

common

generally a matter of chance where

boundaries of

fixes the

its

thought comes to a halt and

words.

The meaning of the word blood, for example, is formed in the from the intuition of human blood and that of mammals and birds may, and

in ordinary language,

contents

but by an extension of

;

first ;

place

hence

does, include the colour red amongst its

original

meaning

it

its

might also be

it

applied to the whiteish fluid in other kinds of animal organisms.

At some

stage of formation, however, the meanings of words are a necessary prelimi

nary to the judgment of the individual; stop this fixed meaning

is

whatever the stage at which they

preliminary to naming and to the possibility of

judgments of experience gained by induction. Thus if blood is the fluid in the veins of mammals and birds, then red forms a part of its meaning, "

"

and when we take

it

as fixed in this

way we cannot use

it

to

name

fluids of

another colour.

Thus before we can

give utterance to a

a judgment of experience including later),

a simple

judgment must have preceded

single idea denoted by a given word is,

judgment having the meaning of cases (of which we shall speak

many

in the first instance, a rule

of

;

to unfold the contents of the

the general rule to be found herein

naming which forbids us

to call

anything

/I!

LOGIC

92

blood which

is

The

not red.

inductive judgment

discovered common

first

appears

when anew

which are denoted by the attribute is with the attributes is connected that we same name, when invariably say idea not of the the contents which make up A, subject having been pre A. with in thought viously connected to all the things

B

B

Such an explicative judgment can contain the statement of a rule con cerning things themselves only in so far as the idea of a permanent and lasting thing, together with the possibility of variable attributes,

denomination

in the substantival

;

and the rule

is

is

contained

that the predicate always

and constantly belongs to the things which fall under the denomination, and is invariably connected with their other attributes. When the judg

ment extends to everything

to reality

it

is

this invariability of the

which can be called

"

blood

"

to

which

red colour belonging it

really refers.

Verbs occupy a peculiar position here, Strictly speaking, the only 3. case in which a verb can be the predicate of a general subject is when we are speaking of an activity which is continuous, and which lasts as long as

comprehended under the subject-idea (fire burns, the wind blows); when, on the contrary, the verb expresses a variable activity, begin ning and ending in time, it is only as a figure of speech that it can be the

thing

used as predicate (the sheep should really denote

which the 4.

we

activity

horse neighs) ; what the expression a merely faculty or a habit, i.e. an attribute from

is

may

bleats, the

proceed, and not the activity

When we compare

this class of

itself.

judgments with those

first

are chiefly struck by the fact that their validity does not

considered,

depend upon

the existence here or there, at this time or the other, of a thing correspond Hence they are not valid for some given time, ing to the subject-idea. but can claim unconditional to ideas. refer validity just because

On

the other hand,

all

merely they merely narrative judgments are temporarily valid.

Here there appears a characteristic difference in the meaning of the .5. Present tense, according as it is used for the statement of unconditionally valid judgments or of those amongst temporarily valid judgments which refer to the present.

When we

having a particular existence

think of a thing

as

we have thereby assigned to time which embraces everything, and is the same for all

presented and as it its

;

by

place in that its

existence

stands amongst other things which are contemporaneous, or precede or follow it; and by its which our is it

it

quality, concerning made, judgment occupies a definite point of time and thus stands in a definite temporal relation to the moment of our judgment.

SIMPLE JUDGMENTS But when the subject of our judgment

meaning of the word, this idea

Removed from

plex.

present, in

the idea which constitutes the

is

disengaged from the temporal com

is

the changes of time,

which there

is

no

93

it

stands before us in a mental

and

distinction of yesterday

which the consciousness that our idea

will

be the same

to-day, but in

at every repetition

annuls

all temporal distinctions between the particular occasions upon which we actively think of it. When thought in this way the subject has predicates which belong to it independently of time, which belong to it as

often as

it is

state of the

thought

The

of.

sky at the present moment, and

really in the present tense; but

ment,

different

meaning

object of

my

my

is

In

always blue.

The

is

blue

is

denotes the

as a narrative

thus,

judg

also have the completely

may

this case

validity of the

"

and

it,

as the fixed

no past nor

judgment

future

is

not estimated

is

perception of the object in a given momentary state, but by the

which

invariability of the ideal content

the

it

the sky

that the sky as I generally think of

thought,

contrasted with the present.

by

"

proposition

word

an invariability which

I

am

connecting once

the condition of

is

all

my

for all with

speech or

thought.

III.

THE ACT OF JUDGMENT

AS EXPRESSED IN LANGUAGE.

17-

The

verbal expression of the unification of subject

takes place in the judgment

be found

and predicate which

developed languages in the form of inflection of the verb, which has itself arisen out of what was originally a is

to

in

mere juxtaposition. Even where the verb be "appears as the link between a substantival or adjectival predicate and the subject, the act of judgment is "to

expressed by the verbal ending alone

;

the verb

"

to

be

"

forms a part of

the predicate. i.

Less developed languages, and, in simple cases, even advanced ones,

are content to express such a unification as takes place in the

judgment by

the mere juxtaposition of the two words which stand for subject and predi cate.

This juxtaposition must not only indicate that the corresponding

ideas are at the

moment

unified

by the speaker,

it

must also express the

Accentuation alone can distinguish the statement from the question, or from any other mode of connection, such as the attributive which expresses a unity of two ideas which is already objective validity of the judgments.

present.

When, on the

contrary, the

development of the

linguistic forms has

LOGIC

94 followed

the logical distinctions, then in the case of verbal predicates

all

the meaning of the personal ending (which blends the pronominal equiva lent of the subject immediately with the stem of the verb, thus making it

agree in person,

number and gender)

is

denote the connection of sub

to

and the indicative mood, combined with and predicate in judgment the emphasis and arrangement which distinguishes the statement from the

ject

;

question, states this connection as objectively valid. indicates the time for which the

judgment

is

to

be

The

tense, again,

valid.

would denote by the expression copula, that element can combine words into a proposition, and so into the of language which

That which

logicians

expression of a statement,

lies in

The meaning

in this alone.

the personal ending of the indicative, and

of the unity of subject and predicate which

is

expressed by this terminal inflection differs according to the nature of the ideas connected. 2.

Judgments

in

which the predicate

is expressed by an adjective or mere juxtaposition (as ino /xei//?i o9 to be is employed. But this is not

substantive are not generally formed by /fyaxv?,

fj

8e

ri^y-ifi {jLaKprf)

virtue of

its

the verb

;

"

"

meaning the element which expresses the formation of the

by judgment; the function of judgment is contained in the form of inflection alone. The verb to be is the means by which we give the form of a "

"

verb to the predicate, and thus enable

it to take the ending which is the outward sign of its predicative relation to the subject. In the judgment cinnabar is red," nothing is added by the meaning of the verb to be which is not already contained in as an adjective it involves red," for "

"

"

"

reference to a subject of which

ness is

"

"and

red-being"

it is

the attribute.

As

abstract nouns,

would have just the same meaning; the verb

"

red

"to be"

is not merely used to express the fact that thought of as independent In this way the verb abstract, but is predicated of a definite subject. "red"

and "

to

be

"

certainly serves to facilitate the expression of this use of the word to show that it is a red," predicate, as contrasted with the merely attributive relation which might be expressed by juxtaposition ; but in so

and

"

doing it is a mere vehicle for the copula, not the copula itself; it does not constitute the judgment, but merely prepares the way for it. This function of to be," to denote the in which a word is to be "

meaning

still

more

tives,

by

its

that

used, appears

clearly in the case of substantives.

These do

not, like adjec

carry in their form a reference to something else, yet their meaning, nature, enables

meaning

is

them

to

a general one

fulfil

the function of a predicate, whenever

and only appropriated

to a definite particular

SIMPLE JUDGMENTS by means

of a denominative judgment.

nite individual, although in

its

meaning

;

Man

"

is

name

at all,

name

into the

man

of a definite

contrary, converts

it

;

included

and

it

word

article converts the

the use of the verb

into a predicate,

of a defi

is

but the sign of a definite ideal-con

Only the demonstrative adjective or the

tent.

name

not the

the idea of the figure of an individual

not a

it is

"

95

"

to

be,"

on the

cannot be a name before

it

has

been a predicate. Thus Mensch," as a general idea awaiting its refer ence to some definite individual, and Menschsein have the same mean "

"

"

ing

;

the verb

"

sein

"

serves only as the outward sign of the function of

the idea as predicate, which might also be

Thus

tuation.

function

its

is

shown by

its

position

and accen

that of a formal element of language

but

it

not that formal element which expresses the act of judgment and merits the name of copula. is

But how does

3.

it

that

happen

be"

as

an independent verb, when

function, which

just the verb

it is

use in this way? and what connection it

be"

which we "

has in connection with adjectives and substantives?

it

In the fourth chapter of the

book of

first

attention to the ambiguity contained in the it is

"to

there between the meaning of to stands alone as predicate, and this

is

his Logic, J. S. Mill

word

"is,"

draws

inasmuch as when

used as the so-called copula, it certainly does not state that the subject but only denotes the relation of predication. Such a sentence as

exists, "

A

centaur

centaur

is

;

is

a fiction of the poets

and he

looked by almost

is

"

directly denies the statement that a

surprised that this ambiguity should have been over authors, although existing in

all

modern

as well as in

ancient languages. little attention to Herbart as to other German philoso 1 Herbart, following in the footsteps of Fichte, has shown, with his

Mill has paid as phers.

53), that the judgment A is B, and do not contain the statement (which, though

usual acuteness (Einl. in die Phil., the question

commonly whatever

There

is

is

is

A Bt

certainly

attributed to them, said about

A

by

no doubt that

been disputed. 2

A

is

itself,

this

really quite alien) that

nor of

remark

its

is

correct,

judgment of the form

A

is,

for

nothing

existence or validity.

"A

and should never have

is

B"

can never, by the

1

I, a passage of which I have Grundlage der gesammten Wissenschaflslehre, part i. been reminded by Bergmann (Reine Logik, i. p. 235). 2 It is urged against this (cf. Ueberweg, p. 162) that God is propositions such as the soul is immortal," "true friends are to be valued," must involve the state just," "

"

ment

that there are such things as

contained in the indicative

mood

;

God, a soul, true friends that this presupposition is that any one unwilling to accept the presupposition ;

I

LOGIC

96

mere

fact that the subject

and predicate are connected by

the statement of the judgment would have "

to

in case there

when

"A

exists."

The

"

is,"

function of this

include "is"

is

add clauses to those propositions which should make them hypothetical Such a clause, it is said, can be dispensed with only is a God," etc. :

the context (as in a romance), or the recognised meaning of a word (such as Zeus, is merely feigned, or that the statement is Chimsera), shows that the reality

Sphinx, This objection is so far true that the reality of the a name. merely the explanation of those who speak or hear such judgments; otherwise subject is generally presupposed by But this is quite another thing there would be no motive present for uttering them. from saying that the judgment itself, as it stands, involves the statement of the reality of the subject, i.e. that this is necessarily stated by the words of the judgment, and more If it were so, it would be incomprehensible how mood. especially by the indicative there should be any exception to the rule, for if the indicative of the categorical judg

ment containing

"is"

has the force of stating the reality of the subject, then

it

must

The exceptions which Ueberweg have this force always and under all circumstances. admits themselves prove that it does not depend upon the form of the judgment, but attach to the meaning of the subject- words, without upon the ideas we unconsciously utterance in the judgment, whether or not the presupposition of their existence their finding as a rule

And, indeed, what meaning can the statement of existence accepted. have when the subject does not denote individual beings as such as in the proposition but is of a universal form ? When true friends are to be valued or God is "

is

"

"

"

"

just,"

what sense does

judgment involve the statement that snow exists ? Certainly not in the sense indicated by the present tense of the indicative when used of definite things having a particular existence, for then the statement would But the judgment, "snow is white," is true be that snow exists now at this moment. in summer and winter alike; and yet it is not held that the judgment tells us that snow always exists. Again, if the statement is said to be, that such bodies as those of which I think when I say snow, have actually existed somewhere and at some time, it can be is meant. This alone can be stated, nor only the existence of definite "snows" which But the judgment, snow is white," can it be said of snow in general that it exists. does apply to snow in general and not only to this or that snow. Still it is true, that the recollection of actually perceived snow is always connected with the idea which we attach to the word "snow," and for this reason, because of the way in which I have attained to the meaning of the word, it is presupposed that we are I say, "snow is

white,"

in

this

"

But suppose I take the analogous judgment, dealing with something which exists. is as firmly connected with the idea which I "Pegasus is winged," the idea of wings So far, however, I attach to the word Pegasus as that of white colour with snow. have never seen an existing Pegasus indeed, I know that it is a creation of fancy, and for this reason the existence of Pegasus is not presupposed. But the judgment itself tells me neither that Pegasus exists, nor that he does not exist ; only how the idea is Take the judgment, constituted which I connect with the word. The branches of the hyperbola are infinite," it is undoubtedly a valid judgment, although it can have nothing to do with the existence of the branches of this or that particular hyperbola. The infinite branches of the hyperbola exist in exactly the same way as all other subjects of ;

"

judgment, that is, they exist as objects of my thought, of which I assume that every one else thinks alike. \V. Jordan has treated this question more carefully in his treatise, iiberdie Zweideutigkeit der Copula bet Stuart Mill (Stuttgarter It is true that on Gymnasialprogramm, 1870). The is certainly includes the concept of existence." But he gives a page 13 he says,

my

"

much wider scope than Ueberweg

to this

concept of existence,

when on page 14 he

says,

SIMPLE JUDGMENTS exactly the

97

same whether we are talking of existing or of non-existing

things,

of subjects which are thought of as particular, or of subjects which are

thought of as general

(to

general, particular existence cannot

these, as

Whenever the thinking

subject finds something present which is independent of his of thought, whether it is in the material or spiritual world, Logic will permit the If we take this explanation literally, it is certainly true that every act use of the is. "

act

"

it presupposes, and does not create, the subject of the judgment recognises something which is independent of this act of thought, and this something the idea denoted by the subject-word. Such a reality of ideas is presupposed whenever

of judgment is

so far as

a judgment finds expression in language, and it is presupposed moreover that it is common Thus the question would disappear if such were the reality many individuals.

to

is would be justified wherever the subject-word, and therefore the intended, and the But just for this reason the judgment would have nothing judgment, had any meaning. whatever to do with the statement of the actual existence of the thought denoted by the "

"

subject-word, in the ordinary sense of existing. However, this is not what is meant. Jordan attempts in opposition to Herbart and the meaning of real existence. This he does in the first Mill to preserve for "is"

place by saying that the reality in question belongs to the predicate, but not to the moderation is difficult," In such propositions as "self-defence is forbidden," subject. there is no doubt that the existence of the subject-idea is left undecided, while in the "

predicate,

whole

is

on the contrary,

allusion

is

made

to

an existential proposition in disguise,

forbid self-defence,

circumstances which

begin to paraphrase like

this,

we

something which actually i.e.

exists.

The

which we once

there are laws, or grounds,

make moderation

shall find at last that

But

difficult.

if

even the proposition, square there are logical laws which make "a

an existential proposition ; a square circle impossible." This, however, is to abandon the ground of dispute, for We are far from denying the question was, whether the reality of the subject is stated? circle is unthinkable,"

"

is

every statement, just because it claims objectivity, contains the recognition of and laws but we do deny that for this reason the existence is ; objective grounds stated of a thing (or attribute or event) which corresponds to the subject-idea. Jordan s Such a other distinction, which he applies to Mill s example of the centaur, is better.

that

"

"

"

"

"the centaur is a fiction of the poets approximates to a definition. amongst definitions Jordan distinguishes a particular class which he calls "recti and these are the definitions which deny the idea which the subject stands for, fying," and replace it by another. The proposition says, "the centaur does not exist in the "

proposition as

Now

word of actually being, but the idea of the centaur is a fiction." number of such predicates which di-gradc the subject-won! into the sign of a merely mental thing, when, by its customary meaning, it might be taken to denote an existing thing. But we must not forget that at the head of these predicates to exist. there stands the verb to be Whenever I expressly state of a subject that it exists, the and my predicate states that subject- word is, for me, the sign of an idea sense indicated by the

No

doubt

there- arc

a

;

an actual thing corresponds to this idea. The view that the meaning of the word "to be is always the same has lately received determined support from Fr. Kern {Die deulsche Satzlehre, p. 64 sq. ), who pronounces In the propositions wooden iron is non against distinguishing two meanings in it. a square circle is a contradiction, the existence of the wooden iron and of the sense, "

"

square circle is stated with just as much clearness and emphasis as the existence of the the boy exists But while boy in the proposition the boy is in the garden. outside my thought as well as within the iron and the circle exist only in my idea. They exist, moreover, in connection with the property of being nonsense or a .

.

S.

L.

.

.

.

.

H

LOGIC

98

of predicates which can belong to an existing thing, or of predi cates which deny existence by their meaning. In each case its one function

belong)

put the predicate into such a form that

to

is

and

;

to enable

can be used

it

The nature

to take the personal ending.

it

in the

judgment,

of the subject

and

predicate-ideas alone determine the sense in which subject and predicate are unified, and whether the existence of the subject is presupposed, left uncertain, or denied. logical identity,

"

is

"this

The square

is

my

real identity

watch,"

a regular, tour-angled figure is "gold

;

a

"

means

metal,"

sub-

sumption under a more general idea ; "gold is yellow," the unity of thing and attribute ; A is a mile away from B" a relation ; the movement is "

"

slow,"

the unity between a general idea

and so on.

"Socrates

because Socrates

and

"

"

is

ill

"

is

winged

not

is

the

Pegasus in

more exact determination,

its

presupposes the existence of the subject,

of an individual

who

is

thought of as existing, "

leaves the existence of Pegasus uncertain for any one the

"

being.

ill,"

name

and

a condition thought of as actual at a given time.

know whether

subject;

is

is

name

is

an actual or of a merely

that of

a mythological fiction

every instance

"

Pegasus

who does fictitious

denies the existence of the

our information

is

obtained only from the

meaning of the terms, either of subject or predicate. With reference

4.

two

to the predicates

we may here

distinguish between

classes.

which property I have recognised and stated ; and thus they cannot pos be found in any reality which is independent of me." But the ambiguity of the word is immediately granted by this distinction between a which exists in a reality external to me, and one which exists subject only in my idea. contradiction,

sibly

For when the word

"

"

is

stands alone in the sense of

subject does not exist only in "

God

my my

"

exist

idea, but independently of

"

what

it.

it

states is that the

In such a proposition as

but only in idea" the clause directly denies the meaning in which we impelled to understand the words "God exists." But it is not even true that a circle exists in my idea," for who could square imagine one ? The contradictory is im possible in my thoughts, as well as in the What the reality which is independent of me. a contradiction" predicate really tells us is, that I cannot think of anything corre sponding to the -words square circle it denies existence in thought as well as in reality. In p. 74, it is brought forward as an instance, that to any one who doubts it we say with emphasis A is the person who did this emphasized is being meant to lay stress upon the existence of A as the person who did it. But it is obvious that the existence of was never called into question, hence that there is no reason to stress are, at

exists

first,

"

"is

"

";

"

it,"

A

lay special

upon

It was the action of A, and not his existence, which was disputed, and the question whether we had any right to predicate of A (whose existence is undisputed) that he is the person who did it. If this is not so, then the A is not the person who proposition did it must be meant to of but the existence of A. deny not merely the it.

"

"

quality

Concerning Bergmann

s

wiss. Philos.y v. 113 sq.

objections (Reine Logik,

i.

p.

agency,

235

sq.), cf. Vierteljahrsschrift fiir

SIMPLE JUDGMENTS

99

All modal relational-predicates, which express a relation to my know ledge (with the exception of those appertaining to the senses, such as visible, or tangible), by their meaning make the subject-term the of sign

a mere idea which does not involve real existence

whether the predicates themselves affirm or deny

When

undecided. etc., is

of anything,

I

I

use the predicates true,

denote that

to give information concerning

its

this is the case

existence, or leave

its

false,

it

credible, incredible,

only an idea, and that the predicate

is

it

and

;

relation to

me

and

to

my

subjective

u Such propositions as "Tail s apple-shooting is a the Trojan war is an historical event," "atoms are bodies which actually if and are could by themselves state exist," would be impossible

thought.

fact,"

"

"

"

"is

the existence of the subject.

But the verb is

of the subject

word

"to

modal

a

itself

it

be,"

when used

absolutely

and

as

meaning

"to

exist,"

expressly stating the existence

determines the question whether that which the subject-

denotes merely as an idea

first

By

relational-predicate.

also

is

an actual

Cf. above,

thing.

12, 7, p. 72.

But with other predicates everything depends upon what the subject is in which it is used ; and this cannot be seen from the mere

and the sense

external form of the judgment

and the use of the word

"is."

If the

used as general and is not introduced as the name of one or more definite things, then the predicate which is formed by means of the subject-term

verb

"to

is

be"

can state nothing but the contents of

nothing whatever "

is yellow"

gold

this

subject-idea,

is

said as to the existence of the subject.

or

"atoms

are

indivisible,"

do not declare the existence of

and

I

say

the being yellow or indivisible

appertains to the idea which I denote by the subject-word positions

When

particular things.

;

but the pro I

must learn

from some other source whether or not the subject-term is applicable to such things. Bat if the subject-term appears from the first as the name of things which have a particular existence yellow,"

word

"this "

"

however, but

is

5.

This

but to

all

attributes,

horse

is black"

"ambiguity

is

this

piece of gold

is

presupposed; not in the

"

in

this."

of the

copula"

applies not only to the verb to be,

predicates which can by themselves denote real states and inasmuch as they sometimes state that which actually takes

place in a particular case

and sometimes

or activity to the subject-idea.

tense

then existence

"

e.g.

which

is

ambiguous

;

that

which belongs as attribute

Strictly speaking,

for this

it

is

only the present

sometimes expresses the empirical,

LOGIC

TOO

The pro

the general necessity of thought. temporal present, sometimes position

"great

though

this

souls

pardon

offences"

moment

great souls are at this

pardoning. a great soul he must pardon offences.

is

speaks,"

states the existence of Socrates in "

"Socrates is ill

;

we can speak

nor that some

the act of pardoning

in

presupposed

is

states neither that great souls exist

of

All

tells

it

us

is,

that

if

man

a

But the proposition, "Socrates the same way as the proposition

him only

in so

just

far as

he

exists,

because the word Socrates denotes an individual having a particular exist ence,

and any

his existence. /

attributes or actions

which are ascribed to him must involve

1

to which is the ex happen that the verb a formal function assumes actual of existence, whereby it loses pression it? The remarkable to contradict seems even its meaning thing is nay, not that the ambiguity in this respect has been so little noticed, but rather

But how does

6.

that all

"

it

be,"

known languages agree in containing it. As Ueberweg (p. 162) rightly notices,

difficult.

sized

above

(p.

95

which we speak not interested to

it is

sq.) t

exist

;

is

explanation

and, as

not

we have empha

as a rule taken for granted that the things of

there

know

The

no need of any express assertion ; we are what and how they are. When

is

that things are, but

now, it is desired, not merely to express predication by mere juxtaposition, but to give the form of the verb to the predicate, the verb to be offers "

"

itself just

because

always presupposed

it

;

is

know, we need to have "being

thus";

exactly as

"

so general and has by itself no contents.

It is

we may know what we wish to determined more exactly as "being and

but in order that it

just as

being here

"

this"

the statement of existence

and

The

"

being

now."

is

determined more "

predicate

red,"

which

by its form already denotes something appertaining to something else which exists, now appears as a modification of Being, being red.

Now as the present tense denotes on the one hand the empirical, sensual present, and on the other the timeless present of our thoughts ; so the meaning of being in this connection is also extended. The attribute has the same relation to the thing which is thought, and to the thing which in its existence is perceptible to sense ; as the presupposition of

Being was only implied before, of

my

this 1

and being-thus remain so The

it

can

thought, things do not alter

;

now be their

far as I retain

theory according to which the judgment in order to get the inevitable copula

speaking."

abstracted from.

being

them "A

"is,"

may

As

objects

cease, their being-

in thought.

speaks"

may be

is

altered to

held to be obsolete.

"A

is

SIMPLE JUDGMENTS Nevertheless the verb has kept a part of

its

101

original

meaning, and the

most important part. The verb to be originally implies That which exists holds good independently of "

"

my

real existence.

thought,

and holds

This objectivity of the connection to which my judgment gives utterance is an essential factor of the judgment itself. This it is, and not the existence of the subject, which forms a of the

good

for

every one.

part

statement; and for this

By this

extension of

"

its

"

Being is a very suitable expression. fundamental meaning it strengthens the assertion

of objectivity, of universal validity, already contained in the inflexional form.

CHAPTER

III.

ARISE, AND THE DISTINCTION BETWEEN ANALYTICAL AND SYNTHETICAL JUDGMENTS.

HOW JUDGMENTS

18.

/

IMMEDIATE JUDGMENTS are those which presuppose nothing but the ideas connected in them, in order that these ideas may be united as subject and ; MEDIATE, or MEDIATED JUDG which some further element is necessary in addition to

predicate with a consciousness of validity

MENTS

are those in

these ideas.

Kant

s

distinction of analytical

and synthetical judgments and the concept which

the relation between the predicate

and assumed

the subject-term

as given.

those judgments in which the subject

is

It

is

refers only to

denoted by

is

not applied by Kant to

a particular, intuitable idea.

All

must be regarded as synthetical from the Kantian point of view, even when based upon the analysis of a complex

relational judgments, moreover,

presentation.

When,

i.

ment

after analysing the functions

takes place,

we ask about the

concerned with the origin of the ideas united by the judgment

through which the simple judg we are not

origin of the judgment,

whether subject or predicate

speaking merely of the analysis of the act of The question concerns only the judging we assume these to be given. that of the genesis of the act of judging itself, and this has two aspects ;

in

:

connection or unification of subject and predicate, and that of the con sciousness of the objective validity of this connection.

This genesis

when nothing

is

may be

ideas connected in

it,

of objective validity. addition of

either

immediate or mediate.

It

is

immediate

presupposed in the judgment but the subject and predicate in order that It

is

it

may

mediate when

some other elements.

It

take place with a consciousness can take place only by the

this

may be

that without

some mediation

the subject and predicate cannot even be referred to each other in such a

way

that their union in a

judgment might be thought of; or

it

may be

PIOW JUDGMENTS ARISE

103

that at least the consciousness of the objective validity of such unity

be obtained elsewhere.

Let us for the present

must

that which brings

call

about the unification of subject and predicate the Ground of the judgment. Then the immediate judgment is one, the ground of which lies in the con nected ideas themselves, apart from anything else ; the mediate judgment is one which has its ground in these ideas only when taken together with the mediation may at first merely relate subject and predicate to ; each other by raising the question whether AisB; or it may at the same time settle the question and guarantee the certainty of the validity of the others

judgment If the

A

is

B.

ground

lie

entirely in the ideas themselves

which are connected

by the judgment, then, according to what we have said above, their relation must be such that the unity expressed in the judgment can be immediately In a denominative judgment

recognised.

I

am

conscious, without further

mediation, of the coincidence between the idea which

which "

that

is

is

general idea of the activities the idea

idea.

I

is

present and that

reproduced and denoted by the predicate-term ; when I say a fir-tree," I find in present intuition just what agrees with the of attributes and

In immediate judgments

fir-tree.

corresponding to the predicate

is

a part of the subject-

analyse the latter and emphasize a certain element,

e.g.

colour,

and

this I recognise as agreeing with a colour already known. Here, again, nothing beyond the complex idea given as subject is needed in order that I may discover in it the element which corresponds to the predicate.

In the case of relational judgments,

it

is

true that an

analysis of the

subject-idea by itself cannot yield the element which agrees with the predi I may turn and twist as I will the idea of the lamp which stands cate.

before me, left

I

can discover in

plex intuition containing this into its

elements

I

it

But

of the writing desk.

nothing which

tells

in this instance that

me

that

which

is

it

stands to the

given

is

a

com

two objects and their relation and by analysing obtain the judgment, for which no more is needed

than the ideas connected for the statement that the

;

in

it.

The complex

lamp stands to the

presentation left

is

the ground

of the writing desk.

Thus all immediate judgments are of necessity analytical, if those judg ments are analytical which only re-unite the elements obtained by analysis of a presentation, judgments, that is, in which either the contents of the predicate are already presented in the subject, as in those of naming, attributes or of activities ; or in which subject and predicate, together with the relation between them, form parts of a complex presentation, as in

rf 104

f

I

I

then synthetical judgments must be need some other ground lying which and those

If this

relational judgments.

those which are inferred,

is

so,

of the outside the ideas given, in order that the synthesis

judgment may

take place.

immediate judgments should be analytical in this sense contradicts the essence of the judgment, which is to be a

That

2.

no way

all

For the analysis or decomposition

vowdTw.

is

only the preparation for the

work of judgment

act of judgment, not that act itself; the

is

union between the elements which have been thus distinguished

to restore (cf.

81).

to use the terms analytical and synthetical simply in this sense

Still,

3.

forbidden by the use of them introduced by Kant.

is

in

The above

distinc

tion between immediate and mediate judgments is based upon a ground different from that of the Kantian distinction between analytical

essentially

and

In the former case

synthetical.

depends

it

entirely

upon how the

any time in the judging subject, whether it is immediate judgment it has its origin in the separation or combination whether and or mediate, cannot we and of elements generally discover what this genesis is from arises at

;

the verbal expression of the judgment. in the

first

instance

Kant, on the other hand, depends

the presupposition of definite concepts which

upon

are expressed by the terms appearing as subjects. "

(ed.

In i.,

he says in the well-known passage of the Kr. d. r. V. which we think of a subject as related to

all judgments,"

p. 6

;

ed.

the predicate,

it

ii.,

Int. IV.),

A

belongs to the subject this

"in

two ways. Either the predicate something which is contained (implicitly)

may be related

concept A, or else In the it.

outside of

as ,

in

though connected with the concept A,

first

lies

B in

quite

case I call the judgment analytical, in the

second synthetical. Thus analytical judgments (affirmative) are those in which the connection of the predicate with the subject is conceived through identity, but those in which this connection is thought without identity are

We

be called synthetical.

to

might also

call

others ampliative, judgments, for the former

the former explicative, the

add nothing by the predicates

to the concept of the subject, they merely break

it up by analysis into its which were component concepts, already thought (although confusedly) in it the latter, on the contrary, add a predicate to the concept of the sub ject, which was never included in the thought of it, and could not have ;

been obtained from "

all

it

by any process of

bodies are extended

"

and

"

all

analysis."

The two

propositions.

bodies are heavy/ follow as examples.

In order to obtain the former judgment

I

need only analyse that concept

HOW JUDGMENTS (of body),

i.e.

think in

in

it,

hand, when different

I

ARISE

105

only become conscious of the manifold which order that "

say

I

may

bodies are

all

from that which

heavy,"

the predicate

is

I

On

find this predicate therein.

something quite

think in the mere concept of a

I

always

the other

body

in

general.

Just for this reason, he adds in the Prolegomena,

propositions are judgments a priori, even rical

a yellow metal

is

gold

e.g.,

;

for in

;

when

2, 6,

all

analytical

their concepts are

know

order to

this, I

empi

require no

my concept of gold, as yellow and a metal, which is what constitutes the concept. just as such," continues Kant in the 2nd edition, Judgments^ofxperience, experience beyond

"

"

are

upon

all synthetical.

It

would be absurd

experience, for in order to

to base

an analytical judgment I have no need to pass

form the judgment

concept or to appeal to the testimony of experience. That a extended is a proposition which is established a priori, and no body of judgment experience ; for before appealing to experience, I have all the

beyond

my

is

conditions for

my judgment to

predicate according

become conscious of

in the concept,

from which

I

can extricate the

the law of contradiction, and at the

On

experience could never have taught.

same time

a necessity which

the necessity of the judgment

the other hand, though I

do not

include the predicate of heaviness in the concept of body in general,

denotes an object of experience by one of

this latter I

may add

can

in

other parts of the

the

first

place

same experience

know

the

concept

its

Then

I

extend

my

parts,

as belonging to the

of

body

still

to this first.

I

by the which are all con

analytically

characteristics of extension, impenetrability, figure, etc.,

tained in this concept.

and

knowledge, and on referring to

the experience from which I had derived this concept of body, I find that

heaviness

add

it

is

always connected with the above characteristics, and hence

synthetically as predicate to that concept.

upon which the the concept

Thus

it

is

I

experience

possibility of the synthesis of the predicate heaviness with

body

is

for though the one concept is not contained belong to each other, as parts of a whole i.e. of itself a synthetical connection of intuitions, although

based

;

in the other, they still

experience, which

merely

We

is

accidentally."

have given these passages

realizing the presuppositions first

place

Kant

in full,

upon which

because of the importance of In the distinction rests.

this

according to the received way of regarding the judgment

has in view solely the concept, which

is

denoted by the subject-word, and

LOGIC

io6

which constitutes

its

The

significance.

is one of the characteristics which although confusedly," or whether "

now

as I

think

I

question

is

whether the predicate

think in the concept of the subject,

it is

not yet contained in this concept

In the particular judgment also,

it.

bodies are

"some

which is used as an example in the Prolegomena instead of the heavy," universal judgment of the Kritik, the point dealt with is only that the predicate heavy

not really thought

"is

Here Kant presupposes,

the general concept of

in

body."

the examples chosen by him, that the concept

in

derived from experience, but contains only a part of the experience of

is

this object

as he expresses

or,

;

experience by means of the

concept

characteristics

which

it is

it

a part of

formed through

is

(as

common

in the first edition,

denotes the complete

This implies two things

it.

:

that

first,

a process of abstraction, whereby of the

characteristics

abstracted) have already been fixed

;

its

from

different things

and secondly, that we are

not dealing with an exhaustive concept which expresses the whole nature of an object of experience, but with a purely subjective image, in which from causes which have no necessary connection with the nature of the

one part of the characteristics actually appertaining to the given Thus the only is made use of to denote the class itself.

thing

class of things

ground

for calling the

the other synthetical,

judgment, is

"all

bodies are

a generally accepted

extended,"

meaning

analytical

and

(actual or assumed)

of the word body.

From

no doubt evident

that

as a matter of chance, so far as empirical concepts

were

the Methodenlehre

Kant regarded

it

(p.

721

sq. ed.

i.) it

is

concerned, which characteristics are employed for their formation. there

shown

that in the empirical

domain there are no

It is

definitions in the

since the characteristics which belong to the object e.g. gold can never be exhaustively enumerated, and hence the rule that the definition should be complete can never be complied with. In our strict sense,

or water

concepts we include such of the characteristics alone as are sufficient for distinguishing the objects;

same

it is

never certain that a word, while denoting

mean for us more of its characteristics at one time than at another. The so-called definitions are only verbal determina The same view is taken in tions, nominal definitions. 99-106 of the the

object, does not

Logic.

In calling the judgment, bodies are heavy

nominal

"all

"

definition,

synthetic,

bodies are

Kant has

extended,"

analytic,

and

"all

therefore no other ground than a

which happens to be universally received.

This

is

the

HOW JUDGMENTS

ARISE

107

main point against which Schleiermacher s criticism is directed when he declares that the distinction between analytical and synthetical judgments because the concept is^pnly relative,

The same judgment

(ice melts)

included in the concept of ice

is

always in the process of formation.

may be

analytical

when we have

already

dependence upon definite relations of thus the temperature, and synthetical when we have not yet done so difference represents merely a different stage in the formation of the con its

;

cept.

Apply

justifies

me

this

to the

Kantian concept

in the proposition,

"

all

:

before the experience

bodies are

concept only from the characteristics of extension,

and must include the it

may

heavy,"

my

etc.

my

;

which

have formed but after

concept "

concept,

it

I

my can

in

order that

all

bodies are

With this concept I might now proceed might go on to say that all bodies are electrical, If my concept were the expression of a complete

thus becomes analytical.

to further experience, all

characteristic heaviness in

express the complete experience, and

I

heavy,"

e.g. I

bodies are warm.

knowledge, which indeed were impossible before all knowledge had been attained, then all judgments of this kind would be analytical. This criticism is fully justified by Kant s own statements. I can never

determine whether a judgment concerning empirical objects is analytical or not unless I know the meaning which the person making the judgment connects with his subject- word, the sum-total of the characteristics which, at this particular stage of the

hended

in

ground

for a universal

formation of the concept, he has compre

His progress from one meaning of the word to another takes means of a synthetical judgment. This judgment, we must be place by careful to note, is the result of an inductive inference, the only possible it.

judgment drawn from experience

reason (as the Methodenlehre expressly emphasizes, necessary and apodeictic.

p.

;

but for this very 721)

it

cannot be

In the case of mathematical concepts

this

un

certainty disappears, but only because these are formed for a purpose and contain an arbitrary synthesis (ibid., p. 729).

Before a judgment, considered in itself and independently of all other considerations, can be regarded as analytical, it must evidently be assumed that there are

no subjective differences between the concepts which differ same word. Assuming, then,

ent individuals connect with one and the

words have a completely fixed and circumscribed meaning, there may be judgments which are certainly analytical ; in this case they are to be found in the accepted meaning of the word. The Kantian example is that

strictly correct, if

it

is

presupposed that with the word body every one

j

!

LOGIC

loS

and no one ever connects

"

always connects the characteristic

extended,"

the characteristic heavy.

But

is

it

that just as evident

this is the

if

case

I

can no longer have any

rational motive in giving utterance to such judgments,

truisms and convey no information.

Who

which are mere

would trouble himself with such

A squares square"? triangles are triangular," judgments as can never be uttered except to judgment which is analytical in this sense some one who is in danger of forgetting the meaning of a word, of think ing the characteristics of the concept only

beyond

its

sphere,

are

"all

"all

etc.,

to

i.e.

some one

for

"

confusedly,"

whom

it is,

of extending

strictly

it

speaking, no

longer analytical; for so long as he himself thinks the characteristics only

make the judgment. Thus judgments which are

confusedly, he cannot even

analytical in this sense lead naturally to those

hended meaning of a word

make statements about analytical for

it

the ignorant

which impart the uncompreto those which no longer

thought, but only about words.

any one who

learning

only

to

makes

is

master of the language

synthetical

being grounded not upon his

own

;

They

are strictly

but any one

who

is

his

judgments, however, knowledge, but upon a belief in the

judgments

;

statements of other people.

But so

4.

far

both Kant and Schleiermacher have failed to

tell

us

how

the matter stands with those judgments which are not covered by our pre that

supposition, judgments,

and

is,

of which the subjects are not concepts

which the verbal expression does not show what idea is present to the speaker, inasmuch as he is speaking, not of the contents of the idea denoted by the subject-term in its generality, but of a concrete at

all,

in

thing which, though

falls

it

under the general concept,

is

particular

and

and hence cannot be completely denoted by the subject-term. 1 actual and primitive judgments of experience are of this kind. Our

concrete,

But

all

experience

judgment

is

gained from the particular, and the synthesis in the synthetical bodies are heavy" is dependent on judgments of which the

"all

and in the last instance on particular percep Let us realize the process which underlies any

subjects are definite bodies, tion

and observation.

judgment of perception, quite evident,

if

e.g. this

we consider

rose

the words

is

yellow, this liquid

and

is

sour.

It is

meaning, that there is a synthesis here, for yellowness is no part of the concept rose," nor sourness of the concept which expresses liquid ; nor from the meaning of this," a mere relation, can But then we are not anything further be derived. their

"

"

"

"

1

Cf.

Trendelenburg, Log. Unters., 2nd ed.,

ii.

241

;

3rd ed., 265.

HOW JUDGMENTS concerned with the meaning of words rose

"

ARISE

109

these are always general.

;

denotes a concrete thing which, in

its

This

"

concrete particularity, can be

only very imperfectly denoted by the word

the demonstrative

;

"

this

"

draw the attention of some one present to an intuition incommunicable by words, and this intuitable thing is the subject of my serves merely to

judgment

of

it is

;

it

that I say

it is

:

yellow.

might content myself with saying: this

I

is

When

in language.

pressed

speaking, a double synthesis. "

this

a

is

rose,"

by which

"

I say,

still

this rose is

First, there

more

subject of

there

yellow,"

is,

my

form, structure,

judgment only

is

The

But

with the general image.

made

only incidentally

does not

it

;

itself

this

whole of

denominative

appear directly, but

the subject-word by which I denote this thing.

in its result

rose,

etc.,

properly

concrete idea under a

general image, finding that the concrete intuition agrees in the its

my ex

indefinitely

a denominative judgment,

is

have subsumed

I

The

yellow.

judgment would be the same, but would be

actual

judgment before us, however, states that this, which I call a Upon what ground ? Not on the ground of a synthesis yellow.

is

between

rose

"

and

"

but on the ground of an analysis of

"

yellow,"

my

form and structure, is included the yellow colour in an undifferentiated unity. One element of my intuition is

intuition, in which, together with

identical with

what

I call

yellow,

and

this I

then predicate of the whole in

an attributive judgment. Or,

more

exactly,

have

intuition I

first

if

we describe the process from the beginning

noticed those elements in which

general image of the rose, hence the

and hence the judgment. The relation between the concepts If comes into consideration as well. tained in

"rose,"

as white

is

in

to the

denomination

my

"rose."

rose

and

"

"

"

yellow

"rose."

hears

my

have then

"

yellow

of course

were analytically con

ice, then, it

But since

intuition completely,

Whoever

I

;

"

for expressly stating

been already expressed by the name

in

not expressed by the name,

is

snow, or cold in

should have had no motive

must, in order to describe

"

:

coincides with the

naming of the subject

noticed one further element, which as yet

ing, I

it

generally speak ;

it

would have

this is

not

so, I

add the predicate yellow

my judgment

in the

course

performs a synthesis as he adds the particular de termination of colour to the image which the word rose has awakened in

of a description, say

him.

But

subject.

I,

the person judging, have merely analysed

my

idea of the

LOGIC But the other example

this liquid

:

is

Is there

sour.

no synthesis here

?

This judgment the judgment, not by means of it. Certainly, but before one by the fact that different senses is distinguished from the preceding

am accustomed

I

to determine

by sight whether or

are concerned in

it.

not anything

a liquid, and thus the denominative judgment that

tongue and discover "

Now

put the liquid to

express

my

perception in the

can make

this

judgment have already referred

judgment

sour taste, and

its

this liquid is

Before

sour."

I

I

sensation of taste to the object which was

my

is

I

confined to visual ideas alone.

is

presupposed

my

is

must

I

known

must be certain that what has touched

my tongue is have no subject for the and cannot make a judgment, cannot refer the predicate predicate sour to the subject liquid, and express this reference in an attributive to

me by

what

sight

I

;

saw before

I

Otherwise

the glass.

in

I

"sour,"

Thus my judgment analyses an

judgment.

the process of perception

stitutes

the sensation of taste to

its

object

is

not the same as the function of the

If we expressed the former in a judgment, it would run judgment. which tastes sour is the same thing that I saw before as a liquid

liquid has

"this

latter,

the attribute of being

cognised sourness as belonging

To

return to the Kantian

shall find that there

by Kant himself are

heavy,"

body,"

is

to justify

example

him

really a relational-predicate

my

;

lies,

refers

and

same way of each

as being alone in

we look more

Looked

at carefully, is

"

"heavy

in itself as

thought, but to what

my "

we

"

all

bodies are

it is

extended,"

in is

particular one, even though I should

the world; the judgment,

expresses a reference of each particular one to

hence

cannot be already contained in the

If,

closely,

all bodies judgment, however, not in the concept

heavy,"

it

re

can

though nowhere indicated

not to what a body

The judgment,

relation to other bodies.

it

it

intuition

I

valid in just the

if

:

in saying that the

This ground

synthetic.

the isolated object of

think of

the

;

must have

I

in the liquid, before I

a sufficient ground

is still

but in the nature of the predicate.

"

is

and being

sour."

"that "

it.

predicate 5.

to,

con

act of combination which

but the function of the reference of

;

"

"all

all

bodies are others,

concept of body in

and

general."

as I believe, this, together with the historical influence of the old

Cartesian definition of body,

unmotived a

priori"

ments.

is the hidden ground of Kant s apparently throws light also upon his synthetical judgments the examples which he gives of these are all relational-judg

distinction,

for

That

7

"

it

+ 5 = 12

is

a relational-judgment concerning the numbers

HO W JUDGMENTS ARISE represented by "

predicate

7

5

A

B

is

thought at

and by 12 B"

;

necessary as well as that of It

all.

The

the judgment asserts their equality.

;

can of course never be contained and thought of taken by itself, nor discovered by any analysis of it for

equal to

in the subject

the idea of

+

1 1 1

is

in order that

that equality with

again,

quite true,

A

+

may be

it

12

is

not

but must be discovered by an actual addition, by proceeding to a number which is 5 more than 7. The judgment is impossible until the addition has been completed, and analytically contained in the expression 7

two numerical expressions given thereby far as the intuition

but then

number of

of the equal

it

is

analytical in so

which may be reached

units

one way or the other furnishes the ground of the judgment.

in either the It is

;

5,

not in the judgment

itself that

we pass beyond

the presentation

7

+ 5,

but in what precedes the judgment and makes the comparison possible so soon as this is possible the judgment becomes a mere analysis of the

;

It is the

given relation. straight line is

is

same with Kant

the shortest

s

geometrical example

way between two

also a relational-predicate,

"

points.

which cannot be contained

The

:

that the

shortest

"

way

in the idea of the

But presupposes comparison with other lines. the straight line can never be presented in intuition apart from the space straight line

in

which

beside

by

it,

it.

is

it

by

is

itself;

drawn, and which contains the possibility of other lines

That which forms the ground of the judgment and is analysed the total intuition in which the straight line appears between

others connecting the

ments a

it

same

points.

So that even these synthetical judg

priori, so far as they are immediate, are really analytical; they

are not concerned with the explication of the concept expressed by the

when taken alone, but with a complex object which, though denoted partly by the subject-word, contains something beyond the subject

subject-word

of the judgment. object which

Of 6.

is

The ground

of the judgment

lies

in that part of the

not denoted by the subject-word.

we must speak later on. In the sphere of empirical notions the Kantian division of judg

the principle of causality

ments into analytical and synthetical

refers to

judgments having

different

kinds of subjects, and therefore having also a different ground for their validity.

His analytical judgments are those which merely unfold the

contents of a concept which has received some fixed meaning in a word, without any regard to the existing object of intuition. His synthetical

judgments presuppose in

experience

;

intuition,

their subjects are

and the

synthetical connection of intuitions

"

things,"

which

fall

under the word but are

LOGIC

II2 only incompletely denoted by

it.

The former

are explicative, the latter

narrative.

We

have shown that an analysis takes place even in judgments of per an analysis, however, not of the concept, but of the intuition which ception

was formed by a synthesis preceding the judgment and not in it. We have still to test the Kantian statement that in analytical judgments we think the connection of the subject and predicate through identity, but not

Accepting for the present the term synthetical judgments. which we showed above to be inappropriate, we still fail to see

so in

identity,

how any

(affirmative)

judgment can be expressed without identity

relation

between subject and predicate

The

the same in the judgment of

is

perception as in the judgment which deals with concepts

ment if

we

to the

that identity

is

look, not to the proper subject of the this

is

and the

so far right that there

is

state

true only

judgment of experience, but

subject

arbitrarily limit the notion of identity to the

But Kant

;

absent from the judgment of experience

meaning of the word by which

i.e.

;

without the consciousness of the unity of subject and predicate.

is

denoted; or when we

sphere of mere concepts.

a different ground for the validity

is

of his analytical, and of his synthetical judgments a posteriori. The former presuppose only the habit of connecting certain ideas with a word ; hence, in order that such judgments may be repeated, nothing is needed but The latter have constancy of ideas and agreement in the use of language. their final

ground of validity in a fact of individual intuition, which cannot, be made common property. The necessity of the former judg ments has its ground in the stability which we find in our general ideas as such,

;

the necessity of the latter in the laws according to which of the particular, and are conscious of their objective

we form

reality.

again

we come upon

the difference in

meaning

to

be found

in

And

ideas

here

judgments,

owing to the ambiguity of the copula. In the judgments which Kant calls analytical, nothing whatever is said as to the existence of their sub jects, in those which he calls synthetical the word denotes subject-

of a possible

"objects

experience."

I9

.

c^,,,.^,--

Before a judgment can be passed in which the idea of the predicate is not immediately recognised as one with the idea of the subject, we re quire

some mediation, both

to bring about a relation

between a subject

HOW JUDGMENTS and a predicate which

lies

outside

it,

and

ARISE

cause us to recognise this

to

relation as a unity in the sense of the judgment,

The

i.

and most

first

which a predicate

hended

in

is

it,

is,

for

familiar

the

first

113

and

to

be certain of

it.

example of a mediated judgment by time, added to a subject and compre

the mental act of a person

who

hears from

some one

judgment which he himself has neither occasion nor ground

for

else a

making.

is mediated judgment. The Socratic Maieutic, indeed, from the principle that there is no such thing as learning, nothing but recollection, is content to call into consciousness the ideas of sub

All real learning starting

Thus

and predicate by means of questions.

ject

the materials alone are

form his judgments himself, and his conviction of their validity being based upon his own discernment. And if this process were perfectly carried out, then, indeed, all judgment provided, the person questioned being

elicited

would be immediate and

it

by

The

the subjects without assistance.

left

to

analytical, finding the predicates in

questioner would merely take upon

himself the work of the psychological laws of reproduction, bringing to the subject just that idea which in

its

is

But teachers and taught have seldom time the truth to say that

all

mind

appropriate as predicate, for the

make

continual eagerness to form judgments to

use

of.

for this process

;

it is

nearer

learning begins with tradition, where the learner

accepts the judgments he hears, and repeats them himself.

In so

far as

he

learns, what happens is that he hears a proposition, the idea of a subject is aroused in him by the subject-term, and he includes in it a predicate in

respect of which the subject

any one learns that

mode

ice

is

had

as

yet

frozen water, ice

When

been undetermined. is

given to

him

in intuition,

unknown, and no reference to water con For the person who learns that the earth moves, a completely new determination is added to the idea of the earth that of movement, and he is called upon to unify subject and predicate in a way but

its

of formation was

tained in his intuition.

contrary to his habit of thought.

has heard,

i.e.

result of his

really

made

Not

until

he has understood what he

the synthesis demanded, does he reach as the

mental action that from which the teacher

set out,

the unity

of subject and predicate in the sense determined by their category.

viduals

;

for

In

be a difference between teacher and taught as indi on the one hand the words are not absolutely fixed and equiva

deed, there will

still

meaning for both ; on the other hand, even if they were, they leave more or less room for choice between particular degrees of meaning in their

lent in

application to particular things. s. L.

i

LOGIC

I14

his words In proportion as the individual is ignorant, and connects with he must have recourse knowledge, based ideas incomplete upon only meagre and by means of this his words become ; to such

judgment

synthetical

more

gradually

significant as

he learns to connect with them more par

At the word

ticular determinations.

"

lion

"

the child at

first

thinks only

of the outward, visible form which his picture-book shows to him ; from tales and descriptions his idea becomes enriched with all the attributes and habits of the animal ; while the zoologist possesses the idea complete.

The more

and the richer therefore the meanings

perfect the knowledge,

room

of words, the less

there

syntheses such as these, in which

is for

some

In the end synthetical judgment would be limited to the particular to that sphere which can never be denoted by words fact as it is for any one who has not observed it himself, and to the par

new

thing

ticular

is

learned.

changes and relations which can only be expressed by temporarily All judgments about the meaning of the word, the

valid judgments.

general idea of the object, are then analytical.

macher means when he sphere of particular

what Schleier-

the proper synthetical judgment to the

limits

facts.

is

(This

155, pp. 88, 105.)

Dialectik^

In learning by tradition the ground which the learner has for the certainty of the judgment is merely the authority of the teacher; objective 2.

validity

is

believed.

accepted from confidence in his knowledge and veracity Since

all

be inferred from

it)

he

is

narrative judgments are necessarily synthetical for the

hearer, they are those which, belief of the hearer.

;

by

their nature, appeal to

Besides one there

is

s

own

and demand the

perception (and whatever

no knowledge concerning the

may

particular ex

way of belief, which, in this case, is historical belief. There is another process, similar to those of teaching and narrating, which adds predicates to a subject capable of further determination, and cept by 3.

calls

to unify them. It is introduced by the inward play of our determined by the laws of associative reproduction, and the

upon us

ideas,

as

When we

activity

of imagination

of

object through perception or recollection

any

as led

by

similarity.

are

conscious

does not

merely up those predicates which agree with its contents as now presented and lead to immediate judgments. Recollection, association, and it

call

analogy bring forward other ideas, which tend to combine as predicates with the subject, although they are not as yet contained in the idea of the

subject

now

present.

already dealt with in

9, p.

From one 55,

is

point of view the

an instance of

this

common

case

the case in which

HOW JUDGMENTS

ARISE

115

visual images of particular objects call

up the recollection of their other and these are forthwith attributed to them as predicates. (This

qualities, is

a bunch of grapes

though,

in

this is

when

certainty that

the judgment

already complete, we do degrees, in called

sweet; this

is

a stone

hard, etc.)

such instances, association takes place with such

made

is

the idea to which

But

absolute

it

refers

is

from these by imperceptible which the fusion does not take place at once, but the idea

up remains

to use

find cases differing

s phrase in suspense, and only brings This is most obvious when different and

Herbart

the expectation of a judgment.

mutually-exclusive ideas are excited at the

same

time,

and a

struggle takes

place between them, as, for instance, when I see a human figure at a distance, and it excites in me the images of both A and B, seeming to resemble first one and then the other.

Upon

such associations are founded

which extend

present, but are melt."

add

in

4.

new

more

all

particularly

judgments

They can never proceed from analysis of the mediated by some process of inference. The snow will

to the future.

"

I cannot tell this by looking at it, but, led by former experience, I thought to the present intuition a predicate not yet contained in it. The universal tendency to form judgments and to connect what is

with what

is

familiar,

is

so strong that,

when

same processes which suggest the predicate may judgment

;

i.e.,

they

may produce

there

no check, the

is

also give rise to

the

belief in the objective validity of the

In proportion as thought is undisciplined it is in proposed synthesis. cautious, and slow to recognise the difference between purely subjective

and psychological combinations and those which are objectively valid there is a greater tendency to believe everything which occurs to one,

;

especially

when

strongly supported by a wish or an inclination.

recollection of one or a few cases in

subject A,

is

generally sufficient to

every subject which at

first

which a predicate

make

B

us attribute the predicate

sight resembles

A; and we

The

belonged to a

B to

are often scarcely

conscious of the process of inference by which the synthesis of the judg This credulity of our natural thought, while

ment has been brought about. the source of

many

deceptions, hasty assumptions and superstitious opinions,

same time the indispensable condition on which alone we can profit by experience, and learn to pass beyond what is immediately given. As we found with the generalization of ideas that the process has not to be is

at the

learned but rather to be checked, and the power of distinguishing cultivated, so

it

is

also with

judgment when

it

passes beyond what

is

given.

Our

LOGIC

Il6 natural tendency

is

always to think of

predicates and attribute

many

them

to the subject; what we have to learn is caution and doubt, to distinguish between the valid and the invalid, and to enquire as to which of these and which are merely forced upon us syntheses are objectively necessary,

by nature and

habit.

check prevents the judgment which passes beyond what immediately given from taking place, there arises the question. This may be in two ways. In the one case we seek to complete a given idea

When some

5.

is

accordance with some previous experience, the desired completion not

in

Such is the case being offered by any absolutely certain association. I cannot recall any idea agreeing with a new and unknown object

when what

is

who

Or when I seek the subject to a given attribute or activity speaking ? What is that shining ? Or again, when I am uncertain

that ? is

what attributes or what does that

activities

taste like ?

belong to a thing besides those perceived In the second set of cases a completion

offered by association, but the certainty of

judgment In

this

is

way

sketched out in thought, but

at

is

validity

is

there arises the question which seeks a decision as to the

validity of a given predication

is

A

really

Both the question which aims

6.

is

wanting; the not passed as a judgment.

its

at

B

?

completion, and that which aims

confirmation, presuppose psychologically

the

simple and immediate

judgment which is inseparably connected with the consciousness of its I can only seek for that of which I have at least a general and validity. indefinite idea

me

;

nothing but experience of perfect syntheses can create in

the desire of completing an imperfect idea by the addition of

further element.

I

some

must have acquired the habit of referring sensations to

definite things before I

ing to a sensation which

can arrive at the point of seeking the thing belong is presented without any certain reference.

In the same way the question which demands yes or no for an answer seeks a certainty which must have been experienced in immediate judg

ments before

it

can be sought.

Its

search for an

answer implies the

thought of the certainty connected with predication in other cases. In simple and immediate judgments that is a tree, that is red, snow white, coal

is

black,

synthesis of subject

snow

am

the certainty of validity

and predicate.

I

white, whether the object before

conscious of the two idea s I

synthesis between them.

am

is

cannot ask whether coal

me

is

is

given inseparably with the

red or a tree.

is

black, or

As soon

as

I

also conscious of the necessity of the

HOW JUDGMENTS

ARISE

117

It is not until we attempt to pass beyond what is given, not until we would unite with the idea of the subject an element not yet contained in it, that the two elements which are united in the immediate judgment, the

simple or complex synthesis between subject and predicate and the con sciousness of its necessity and objective validity, can be separated. The "

is

question

A

really

,5?"

can only arise

that sphere of thought in

in

which judgments are formed by a process of mediation.

Hence

it

follows that the

first

psychological starting-point "predication

without

stage in the formation of judgments

not invariably (as

is

a mere

quality,"

e.g.

"idea"

in

Bergmann holds

critical reflection

"

upon

its

validity

is

added.

)

)

a

which subject and

predicate are thought together, the judgment taking place only "

our !

when

:

the

In the simplest cases the

two elements are not found apart, and we cannot show the meaning of predication in general unless we start from objectively valid predication as it

occurs in the immediate positive judgment

"

A

is

B.

n

All such theories overlook the fundamental importance of the distinc-

between immediate and mediated judgments, a distinction which in logic is not less important than that between analytical and synthetical

.

tion

judgments in the transcendental philosophy. In the question A 2??" the elements and the connection 7. "is

between them have the same meaning

as in the

expresses the expectation of a synthesis between

judgment.

A

The

The judg

of a valid synthesis, not merely of an arbitrary combination.

ment

is

already conceived, but

for the certainty of validity

is

it

still

wanting.

question

and B, and moreover

needs the seal of

its

confirmation,

This invention and essaying of

judgments which pass beyond what is given and the immediate judgments based thereon, represents the active movement and progress of thought in inventive action in the sphere of the

judgment.

We may

say at once,

Doubt, conjecture and expectation are only particular varieties of the same state. They differ in the degree to which we are conscious of the absence of a ground for the completion of the questioning

is

thinking.

judgment they are alike so far between subject and predicate. ;

8.

The

as concerns the

decision of a question

1

meaning of the synthesis

may sometimes come from

the elucida-

Reine Logik, 1879, p. 42, 169 ; cf. the objections raised by Schuppe, Vierteljahrsschr. filr wiss. Phil., iii. 484 ; my own article, Vierteljahrsschr. filr wiss. Phil., v. I, p. 97 ; and Bergmann s reply in the same journal, v. 3, p. 370. Brentano s view is dealt with in

my

Impersonalien, p. 58.

j

LOGIC

n8 tion

and completion of the subject-idea

we

itself;

when

this

idea

is

the

means of more exact appre hension and observation what was not formerly observed. Such is the case when, seeing a white powder, I ask whether it is sweet and put it to my intuition of a particular object,

discover by

tongue I have then made an addition to my perception, and is an analytical judgment proceeding from the new perception. ;

not given in intuition, reflection

subject-idea

is

recollection,

and again enable me

these attempts

fail,

to

make an

may

bring

my answer When my

more complete

analytical judgment.

then the only way of arriving at a decision

is

But

if

to seek

which may confirm the attempted synthesis, and the mediation to which the spoken question appeals in the first instance is for mediations

information from It

9.

enable

it

may be

some other person. ground for the desired synthesis, which would form of a judgment, can be found neither by the

that a

to take the

elucidation or completion of the subject-idea, nor yet by mediating ideas.

Then

either the question remains unsettled

of

objective validity, or else the negation arises, from the fact that the

its

and we

fail

to

become conscious

subject-idea immediately or mediately repels the predicate-idea.

Reserving for a later investigation the former case called problematical

judgment

let

us

now

that of the falsely

turn to the negation.

CHAPTER

IV.

THE NE GATI

N.

THE NEGATION

is always directed against an attempted synthesis ; hence presupposes some prompting, either from within or without, to connect The object of a negation must be either a the subject and predicate. completed or an attempted judgment, and for this reason we cannot regard it

judgment as a species equally primitive with the and co-ordinate with it. judgment, the_ negative

1.

Following the example of Aristotle,

defining the

judgment

aspect a part of

its

many

logicians have

as either affirmative or negative,

This

definition.

is

making

positive

begun by

this

twofold

true in so far that judgments

when

formed can be exhaustively divided into affirmative and negative, and that when we form judgments, it can only be by affirming or denying a pre But the definition is false if it implies that affirmation dicate of a subject.

and negation

as forms of

judgment are equally primitive and independent

of each other, for the negative judgment presupposes the attempt, or at least

the

thought,

of an

attribution of a predicate,

affirmation

and has

its

i.e.

it

presupposes the positive

meaning only

in contradicting or

Or rather, the primitive judgment should annulling such an affirmation. not be called affirmative at all it would be better denoted as positive. ;

The simple statement negative judgment and

but that

we should

A

is

B

is

an affirmation only when opposed to the

in so far as

it

rejects the possibility of a negation

should be raised which must be decided by yes or no, condition of the judgment A is It. 1 2.

When we

consider that only a

finite

number of

affirmed of every subject, while an incalculable is

at

is

Cf.

Beneke, System der Logik,

I,

no necessary

predicates can be

number can be

once evident that the negation has no meaning except 1

;

think of the possibility of a negation, or that a question

140

sq.

denied,

it

in opposition

LOGIC

120

No

at a positive statement.

an attempt

to

one would think of making

the negations which in themselves would be possible and true have no motive for so doing. Before there can be any sense

all

he could

;

in saying

:

this stone does not read, does not write, does not sing, does not think ; is not five-cornered, does not rotate, etc., justice is not blue, is not green,

some one

there must be a chance that

will attribute these predicates to the

stone or to justice. All that the negation aims at

of the

nature

ideas

given

individual thought, which

and

in fancies, questions,

statements extends beyond what a subjectively arbitrary

to confine within limits fixed

is

the subjective

is

fortuitous

of

conjectures and erroneous

Thus

objectively valid.

and contingent thought

by the

movement

it

presupposes

the limitless sphere of the

in just this deviation of individual thought from the which is objectively necessary and universally valid, and it is a thought matter of chance how the negation may arise with any particular individual. It is impossible to lay down universally and exhaustively what must false,

which consists

necessarily be denied of 3.

what

any

1

subject.

We is

cannot farther define and describe what we mean by not," nor the significance of the negation ; we can only recall what always "

The

takes place in the process.

B may, however, be elucidated

meaning of the proposition by contrasting it with incorrect and true

A

is

not

artificial

interpretations.

In the

first

place subject

and

predicate, taken each

in the negative propositions in exactly the

words stand

for

means the same

the

same

as in the

ideas.

When

judgment

same way I say

by

itself,

are thought

as in the positive

"snow is

"snow is white,"

not

black,"

;

the

snow

and black the same

as in the judgment "coal is black no effect is at present produced upon them by the negation, they have their usual contents. The question raised by. Aristotle (De Interpr., 2 and 3) as to whether there is a 6Vo/m do/oiaroi/ ";

(OVK ai/$p(D7ros)

and a

prjfjia

aopLcrrov (ov Ka/xvet)

which could appear as

subject or predicate of a judgment does not refer to the essence of the

negative judgment, but only to the nature of the subjects and predicates which can be used in a judgment, and can be affirmed or denied of each 1

Kant, Kr. d. r. V. Methodenlekre, ed. I, p. 709 (a passage which Windelband points out in the Strassb. Abh.,^. 169), says In respect of the content of our knowledge in general, negative propositions have the peculiar function of simply averting error :

;

hence also negative propositions which aim at averting false knowledge when there is no possibility of error may indeed be very true, but they are devoid of meaning, and for that reason often very ludicrous.

THE NEGATION A

other.

and primitive

natural

expression not-^4 or not-^5, but

may be

never be

denoted by the

always possible that these expressions

serviceable as abbreviating formulae, under which definite subjects,

or at least predicates,

may be

and when a statement

these,

idea can

it is

121

thought.

But then they act as symbols of

possible at

is

all

some predicate

is

affirmed or

denied of such subjects, or such predicates of some subject; the judgment not-^4

is

B

and the judgment and is not

judgments not-A

A or not-^4 is A or not-A

not-.# are affirmative, the is

not not-^ are negative.

Aristotle has given the right explanation of this.

It is true he attempts all with unlimited combinations and subjects possible predicates (De Interpr., 10), but he does not make into a particular kind of judgment those in which

a subject or predicate of the form not-A appears. hand, Kant

places the infinite

and negative is,

as a third

1

When, on

the other

or limiting judgment beside the affirmative

kind (Kr. d. r. V., the soul is not-mortal, that 9) which remains when I take away the mortal

belongs to the infinite sphere

from a view of the judgment which we shall have to oppose its essential aim to be the placing of a subject this within the sphere of a concept. view he is enabled to bring out a By then he

starts

later on, a

view which takes

between the propositions "the soul is not mortal," and "the he does not, however, thereby gain a third judgment addition to the positive and negative, but is himself obliged to allow that

distinction

soul in

is

not-mortal

"

;

is no ground for considering a judgment of the form which a purely negative predicate is attributed to A, to be anything more than an affirmative assertion.

in general logic there

A

is

4.

not-^5, hi

In opposition to the attempts to regard

affirming a predicate not-^# of a subject that the negation affects the copula,

is

all

negative judgments as

the largely accepted tradition

by which we are led to speak of the This is so far true that the

affirmative or negative quality of the copula.

negation does not

lie in the elements of the judgment, but only in the which they are referred to each other. But it is incorrect to If by copula we understand oppose a negative to an affirmative copula. the expression of that mental act by which a predicate is referred in the

manner

in

judgment

to a subject as

agreeing with

it,

as activity or quality, then a

But that which holds subject and predicate apart, and prevents the attainment of unity, cannot be a kind of unification. unification

is

expressed by

it.

1 The name comes from an awkward translation and application of the which Aristotle had used, not of the judgment but of its component parts. Cf. Trendelenburg, Elem. Log, Ar., 5.

d<5/5to-ros,

LOGIC

122

A

bond which divides

nonsense.

is

We

should rather say that the proper

has exactly the same meaning in the copula (in language the verb-ending) that is, it expresses the positive affirmative the in as ; judgment negative of the relation in judgment between subject and predicate, the attributing predicate to the subject,

and

arouses the thought that the predicate

it

thought (which is also contained it is just this attempt at is declared to be false which question) does not convey the The the which copula prevents. negation synthesis There is no such thing as a negative, but is the object of it.

For

belongs to the subject.

it is

just this

in the

;

negation,

but only a negated copula.

Three elements, then, can be primarily distinguished in the simple, These are the subject, the predicate, and the thought positive judgment. of their unity (in the particular sense of the synthesis determined by the being the object of the certainty which finds utterance judgment. The same three elements are present, and have

categories), this latter in the positive

the

same

force, in the negative

judgment

;

fourth in language as well as in thought.

the attempted synthesis as valid, and proposition

A

is

The

B.

but the negation is added as a This prevents the completion of opposes its No to the whole "

"

it

object of the certainty, which gives to the negative

proposition as well as to the affirmative the force of a statement,

The judgment

"

No."

believed that

A

is

B

"A

not

is

B"

means,

"it

is

false, it

is

just this

must not be

hence, immediately and directly, the negation

"

:

is

a

judgment concerning a positive judgment that has been essayed or passed only indirectly

we had

were formed by means of a negative copula is not 2? not" in the judgment

to regard the

"A

"is

pression of a simple act of thought,

who

ascribe to the

"

"

is

denies the existence of the subject.

when

judgment^

if, "as

there-

the ex

then, to be consistent, those logicians

of the affirmative judgment the force of stating the

existence of the subject should hold that the

a rule, the

;

a judgment concerning the subject of this judgment. 1

If the negation

5.

lore,

is it

is

not

B

But

"is

not"

in negative

this is certainly

judgments

not the case.

presupposes the existence of

A

As

in all cases

in the judgment A is B ; i.e. whenever it is meaning of the words. But the negative judgment in itself no more concerning existence or non-existence than the affirmative

it

would be presupposed

part of the states

"Socrates is not presupposes in the first place the existence of Socrates, because only on the presupposition of his existence can there be any question of his being ill. But since the negation only declares it to

judgment.

ill"

1

See Appendix A.

THE NEGATION

123

be

false that Socrates is ill, the presupposition contained in not so definite as in the affirmative judgment Socrates is

it is

may

because Socrates

also be denied

is

dead.

certainly

"

"

ill

;

for this

(For further, see below,

25.) 21.

The negation has for

its

follows the different forms of the positive judgment,

and

object those different relations between subject and predicate

which constitute the different meanings of the unity between them. Hence, the judgment contains a manifold synthesis, the negation is ambigu

when ous.

Directly

it

can express nothing existent

neither attribute, activity,

nor relation. i.

In prohibiting an attempted statement, the negation adapts itself to and whatever these may state, it ;

the different kinds of propositions

all

declares to be false.

To

the

judgment which would allow two ideas to coalesce as wholes, Such propositions as apes are not

the negation opposes their difference.

red

"

men,"

is

not

freedom

"

blue,"

"

is

not license

"

prohibit a threatened

confusion, or a conscious annihilation of the distinction fixed between the

This negative judging brings into consciousness by an express in the formation of our

objects.

what was already contained unconsciously That is, ideas and in their verbal denotation. act

that distinction

between

it

makes us conscious of

different ideal contents which, being always

same way, gives us a fixed plurality of ideas and difference of words corresponds. This act of

in the

to

which the

drawn

plurality

distinguishing, through

which our ideas are formed, must have already taken place before it can be brought into consciousness and confirmed by the negative judgment.

When

opposed to the qualitative judgment, the negation prohibits the between a subject and an attribute ascribed to it. The

relation of inherence

relation of inherence in itself even forms the

The proposition

ground

for the negative

judg

does not deny that the subject is a unity of thing and attribute, but that the attribute, which really belongs to the subject and which is not expressed in the statement, is the one in ques ment.

tion.

I

cannot find

"

lead

is

not elastic

in the subject

"lead"

"

the attribute denoted by

the actual attributes of lead are other than elasticity.

what the negation qualitative ideas. activities.

finally

emphasizes

The same

is

So

"elastic";

that here, also,

the fixed difference of certain

holds good of judgments whose predicates are

LOGIC

I24

Now

2.

according as the

movement

of thought (see

the attribute or activity to the thing to which

it

n)

passes from

belongs, or the reverse, the

also varies (the variation being expressed verbally object of the negation It may either lay stress upon the fact that a or position).

by emphasis

does not possess the attribute or given thing, with fixed determinations, the fact that it is not this thing to which a or in emphasize question, activity given attribute or activity belongs. false when no one has shouted at shouted. In the

first

in the latter, the subject

;

or the negative placed before

to

is

the

"

can the predicate

it is

burn"

no "

it

the

false that

;

generally emphasized, it

was not

I that

that neither predicate nor

"

is

to find the

and

burns,"

How

a contradictio in adjecto.

be denied of the subject

we expect

fire

may mean

does not burn

fire

"

not hesitate to say "

denied, in the second

Starting from the general view of the negation,

be found.

the proposition

is

is

(/have not shouted;

Finally, the negation

shouted).

subject

it

"

"

case, the reality of the predicate

relation to the subject

its

The judgment I have shouted is as all as when it was someone else who

And

fire?

burning

fire,

yet

we do

the negation says

this proposition is true

when

there

is

This applies especially to the negation of the Impersonals. does not thunder means either that the name given is false that

fire at all.

"

It

what

heard

is

is

not thunder, or

indicated by the predicate

it

denies the

phenomenon

itself,

which

is

the negation extending also to the presupposed

reality of the subject. 3.

Similar modifications appear in the case of relational judgments.

judgment being here threefold, we from the simple negation of the relational judgment what the statement of the negation is primarily aimed at, nor what is the point which That

the synthesis of the positive

is,

cannot

tell

the person making the negation has in view.

If the judgment "A is be may merely the direction in which he walks, or it may be the kind of movement (if he is riding or driving), or the fact that he is going away at all or, finally, it may be home"

walking

be

false,

what,

is

denied

;

disputed that

walking

home

it "

is

A

who

is

walking home.

may have any

The

of these meanings.

"

proposition

A

is

not

This ambiguity of the

negation, which at best can only be dealt with by emphasis, is a new proof that its only force is to state the falsity of the positive judgment as a whole,

and

that

it

is

unable by

itself

to constitute

any definite relation.

In

the case of causal relations, which are expressed by transitive verbs, the

negation activity,

may be which

directed merely against the particular object

itself really

takes place, or against the activity

of the

itself,

or

THE NEGATION against the subject to which the activity this

may

sentence"

either

been written, or

has

is

125

ascribed.

"I

have not written

deny the whole fact that the sentence in question

it

either

may emphasize

this

sentence, or

"

/.

I

have written nothing denies all writing whatever by the negation of every I drink no wine denies only a possible kind of object of writing ; "

"

"

particular kind of object.

In the same way, when an unconditionally valid judgment is denied, tells us that the statement made by the unconditionally

4.

the negation merely valid in

judgment

the

is false,

do not

(plants

ambiguous

feel

(e.g.,

;

the statement being that the predicate

contained

is

which constitutes the meaning of the subject-term

subject-idea,

How far such negations may be not equilateral) will be discussed below,

light is not matter).

the triangle

is

25-

When opposed

to temporally valid judgments, the negation applies only

to their validity for the time stated, to the condition of the subject at

watch

is

not

watch

is

going

now

this

;

going"

therefore say anything as

The judgment

declares that the temporally valid

"

is

and cannot

any other time.

false

;

and what

negation leaves

it

it

means by

that

is

"this "

judgment

that

this

not going

it is

undecided whether or not the watch goes

at

other times. 5. Attempts have not been wanting to supplement the poverty of the negation as merely annulling some other statement by giving it the force

In this way, what is stated by the would stand negative judgment opposed as independent and valid in itself to what is stated by the affirmation and thus negation and affirmation, of a directly significant statement.

;

would occupy the same rank. himself has to some extent given a precedent

as forms of statement, Aristotle

for this.

makes the affirmation and negation (particularly in the Metaph. b i sq.) correspond to a unification (a-vyKelcrOai) and separation and

in so

doing he makes

subject and predicate

it

the primary

meaning of the

in the affirmative

judgment

compounded (from substance and accident). 80 sq.) shown this view to be impossible,

We since

,

He

10, 1051,

(StypyvOai),

relation between

to express something

have already

(

14, p.

the predicate of the

judgment can never be looked upon as something existent least of all as an existent thing which can be thought apart from the subject. There is no meaning in saying that, in the existent, commensurable is always ;

"

"

separated from the diagonal of the square

belong

to thought alone.

But, for the

;

separation and unification both

same reason, neither can the nega-

LOGIC

I26

any separation. In the first place, elements actually could have no mutual reference whatever and it separate in the object would be inexplicable how these separate elements should be found tion correspond to

;

Moreover, here again, since the predicate never stands for anything but an idea, we cannot say that it exists anywhere in such a way that it can either be united with the subject, or remain together in one act of thought.

separate from

it.

The view

that the proposition

"

man

is

white

"

is

the

expression of a unification of the substance man with the idea of white," because the latter has an independent existence, would be impossible, "

"

"

It is due to except as a consequence of the Platonic doctrine of ideas. between a and a the relation this alone that predicate which is thing

incompatible with

it

can be denoted as a

l

"

perpetual

separation."

On the other hand, Spinoza well-known proposition Determinatio est has been made use of to express a view which goes so far as negatio "

s

"

to transfer the negation into the nature of things themselves, thus ranking

the negative judgment as the original expression of knowledge of these.

Trendelenburg has rightly drawn attention to Thomas Campanella as one of the most decided supporters of the opinion that all things consist in yes

and no, being and not-being because

he at "

is

it is

only

not something

man because he

is

once being, and not-being. Determinatio est negatio

;

that everything

else.

"

;

"

Man

is,"

not stone, not

is

this particular thing

that

lion,

is

his affirmation.

not donkey

Spinoza has the same meaning a figure

is

determined in so

only

But

hence he

;

when he

far as

it is

is

says

not the

space surrounding it, and thus it can be thought of only by the aid of nega as a limitation, i.e. negation of the infinite. tion But such views always involve a confusion between the negation itself as a function of our thought,

and the presupposed objective ground of this negation the exclusive individuality and uniqueness of each one among the many things which are That which they are not never belongs

to their being and nature ; only our thought, which, in making comparisons, brings such alien elements into contact with them. All that concerns us is to recognise why we have need of these subjective expedients in order to know the world of real.

is

it

which no counterpart of our negating thought is contained. It only by a constant confusion between negation in thought and those real relations in being which are very imperfectly expressed by mere negation

reality in is

1

Prantl has very justly noticed the deficiency of the Aristotelian theory in this respect in his Geschichte der Logik, i, 118, Elsewhere Aristotle

14454.

that the negation belongs only to the sphere of thought (Metaph.,

expressly recognises

vi. 4).

THE NEGATION that the Hegelian logic succeeds in presenting

nature of things

but unless we

;

may admit

127

as a real power,

it

and

confusion once for

this

as the

/

as

all,

j^eJ

(

may

well be

done

after

s

Trendelenburg

penetrative criticism,

must be

it

pointed out at almost every step of the Logic.

When

the attempt to attribute a predicate to a subject

is

prohibited by

the negation, the ground for this prohibition lies either in the fact that the

predicate in question

is

wanting to the subject

(or, in

relational judgments, the subject to the predicate)

the subject, or at least one of

The mere statement

cate.

the two

elements,

of the

is

;

incompatible with the predi

does not show which of

negation

it is.

Further, the negation plete

its

the case of certain

or else in the fact that

expression

equally unable to explain, or even to give

is

those

to,

relations

com

between ideas by virtue of which

they are incompatible (the so-called contradictory and contrary opposition).

When

1.

is

negation

a negative judgment

is

not inferred

when, therefore, the

we have nothing but

not mediated by interposed terms

the

given subject, and the attempted predicate, as materials for our negation.

Hence which

the ground for prohibiting the predicate must

There are two ways wanting in

(or

my

in the

wanting

in the relation

in

which

this

be.

may

Either the predicate

is

judgment, one element is excluded by the subject-idea

subject-idea (or, in a relational

whole ideal complex), or

by the ideal complex present).

either

lie

given between the ideas of subject and predicate.

is

a deficiency

(ore/oiyo-is,

it is

The ground an

or

privatid)

of the negation

opposition

may be

(ei/ai/ridr^?,

oppositio). 2.

It

may be

that the subject-idea

is

concrete and particular, an object

of intuition, and the attempted positive judgment a temporally valid one

which

is

to

be denied

in

the

same sense

in

which

it

was supposed to be

In such a case the negative judgment rests upon

asserted.

ness of not finding the predicate in

my

intuition

my

immediate knowledge of the difference between the subject as and another conceivable thing possessed of the predicate, consciousness, that "

This watch "

moving,"

is

not

the sun

is,

it

upon

really

is,

upon my

of a deficiency of determination in the subject. "

going,"

is

conscious

of the subject

not

this flower

warm

to-day,"

has no all

"

scent,"

the invalid

is

not

these judgments proceed from

}

I

j

\

J

LOGIC

I2 8

my consciousness thought

of,

of difference between what

between

this

and one with a scent idea to what

is

;

is

watch and one which the fact of

it is

my

is

given and what

rise is

to

my

from the complex same portion of space) from the portion of space in which (Socrates is absent differs

deficiency

becomes more

In the

judgment.

not here), the complex of

judgment (Socrates and myself

things expressed by the attempted

merely

bringing a more fully determined

actually given which gives

case of relational predicates, again (Socrates

The

is

going, between this flower

given I

to

in the

intuition

am).

striking in proportion as the

more com

easily produced comparison, and in propor plete idea is familiar to seems tion as the missing predicate belong more closely to the whole

and

for

complex. The absence becomes a deficiency in its narrower sense the absence of something which should be there when reference to a purpose,

demands the completeness of the predicates. Logic such references, which give a colouring of disappointment to ally, however, as "he does not see," "he does not hear," "he will not such judgments or an aesthetic law,

understand

draw

"

this,"

the sentence has no

and

attention to the deficiency,

meaning,"

They form no ground

of comparison.

have no value except to

to enable us to realize the standard for

any particular kind of nega

tion as such.

The same absence of a predicate takes place also in the case of The negative judgment may be based upon the fact that general ideas. the predicate does not form a part of the idea which constitutes the mean 3.

ing of the subject term

"

plants

:

do not

"

feel,"

water has no

etc.

taste,"

Comparison with things related in other respects, of plants with animal organisms and of water with other liquids, forms the ground for the priva tive

judgment

;

something which, to judge from the nature of the subject might belong to it, does not belong.

in other respects,

The same ground for a negation would be present, if the attempt 4. were made to attribute to a more general idea predicates belonging only to the particular ideas which is

no

fall

under

it,

and are more

part of the general idea of the triangle that

spherical

nor

;

is it

is

it is

determined.

plane, nor that

part of the idea of the plane triangle that

angled or acute-angled. that he

fully

It is

not contained in the idea of

man

either black or white, straight-haired or woolly-haired

general idea of motion that express this

it is

progressive or rotatory.

Still,

;

it is

It it

is

right-

in general

nor in the

we cannot

mere indeterminateness of the subjective general idea by the

simple negation of those predicates.

The

"

propositions,

the triangle

is

not

THE NEGATION not

"is

spherical,"

the predicate was wanting to

is

not

"motion

black,"

is

not

in a quite different sense, as stating that

all

the objects denoted by the name.

So

the habit of passing at once from general ideas to the most

is

strong

"man

right-angled,"

would be understood

rotatory,"

129

concrete and proposition

determined ideas in which they are contained, that the triangle is not rectangular," though quite true in itself,

"the

would be misunderstood. necessarily

It

or

rectangular,"

"

must be expressed

not

all triangles

are

"

the

triangle

is

not

Cf. below,

rectangular."

25-

With the negation which

5.

based upon the privative relation, and

is

hence upon a simple difference, we may contrast that which arises from the fact that _one element of the subject-idea repels the predicate-idea.

Here we cannot even predicate might belong

case of relational- deas

A

is

not near

B at

all,

we do

think, as

it is

;

false that

or because

it

in the case of privation, that the

(The same thing takes place

to the subject.

A

is

in the

B either because of B the one rela

to the left of

stands to the right

;

This brings us to those relations between ideas of which virtue are able to exclude each other as predicates of one by they tion prohibits the other.)

and the same

subject.

Suppose we are dealing with a denominative judgment, in which the attempt is made to unify subject and predicate as a whole with a whole 6.

;

then the exclusiveness of the relation between different ideas fixed determination

our ideas since

"

the condition of the continuity and

Socrates

not

is

to the

differentiation (within the different categories) of

a determination and differentiation presupposed in

it is

itself.

and

due

is

not

"

Crito,"

wood not

harmony

not

is

all

judging,

of consciousness

red

"

iron,"

is

not

blue,"

such judgments are based upon the fact that we have a multiplicity of ideas distinguished from each other with certainty, and guarded against all confusion and mistake ; and

"seeing is

all

hearing,"

the judgments can

present

(

earlier

than

21, i).

the

is

"right

do

is

to

left,"

remind us

that these differences are always

The knowledge that two knowledge of how they

ideas differ differ

for

;

is,

indeed, generally

in

order to show

how they differ I must finally have recourse to elements of which I simply know that they are different. I distinguish with certainty between my friend

A

and

my

friend

B before

I realize

to myself

what

it is

wherein they

Suppose I did realize it, and become conscious that the one is fair, the other dark the one of a round, plump figure, the other lean and differ.

;

angular s. L.

;

the difference between

fair

and

dark, round

and

angular, lean

K

and

LOGIC

130

plump would differ,

(

still

remain; and here

all

that I can finally say

is

that they

not how.

In treating of the affirmative judgment 14, p. 83 sq.), as the presupposition of

we were obliged

down

to lay

possibility, a principle of

its

agreement, according to which ideas are recognised as like with unfail ing certainty,

and upon which

We may

judgment depends.

possibility of certainty in

all

find a similar

an affirmative

for the negation in the

ground and unfailingly recognised that there should be any mistake as impossible

proposition that different ideas are immediately as different,

and

that

it

is

If the whether two ideas present in consciousness are different or not. formula "A is not A had not been misapplied to denote everything and to

"

anything,

we might make use of

ideas; that everything which

would then

A

to express that

different

is

from

and no

all

other

other.

It thought law of our differentiating thought and a funda

state both a

mental psychological

it

is

is

just itself

fact.

Does any one appeal, in opposition to this, to the fact that we do confuse many things, and so fall into error ? Then we answer, first, that confusions with reference to things take place because their differences are not repro

duced by our momentary ideas as e.g. when I mistake an for a natural one, because I have observed it superficially ;

ideas

do not

complete.

differ as

they would have done had

my

artificial

flower

in this case

observation been

my

more

Secondly, that confusions take place in consequence of the

imperfect reproduction and constancy of our ideas, one substituting for the other in

course of time.

Thus

acquaintance because the image of the impression of what I

does not mean that

it is

now

see

my is

I

may

itself

greet a stranger as an old

acquaintance has faded, and under represented as different.

But

this

possible to hold that two ideas are not different

when they

are present as different in consciousness, and are retained undisturbed during an act of judgment. On the contrary, all unity and clearness in self-consciousness depends

upon this power of the negation to hold asunder the manifold presented to us, and to guard it from blending in confusion ; and in the same way the one possibility of being certain of and hence the possibility of judging, depends upon an immediate and perfectly certain consciousness of difference. Where this could not be presupposed, as, say, in a case of insanity, all community of thought would cease.

the validity of a judgment,

7.

In the case of attributive judgments,

the conditions of the negation.

it is

The same

more

thing

difficult to investigate

may have

different attri-

THE NEGATION butes,

and

different things the

because

B

The

A

A

has

it

question

is

;

:

B

that attribute

when one

attribute for

A

snow

on a surface

the fact that a line

and so

This

on.

is

8.

The

/3

of thing

A

or for denying attribute a of

me

expressions

;

and

if

Thus one par

subject.

other colours.

all

The

other colours of

it

deny the predicate curved of

it

all

relational predicates.

right

and

the one

is

left,

;

;

Sitting

equal and greater of any thing, the

true

it.

and

"opposition"

become almost

to

and walking,

still

same

once to deny

at

mutually exclusive

all

;

excludes

true also of verbal

is

other must be denied of

identity,

me

straight enables

and standing, standing or smaller, are

white

e.g.

white enables

is

simple difference in the

stands in such a relation to attribute B,

that they cannot both together belong to the

fact that

this

though there is ground for saying A is not B, a is not what is necessary in order that we may say of a thing cannot be united with it ? Clearly it can only be said

of the attributes of

ticular colour

;

denying attribute

possesses the different attribute a

it

because

(3.

same

no ground

ideas of attributes affords

131

.

useless

"opposed"

to the different

owing

have, like that of

meanings given

to

them, and owing to the frequently vague relation between what was called opposition and negation on the one hand, and difference on the other. conflict of particular ideas has

The

been confused under the same name with

the contradiction of judgments; and with reference to the more special relations

the

of conflicting ideas there

Tower

is confusion of language like that in Let us attempt to formulate the distinctions from

of Babel.

the nature of the case.

There can be no reasonable ground the mere difference of ideas which

is

for

denoting as conflict or opposition

the condition of

as all sorts of things co-exist without conflict in space, different attributes the varied

all

thought.

and present

Just

in their

image of the world, and its perpetual change an incalculable manifold

in their various activities, so our thoughts contain

of ideas between which there as particular

and indeed

suffices to give to

each

is

no

conflict,

differentiated. its

due.

between the ideas of man and

although each

is

looked upon

Negation distinguishes them and is no more conflict

In themselves there

lion than

between those of black and

red, or

made upon the same thing; and a relation of conflict between ideas is found only when Thus they meet as attempted predicates of one and the same subject. black and white.

conflict

Conflict arises only

when

rival

claims are

can appear only in the sphere of subjective thought, which

trenching upon

the

false,

for in the truth every subject

is

in

is

undisputed

LOGIC

132

The members of definite, larger or smaller, possession of one predicate. in such a way that, when tried as predicates of groups of ideas are related same

the

subject, they repel

and exclude each other

;

and

this

not because

of something peculiar in the nature of a particular subject, but because of will call them by a current term their own contents. incompatible,"

We

"

which would most accurately express the case, has for incompredicable," This relation exists originally between ideas of too unfamiliar a sound. relations derivatively it exists also between ideas attributes, activities and "

;

of things, in so far as these appear as predicates in judgments of denomi nation and subsumption, for two substantival ideas are contradictory in so 1 they contain determinations which cannot be combined. what are rule ideas from We cannot deduce any general incompatible

far as 9.

;

determined by the actual nature of the ideal-contents and their re It is possible to imagine our sense of sight so con lations to each other. this is

stituted that

we should

see the

same surface illuminated by

different colours

does emit light of differing refrangibility) just as we distin guish different overtones in one note, and the particular notes in one chord. It is purely matter of fact that different colours are incompatible as predi (as,

indeed,

cates of the

the

it

;

same source of

same source of sound

light,

and

are not so,

that different sounds as predicates of

and

that the tactile sensations of

tem

perature and pressure can be referred to the same subject in the most different combinations (cold and hard, cold and soft, etc.).

Nevertheless a general statement can be

made

of the ideas in reference

which we are most frequently conscious of incompatibility, and which are most liable to come into actual conflict. Evidently they are those because they are most homogeneous and most nearly akin, because

to

they belong to homogeneous and similar subjects, can be most easily tried

(which, as

predicates together; those which, just because they are akin, present

;

,

themselves together as the more special determinations and modifications of a general idea.

we

are

It is for this

most familiar

same general idea

;

is

reason that the incompatibility with which

that of different determinations

sense of touch, of forms, numbers, etc.

which

which

fall

under the

such as the determinations of colours, of qualities in the It is

the incompatibility of these

once obvious to us because we have had most frequent oppor of tunity becoming conscious of it. No one thinks about the incompati bility

is

of

at

man and

kangaroo, of melting and flying, because no one will ever

Plato, in the Phcrdo, ch. 52, fravria ctXXT/Xa ov

103 D. sq.,

investigates in a masterly

manner

TO,

THE NEGATION

133

man

or a kangaroo, or whether

have occasion to ask whether a creature

something

melting or

is

young and

white,

The

flying.

old, standing

and

is

and

may be

raised whether something

is

old or young, whether something

is

Hence

standing up or lying down.

a

lying, strikes us constantly, for the cases

are innumerable in which the question

black or white, whether a person

is

incompatibility between black

the delusion of thinking that in the

different determinations of a general idea

we come upon

of incompatibility, which belongs to

quite apart from any judgments

them

a specific relation

and white, straight and crooked, had some special enmity to each other as being sons of the same father.

as if black

10. Incompatibility has no degrees; and when we are dealing merely with the ground of the negation, the relation between black and invisible

does not

from that between black and blue, nor the relation between But with the relations

differ

black and blue from that between black and white.

upon which incompatibility to the

merely

the relations which are

it

are

opposed

finally

there

;

maximum.

It

Black and white

called opposites.

sense from that in which black and blue

the difference between the two relations

reaches a

is

commonly

between homogeneous

mouse and

based are connected others, which refer and are easily confused with

in quite a different

are opposed interval

is

magnitude of the difference,

is

based upon the

ideas, which interval gradually increases and is in this sense that we oppose day and night,

elephant, a drop and an ocean, to each other.

For our

feeling

a sharp distinction between the sudden transition from one extreme

and the

to the other,

transition to the idea nearest in similarity, particularly

where transitions constantly take place, and so establish a connection be tween the more proximate differences. And when the impressions upon our feeling are themselves of an opposite nature, being beneficial and and displeasing on the other, the im

pleasing on the one hand, painful

is ren pression which is given of the magnitude of the objective difference dered especially intense by this effect upon feeling. Thus it is that light

and darkness, good and bad, pain and pleasure, beautiful and ugly, are opposed to each other and we need not point out that it is always pre supposed that such ideas are homogeneous and fall under a more general ;

idea which trast, to

is

common

to both.

avoid confusing

it

But we should prefer to

with that of incompatibility.

by Aristotle, and has been shown with 1

Trendelenburg,

Arist. with

10.

Logische Unters.,

It

con

was noticed even

acuteness by Trendelenburg,

1

2nd ed., II. 151 3rd ed. 171. Cf. El. Lo?. and the passages in Waitz with Cat., n b, 34.

xii.,

Arist. Cat., 6. 6a 12,

much

call this relation

;

LOGIC

I34

The

image.

spatial

is

and gains a physical action and reaction, and

counter-pressure,

But

will as contrast is in feeling.

trast,

istics

is

distinguished from the

represented to us by a spatial

maximum

represents geometrically a

"opposite"

difference in direction

own

of ideas, and

increase of difference in such an ordered series

that the

the position of the extremes of the series,

many

this

significance from pressure it

of

and

finds itself re-echoed in our

relation also, like that of con

incompatibilities only by character

which have no direct reference to the negation. This

ii.

express, by

is

most obvious

in the

attempts to understand, or at least to

means of the negation, those

relations

which go by the name of

Opposition was held to proceed originally from the negation, a i\ot-A taking up its place by the side of an A. By dragging in a term opposition.

which was originally framed to apply to two opposite judgments (v. below, 23) a distinction was drawn between the contradictory and contrary

we

Ideas which are contradictorily opposed,

opposition of ideas.

are

A

and not- A, so that the one idea contains only the Those which are contrarily opposed, negation of the contents of the other. on the other hand, are so related, that though the one annuls the other, it taught, are related as

also contains a positive determination.

Equal and not equal, white and white and black, good

not white, are examples of contradictory opposites

;

and bad, of contrary opposites. test the truth of this theory, we must first insist that nega no meaning except in the sphere of the judgment. Every negation is the no and negative answer to a question, and prohibits a predication not have no place except when opposed to a proposition, or in a proposi

In order to

tion has

;

Taken literally, the formula not-A, where A denotes any

tion.

meaning whatever.

There

is

no such thing

as

pure negation of the contents of another idea. putting aside (Aufhebung\ then indeed an idea

may be and so is

not

fies

is

If negation

is

only the to

mean

man, heaven, blue, green

there or not there, consciously presented or not presented at

But the

"

itself

put

aside."

fact that the idea of

man

an idea, 1 and the formula cannot mean that OVK

that the idea of

idea of the

far

man

man must be

same way

as

Kant

is

s

is

Thus

memorandum,

the formula "

fails

Lampe must be

of

ai/#/xo7ros

its

A

alone,

signi it

the

purpose in

forgotten."

If not-A were taken to denote everything not present in our ideas

we form the idea of

all,

not present

not present, for in order to understand

present.

no

idea, has

an idea which

when

everything therefore the idea of which

voflv ^77 voovvra eV.

Arist.,

Met. T, 49. IOO

b,

6lO.

is

THE NEGATION not immediately given with the idea A, then

denote incompatible determinations, and

When

are mutually exclusive.

me

thing before is

then

not-v^,

it

the idea

but the colour.

"

A

135

and

not-^4

would no longer

would not be true that they white is present I have no "

which

If everything

not this colour

is

includes round and square, heavy and soluble in sulphuric

it

acid.

These are

these

predicates are in no

not

"

all

white,"

something other than

i.e.

way incompatible with

But

"

white."

white,

i

and form no |

opposition in the ordinary sense of the term ; for that, we should have to white" by pass from "white" to all white things, but does the word

:

"

itself

ever

But thing, is

not-^4

if

and so

what

is

a

white things

all

were a

?

real negation, the idea

pass, either expressly or tacitly,

meant

really

A

of which or

mean

iiot-A

;

of negative

Thus

subjects

upon

to

then, any idea

If,

indirectly.

must come from somewhere

deny all

thought

would be

A

concerning

is

;

to

s

cates that the subject

but that

it

lies

not-mortal

is

"

this

subjects

be present.

order to deny

A

I

not-^4, these

we

fact that

possible things the positive objects denoted by not- A.

we consult Kant

unnamed

formed of

to be

mere

were any use in this, it would be an impossible an oi/o/xa dopioroi/. 1 right in calling the expression If

And

not A, that

the ground of these negations

the

does not cause them in

is

presupposes a negative judgment,

it

judgments,

which can be denoted as not-^4 only upon

and very

must be denied of some

taken to denote that which

is

must be denied.

number

A

into a judgment.

are called

must review

But even

task,

and

in

and these

of them,

if

there

Aristotle

was

Logik we are told that not- A as a predicate indi not contained within the sphere of a predicate,

is

somewhere outside places the soul

The

in infinity.

among

"

proposition

the unlimited

number

the soul

of undying

when I subtract all beings which remains from the totality of possible beings for a to seems This the mortal. realizing what belongs simple receipt give to not- A.

But

it

is

only applicable

when we

are dealing with predicates

which can be used to denote particular beings, for then we can look upon the world as an infinite number of such particular beings from which we subtract the

number

of the

A

s.

But how

shall

we

deal with concepts

which are of an abstract nature and whose extension can never

beings into 1

With

signify a

A =

mortal, and I divide the extension of possible mortal and not-mortal, where will justice, virtue, law, order,

number of beings ?

If

reference to this not-/*

Lotze, Logik, ed.

2, p.

61 sq.

compare

also Prantl,

Geschichte

der Logik,

i.

14}.

\

,

LOGIC

36

distance, find a place

They

?

are neither mortal beings, nor yet not-mortal

not beings at all ; they are attributes and relations of can and belong to both mortal and immortal beings. If they are not beings, to be counted under not- A because they may belong to a mortal being, still beings, for they are

\ve

cannot include them under A, and contrary to the presupposition from set out, we are left in possession of a territory lying midway

which we

between

A

and not-A.

A stands

If

for

man, then

it

seems easy to put

men on one side away from the rest of the world, everything which remains But all is not-man. sun, moon and stars, minerals, plants and animals ;

where do the attributive concepts black, green, soft, hard, belong ? to A or The intended division of all possible beings into A and not-A not-^4?

U

that every quite overlooks the fact that there are different categories concept stands in relation partly to concepts of like categories, partly to ;

concepts of differing categories, and that the lines which divide them cross in all directions.

But even supposing

possible to think of

it

all

that which

not-A as

is

anything which would have a meaning as a predicate, where should I find a reason for denying A of everything which can be called not-A ? Not in the fact that it is not-A this can only be anything comprehensible,

and

said indirectly

derivatively

vents us from predicating

A

of

;

it.

but in that which

The

it is,

that

which pre

opposition said to be expressed

and made comprehensible by not- A is, on the contrary, the presupposition of the not-A, which is itself merely a derivative sign of the opposition, not its essence and ground.

The same we is

indefiniteness into which contradictory opposition resolves

attaches also to the contrary opposition of the ordinary doctrine.

If

say that everything which can be expressed by the formula not-A

+B

itself,

contrarily

opposed

idea A, then red and virtuous, black

to an

and im

mortal enter into contrary opposition, not to speak of the strange confusions

which is

A

arise

when

A

and

B are

taken from different categories.

And

this

not excluded by the formula which denotes everything included in notand denoted not merely negatively but directly ; so that grass-green

and algebra, emotional and examples must be excused

ellipse,

fall

into contrary opposition.

The

no other way can we make obvious the formulae which are dragged over from one treatise ;

in

want of meaning in on Logic into another.

12. The view that negation can only take place where there is a reason able possibility of question and of affirmative answer has led others to

THE NEGATION abandon not only

this

contrary opposition

as

not-

well as contrary opposition fully

line

not-^4, but

vague

A + B.

common

explanation of

them, contradictory as According found only when a general idea is more to

to be

is

also the

137

determined by mutually exclusive differences ; where, for instance, a determined as straight or crooked by differences of direction, or

is

the state of a body in space

is

determined as

ing to this view contradictory opposition

is

movement.

rest or

Accord

found where only two deter

minations are opposed to each other where therefore the negation of the one definitely implies the other a line which is not straight must be ;

crooked

;

while contrary opposition

is

found where several determinations

appear on an equal footing, as in the case of colours. Thus, under the names of contrary and contradictory, the distinction is again introduced which Aristotle made (Categ., 10. n, 33) between opposites which

admit of no intermediates, such as even and uneven

numbers,

illness

and health

in

a living being

of an intermediate, such as black

and

;

in the case of

whole

and opposites which admit

white. 1

This way of putting the doctrine is more rational because it at any rate But in return it gives us a subject for the negation in the general idea. conceals another danger, that of believing it possible to produce opposite concepts idea by

A

and something positive therefore by determining a general But the general idea does not exist before its deter not-^4.

and

minations, but only together with them.

we could determine

There

is

not

a line in

first

be straight or not straight it is part of the nature of the space containing the line that both straight and crooked lines are possible in it. Thus, it always depends upon the nature

general, which

to

;

of the objects comprehended in a general idea what are the determina tions they permit,

with one which

and whether another predicate

we recognise

as

is

permissible together

In the same way

it depends upon the nature of the objects how great the range is of these compatible Here again the negation and the formula framed from it determinations.

possible.

Some have even gone so far as to confine the name of contrary opposition to those terms in such a series of differences which are furthest apart thus, in the case of colours, only black and white are said to be in contrary opposition, while red and yellow are This was the view taken by Trendelenburg in his Log. merely disjunct, not contrary. Unters.^ chap, xii., in accordance with Aristotle s dictum (Categ., 6, 6a, 17, and elsewhere 1

;

;

vide the passages in Waitz, Org., 5teoT7?/c6Ta rSiv tv T avry y4vei.

i.

p. 309)

But

this,

i.e.

that the tvavrloL are r&

according to p.

I

So,

-rrXela-Tov

introduces a

dXATjAwi/

new point we have

of view, that of a comparison of the intervals between our ideas, and with this nothing to do when considering the grounds of the negation.

i

LOGIC

38

can only interpret for us that which lies in the nature of ideas it cannot On the contrary, the incompatibility of this nature beforehand. ;

determine

our present observation, to be an empirical speaking, has never done more than describe.

.certain ideas continues, for

which Logic,

relation,

The import

strictly

of the procedure by which

a general idea, as

in

A

we

give expression to differences

and not-A, can only be treated of under the

.doctrine of the Concept.

In one case, however,

13.

origin in negation

purely negative

when, that

:

is,

seems undeniable that opposition has its one term of the opposition has really a

and

definite

itself

and crooked are two

Straight

significance.

each in

intuitions,

it

positive

;

and

it

may

different

be

at least

questioned whether in the case of rest and motion the one

the

is

mere

1 negation of the other or not, either the one or the other being taken as

But how about

positive.

speechless, unfeeling,

and

unhappy, unreasonable, unwise, and

blind, deaf,

the numerous epithets formed with

all

"

un-"

and blind be expressed except by saying that blind means not-seeing, the simple privation of sight ? and is not this an opposition which has arisen entirely from negation and one

Can

"

?

"-less

the relation between seeing

term of which means nothing but a not-being ? And has not language, by thus blending the negation with the predicate, justified the not-^4 of

beforehand

logical theory

If this

were

so,

then

it

?

must be

fully equivalent

term of the opposition or affirm the other or

see,"

"

"this

needed that sees"

is

then

is blind,"

this is

false it is

A

is

not

not the case.

happy,"

If all

and the mere words

not said

why he does

or

;

"A

we know

"A

I

I

deny the one

"

say

is unhappy." is

does not

not see.

whether

whether

does not

this

No

proof

see"

is

judgment A never tell us more

that the

"

But blind denotes a

definite

an organic change of the apparatus of sight, in con sequence of which seeing does not take place. By denying sight, then, state of the subject,

we do not

affirm blindness, as

must be the case did these

vative predicates really contain nothing

so-called pri

but the expression of a negation.

Here

It is again, then, negation is not sufficient to explain opposition. only because our negations are almost always based upon such oppositions

that negation, working according to psychological laws, excites mainly the

idea of opposition.

and 1

Language, which makes use of psychological

arbitrarily curtails the

Spinoza

upon

tells

original

meanings of words,

is

forces,

able to turn this

us (Tract, de Deo, ii. 19) that rest is not a mere negation (nothing), and whole of his physics is based.

this proposition the

THE NEGATION and

habit to account,

39

denote oppositions by negations.

to

always means more than

it

and

says,

logical

But language

analysis intervenes to dis

between the necessary meaning of the negation in itself, and its ordinary meaning which attaches to it only from association and on the tinguish

ground of the known

relations of the predicates. 23.

The PRINCIPLE OF CONTRADICTION judgment and

tive

its

negation

the negation by saying that the judgments

cannot both be true together.

known

proposition usually

which

We

give the

name

This statement

Bn

"

differs essentially

its

(A

from the

is

notnot-^4),

subject,

and forbids

opposed to the subject.

of avrfyaa-is, contradictio, to the relation between a

judgment and

which stand

is

"A

between a predicate and

that the predicate should be

positive

and meaning of and "A is not B

as the principium contradictionis

refers to the relation

between a posi

refers to the relation

expresses the nature

if

;

its

negation (and hence also to the two judgments They are contradictorily opposed to each

in this relation).

other (di/nc/xxTiKws arrLKelo-Oai, contradictorie oppositum

esse),

A

confusion similar to that concerning identity and opposition exists with respect to the so-called principium contradictionis. Aristotle, in a i.

familiar passage, 1

1

formulates

it

as follows:

T6 yap auTb Metaph. F, 3. 1005 6, 19 aury K.a.1 /card TO ai/ro (/ecu ocra &X\a :

Tip

"

It is

UTrdpxeti/ re /cat

a^tta

7rpo
raj Xo7t/cds

OVTWOVV

5i>
avrrj

STJ

TTCKTWJ

TO.VT OV inro\a.p.^dvei.v elvaa /cat

ecrrt

efoTi

tvavrla 5 elvai.

/cat

tcrrl

Ai6

TOUTOV.

apx^l Kal TUIV

a\\wv

auro

ot

aTroSet/crwres

ct.^tw//.drw^ avrrj

avrb avdpwrrov

elvon,

<j>avepbi>

yap

afj.a

^x oi

ai>

rwv dpxuv el

inroXafJ-pdvet.?

Tjfuv

6

avrifidafus,

rrjs

r]

r6

TrctJ/Tes

elvai elirtiv TO

\eyw

do^a eli/at

/u.rj

/cat

n

/cat

rg

ravrrj

a$tiva.Tov a/J.a

TaJ evavrlas

.

/J.T]

e^Sexerat

elwdora) VTroXa/j-jSaveiv rbv avrbv dieij/evfffj.evos 5oai>

:

elvai avOpwirov (cf. also 3>v

a/j,a

TO,

-rrpoTdffet.

l>,

fj.7)

Trpos

\yeiv Hpd/cAetroj

5

ra^r^v dvdyovcnv e(rx_a.Tt}v TT&VTWV. OVK apa e^5^x era 4 1006 33

/cat

a

dovvaTOv yap

.

.

56^as 6

els

5e a7ro5et/crt/cds rdr KOivds 56^as,

dduvarov

UTrdpxetj/

/xrj

aV, ecrroi jrpoa di.opiafj.ei

Kaddirep Tives oiovTon.

etVai,

(Jir)

u.e#

/3e/3atordr77

yap dvayKdlov, arts \eyet, raura irrdpx*w T$ ai/rui rdvavria (TrpocrStw/Jtcr^w 5 OVK

impossible that the same

(pv
a/J.a

irepl

yap

d\r}0S

Metttph, j3, 2,99^ airavres SeiKv^acnv , olov OTL irav dvayxaloit ^>

3"

r)

Here Aristotle makes use a7ro0dj at, /cat dovvarov a/j.a elvai /cat fj.ri etvat). of the phrase that contrary attributes (evavrio.) cannot belong to one subject both together, and he seems to employ it as a proof that one and the same person cannot di>ai.

T)

But he must not, of course, believe that anything both is and is not at the same time. be understood as intending to lay down a principle higher than, or independent of, the he not only denies this in the same passage, but refers again principle of contradiction ;

e?ret 5 dduvarov rty afterwards (Metaph., iv. 6. ion d\r)6eveaQaL 15) &IJ.a Kara rov avrov, (f>avepbv OTL ovde TavavTia a/u.a virdpxew ev5ex.Tai ry ai ry ; here the other stating that the principle of contradiction is the original principle upon which

to

it

depends.

:

l>,

The above proof should

the Aristotelian sense

;

i.e.

,

di>Tl<pa
rather be called a mere av\\oyi.
viroBecrews in

to

show

that

LOGIC

140

and not belong

(predicate) should both belong

same way

to the

same

...

mental principles

man

is

same time

at the

in the

the most certain of funda

and

is

impossible for any one to believe that

it is

is

.

who

every one

brings forward an argument,

falls

.

.

back in the

last

instance

which by its nature serves also as the principle upon other axioms depend."

this proposition,

upon which

all

That not

for

This

.

.

not (as some think Heraclitus says, for does not necessarily really believe what he says) Hence

the same thing both a

.

thing.

is

to say then

B cannot both

:

B, we must declare the proposition proposition

This

2.

A

B and

is

If

we

is

B

the proposition

state the proposition

be

to

false

and

;

if

B to

we

A

A

is

is

not

state the

A

is

is

nothing but a statement concerning the significance of the

Its

negation.

A

the proposition

be true together.

we

,

declare the proposition

A

not

is

down

nature and meaning are laid

be

false.

in a proposition

which

be expressed without negation, and which is, therefore, only of value as making us conscious of our own act when using the negation.

cannot

itself

we connect

If

same meaning

the

we may indeed

"

not,"

as

say both that

and maintain

A

every one else does with the word is

B

and that

cannot believe

it

words make

appear that both are true together

words this

it

reason

that

That

"

Aristotle at the

guards his proposition so

same time

"

and

"

in the

Aristotle intended his principle to have

to the nature of our thought

movement

sole origin in a

and endeavours

A

not Z?, but we we may by our

is

Or, again,

seriously.

but only by using the ; It is for meanings, or by speaking of different times.

in different

determinations

it

to

same

carefully

by the

sense."

immediate reference only that the negation has

its

of thought which extends beyond that which

is,

is

as certain as

combine incompatible

it

is

This

things.

"

shown by his the same thing,

is

argument it is impossible that any one should believe that at the same time, both is and is not." It is shown again (Metaph.,

when he

be and not to

to

who

says that those be,

and

that

say that it is

it is

possible for the

possible to believe this,

possibility of thought

iv.

4)

same thing both do away with all

and of mutual understanding for these require that every word should have definite meaning, and that the speaker should keep to this meaning, and not contradict it. 1

the recognised proposition involves the proposition

"

and not belong 1

to

;

"

contradictory attributes cannot belong to the same thing one can believe that the same attribute can both belong "

No

one and the same

thing."

Cf. Prantl, Gesch. der Logik, I.. 131 sq., 134 : The ence to objectivity always arises out of the relation

corresponding principle with refer

which

exists

in subjective speech

THE NEGATION 3.

If this

what Aristotle meant by

is

the positive interpretation of

it

is

141

his principle of contradiction, then

also

obvious.

It

can be none other

than the proposition that every one who consciously makes a statement that what he says must have a states just that which he does state ;

and I

another meaning

is substituted whilst he speaks he does not really say anything. It must be true that what what I say, that I do say." But it is have written, I have written

fixed meaning, because,

if

"

thinks,

;

evident that this

is

constancy of ideas

;

only a corollary to what it

is

we have

called

above the

the unambiguity of the act of judgment.

This

unambiguity of the act of judgment would form the content of a principle of identity which would be the positive rendering of the Aristotelian

But

principle.

negation that

it

we

us nothing which It is

is

through the rejection of simultaneous affirmation and become conscious of this unambiguity, and it tells

first is

not already stated in the principle of contradiction.

then quite natural that only the principle of contradiction should be

ranked by Aristotle as a principle, while its positive rendering finds merely an incidental expression. 1 For a long time indeed it was the Aristotelian

was principle of contradiction which

meant by the principium

identitatis.

and belief, and this is in accord with the subjective origin of human judgment. No is impossible that the same thing should doubt when the principle takes the form both be and not be" it does seem as if we had to do with a principle which is and logical only in a secondary manner Ueberweg, for instance, primarily metaphysical, takes this view when he divides the sayings of Aristotle into those which state the But there can never have metaphysical, and those which state the logical principle. been a division such as this between metaphysics and logic as Aristotle understood them, "it

;

if only because he regards the true judgment as always the expression of Being, and, Nevertheless, if indeed, frequently denotes the ecrriv of predication simply as a being. we remember his express statement (Metaph., vi. 4) that truth and falsehood appertain to thought, and not to things, a proposition which declares that of two propositions one

and can only refer originally to the activity of thought in its follows from this as a matter of course that the same thing cannot both be and not be at the same time, nor the same attribute both belong and not belong to the same (objective) thing at the same time ; for if this were not so, then, owing to the Aris For totelian conception of truth, the logical principle would also be without validity.

must be

diaipeffis.

Aristotle,

false

It

both modes of expression are ultimately exactly equivalent in meaning.

Cf.

Zeller, Phil. d. Gr., II. 2, 174. 1 Aet 9, quotes from Anal., I, 32, tfa, 8 Trendelenburg, Elem. Log. Arist., TO a\7)ds aiirb eavrtf b^oKoyov^vov eiVcu iravrri ; but this is introduced for the sake of Sucli the later doctrine, and where it stands has not the significance of a principle. vi. 4 sq., and the significance can be attributed only to the propositions in \\\Q Metaph., p. contents of these are correctly formulated by Prantl, Gesch. der Logik, I, 131, as the :

irai>

statement that every assumption concerning a vTrdpxov (I should only have said birdpxew) remains constant with itself; and this again is only possible on the assumption that our Baumann has lately endeavoured verbal denotations are conceptually determined.

i

LOGIC

42

The prindpium

4.

Leibnitz and

Kant

)

of

contradidionis

in the formula

!

modern

logicians

A is not not-^4,

(particularly

differs entirely in

mean-

This

latter refers to

the relation between an affirmative and a negative judgment.

According to

from the Aristotelian proposition. ing and application

Aristotle,

The

contradicts another.

later proposition refers

one judgment between subject and predicate in a single judgment; the Aristotle states that one judgment is contradicts the subject.

to the relation

predicate false

when another

is

true

;

the later writers state that a judgment

is

in

itself and absolutely false, because the predicate contradicts the subject. What the later writers desire is a principle from which it can be known

die Welf) to re-establish the true Aristotelian meaning (Philosophic ah Orientierung iiber of the logical principles, but he nevertheless diminishes the importance of the law by Es it refer to the merely empirical fact that something has been thought of

making

("

dru ckt nichts aus, als dass die Thatsache des Vorstellens stattgefunden hat in der Weise, and by stating it as merely a special case of factuin wie wir sie vollzogen haben The law is not intended to establish in a subsequent judgment infectum fieri neqtiit. the fact that something has been thought for this subsequent judgment itself is governed by the rule that it must have a definite meaning, its meaning being that just this mental "),

;

It is really intended to show how any act of judgment act and no other has taken place. has taken place, that it contains one definite single meaning, that if we affirm anything we can affirm it in one sense only, and cannot in the same act of judgment hold the

opposite view also. 1 I do not know

it was that the name of principium identitatis was first given A, or Ens est Ens, instead of to the Aristotelian principle, which was so denoted throughout the Middle Ages (see Prantl s References} nor when the

to the formula

A

when

est

;

principium contradictionis (and the princ. exclusi tertii] received its altered meaning We can see very clearly how Leibnitz passes the two changes were no doubt connected. from the one rendering to the other. In the Nouveaux Essais, iv. 2 (Erdm., p. 338, 9), we find as the principle of identity A est A, chaque chose est ce qu elle est" while une proposition est ou vraie ou the principle of contradiction, on the other hand, is I. "que le vrai et le faux ne sont fausse." This, he tells us, contains two propositions point compatibles dans une meme proposition, ou qu une proposition ne saurait etre vraie 2. et fausse a la fois que 1 oppose ou la negation du vrai et du faux ne sont pas compatibles, ou qu il n y a point de milieu entre le vrai et le faux, ou bien il ne se ;

"

;

"

:

:

"

"

;

Here, as in the Theod., I, 44, pe ut pas qu une proposition soit ni vraie ni fausse." ce qui est But his first example is Leibnitz is in essential agreement with Aristotle. A ne saurait etre non-,4 ; and though we may still recognise in this the two judgments the same thing is A and is not-,4," the use of the term non-,,4 has very nearly con "

"

"

This formula actually appears together it into the formula A is not non-,4. est impossible with the other in the Nouveaux Essais, i, 18 (Erdm., p. 211) qu une chose soit et ne soit pas en meme temps." In the Princ. phil., on the other hand, verted

:

he

states that the

import of

&& principium

contradictionis

that everything which contains a contradiction is opposed to the contradictory or false is true.

is

false,

(

and

"il

31) is to enable us to say that everything which

Here, then, the contradictio is in the that the opposite of an identical proposition contains an express contradiction, so that "A is and is non-^4 are opposed to each other as necessarily true, and necessarily false. predicate.

Finally, in

45,

it

is

said

A

"

"

A

"

THE NEGATION

143

whether certain propositions are in themselves true. From the Aristotelian proposition we cannot immediately infer the truth or falsehood of any but

particular

proposition,

affirmation

and negation

Kant

the

only

polemic against Aristotle

s

is

of

impossibility

same

at the

both

believing

time.

then quite misdirected.

According

him (Kr. der r. Vern., Hart, p. 166 sq.) the fundamental principle To no thing can there belong a predicate which contradicts It

to "

it."

universal

that

knowledge whatever, irrespective of is

knowledge

a judgment

entirely annihilated

may

be

still

contradiction

knowledge of the

false or

given since

its

It is

is

by contradiction.

It

and

It

does not,

;

truth,

when

it is

free

the principle of contradiction always

We

must always be

contained and thought of in

this

for

impossible

point of view, then, that

anything

from

it

the concept of the object as

Kant

itself,

rejects the formula,

same time both

the

at

a

affords

denying the reverse

right in

knowledge, and we must necessarily affirm the concept opposite would be in contradiction to the object.

from

is

states

may be of positive use towards for when the judgment is analytical, let it be

sufficient test of its truth.

to

contents,

groundless even

nevertheless

affirmative or negative,

of whatever

its

:

a

go so far as to guarantee the truth of a proposition, for

indeed, as a rule,

internal

criterion of all truth.

though indeed, merely negative

valid of all

is is

and not

to be

to

"

it is

be,"

as

containing a synthesis which has slipped in from carelessness and quite The proposition, he says, is affected by the condition of unnecessarily.

and

time, at the

not- B}

as

much

as to say

same time be one

after

not-j^

this

;

;

"

in is

is

attributed to

but the contradiction

is

is learned,"

its

entirely contrary

on,

statements to timeto is

the intention of

due

entirely to the

;

if,

at

the

same

time, an opposite pre

the subject, then a contradiction arises

between the one predicate and the

between predicate and subject.

man

limit

A predicate (e.g. unlearned) is synthetically

connected with the subject (man)

unlearned

no way

The misunderstanding, he goes

use of synthetical propositions.

dicate (learned)

it

But the principle of contradiction, being a

must

such a formula, then,

principle."

is something B, cannot can very well be both (B as well as

a thing A, which

but

another."

purely logical principle, relations

"

:

If,

on the other hand, we say:

the truth of this negative proposition

;

other, not

is

"no

obvious

the from the principle of contradiction, without the addition of In his Logic, also, Kan t^ deals in the same same time as condition. "at

"

way with the

principle of contradiction.

i

LOGIC

44

needed to show that Kant is speaking of something quite from the original principle of contradiction. Leibnitz divided truths into necessary and matter of fact, and offered a special principle of Little

is

different

truth for each of the two classes

are sary truths, which identical propositions

all

the principle of contradiction for neces

:

them

of

the last instance what are called

in

the principle of sufficient reason

;

Kant proceeds

same way with

the

in

matter of

fact.

analytical

and synthetical judgments; what he

is

his

for

truths

of

two classes of

looking for

is

a principle

Now analytical judgments are of analytical judgments. always concerned with subjects which are concepts, and they state what is for the

truth

hence quite independently of time

thought in these subjects as concepts

;

the predicate of an analytical

judgment is always already contained in the But what the principle of contradiction subject.

concept which forms its Kantian sense states

in the

tributed which contradicts their subject is

known by

would be

"

is,

no concept must a predicate be

to

In so

it."

far,

then, as other

man

by means of a concept

(in

the concept man), the

principle applies to

self-destructive

if

"

this

is

will

investigate hereafter

a universal logical

At present

it is

also

that

subject

falls.

meant by contradicting a concept, principle can be grounded upon this con

what

tradiction.

is

clear that, starting from

these premises,

from

excluding time-determinations

certainly right in

them

; they they attempted to attribute to a subject a

and whether

is

the object

learned,"

predicate contradictory to the concept under which

We

at

judgments express

his

Kant

principle.

But when he accuses the Aristotelian formula of a misconception in u its at the same time," it is due only to his own misconception

containing in

thinking Aristotle

certain that Aristotle

s meaning to be the same as his own for it is meant to prohibit, not indeed contradiction between ;

two predicates, but contradiction between the affirmation and negation of the same predicate. It

5.

may

differing so

fairly

be asked here,

greatly as

do the

"

How is

Aristotelian

it

possible that two principles,

and the Kantian, should be

regarded as one and the same fundamental law of human thought? And is there really no connection between them?" Some connection there certainly is. The ordinary principle of contradiction generally

by which the validity of negative judgments may be seen that a negation generally rests upon the exclusion of the predicate by the subject, and it is fancied that this relation of incom

aims

at giving a rule

tested.

It is

patibility rests

again in

its

turn

upon the negation

;

hence

it is

thought

THE NEGATION

145

But

that universally valid negations are all reducible to contradiction. this

way we

see that the formula really

"

moves

But what can be the meaning of saying A ? That a proposition which

subject

involves a contradiction

diction can take place

B

when

is

B

contradicts

B

attributes a predicate

The

?

in

circle."

that a predicate

a subject

A

in a

in

only way

to a

which a contra

the judgment which attributes this predicate

A contradicts another judgment (presupposed, if not ex which denies the predicate of the subject A. This latter pressly stated) is not judgment (A B} being accepted as needing no proof, or as known to a subject

B

from some

judgment

down by

other source, the

and

;

it

does

so,

contradiction

moreover, according

Kant

way

s

example,

"an

"

"

judgment

the proposition

and the same

learned,

X

stating that the subject

is

learned

;

is

false,

and

i.e.

if it

is

it

In

not learned.

X

is may be reduced to the two judgments, is not learned. These two judgments are both

stated by the proposition, which therefore contains a contradiction,

therefore

laid

be true together. Why is the unlearned man is learned," a con

"

implicitly contains a this

first

Because the predicate learned is attributed to a subject denoted by the subject-term unlearned man," a term which

tradiction? is

the

to the proposition

Aristotle, that they cannot both

proposition in

which

annuls

certainly

is

true

false that the

that

he

is

same man

not learned,

is

it

and

learned and not

is

that

false

he

is

learned.

A is

contradiction, then, can only take place in so far as a judgment

This

already implied in the subject.

the analytical propositions which

positions of which alone the school logic

have seen above, Kant

s

is

Kant has is

certainly the case both with

and with those pro

in view,

accustomed to

As we

treat.

on the

analytical propositions are possible only

presupposition of concepts which are the same for every one

;

on the

i.e.

presupposition of universally valid judgments concerning the meaning of

words

;

judgments which state that body means the same as extended denoted by the word body" contains the idea "ex

thing, that the idea tension."

If I say,

thing which I call

"

"

bodies are

all

body

I

must

extended,"

then that means

also call extended

"

;

"

every

the denotation of

X

If now I say is extended." any AT as body contains the judgment, then a body is not extended," or even this body is not extended" this is extended, and this is not extended there is a contradiction "

"

"

"

"

:

and

as

it is

absolutely established that anything which

the contrary s. L.

is

;

is

body

is

extended,

necessarily false.

L

i

LOGIC

46

So

:

not B.

is

B and

appear the contradictorily opposed predicates tradiction between affirmation and negation

A

"

affirmations false that

A

is affirmation and negation opposition has been between But now, instead of contradictory propositions, there

far the

B and A

A

B

is

"

and

A

"

is

not-,5

if it

and the con

;

is

the two

to

A

true that

"

;

not-./?

transferred

is

is

B,

it is

not-/?.

is

these presuppositions alone can a contradiction take place between the falsity of a proposi subject and predicate ; and we cannot recognise tion from the contradiction between its predicate and the concept forming

On

the subject, unless are formed

is

when we

and,

is

it

infallible,

presupposed that the process by which concepts and their denotation by words absolutely fixed

j

the process of the sub-

are treating of the particular, that

Now, so sumption of the particular under the concept is also infallible. which Kant with the do have to we as subjective upon image merely long bases his analytical judgment (v. p. 104) no doubt it is easy to form a body concept and to combine in it certain characteristics to say is Then the judgment is bodies are extended extended thing." "

"

"

equivalent to

the extended

"

is

Here, as Hobbes holds, we

extended."

have only equations between the arbitrarily framed meanings of words. Even the statement all bodies are extended involves an unauthorized "

"

for

assumption,

it

assumes

tacitly

and

that

that I can safely

my

make

is

concept

this

to

applicable in

any par for this is the only meaning of ticular case Finally there can be absolutely no question raised as to whether I should say more concerning possible things,

application

"

all."

what

I call

become But

body than

identical,

it is

i.e.

is

already contained in the

name

just at this point that the formula

"

A

is

between a predicate and

The

is

"A

A"

its

subject

is

reduced to

this

judgments must admit of being and that our absolute measure of truth lies

assumption that

true

all

propositions

not not-^4

as the expression of the principium contradictionis.

to

all

;

without meaning or importance. "

appears

contradiction

formula by the reduced

finally

in the finished

system of concepts in which alone our thought and knowledge move. But the first weak point in the formula is its ddpto-roi/ non-A. An attempt

might indeed be made to explain

this

away.

principle of identity, the proposition can

not

A

"

;

because, that

is,

it

-non est

A]

;

"

it

is

false that

contradicts the true proposition,

a slight perversion of language this

non [A

Starting from the so-called

be made,

the given

A

may be still

A

is

A.

A

is

By

contracted into the proposition

remains subject, and

it

is

:

denied

THE NEGATION A

that

as predicate can be denied of

would have a meaning if this is not what is meant dictory

From some

of A.

and in

as

and what

is

In the same way the formula

it.

were taken as the sign of a proposition. But Non-A is introduced deliberately the contra :

of concepts

opposition

propositions,

A

147

now

is

substituted

prohibited

points of view

is

for

of

contradiction

the

that non-^4 shall be predicated

we might be content

to accept non-^4,

acknowledge the formula as theoretically correct but it is useless We seldom meet with the contradiction in such a crude form practice. to

;

"gold

is not-gold,"

speaking

rally

so easy

when

"green is not-green,"

it

must be discovered under

A

is

Gene

not-Being."

Would

that

it

were

given to decide what determinations are included in

non-A and therefore contradict But now we see

"Being is

disguises.

A

\

that, like a

proper oracle, the principium contradictionis what is it which may not be stated gives us no answer to the question

\

"

;

we take refuge in saying that A as a concept contains the characteristics a, 6, c, d, and that therefore non-a, non-, non-d must not be attributed to it, the difficulty of the r\on-A is only multiplied If

of^f?"

non-
;

and

if

we

are content to say a,

b,

c,

d must

not be denied

Aristotelian principle applied to judgments,

well, that

is

the

which we already acknowledge

to be valid.

But the Kantian Logic can contain no universal formula by which determine what

Kant

s

is

opposed

to a subject

for

to

our concepts, according to

express teaching, generally denote the nature of their objects by a

part only of our experience of them.

the fact that something

belong to the thing

;

is it

contradict the concept,

it

Hence we can never conclude from

not contained in the concept that

it

does not

never follows that because something does not It is moreover a does not contradict the thing.

fiction that all the relations of

tion

;

concepts are and exclusion are concerned.

known

to us so far as opposi

because the Aristotelian principle refers only to what we know the function of negation and does not confine itself to judgments having It

is

concepts for their subjects, that it is a first principle, absolutely uncondi all our judgments. Because, moreover, there is

tioned and applicable to

it so far as we have any knowledge of the relations of op the ground of the impossi and position incompatibility among concepts

contained in

bility of attributing to a

But

all

that

proposition

is

concept a predicate excluded by

it.

the ordinary principium contradictionis can say

false if its predicate is

is,

that a

incompatible with some determination

j

\

;

,

i

LOGIC

48

of the subject

;

and

therefore prohibits us from attributing to

it

Thus

presupposes a knowledge of what

it

compatible predicate. and cannot be an unconditioned

patible

according to the principle of the its

in

incom

principle sufficient in itself

first

doing which

to establish the falsity of a proposition (by

an

it

is

it

would

also,

excluded middle, establish the truth of

contradictory opposite). 24.

To

interpret the nature of the negation completely

is

It is

i.

deny a negation

affirmative, that to

the same predicate of the

to the

the further principle that the negation of the

principle of contradiction

negation

we must add

same

is

equivalent to affirming

subject.

has found no

strange that logic

place for the proposition

from duplex negatio affirmat? which has been abstracted by grammar Probably it has been looked upon frequently recurring forms of speech. as a consequence of the principle of excluded middle ; but its position "

is

rather that of the indispensable link leading from the principle of

The

tradiction to that of excluded middle. states that

together

;

con

principle of contradiction

impossible for affirmation and negation both to be true if the affirmation holds good, it leads to the falseness

it is

in this way,

doing it does not state what is meant by stating Only because the denial of the negation is the there no medium between affirmation and negation.

But

of the negation. that a negation

affirmation itself

in so

false.

is

is

between the two by treating^ completely parallel and co Owing to this he failed to give a satisfactory

Aristotle lost sight of this simple connection

affirmation

and negation from the

ordinate forms of statement.

account of the negation

first

as

left

and, strictly speaking,

itself,

no room

at

all

But as soon as we see that every negation

for the negation of a negation.

its only object being to declare this soon as we see that the negation is a particular act in

presupposes a previous synthesis, synthesis invalid

which the (either

as

;

"not"

has the force of a judgment concerning a judgment then it becomes clear how far the nega

attempted or complete)

tion of a negation

the proposition

A

"

is

possible.

is

B

is false,

nations incompatible with

turn be denied.

"

B

not

"

contains the statement that

that other determinations than

^determi

B

B

It is false that

state that the proposition

B

is

belong to A, that it is impossible to unify This statement, or the attempt at such a statement, may in its

with A.

than

A

to

A,

"

A

is

A

B

is

not

B"

"

is false,

to prevent the unification of

A

says that

to ascribe

and B.

it is

impossible to

any other predicate

And

if

the objections

THE NEGATION to the

good.

A

synthesis

is

B

149

are impossible, then this synthesis must hold

1

2.

It is in this

negation

it is

property of the negation, that

when we

to that extent a positive statement, that

directed against a first

become

fully

aware of the completely subjective character of the whole movement of thought when concerned with negation. By the process of negation no

produced and nothing can be created which did not exist in The presupposition of its validity is that a combination dependently of it. should be attempted which is merely subjective and peculiar to the indi vidual, and which is prohibited by the immovable necessity of thought truth can be

;

and when the negation has been attempted without sufficient ground not vanishes, leaving no trace behind the repeated only serves "

"

;

it

to

indicate the circuitous way which the thought of the individual has taken, For in in order to reach a truth which might have been reached directly.

the last instance

always out of some positive knowledge that we declare false, and in this positive knowledge is contained the

it is

a negation to be

ground for the overthrow of the negation. But it is not altogether to no purpose that 3. In grammar

taken.

it

this circuitous route is

has already been recognised that resisted attacks

increase the psychological firmness of conviction

;

the affirmation which

negation seems to stand firmer and to be more may gain but it can never gain so as to contain more

has fought through a

So much

certain.

it

;

u ^4

than before, or to be richer in meaning. information whether is

not

B

that

is,

it is

known

so long as

A

directly or

and

B keep

is

is

B

"

gives just the

same

the result of the negation of

the

A

same meaning, and we do

B

for not substitute the affirmation of a positive characteristic opposed to If we did this, we should of course have A is not the mere negation "

B."

gained something new, inasmuch as A would have come into relation with Is it false that light is not a kind of motion, then a new predicate. the proposition we have gained tells us no iota more than the propo sition

"

another

light is a "

light

is

for other reasons,

kind of

motion."

a kind of

matter,"

If for our

first

proposition

then the denial of this might give us

a distinction between

"light"

and

we

substitute

on the ground of a disjunction accepted

"matter";

new

information,

i.e.,

but this would not be due to

the twofold negation. The Principles of Logic, 1883, p. 149 sq. ; special weight is laid upon Cf.. Bradley, the position that every negation must be based upon positive knowledge ; the only ground This knowledge is B. is our knowledge that upon which we can deny that A is not 1

B

is

therefore included in the double negation.

A

LOGIC

I5 o

25-

of itself from the principles of contradiction

It follows

and of twofold

two contradictorily opposed judgments one is necessarily true ; hence that there is no third statement besides affirmation and nega This is the PRINCIPLE OF THE tion which would imply the falsity of both. negation that of

EXCLUDED MIDDLE, which, like the two previous principles, aims only and meaning of the negation. Interpreting more fully the nature

The

ordinary interpretation of the principium exclusi

A

tertii is

at

by the

B

aut non-JB, according to which every subject but this is as possesses one of two contradictorily-opposed predicates ; different from the original and genuine principle of excluded middle as the formula omne

aut

est

ordinary principium contradidionis

is

from the principle of con

different

tradiction.

j#"and

is

"A

not

B"

one

necessarily false,

it

;

not be denied together. tain that

A

is

B

not

If I

while

A is B. that A is B

maintaining that

deny both

to

is

"

and by so saying it fixes the meaning of the negation. follows immediately that one is necessarily true because both can

maintained together

But

judgments A is because both cannot be

principle of contradiction tells us, that of two

The

1.

that

A

deny that

B, then by so doing

is

A

not B, that again

is

main

I is

only

attempted at one and the same time and that A is not B, I should by one negation If then I

not .Z?, and by the other that A is thus falling into a con Thus there remains no middle statement between affirmation

A

say that

deny

if I

is

tradiction.

,

and negation, which could contain any reference of the predicate B to the and A as predicate subject A and any judgment which tries to combine

B

;

and

subject,

must

either affirm

A

or

deny

contains a petitio 1

<j)dvai

iv.

7)

ion

b,

23

aTrofidvai.

:

v

it it

A. in the

(one,

most important however, which

as needing

no

1

proof.

AXXa ^r\v ov8 /j-era^v avn^acrews fv8^x Ta L Ka8 evos OTLOVV SrjXov 5 irpQirov fj.ev opiffa^fot-S T L rb -

^euSos* TO jj.ev yap Xeyew TO ov /irj elvai rj TO ov fjii] elva.1. a\T)6es, &aT 6 Xeywi TOVTO elvai ^

/ecu

TO ov XtyeTai

and

;

Arist., Metaph. T, dXX dvdyKri r) f)

fjL^j

B of

he attempts a proof of prindpit) elsewhere he gives

passage (Metaph.^

d\7)des

of

Aristotle repeatedly states this principle,

2.

Kal TO

B

/J.T]

ov elvai

i/

euSoj, TO Se TO ov etVcu

/A?; d\r)dei>(reL rj

^eixreraC

dXX oure

This passage has received various interpre tations ; its meaning is there is no intermediate between the members of a contradiction ; This is obvious as soon as everything must be either affirmed or denied of everything. we define what true and false mean. To say that the existent is not, or that the non H.T)

elvcu,

f)

elvai, oi/Ve

TO

/ATJ

ov.

:

existent true.

is,

is

false

;

while to say that the existent

Thus when we

say that this

(i.e.

some

is

and that the non-existent is not, is which is either existent or

definite thing

THE NEGATION

151

is shown by the even Aristotle gives formulae containing both, while Leibnitz exincludes them both in the formula A proposition is either true jDressly or false." i But the either-or conceals an ambiguity in an apparently

Its close

connection with the principle of contradiction

fact that

"

:

"

"

simple expression, and the dependence of the derivative proposition sight

It

of.

is

more

therefore

is

lost

natural to give the principle of excluded

middle a special place as a corollary to those principles which immediately but it is incorrect to rank it beside ;

unfold the meaning of the negation

upon which

the principle of contradiction

immediate, especially as

its

application

depends, as

it

is

if it

were equally

easy and evident than

less

that

of the fundamental principle. 3.

It is

owing to the weakness of the mere negation, and the incom

pleteness of the information which

seem

denial, that difficulties

meaning of

gives us as to the

it

its

excluded

to arise in applying the principle of

middle.

The more

familiar difficulties,

arising

from continuous transitions and

When

the many-sidedness of the subjects, are indeed easily solved. is rising,

may be

two propositions

either of the

true,

"it

has

according as we apply the term

the horizon of the upper or lower edge.

It

"

risen

may

"

"

or

risen"

it

the sun

has not risen

to the elevation

"

above

be said that in the moment

non-existent) is or is not, we speak either truth or falsehood. But if we suppose a middle statement between affirmation and negation, it tells us neither that the existent, nor that the non-existent, either is not or is; for if any one of these statements were made, it

would be an affirmation or a negation, and

either true or false.

The middle statement

could say nothing either of the existent or of the non-existent, nor could it therefore be But that which is neither true nor false is no statement at all, for it either true or false. a part of the nature of a statement to be either true or false (wore oiire d\rjdev
is

the classification of judgment into affirmative and negative, that there is no fj.era^v, if no more can be stated than that the existent or non-existent is or is not. The passage can not therefore be regarded as a proojj_ it serves merely, together with the rest of the course. chapter, to point out that it is always presupposed that there is no middle eirl u*bvuv TOVTWV Cate., IO, 13 a, 37 "Ocra Se wj /cara^acrts /ecu ct7r60a
:

.

.

/>,

Metaph.,

(TTiv

K.

1069

a, 3

a,

:

:

TU>V

^s brqovv ddrepov

dir^acrews

oi}5

ava

OVK e xownjs ovdev fj-era^v. a similar passage, Phys. ausc. v. 3,

TrdpeffTLf,

/m.6pioi>

fj-foov,

there

is

a, 9.

In the Analyt. post., as the basis fjibpiov, 1

33

avrideffis

dvTi(pa<ns,

12,

227

1057

I, 7,

upon which

dvTi<pa
See note,

p.

5

I, 2,

dvriQecris

142.

72

a,

to explain rjs

OVK

n,

the opposition

what a judgment Zcrri fj.cra^v /cct#

which excludes a third

is

:

airb<pa.v
avrriv.

Cf.

De

is

even used

dvTi(f)dffeus oiroTepovovv

tnterp., 9,

1

8 a, 28.

LOGIC

I52 of death

this again is incorrect, for

and

lives,"

he does not

"

"

live

;

but

expresses a state which continues, and the

"

"

he

"

equally false to say

it is

life

And all cases in which we dying man in articulo mortis does not live. have to deal with spatial and temporal limits may be similarly treated. it is false that a chess board is Still more clumsy are such examples as "

black and false that

it is

not black

then the negation

true

;

two propositions.

is

"

if

;

the predicate applies to the whole,

not, then the subject

if

not the same in the

is

But these are not the only difficulties which arise. what is the relation between

1

Aristotle himself raised the question as to

the two propositions

"

Socrates

Socrates does not exist at all;

and

ill,"

and whether

decision he

"

Socrates

it is still

comes

not

is

ill,"

when

the case that one of the

is

the

two propositions expressing the material opposition, "Socrates is and "Socrates is well," would indeed both be false; but that the mere

necessarily true.

"

negation

.

The

is

two

ill"

;

2

Socrates

is

not

"

ill

perfectly satisfactory

"Socrates is

not

ill"

|

answer the question

;

for,

means

"

is

ill,

we

as

This solution does not, indeed,

"

Socrates

possible

;

words do

ill

?

by yes or no, then

If

we

It

may

still,

however,

by calling such an answer ambiguous, we admit that the in themselves, exclude the other meaning ; and that form

not,

We may

the truth of the proposition

admit

this justification,

done with the

is

incontestable.

and nevertheless draw from judgments there

principle of excluded middle.

as to whether Socrates existed at all

be

ill.

according to

we accept the presupposition upon which and if we say of a dead man that he is not

lesson, that in the sphere of temporally valid

sitions

not

is

that,

ally, therefore,

to be

the proposition

commonly understood,

are guilty of using our words ambiguously.

be claimed

4.

is

that in this instance

that Socrates does live but

our usual way of speaking alone the question

is,

remains true even in this case, thus pre-

serving the universality of the principle.

seem

to

;

if it

The

is

not

question

it

the

much is

not

were, then, of the two propo

Pegasus is winged and Pegasus is not winged," the latter must His existence is presupposed in the proposition, but existence

"

"

true.

at a previous

time,

and the

"

difficulty applies to the present.

Because

temporally valid judgments state their affirmations only for a given point of time, it remains uncertain whether the negation of such judgments applies

only to this point of time, or to the subject throughout 1

p.

With

205 sq. 2

reference to these ;

and similar objections

Drobisch, Logik,

Categ. t 10, 13 a, 27-^ 35.

60, p. 66.

cf.

Ueberweg

its

78-80,

whole more

exist-

especially

THE NEGATION ence.

It

is

uncertain, therefore, whether what

past or future, or the predicate altogether "

propositions

other die

is

to

up

he

he

will die

will

not

and

die,"

But the proposition does not

false.

"

true because he

heaven

153 is

false

is

only present,

at all times.

one

tell

is

Of

the two

necessarily true, the

us whether

"he

will

not

already dead, or because he will be carried

is

in a whirlwind like Elijah. 1

When,

therefore,

we can

attain

principle of excluded middle to the truth of an affirma

by means of the

tion, the principle

has

its

value even in the case of merely temporal judg ambiguous. But it is not worth while to

ments, for affirmations are not use

it

5.

for the sake of

There

is

mere negations.

less difficulty with respect to

judgments of unconditional

Since these apply to the contents of the subject-idea, there validity. In would seem to be no room for ambiguity in the negation of them.

such judgments as "

is

infinite

and

"matter is

"space

is

heavy"

not

and

infinite,"

"matter

is

not

heavy,"

"space

neither affirmation nor negation

be ambiguous. But here a difficulty of another kind presents which one we have itself, already touched upon above ( 22, 3, 4, p. 128) and which rises out of the generality of the subjects. Owing to this

seems

to

we

generality

are constantly tempted to extend our judgments to

all

the

under the subject-idea but though the Predicates of affirmative judgments are of course true both of the general idea and of the particular objects which fall under it, we cannot in like definite particular things

manner deny of

which

fall

;

the particular objects everything which does not form part

of the general idea.

It

is

no part of the general idea

triangle to

be

nor of the general idea man to be white but we cannot on that account deny that any triangles are equilateral or any men white. equilateral,

;

makes a strange exception with reference to the future when he says (De 8 a 27) that when one person says that something will happen, and another person denies it, it does not follow that one necessarily speaks the truth, for if it did all But here as the future would be necessary and deliberation would be superfluous. Zeller allows (Gesch. der griech. Phil., II. 2, the Stagirite. has committed an over 1

Aristotle

interpr., 9,

1

p. 157)

He

is necessary that the one or the other should be speaking the truth, with the statement that one or the other speaks necessary truth, i.e. speaks the truth because what he says is necessary or necessarily not ; while all that is necessary is that the actual, perhaps fortuitous result should prove one of the two to have been right. What Aristotle means is that the statement that one is necessarily speaking truth involves that the truth or untruth is already determined, while really the one state ment is as uncertain as the other, and neither &TTCU nor OUK ftmu can be properly used in

sight.

confounds the statement that

it

We see here how he, with his habit of referring every proposition can find no correlate for a statement which leaves the alternative between Being and Not-being undetermined.

the sense of knowing. to Being,

LOGIC

I54

Hence

there

something wrong about

is

are

"

judgments

triangles

The negation

is

meant

not

is

It

subject.

the

is

the

not

are

triangles

equilateral

between

opposition

the

equilateral."

denies generality, and again ambiguous, for now it only cannot be united with the to state that the predicate divisive the at this point that first judgments, and then grounded upon them, appear; the former

judgments

disjunctive

different predicates with the general idea, the stating the compatibility of

amongst themselves. According to the ordinary formula of the prindpium exclusi tertii the proposition that of two contradictory judgments one must necessarily

latter their incompatibility 6.

be true "

A

(either

B or A

is

not B, holds good)

is

rendered as follows

is

of two contradictorily opposed predicates one must belong

ceivable subject

A

"

is

(A

either

transferred to the predicates,

B

or

and

In

not-.Z?).

strictly

this

speaking we

to every

:

con

way the negation

is

obtain two affirma

After this transi judgments, which allow of no third intermediate. use of it for Kant made tion had been made by the Wolffian Logic, tive

his

own

to

He showed

purposes.

dicates are

that since,

when

all

possible

pre

compared with their opposites, one of each pair must belong

every subject, this principle passes beyond the sphere of the merely

logical,

and

totality of

the

upon

question

as

clearly

whether

to

all,"

how Kant understood

in order to see

all

B or

transition

need not here enter does not contain a

;

not-.Z?

in

the principle

possible positive

by which of these

either

is

this

which

"

the reference of a subject to

"A

We

one place is used as a completely At any rate, it the other as a definite number.

in the

indefinite generality, in

sition

determination presupposes a

predicates as the total possibility.

quatemio terminorum

shows

of complete

as the principle

all

it is

to

i.e.

as

concerned with

and negative predicates, Thus the propo

be determined.

instructs us to substitute for

able predicates one after the other.

B all

conceiv

But even apart from the question as

we never gain any deter ; remains or notundecided whether always OT notto the subject. Even if we could decide between B, belongs the alternatives, still, so far as the great majority of such predicates was to the justification of not-.? this

mination in this way, since

X

is

a barren task

B

it

A"

concerned,

no

conceivable

combination

affirmative form of the predicate,

would

and thereby challenge a negation.

regards general concepts the difficulty would

both

B and not-^5 are

the principle

is

compatible

enable us to try the

;

still

As

remain that with them

so that for this reason also the value of

considerably lowered.

THE NEGATION But the principle of excluded middle

7.

155

really derives

its

reputation

mainly from the fact that it is a special case of a relation which is certainly most important and rich in consequences i.e. the relation of disjunction. It is due to the nature of ideas that we are often in a position to limit our choice

among

the

particular

same subject

different statements concerning the

We

two only.

often to

to a few,

knowledge and of predicates, to frame two

are able, on the ground of our

of our

contents

subjects and

which we know that they are so far related like contradictorily opposed judgments that while both cannot be true to and in this case we gain, by denial of gether, neither can both be false positive statements, of

;

member

either

Now

of the disjunction, a

definite,

the principle of excluded middle

can attain

easily,

and

such

at little cost, to

we need but say that every proposition we have an incontestable truth and a

make

understood as

it is

;

if it

either true or false,

is

upon. "

"

we could

solve "

It is either

so or so

trancher

question

"he

or

itself

unnoticed for the

to tell us

more than

it

applied to the truth of the proposition

difficult

it

as a rule really based

is

questions by starting right off with

proceeding of which we might use the phrase even more fitly than the French themselves use it)

either mentally healthy or diseased in

is

odd

either

and there

(a "

la

all

we

these;

sure basis for strict investigation.

with the opposite predicate, this being what If

us think that

fruitful disjunctions as

But the opposition of predicates has substituted mere negation, and the negative statement seems really does

affirmation.

unambiguous

apt to

is

then indeed the

even,"

would be an invincible weapon.

But

mind,"

in itself

it

"the

number

of excluded

principle

is

middle

can never really do more

than oppose the affirmation by the negation in its poorest and most and though the view that there is no intermediate between barren form ;

affirmation

negation

and negation

itself,

yet

the

important as interpreting the meaning of the as a special proposition cannot be dignified

is

principle.

The

8.

its cogency from ends by inferring an

indirect proof, again, does not really derive

the Principle of Excluded Middle.

It is true

affirmation from the falsity of a negation

;

that

but the

it

falsity

of this negation

must have been shown by substituting for the purely negative and there fore indefinite contradiction one which was definite and based upon a disjunction,

and

this

the disjunction was in itself sufficient to support

1

proof. 1

While reserving a

fuller

treatment of the question for a later section,

we may,

in

|

LOGIC

I5 6

passing,

show by an example In Euclid

the indirect proof.

that the principle of excluded middle is unnecessary for I. 29, it is proved that when a straight line falls on

For if the angles were not equal alternate angles are equal. parallel straight lines the would follow that the inner angles were together less than two right angles, therefore

it

The contradiction according to the accepted postulate were not parallel. of this with the hypothesis from which we started shows that it is false that the alternate are equal. Expressed in this form, the angles are not equal ; true, therefore, that they But it is not really so. proof seems to rest upon the principle of excluded middle. that the lines

Unless

we

"angles

is greater than the other" "one angle for the The hypothesis which get no further with our proof. that one angle is greater than the other ; and it is from the falsity of

substitute

are not

the statement

equal,"

proves to be false

is

we can

The ground of the proof, therefore, get the truth of the proposition. that of the two propositions the two angles are equal this that

we

is

not

:

one must necessarily be true

;

the two angles are not equal but that of the propositions

:

the two angles are equal the one angle is greater than the other

one must be

The

true.

disjunctive proposition includes the clude the disjunctive proposition, and it is

mere negation, but the negation does not upon the latter that the proof rests.

in

CHAPTER

V.

PLURAL JUDGMENTS, BY

Judgments we mean those which,

Plural

in

one proposition,

state

one

predicate of a plurality of subjects. i.

AFFIRMATIVE PLURAL JUDGMENTS. 26.

When

simple judgments repeat the same predicate of a

number

of

and the person judging expresses his consciousness of this agreement by making one verbal act of predication refer to several sub subjects,

jects,

then the

P (Copulative When

A

are enabled

first

form of judgment which arises

and

B and C

Judgment

indefinite statement of the

one verbal expression i.

Our

A

B and

and

Care

under the same denomination JV so that we

fall

or induced

arises the Plural

material

is

Judgments). t

enumerate them as several

to

in the

desire to form

and occasions

s,

then there

narrower sense, which, with a definite or

number, includes the

(several

W

TV s

plurality of subjects in

are P).

judgments exercises

offered psychologically.

itself

The

according to

first

result

is

the

a series

of acts of judgments, connected only by the fact that they follow one in the judging subject, and are comprehended by one consciousness which, in passing from one to the other, does not im

upon the other

The verbal connection of mediately lose sight of the previous acts. all forms the most primitive and least signifi and," of "

propositions by

cant, states originally nothing but this subjective fact of co-existence in

one consciousness.

Thus

equally to connect the

it

has no objective significance;

most heterogeneous and the most

"and"

serves

closely allied.

But according to psychological laws those judgments tend to group themwhich either state different predicates successively of the

selves together

same

subject, or the

same predicate of

different subjects.

the former kind, which presuppose that the attention lingers

of

Judgments over one and

/>

o

)

i

5

LOGIC

8

into the conjunctive form, the same subject-idea, link themselves naturally not does this and etc. and merely imply that the predi C and is D,

B

A

;

one and

cates

all

to the subject, but also expresses the conscious

belong

To

ness of this co-existence of different determinations.

more than

us

tells

its

this extent the

component

parts taken^ conjunctive judgment is no occasion at present to consider this form more at there But singly. It becomes important only when applied with a consciousness of

length.

to narrative logical claims either

or to explicative judgments,

The combination

2.

cate, that factor of the

of judgments which ascribe the

judgment which

referring

them

each other

to

Care

P has

the

Thus

same end before

appropriate the manifold and present

and

firmly

The

to

upon the predi the mind as a general

actively

comparing ideas and to

the

judgment of the form

as all

it

judgment

;

it

A

and

attempts to

the aid of ideas which are already

and

therefore

it

represents

a

higher

compared with the simple judgment.

development of thought as 3.

new by

established,

is

same predicate

fixed

seeking to connect particulars

;

recognise agreement in difference.

B and

is

present in

is

This further implies that our thought

idea.

serves as a description,

it

serves as a definition.

it

presupposes that our attention

different subjects

and

judgment, when

when

simplest case in which

we have a

repetition of predicates

is

the

which are named by the same word. These things may be perceived as discrete, and form a or they may be recognised as differentiated spatial or temporal series intuition of a plurality of like or similar things

;

parts of a whole, as

members

of a group.

The

and the same denomination comes

intuition

distinction of the

many

As

from one

A

repetition of the

same

into consciousness in the

verbally in the formation of the

plural.

When we

we have

seen, there follows a denominative

are interested merely in the question what

it

is

which

in the plural (those

judgment But by every plurality of the homogeneous we are instigated to count and to make numerical comparisons, and an are sheep, those are letters).

or

indefinite "

question

definite

how

numerical expression appears in answer to the In the judgment these are three shots either "

many."

the numeral or the

noun

is

the speaker, according as the 4.

that

As a

rule the act of

we form no

the real predicate, which

name

or the

"

is

emphasized by

number precedes.

naming takes place so rapidly and unconsciously,

judgments in the process, but merely assert the name in the word by which we denote the subject. Generally also the distinction of unity and the of small plurality, counting numbers, and the special

PLURAL JUDGMENTS estimation of different degrees of plurality

We make

as quickly.

pass

how many

the question arises

between the

is

;

some, several, many,

-few,

when we wish

then the synthesis which

plurality

which

is

etc.,

when

of these only

predicates

there are, or

doubtful or disputed statement the judgment

special

159

to establish a is

contained in

presented and

now counted

definite or indefinite numerical idea. 1

and the

Generally this again finds expression only as part of the denotation of the subject, as a completed result ; and what we are concerned with is the statement to be made about

such and such a number of subjects.

What

5.

is

the nature of the function of judgment,

way such judgments as

this

visible

coming

The

is

that

summed up

in

are falling

men

when

there arise in

some

stars

are be

are wounded"?

up fifty which regards the plural of the verb

and there

as the sign of a plurality of acts of judgment,

fore the copula also

are

hail-stones

trees are rooted

many

view

first

"

common

one

Before

expression.

I

can

which "

say,

some

must have seen one here, one there, another there. visible," The predicate belongs to each one, but either I do not know their names, stars are

or I

I

do not wish

to

and a Bootis are

common name It is

refer.

only

only

arises in this way.

in

name them visible, ;

but

one

it

I

instead of saying a Lyrae and a Cygni denote the particular individuals by their is these definite particular stars to which I ;

set of cases,

however, that the plural judgment is perceived as a plurality, as it

In others the subject

one glance, and the predicate

were, at synthesis

is

is

stated of this plurality; the

then, as a matter of fact, simple.

This

judgments where the predicate cannot belong Numberless birds fill the wood with by itself. in

"

"

is

particularly obvious

to the particular subject "

the trees song these are not judgments which can have arisen their

"

grow thickly together from a summation of many judgments. It

is

different

when

the numerical term

is

the real predicate.

The

1 Those logicians who see in every judgment a subsumption of the subject under a more general predicate concept which is its genus, might be puzzled to say what the particulars are in respect to which three, or seven, or a hundred are general and what three" Does the extension of extension is to be ascribed to these concepts. comprise Or must we not everything in the world which I can enumerate as one, two, three ? "

rather say that three is in itself a fully determined idea, in which there can be no question of extension, because, as we always count in the same way, the number itself is always absolutely the same ? Again, when it stands as predicate is it really the predicate of the

things concerning which the statement is made, or is it not rather the predicate of their number, this number owing its existence to the fact that I am at the moment grouping

together and counting just these things and no others?

LOGIC

i6o

"many

proposition

A

that

B and

and

men

are

me

not intended to inform

is

short-sighted"

indeed C, etc., are short-sighted, nor

is

it

meant

as a

The information offered is the statement about definite individuals. are many/.*, many, comparatively the that fact short-sighted lamentable

When news arrives from with the total number. speaking, in comparison the battle field it is taken for granted that some have been killed, or at the question is how many, and the construction of the least wounded is logically the most correct. Dead 10, wounded ^L telegram, We need not point out that repeated activities give occasion in the ;

"

50,"

as things for plural judgments.

same way

no doubt, that several particular judgments must precede all before I can count, each particular one must

It is true,

such statements of number

A

have been observed, counting them

who

upon people, and observations

know merely

retain the

I

definite

homogeneous

upon

magnitude.

B

short-sighted,

that

have made

I

number of

them

my

I

;

determining

who

fills

in

forget

observations

repetitions of the

individuals,

like the statistician,

proceed

But

short-sighted, etc.

is

disregard everything which distinguishes

I

short-sighted, I

is

;

is

same

relative

its

his schedules

with

and who cares nothing as to who are the subjects of the enumerated births, deaths and suicides ; the predicates of his judgments numbers

only,

also are numbers.

necessary to treat of these obvious points at length, in order to

It is

throw some versal

light upon the obscurities of the and particular judgments.

traditional doctrine

of uni

27.

The

As

by which the subject of the so-called universal judgments

"all"

are

B)

is

bound

together, signifies, according to

its

original

(all

meaning,

number, and a judgment beginning with all presupposes a limited number of particular objects which can be counted. Thus, a

"

according to

its

"

original meaning,

all

A

"

"

(the

We

must

j

B

number of .*

/6

As

"

which are

distinguish between

can only be said

in

here from a logical point

this

B are

all

^

s).

EMPIRICALLY UNIVERSAL

JUDGMENT and that which is UNCONDITIONALLY UNIVERSAL. In the latter we attempt inadequately to express the necessary connection between the predicate

A

carefully

B

are

s

And

reference to definite particular objects. of view the all is the predicate

S

"

^definite

"*

.

(

*

and the subject-idea A, by

the particular. )

<

(If C^

anything f\

t

is

& -

back upon the unlimited must also be B.)

falling

A, 1

/^H- -

^

it

PL URAL According to

1.

ber, for

its

JUDGMENTS

meaning

original

definite numbers are equal to each expresses the fact that two s are B" I must All Before I can pass a judgment of the form it

A

"

other.

r

num

presupposes a definite

"all"

6

1

undertake a twofold process of counting. I must first count the things which then if the two numbers are equal I are A, and then the A s which are ;

B

express "all

in the proposition

it

nine,"

there

the

are

B"

(such phrases as If I

directly of this process).

remind us

"e.g.,

As

"All

then

invited

guests

I

say

"all

know how many

I

four,"

are

"they

all

invited, "

re all count those who are present, and the numbers being equal, the and If I think that a card is missing from a pack, I count them, sults. "

number

the

if

of cards which I hold in

my hand

number

equal to the

is

which belongs It is

to the pack, they are "all there." not necessary that the definite number should be expressly

and named, in order that a judgment may be stated as to a room has been emptied, and I say they are all gone

out,"

me

for

to

know how many people were

gone out

;

Under any circumstances one number and the

no exception.

equally sure of

is

have reviewed

enough

in

has always passed through this twofold

"

all

;

and by whatever method

no exception, whether by

my

Thus

"

all."

it is

is

may them

none escape me,

the formula nemo non, nulhis non, etc.

and not a circumlocution

the process gone through, and

I

directly counting

after the other with the certainty that

really the primitive one,

is

"

I

denies the exception

or only by taking one

am

no

that

out of the question, therefore, whether there

other, "

"All

assure myself that there

I

is

out of the assumption of a possible difference between

It arises

negation.

is

there

thought all who were particular person who was present must hence that the predicate is wanting to none.

none have remained behind, that present, and now know that each also have

It

there.

When

"all."

"

need

known

omnes which

is

;

it

the secondary expression.

speaking the real statement is concerned with the which is the predicate from a logical point of view, even though ^-* "

2.

it

may not appear

which are

A

s,

all."

Strictly

It is this

it is

as such grammatically.

B are all A

s."

It is

The

proposition

is "those

implied by the plural that there are

also implicitly stated that there are

A

s

which are

B

question to be dealt with and to be answered by the judgment

A s to which B

As

many

but the

;

is,

whether

no exception. (When we are dealing, not with things which can be counted side by side in space, but of states or activities which take place at different times, then what we

the

belongs are

have said applies to the s. L.

^

exactly expresses

all

"always"

whether there

and

is

"

every

time.")

M

LOGIC

,62

From

3.

originally apply to particular things

present in a definite

judgment concerning ;

all,"

that these particular things

and limited

adequate expression of my thoughts. A s are In other words The words "all

:

an empirical generality only,

must be

number which can be counted, and

B"

"

"

can a judgment concerning presupposition

only upon this

the words

"

clear that in a

it is

this

all

that

be the

are originally the expression of

a generality attainable by actual counting;

i.e.,

are forthcoming ancTthey can only be used in reference to subjects which and of of which the each be can which in a definite number counted,

predicate can be stated.

They

are the expression of a definite limited

comparison of the cases before us, and they presuppose that I am certain that the judgment is true of each particular one before I can state it of all.

How

4.

are

then are such judgments as

extended,"

etc., related to these ?

"all

men

are

mortal,"

Their meaning

is

"all

bodies

not that before

making the judgment we have gone through all men or all bodies one by one and counted them but that the predicate, mortal or extended, belongs ;

to

whatever

is

man

a

or whatever

is

a body.

But there are two senses in which such judgments may be

really valid.

place, be_expjicati ve judgments (analytical in Kant s They may, of the meaning word), because based upon the recognised meaning of the all animals feel I can state with perfect certainty that subjects-term. in the

first

"

"

without having enumerated the particular animals, if feeling is contained in my idea of animal if therefore I should not call anything an animal to

which feeling was wanting. the thought the

In

this case

"

is

expressed by

all."

it is

The

only in a secondary way that

expression results simply from

analysis of the idea which I connect with the

word animal.

meaning of the word determines the limits within which

is

it

The

applicable,

from the meaning that the predicate to feel must be present wherever the denomination animal is justified (p. 9 sq. above). Because animal feels, all animals feel. The analytical proposition express

and hence

I

can

foretell

ing the meaning which the words have in our thoughts

the

more

is

translated into

familiar language of narrative

judgment concerning particular and by my passing from the general thought to individuals it becomes more intuitable. This is why the expression has become all things,

"

naturalized where

it

experience of

the particulars,

all

nature of the case,

it

is

not original; where, that

and anticipate

"

anticipate an

is,

we only

it

even where, from the

can never be completed.

In other cases the predicate

is

not analytically included in the meaning

PLURAL JUDGMENTS The word

of the word.

"

of

life is

for instance,

man,"

ticular formation of the body,

thinks of asking

men from

include only the par

ability to speak, etc.

life,

not necessarily included in

able to distinguish

may

163

it;

;

a definite length

every one at one stage of his

life is

everything else with confidence, before he

how

When this long they live or whether they all die. is not Nor is judgment all men are mortal analytical.

the case the

"

is

"

it

men "denotes only those judgment of experience in the sense that whom I know and in whom my experience has taught me that I shall find the predicate. But this makes it only the more certain that it is the a

"all

result of

an inference

others, of

either of an inference from all observed cases to all

;

which there

is

an indefinite and incalculable number

;

or else of

an inference from the determinations which are understood as expressed by the word to others which are necessarily connected with them. If we form the judgment, and do not merely repeat it after some one else, can only be as the result of some such inference. We can never tell at all from the verbal expression of the judgment in

really it

which sense

to be taken

it is

cally universal

;

whether

it is

be understood

to

judgment which presupposes a

definite

or as an unconditionally universal judgment; and, analytical or synthetical.

The

an empiri subjects,

the latter, whether as

if

does not hesitate to

ordinary doctrine

regard every judgment beginning with

as

number of

as belonging to the

"all"

same

species. 5. is

If a

clear

judgment concerning all is unconditionally universal, then it that no direct statement is made about the actual existence of the

subjects, if

A

"

"

though

this is

most

certainly presupposed

they refer to actual things at is B" ; or anything is "if

all.

All

A

B"

"

it is

A

It

supposed that some existing particular thing the

name A, but

the plural,

"

fjitrdpao-is eis

aAAo

yeVos,

"

indeed, indefinitely pre

recognised and called by

judgment.

and indeed the whole mode of expression,

inadequate, a free

this is not stated in the

is,

is

by empirical judgments means only what is

B

are

s

Just for this reason is,

strictly

speaking,

a relapse from the sphere of the

and independent thought which moves among our

firmly-established

ideas into the habits of intuition, which deals with the particulars.

adequate expression

is

simply

A

is

B, man

is

mortal, a square

is

The equi

lateral, etc. 6.

The

traditional

universal judgment. stated of the

doctrine

What

is

finds

no

difficulty

generally said

whole extension of the concept

is

A

that

in if

introducing the a predicate

B

is

which forms the subject,

LOGIC

i6 4

then the judgment is universal; if a part only of the extension, then it is If the subject-term is a no men proprium, or an equivalent particular. then

expression, "

judgment

extension

its

Callias

"

rich

is

is

exhausted by one individual

besides the doubtful use of

Nevertheless this simple doctrine contains the nomen proprium as the sign of a concept

consequences are constantly recurring. tension of a concept

is

thus the

;

has so far the character of being universal.

made up

an obscurity of which the

It is generally taught that the

of the concepts contained under

ex

as species,

it

inasmuch as we can form a plurality of more definite general ideas by means But in the discussion of of the differences admitted by the higher concept. the universal judgment

is

it

assumed without

generally

hesitation that the

extension of a concept consists of particular existing things, and that there is

no

sion,

difficulty at all in reviewing, establishing,

because

should be

it is

that

and recognising

presupposed that our concepts are already

this

all

exten

that they

the expression of the nature of things according to

is,

Hence Logic does not as a rule distinguish between those judgments which are based upon the Concept alone (i.e., the meaning of the subject- word), and which in unfolding this meaning their fixed specific differences.

which is named by the subject-word and thus forms a part of the "extension of the concept"; and those which perhaps on the ground of unanimous experience state a predicate of

attribute a predicate to every thing

all

known

things which

have the same

fall

under the same denomination because they

neglecting this distinction Logic obscures the most important point, the transition, namely, from an empirically universal to an unconditionally universal judgment, the process by which concepts attributes.

By

and judgments are formed from experience. The judgment planets move round the sun from West to East" is originally empirically universal; any one giving utterance to it before 1781 meant by all planets, all six; "all

between 1781 and 1801 Uranus was counted amongst them, and all seven were included; from 1807 till 1845 all eleven was what was meant; and

we mean in the same way all the two hundred or whatever the number may have become. But what is meant is always all that are known, the same movement in its orbit being attributed to each. The

to-day

proposition says that direction of

all

the bodies which

movement from West

But suppose that

I

had recognised

of the hypothesis of

Kant

to East it

I call ;

planets have a

that I

as necessary

or Laplace

constant orbits around our sun should

that all

move

know

of

common

no exception.

upon the ground,

say,

compact bodies moving in

in the

same

direction, because

PLURAL JUDGMENTS

165

no reversed movements were possible within the space which can contain then I should have to include movement from West to East in the

them

;

meaning of the word planet then

my

e.g.,

them from meteors

to distinguish

move from West

and

would be

to

judgment, East," planets Kantian sense, and would extend to the unenumerated "all

analytical in the

planets

be discovered.

to

still

It

would mean that whatever can be called

a planet moves from West to East

moving

in the reverse direction

The

7.

from which

;

would not be a

it

follows that anything

planet.

difficulty of finding a place for the so-called Singular

Judgment

which distinguishes universal and particular judgments, clear from what has preceded from the fact that the former

in the classification arises

as

is

no way comparable with the latter. For in the case of universal and particular judgments we have to do with a predicate which implies an

is

in

absolute or relative numerical statement in general, but

;

their

is

genus

judgments whose predicates are numerical

we

case of the so-called singular judgment

not the judgment

But

ideas.

in the

are dealing with the question of

what belongs or does not belong to a certain particular subject, and not of subjects are forthcoming which possess one predicate.

how many In the

first

place,

then,

into singular, particular

we cannot regard

and universal

the division of judgments

as correct

and

second place, we have no ground

for treating

judgments as special kinds

no more reason

;

there

is

In the

exhaustive.

particular

and universal

in the ordinary

Logic

all for a predicate as a special kind judgments having than there is in mathematics for regarding judgments having the predicate or Hence it is an arbitrary pro infinite as a special kind. equal

for regarding

"

"

"

"

"

"

ceeding on the part of the traditional Logic to ask of every judgment whether it is particular or universal. Singular judgments concerning the particular

and concrete have been treated as universal

that there are three kinds generally called singular

ment

broken up

has a ring," and rich," the numerical judgment "one planet judgment of the next section "there is a comet which has while plural judgments have been regarded as particular,

")

;

although in no sense comparing what concept";

and simple

is

given with the

"

whole extension of

explicative judgments, even definitions, were

without a place until they consented to pass as universals.

an important part in human thought ; nevertheless instance it borrows its importance from necessity. plays

of the fact

"Callias is

the particular

the

(in spite

the individual judg

Generality in

the

last

LOGIC

166

28.

The

so-called

"some

As

are

In

this

things. it

aims

way

PARTICULAR JUDGMENT as given

common

formula

establishing an exception to the universal, or at preparing the

at

for a universal

When

in the

may be an empirical judgment concerning particular case it differs from the merely plural judgments only when J5"

judgment.

the subject

not to be taken in an empirical

is

completely inadequate expression for the thought which denote, and confuses the important distinction between

sense it

it

is

meant

is

a to

empirical and

unconditionally valid judgments. 1.

To

the universal judgment the traditional Logic opposes a Particular

Judgment having

formula

for its

A

"some

are

s

B"

and

in so

doing

it

meaning was not the same. TJns^artiular judgment, as ordinarily treated, is one of the most unfortunatejindjncon-^ So far as the words go, its meaning is quite venient creations of Logic. follows Aristotle, though his

and

indefinite,

as a rule

and which

express

it

incongruent to the thought which

it is

obscures.

really

It

true

is

between the universal and particular judgments

that

the

should

it

difference

generally elucidated by

is

pointing out that in the former the concept which serves as subject

taken in

its

whole extension, while in the

extension only (eV

If

//,e/)ei).

we allow

totality of particular individuals,

assumption that we

know

latter

it

taken in a part of

is

is its

that the extension refers to the

then this distinction holds good on the

the whole extension

parts of the extension are actually given to us.

and

that therefore all the

This distinction between

the universal and the particular judgment was rational enough according to the view of Nature taken by Aristotle ; a view which starts from the idea that a system of fixed

constantly realizing

and immutable concepts has realized

itself,

in

empirical knowledge surveys this realisation

And

essential

differences.

because

Aristotle never actually applied

the

distinction

itself,

and

the fixed forms of Nature,

of the concept in

was

all

the

more

and

that all

is

our its

rational

it except when it was justified. Logic dealing only with conceptual relations, and totally dis regarding the material realization of the concept, took up the Aristotelian

But when

later

distinction,

them

and made use of

completely false 2.

its

formulae

or rather of a

bad

translation of

the result was a host of absurdities, rendering the ordinary doctrine

The

if

the words are understood in their ordinary meaning.

Aristotelian nvl virdp^Lv

^

Travrl v-rrapxtiv is generally translated

PLURAL JUDGMENTS by the formula

"

As

some

only when applied

B" but the plural here can have a meaning which are particular and definite, and can which case it presupposes a narrative judgment

of the

;

the

universal,

plural has a

presupposed that the extension of the concept each of which itself contains a plurality of indi is

it

divided into parts,

viduals

same way, when the

the

in

And,

contrasted with the

is

meaning only when is

existent. 1

actually

judgment

particular

are

to things

therefore be counted, in treating

167

whereas there seems no reason why a single individual should

not suffice to form a part of the extension of the concept.

The

first condition is present in all cases where a particular judgment opposed to an empirically universal judgment all planets move in But when we are dealing with abstract ellipses, some planets have moons. subjects, whose extension does not consist in a plurality of things, the is

Must we say

formula leaves us in the lurch, virtues are

"some

have no plural

!

justice"?

Even

"some

in cases

love

virtue

or

is calf-love,"

where number

is

some parallelograms have equal

"

parabolas,"

"

diagonals,"

is

justice

we

but there

not contrary to sense,

Such judgments

the use of the plural shifts the ground of the judgment. as

or

"

"some

some conic

sections are

have a very strange sound from the point of view of geometry

;

geometry we do not think of its constructions as spread abroad in the world in a plurality of instances, so that we can speak of them as of some cats which have blue eyes and some quadrupeds which can fly. The for in

all

parallelograms are divided by the diagonals into

all

conic sections are curves of the second

"

universal judgments,

"

congruent

sound

less

extends

triangles,"

strange, because

"

all,"

when used

beyond the empirically known.

belong to the particular

judgment

;

But

H

Kara

/xe pos

But on the second point the customary plural "

one

man "

sinless

is

sinless

would be

avfyxoTros XCUKOS.

;

is

When

is

as

thought

ala-dya-iv reXeura.

is false

Herbart

much

and misleading

;

is

"

quite right in his correction of the ordinary 62).

a judgment of the form

"

one

A

is

a narrative judgment of empirical origin, then that

^5,"

it

or

"

some

A s are

"

seems to have no other

predicate of one or more word instead of being a general indefinitely by

of stating a

meaning beyond subjects which are denoted 1

as

not

some men are a particular judgment as and Aristotle himself included the singular in his TIS "

doctrine on this point (Einl. 3.

privilege does

this

this necessarily imprisons the

within the sphere of the particular.

degree,"

in the unconditional sense,

Even Kant makes the category

definite

of plurality correspond to the particular judgment.

68

1

named one by

The second judgment does

one.

from a number

plurality

numerical determination the judgment

Still in

not seem to differ in

its

of judgments concerning single subjects, since the is

not emphasized.

"some

men

mistake red for

green"

there

is

some

and Peter and thing more implied than in the copulative judgment "John of the statement definiteness individual The for Paul mistake red green." by denoting John and Peter and Paul, as "some men." But through being denoted by the general name they are placed in a relation to the whole of mankind which challenges a comparison ; and the is

indeed

lost

meaning of the judgment indicated by the indefinite denotation of the all other men differ from others subject, is that those who as men are like and possess some peculiarity In so

far as

it

assumed

likeness.

thus aims at emphasizing differences

judgment becomes

plural

words, that differences

in this respect; in other

of colour-sensation are contrasted with the

But

particular.

is

it

and exceptions the aim is

clear that this

by a singular judgment whenever its subject is denoted by the general name instead of the proper name. The judgment there is a comet which has broken up into two is particular in this

attained just

well

as

"

"

sense.

But the

4.

not meant us that not formula,

all

teaches that the particular judgment

logic

As

are B.

This

generally speaking,

for,

that

just this

is

traditional

to exclude the universal

some

A

s

is

it is

a

"

;

some

As

new proof

are

B

"

is

tell

of the ambiguity of the

certain that what

we do mean

are distinguished from the other

former interpretation has an element of

does not

truth in

it,

A

which

to say

Still

s.

is,

the

that the

judgment may both be proceeding towards a universal judgment to which it is preliminary, and be cut off from a universal as an exception to plural

As

it.

shown

a proof against the apparent immobility of the fixed stars, some of them have a motion of their own, and the

that

it

was

first

copulative

judgment

a Centauri, and 61 Cygni

their

was expressed as "some fixed stars have a movement of It was meant by this not that these three are on this

"

own,"

their

own."

account not fixed stars,

of

we have

them

"

all

-j

to

Sirius

have a movement of

but that while leaving them amongst the fixed

contrary to our old belief

perceived

movement

in certain

the

fixed

meant

stars,

and

judgment was opposed as an exception to the proposition stars are absolutely immovable." It was a particular judgment

express a distinction amongst the fixed stars. But as the number grew and progress was made with observations the

PLURAL JUDGMENTS

169

"some fixed stars have a movement of their own" was able new meaning that it is known certainly of some and is probable The former judgment presupposes the knowledge complete that a

same judgment to take the

of

all.

predicate belongs to

presupposes that our ticularity of the

some

A s and

knowledge

is

is

wanting to others, while the

is merely provisional. But the school logic does not generally take any notice of

5.

latter

a state of growth, and the par

only in

judgment

gress of knowledge through experience of the particular

;

its

this

pro

particular

judgments presuppose fixed conceptual relations and are only adapted But this logic falls into difficulties when to the interpretation of these. called

upon

to

show the

truth of

its

propositions by

Whence do

ciples of identity and contradiction. "

that

some parallelograms have equal diagonals

means of the

prin

obtain the knowledge

I

"

?

Not from

the concept

of the parallelogram, for this contains nothing about right angles ; and so doing I take some to even if I add parallelograms," though by "

"

"

has become only a part of the extension of the concept, the concept itself no more definite than before, and I cannot upon the strength of this addition say of the part anything which was not contained in the concept. If then no particular judgment can proceed from a mere explication, it

must be possible for us to define the idea of the parallelogram more and conceive it in a form which implies the predicate and is one among a number of other possible forms, or else this form must be

accurately

present in thought as constituting the subject of

however

state

it

in

denoting the subject

grams, but denote them merely as

The more adequate have

I

;

mean

diagonals

and

"

I

judgment.

do not

right-angled parallelo

parallelograms.

expression would then be the "

equal

some

my

one kind

of

"

parallelogram can

parallelogram has

equal

diagonals."

we should

Still

are

B

were

"

it

certainly not banish from logic

in the sense that

not for

"some

first

place.

it is

its

formula

"

some

denotes a part of the possible

the constant danger of

things for possible things, for plural in the

A

"

unwittingly substituting

A A

s s,

actual

actual things which are indicated by the

LOGIC

70

2 9.

NEGATIVE PLURAL JUDGMENTS.

II.

Exactly the same rules hold good

denied of a plurality of subjects

when one and the same

and

;

particularly to

it is

predicate

the judgment which denies universally may be either empirically or ditionally universal, just as the affirmative judgment may.

uncon

The COPULATIVE NEGATIVE JUDGMENT, 1 "neither A nor B nor C leads, when A and B and C fall under a common genus,

1.

are

is

be noticed that

P"

the plural negation

to

to the statement

P are many,

are not

"Several

which

TV

refers to the

are a

hundred."

and the negation concerning a

not

are

s

The

The UNIVERSAL NEGATIVE JUDGMENT

are ally

is

s"

number

nite

When

TV s which

this

statement

those

(

26).

A s which

are not 2?

s

originally obtained by the same process of reviewing a defi

as that by

examine a

I

"

again leads

the

exactly the same as was

is

single thing

"

between

relation

explained with reference to the affirmative judgment 2.

This

P."

number of the TV s,

which the universal affirmative judgment is obtained. number of trees one after the other to see

definite

whether they bear fruit, and must answer in the negative as to each one, up to the last, then I obtain the universal negation, which is appropriately expressed in the words "

none

"

one

"none

after the other

is

of

them bear

2

For by means of

fruit."

brought before

me

;

there

this

not one, ouSe

is

els,

1

This must be distinguished again from the conjunctive negation of different predicates with respect to the same subject (A is neither nor C, nor D); the import of this judgment cannot be made clear until later on. I consider it a burdensome superfluity of ,

terminology

to

make

use

of the expression

remotive judgment for the copulative

negation. 2

Thus

"

"no

"

person

no one

"

"nothing,

etc.,"

are not negative subjects such as the

make no statement about nothing" no one." When I no one is good except God alone," the subject of say my judgment is human beings," and their goodness is denied what I mean is there is none who is just, not even one." When I say "nothing hurts me," I do not mean that a thing called nothing hurts me, Aristotelian oik dvdpuiros

;

I

"

"

"

"

"

;

but that everything that might perhaps hurt me does not hurt me. But the appearance of the negation in the subject is most expressive of the way in which I seek, as it were, a subject for my predicate and find none. It is the same when no one"" nothing none," stands in the accusative, I see no one going, no one coming," e.g. gramma "

"

"

"

coming no one," appears as object of my seeing, actually it is the sight of a hear nothing," not only coming person which is denied. Again, in the proposition tically the

"

"I

the object, but the hearing itself disappears" it is false that I hear anything." From this it follows that (as well as "no one,") has no meaning except in a "nothing" to use it out of a ; proposition as the independent symbol of a concept, as famous Being, Nothing and Becoming, must lead to mere playing with words.

proposition in the

PLURAL JUDGMENTS

171

A

ne unus quidem, to which the essayed predicate belongs.

A

single

B would prohibit the universal proposition.

which was

This explains also the ambiguity of the negation, and the different meanings which may belong to judgments of the form no A is B" For on the one hand they pre "

A

suppose the existence of a number of us

is

B

that the predicate

On

fruit.

s,

absent from

is

and what they are meant to tell all existing A s, no tree bears

may be meant

the other hand, they

to

deny the very existence

(within the given spatial or temporal region) of subjects to which the

no tree is casting a shadow, no spring breaks predicate might belong through the sand. When I deny that an A exists which is B, it is pre supposed that I am trying to find a subject A of which the predicate

B

may be

affirmed.

may be

It

case "

when

the

fire is

Thus

:

the predicate

not

the judgment

denial that an

p.

A

"

which

no

A

an

will

s,

be the

were there

(cf.

124).

A

B

is

which

all,

if

burning,"

some

that I succeed in finding one, or

B or that I find no A at B could not be absent

but without the predicate

A

is ,"

It

exists.

immediate meaning the only secondarily, and in cases

has for is

its

where the predicate might be absent from A, that the proposition might are all A be expressed as "the A s which are not

B

3.

From

this

s"

follows again that this formula

it

A

adequate only when particular

s

are in

A

"no

view, and

"

is

the

as

is

result

of

when therefore it represents a judgments concerning particular A s But if we wish to say that the predicate is excluded narrative judgment. by the subject-idea, hence that anything which can be named as A is on ;

account not- B,

that

then

A

the adequate expression

"

is

A

is

"

not

or

only our habit of always return makes us use the uncondition which and the concrete to intuitable, ing universal well as the affirmative) with reference ally negative judgment (as "it

to

is

impossible for

"

things,

particular

either as to

their

to be

even

cannot know the future

question

of

the

subject-word. manded,"

manded."

but

in cases

where no question

number, or even their existence.

no man can know the

existence,

It is

B"

the

future,"

"

;

for

prophet.

existence

my

it

would be more correct

is

to say

"

man

obvious when modal predicates

particular thing

corresponding

to

the

do not say "no ghost exists," "no murder is com murder can never be com ghosts do not exist,"

We "

directly raised

judgment denies the possibility, not the

This

of any

is

Instead of saying

"

LOGIC

iy2

THE NEGATION OF PLURAL JUDGMENTS.

III.

30-

When is

a universal judgment

actually stated in the

is

denied, the negation applies to what

judgment;

that the subjects to

viz.,

are predicate belongs or does not belong The negation of all A s are term.

which

all "

"

means

which the

under the subjectthe A s which are

fall "

B

and the way in which we understand the negation must depend upon whether the judgment was intended as empirically or as are not

As

all

"

;

unconditionally universal.

negation of the empirically universal judgment tells us that there is an exception ; that of the unconditionally universal judgment

The

actually

only that an exception

is

possible.

and

Aristotle taught,

universal affirmative

is

logic

and

constantly repeating his teaching, that

particular negative

and universal

judgments,

negative and particular affirmative judgments, are contradictorily opposed.

This doctrine leads to false conclusions unless attention

is

paid to the

between empirically valid and universally valid judgments. The real character of the judgments we have so far considered

difference 1.

brought out most clearly by the negation. or plural is

subject

is

negation of a copulative

judgment has more than one meaning, inasmuch as that which the whole connection between

may be merely the plural, or and predicate. The difficulty is

false

The

especially great in obtaining

any

If it is from the negation of a negative statement. that neither Peter nor Simon Magus were ever in Rome, that does

definite statement false

not

tell

me

whether both were there, or which of the two ; from the it is false that several comets have brought misfortune I

statement that

do not know whether only one has brought misfortune or none

The

at all.

negation of a numerical predicate disputes the numerical predicate

itself in

the

first

place, but

further.

If

it is

false that ten

less or

none

A

2.

at all

more

it is

left

uncertain whether

it

does not extend

houses are burnt down, then either more or are burnt down.

definite value attaches, according to the ordinary doctrine,

to the negation of a universal

When "

ing

a negation "

all

it

is

judgment whether affirmative or negative. advanced against an affirmative judgment concern

annuls the statement that the number was complete without the universality

exception

;

judgment

says,

"there

is

no

is

denied.

exception,"

Since the affirmative universal its

negation says,

"there

is

an

PLURAL JUDGMENTS is

know

If I

exception."

one which

at least

to

it

is

be

ravens are black, then there

false that all

not black

hence

;

can say

I

173

"

one raven

is

not

black."

Suppose the negation is directed against the proposition "no A is B" according to what was said above this means "there is not an A that is

;

j5,"

so that as a consequence of the negation

which

is

B.

If

is

it

must be true that there

it

no raven

false that

white, then there

is

is

an

is

A

a white

raven.

Thus, the principle of contradiction and of the twofold negation being

(De

interpr., 7, 17

judgment,

i.e.

If,

1

the teaching of Aristotle

"

applied to propositions with the predicate

all,"

6) follows directly from the

meaning of the universal

avTiK^lcrOat Kara^acrtv dTro^durei avrt^artKais rrjv TO

:

aura)

TU>

O

on

ov

oiov Tras

Ka.0dA.ou,

corn rts

ouSets aV0pa)7ros AeuKos

?,

Ka@6\ov

AevKos

avOpwiros

ov ?ru9

This

A.et>K09.

ai/$pa)7ros

falsified by the thoughtless perfectly correct, and has not yet been some for ou TTUS and ris. 1 habit of substituting the plural

formula

is

"

"

But

3.

1

it is

The ordinary

correct only so long as

doctrine

is

that there

Contradictory opposition between,

is

All

and between,

s

are

Some A

s

No A

B

is

These two

latter propositions

Of the judgments

"some

A

B

are not

s

are

B

s

are

No A

s

are B.

cannot both be

true,

B

A

s

are

some

B

B

A

All

contrary opposition between,

passing from uncondition-

:

A

Some A

And

we avoid

s

but

may both

are not

be

false.

Aristotle rightly says aVrimrcu fj,6vov because the ,"

(Anal, pr., II. 15, 63 b, 27) TO TLVI ry ov nvl /caret, TTJV \ei;iv subjects are quite different. To these judgments modern terminology has given the absurd name of sub- contrary ; both, it is said, may be true, but both cannot be false. (If we "

"

A

B

A

B

the subjects are s are not some "some s are the same, the denotation alone being indefinite, then the propositions would naturally s are meant.) be contradictorily opposed but the expression leaves it undecided which lead us bears witness to the difficulty into which the ordinary doctrine seems to

assume that

in the proposition

"

A

;

A

justice of our

view as given above

;

viz., that

the contradiction between universal and par "

as the all judgments of opposed quality is the simple consequence of regarding As an instance of this difficulty, the two propositions "light is matter light predicate. is not matter are contradictorily opposed and one is necessarily true ; while the equiva no light is matter" are said to be in contrary lent propositions all light is matter The difficulty is solved when we opposition only, and may therefore both be false. notice that in the second pair of judgments an entirely new subject is introduced, which "

ticular

"

"

we are speaking of light, not according to its unity but From this it follows that the proposition "all light is according to its differences. matter is after all an inadequate and not completely equivalent expression for "light is involves the assumption that "

matter."

,

LOGIC

74

ally valid

judgments which are empirically valid and

to

judgments

vice

vers&.

The

universal

intended by means of the more intuitable universality when affirmative, the necessary connection of subject and predicate

judgment, which to state,

directed against an unconditionally

may be

negation

is

;

exclusion of the predicate from the subject. negative, the necessary In this case it can deny only what was meant, and says that in the first

when case

not necessary, in the second that

it is

But

to the subject. predicate to belong

to

must not be taken

belong to one or some

mean

to

actual

As

;

not

or does not

would be quite inadmissible

it

The statement

that

is

it

to apply

false that all

are sinners (in the sense of the sinfulness inherent in their nature) does tell

some men

us that

judgment sinned."

"all

If

men

it is

are

false that

some were

On

and the empirical because all have true,

are actually not sinners

sinners"

no man

negation of an impossibility, or

which has nothing have been enumer

B belongs

that the predicate

the relation of contradiction here.

men

not impossible, for the

is

with the presupposition that particular subjects

do

ated,

it

this negation,

it

might is

still

be

entirely bad,

;

"

in

the sense of the

would not on that account be true that one

in reality entirely bad.

the other hand, the negation of an empirically valid particular judg

ment can never be

the ground of an unconditionally universal, but only of

an empirically universal judgment. If it is false that there is anything living which has not had its origin from something living, then the propo sition omne vivum ex vivo is true in the sense that everything living which is

known

to us has

had

its

origin from

something living. (Bu^whether it an absolute necessity, is still that there are men who live over 200 years,

follows from this that the proposition states

disputed.

It

may be

false

but this gives no ground for the judgment in the sense that

it

would be impossible

to

"

no man be a

over 200 years

lives

man and

still

to be

"

more

than 200 years old. It is characteristic of the inferences of empirical science that

they pass

from empirically valid judgments to universal judgments which are un But their justification for so doing can be found conditionally valid. neither in the doctrine of the contradictory opposition of universal particular judgments, nor yet in the ambiguity of the

the difficult task of a theory of induction to ditions the transition

which

is

may be made from an

universally valid.

"

"

all

;

and

and it

is

determine under what con empirical judgment to one

PL URAL JUDGMENTS

1 7

5

The real import, then, of the universal and particular judgment with 4. which Aristotle and the traditional logic were concerned, and to which they attributed so "

viz.,

much

importance, was not that of the ordinary theory, whole extension or to a part of the

that a predicate belongs to the

extension of a subject

is

concept,"

but that the connection of a predicate with the The whole interest attaching to the

necessary or possible.

absence of an exception

lies in its

indication of a binding law

interest of the exception in the fact that

it

;

the whole

points to a plurality of possi

bilities.

This brings us naturally to

and the possible with reference

the closer investigation of the necessary to judgments.

CHAPTER VI. POSSIBILITY AND NECESSITY. to necessary for our immediate guidance, and before proceeding and the the to necessary, to treat of the logical questions referring possible

IT

is

lay

down a fundamental

possible or necessary

is

The statement

distinction.

that a

not the same as the statement that

possibility or necessity of

what

is

assertorial

Aristotelian

proposition

avay/o/s inrdp^fLV

:

;

stated in the judgment.

The Kantian which they

or apodeictic, applies to the former; the

Tracra

Zamv

TrpoTCKrts

rov ei/Se^eo-^at virap-^av

rj

to the

the latter to the objective

distinction of the differing modality of judgments, according to

are problematical,

is

possible or

The former refers

necessary for a predicate to belong to a subject. subjective possibility or necessity of judgment

judgment

it is

v)

(Anal

rov vTrap^eiV pr.,

I,

2,

77

rov

e

24^, 31) to the

latter.

I.

THE

SO-CALLED

MODAL

DISTINCTIONS.

31-

The

so-called

A is perhaps B]

PROBLEMATIC JUDGMENT in so far as the

"

A

may be

B

"

(meaning that

consciousness of objective validity

is

absent,

cannot properly be called a judgment i.e., it is not a judgment concerning that which is denoted by the subject of the proposition. It is a judgment ;

only in so far as

it

states that the

speaker

The so-called ASSERTORIAL JUDGMENT

is

not differ essentially from the apodeictic judgment that

A

is

when we its

in if

B)

;

for

every judgment of which

give utterance to

utterance.

it,

A is B. A is B} does

uncertain as to whether

(the simple statement

we

(it is

necessary to affirm

are completely conscious

includes the affirmation of the necessity of

judgments differ with respect to the way which the certainty is attained, whether it is immediate or mediate; but we were to ground the distinction between assertorial and apodeictic It is

true that the

this difference, then the apodeictic subordinate place, as having only a derivative certainty.

judgments upon

would take the

POSSIBILITY The

AND NECESSITY

177

between a statement which is merely possible and one does not appear in the case of immediate judgments necessary, where subject and predicate are found to agree without further mediation. 1.

which

distinction

is

Such judgments are formed according to the principle of Agreement with a confidence which is not the result of reflection. But it is different with mediated (synthetical) judgment such as takes place

when we form not

ideas of syntheses between definite subjects and definite predicates

These ideas may be due yet contained in the subject-idea before us. either to external stimulus, the questions or statements of other people, or they

may

arise

But

from psychological combinations.

internally

in

may be no ground capable of yielding a consciousness of objective validity in the synthesis, and then what we have is merely the idea of a synthesis which remains in suspense as a question or conjecture,

either case there

and awaits some decisive

Here the judgment necessary at the

is

certainty to confirm or

and

thought of as possible

moment

deny the predicate. means that it is not

this

person thinking about

for the

it

either to affirm

Such a judgment (A is 2?) which is merely thought of as possible and not yet affirmed, may be briefly denoted as the hypothesis A is and the simplest expression of this stage between synthesis and /?,

or to deny

it.

judgment is the question. This is genuine only when expecting yes or no for its decision when asked by one who has already made up his mind ;

for

the

one

sake of testing some

else,

it

not a question, properly

is

But while the question expresses the first seeks confirmation or rejection, it is which the of hypothesis conception if neither is found followed by the consciousness of indecision which is speaking, but an imperative..

n

expressed in the formula

formula so often used

"

A

"A

may

expresses both the objective

This form of statement, then,

(The perhaps B, A is perhaps not B. is ambiguous and misleading, for it be

is

B

"can"

"

(Svvacr&ai)

and subjective

hesitation.)

from the question only by expressing While the question to decide the question. differs

our consciousness of inability contains the wish for decision, this form denotes the resignation which

Both really express the same is obliged to remain in uncertainty. thought that of a synthesis concerning the validity of which we are undecided. 2.

This expression of uncertainty

is

generally called a Problematical

Judgment, and Assertorial and Apodeictic Judgments are opposed to expressing different degrees of certainty. 1

Cf. e.g. S. L-

Ueberweg, Logik,

ed. 3,

1

Kant

it

as

himself, indeed, gives a

69, p. 164 sq., ed. 5, p. 207; Drobisch,

61,

N

62.

i

LOGIC

8

7

somewhat

meaning to the problematical judgment.

different

He

tells

us

to the contents of (Kritik d. r. V., 9. 4) that modality contributes nothing which value the copula has with the but is concerned the judgment, only for

Problematical judgments are those in which

thought in general.

we

accept the affirmation or negation as merely possible (a matter of choice). Assertorial judgments, those

which

in

it

is

regarded as actual (true).

The Apodeictical judgments those in which we look upon it as necessary. Kant to of the extends problematical judgment arbitrary acceptation judgments which are obviously false they have a problematical signifi cance if it is thought that some one might perhaps for a moment accept such ;

a

On

proposition.

ment

to

when

its

the

mean one

1

every judgment

vTrofocris,

moment

not at the

is

validity

which compares the problematical judg

this view,

Aristotelian

we must

of two things, between which

is

problematical

But

expressly stated. distinguish.

this

The

may

reason

is stated concerning the validity of a judgment in Thought be that can be stated, because the speaker has not yet come may nothing to a decision; or it may be that the speaker will not state anything

why nothing

its

concerning

validity,

being to treat a valid

On

certain.

ulterior

purpose leading him for the time

as invalid,

judgment

or an uncertain judgment as

point the traditional Logic has not followed Kant, and

this

Kant himself

some

in his

Logic (Intr.

ix.)

means by the problematical judgment

nothing more than an uncertain acquiescence. But the custom of denoting the proposition 3.

"

"A

is

perhaps

a problematical judgment, threatens to destroy the concept of the

as

judgment

The be

and

itself,

to fall

into

essence of the judgment

and

true,

and leaves If every

it

An

calls for belief.

open

judgment

is

contradiction with

all

other teachings.

to present a statement

which claims to

utterance therefore which states nothing

for the opposite to is

be

true, is

not a kind of judgment.

either the affirmation or the negation of a question,

then an utterance which neither affirms nor denies cannot be a judgment ; for to leave the question undecided is no decision, and to be uncertain not a degree of certainty.

is

1

According

thing which

is

be certain, and

Programm p. 2.

A

:

to Aristotle, the

or it

is

not

;

virbde
the judgment

must be conceded

Beitrdge zur Lehre

justification

introduced above.

may

The law

vom

is is

of contradiction notwithstanding,

a merely assumed judgment concerning some not certain, or at least it is not proved to

if it is to

be used in conversation or proof.

Cf.

my

Urtheile (Tubingen, Laupp, 1870), also be found here for the use of the word which I have hypothetischen

POSSIBILITY

AND NECESSITY

179

A is perhaps B" and A is perhaps not B? would both be true together. So far, then, as concerns A, the so-called problematical judgment is

the two propositions

not a judgment at at a

attempt is

"

is,

is

B

unfinished

in the formula

"A

Immediately,

is uncertain."

instance, this

first

person who

is

:

have no ground either

I

A

the hypothesis

"

made

only real statement

is nothing but a judgment concerning the his relation to the hypothesis A is B, concerning speaking, formula says I do not know whether the hypothesis is valid or not,

the

in

The

The

the

only the thought of one,

is

it

all;

judgment.

B

perhaps

and

"

"

sent condition of

for

it

;

states the pre

it

A.

validity with reference to

We

affirming or for denying

thought, but nothing which could have objective

my

wider meaning to the formula by taking it to mean, not merely that 7 do not know whether A is j5, but that it is not known whether A is B\ thus regarding the uncertainty as something more

might

try to give a

than a fact peculiar to the individual, as always attaching to the proposi But apart from the fact that the words do not mean this, even

tion.

this statement could not lead to a judgment concerning be co-ordinated with positive and negative judgments.

A

which might still have

We

only a statement concerning a subjective attitude, though an attitude not

sum total human many questions we

peculiar to the individual but due to the present position of the

of knowledge, or, which intelligence.

It

is

is still

more

general,

due

to the limits of

quite true that with reference to

can get no further than stating the impossibility of a decision, and that such knowledge has its value when we are measuring our human capacity by the ideal of knowing. Nevertheless it states nothing which could be taken

For an ideal consciousness, an omniscient

as a judgment concerning A,

one proposition is true, the other false ; not until we are certain of the one or the other have we realized the aim of thought, a intelligence, the

judgment which

is

objectively valid.

Until then, the hypothesis remains

only confusing to subsume the expression of subjective uncertainty and the expression of the certainty of the

an unsettled problem, and

objective

Hence "

validity of

the

only

1

is

is

a proposition, under

possible

the person forming

but

it

negation

the judgment

of is

one concept as judgments.

the problematical judgment

not

uncertain whether

Not only Wundt 473

sq.),

(Logik,

I,

p. 197.,

cf.

my

is

,

negation."

reply in the

but Windelband as well (Strassb. Abh.

is

1

certain either of the affirmation or of the

Phil., iv.

A

t

p.

Vierteljahrsschr. filr wiss.

185

sq.),

has defended the

LOGIC

i8o

We

that the so-called problematical judg must, then, cease to teach that the concept of the judgment hold ment is a kind of judgment, if we

The latter endeavours to show from the this view. problematical judgment against been discussed above, p. 122 sq. that the problematical judgment is position which has that it is a third kind of the co-ordinate with the affirmative and negative judgment ; of a given combination of ideas. relation" which is expressed in the criticism "practical "The

critical

of gradual probability

judgment, like

The

variations." ;

these represent

other functions of approval and repudiation, is capable gradation of certainty appears in the different degrees of different intensities of the feeling of conviction, a feeling

all

which applies both to negative and to affirmative propositions.

"We

may

think of

these different intensities of probability as represented by a line ; at each end we have at the one, and of negation at the other ; and these, by certainty, of affirmation

complete

a gradual diminution of the certainty, approximate to a point of indifference where This zero point has two meanings, for the there is neither affirmation nor negation." Total indifference between positive and negative reaction may be either total or critical. indifference occurs,

first,

in all those trains of thought

which are accompanied by no

secondly, in the question where ideas are combined without any decision as to the truth of their combination, but still with the desire for such a decision. Now since the question contains no decision as to the validity of the thought, Windelband

estimation of the truth

;

does not co-ordinate it (as Lotze attempts to do) with the affirmation and negation as But when we are led by consideration of the ideas combined another kind of judgment. in a question to the conclusion that there is no sufficient ground for certain, or even then we get the problematical judgment, which signi probable affirmation or negation, B. fies that nothing is to be said concerning the validity of the ideal combination A This is intentional suspension of criticism, critical indifference. Such conscious refusal,

come to any conclusion is, says Windelband, quite decisive as to the position assumed by the person judging towards the combination of ideas, contained in the question therefore, when we divide judgments according to their quality, the problematical must be co-ordinated with affirmative and negative judgments. Of course I fully recognise the truth of what is here said as to the import of the socalled problematical judgment and acknowledge my obligation for the distinction (which I have adopted) between the problematical judgment and the simple question. But I cannot Even from Windelband s point of help drawing an exactly opposite conclusion from it. view, that affirmation and negation are both alike criticisms of the value of an ideal com The relation bination,! fail to see that the suspension of criticism is a kind of criticism. between the three forms of judgment cannot be that of co-ordination. Either I cannot come to any decision or I can if I do come to a decision, I must decide either in the Thus it is only affirmation and negation which are co affirmative or in the negative. ordinate because they are divergent kinds of decision, and both are opposed to indecision this is what I wished to show. If I have no knowledge on any matter unless I can either to

;

"

"

;

;

affirm or deny, then the

deny is only a knowledge judgment about myself and not about the Nor can I agree that because certainty is a feeling and all Cer feelings present differences of intensity, therefore there are degrees of certainty. tainty, if we take the word in its strict sense, is either present or not anything which is

of

my

knowledge

subjective inability ; subject of my proposition.

it

is

that I can neither affirm nor

therefore a

;

not absolutely certain

is uncertain. It is true that certainty manifests itself immediately in consciousness, that there is a feeling of certainty just as uncertainty, the wavering between opposite probabilities, manifests itself in feeling. But then the opposition is not ;

between certain affirmation as one extreme and certain negation as the other, with un certainty as a transition between the two ; it is certainty and uncertainty which are

POSSIBILITY

AND NECESSITY

181

includes the affirmation of the truth of the statement made, and

teach that a judgment must be either true or

The

4.

traditional doctrine

is

not

much more

successful in

between Assertorial and Apodeictical Judgments.

94;

V.,

Kant

30) that the assertorial judgment

Logik,

if

we

false.

is

its

distinction

says (Krit.

d. r.

accompanied by

the consciousness of the actuality of judging, the apodeictical judgment by the consciousness of in the assertorial

its

necessity; is

judgment

and according

to this all that

is

needed

that a statement should find utterance in

words, the consciousness of the necessity of the judgment being unessen

In the introduction to the Logik,

tial.

again, the assertorial

ix.,

appears as the expression of a merely subjective belief, which for me ; while, on the other hand, that which I know is apodeictically certain, validity for every

one

i.e.

a

necessarily having

even though the object of

should be a merely empirical

universal

is

judgment valid only

said

to

be

and objective

assured conviction

this

truth.

According to this distinction the assertorial judgment would also be excluded by our definition of the judgment ; for in this we make the claim to objective validity an essential characteristic. Indeed, from this point of view the judgment has but one meaning, that every one must affirm and believe the same, because

speech would lose play or that

its

ment

lies

if,

is

wrong

;

false,

i.e.

is

necessary to affirm and believe

serious meaning,

when we

negation

is

all

it

if

and

stated a proposition,

and the

degenerate into

we did not

also

Our

it.

mere

child

mean

to

s

say

making an incompatible state between an assertorial and an

that any one distinction

the former apodeictical judgment were that while the latter is necessary is true former the one is not, that while the latter is true for every only for

me.

Truth has no meaning except

this necessity of

our subjective action.

Even the merely temporal statement concerning the most casual particular phenomenon this iron is hot presupposes that at the moment it is

My

necessary to judge in this way and not otherwise.

connection between

this subject

and

this

predicate inevitable,

question were raised whether or not the iron against for

my

all

sensation

is

hot,

I

makes the and

if

the

should maintain

contradiction that in no other statement could I find expression

sensation.

If the doctrine that opposed, and certainty belongs both to affirmation and negation. we must regard the distinction degrees were consistently carried out,

certainty has

between opinion and knowledge as merely which has degrees.

relative.

It is really

only the hope of certainty

LOGIC

i82

Here, then, there disappears

5.

assertorial

unless perfectly complete judgment that this

is

so

the certainty of

"

;

my

essential difference

all

When

and apodeictical judgment. it

means

in different cases,

grounds

"

say

"this

is

between the

so,"

it is

not a

must of necessity judge

I

statement rests entirely upon the pre

supposition of this necessity. All that remains of the distinction different

I

is

and

that the necessity rests

that

we become conscious

upon of

it

in different ways.

With reference

6.

to the

first

point,

we may begin by

between immediate and mediate judgments.

judgments

(in

specie analytical) the necessity

the predicate of the subject

distinguishing

In the case of immediate of affirming

(or denying)

the principle of agreement

is

grounded upon in the case of mediate judgments, either (or of difference) upon Immediate judgments authority or upon some process of inference. ;

either (as in perception)

upon individual experience as the ground a predicate to a subject, or upon the generally recognised meaning of a word. The same distinction between a ground peculiar to depend

for attributing

the individual and one accessible to

all,

divides mediate judgments into

those which depend upon authority and those which depend upon a process of inference. The fact that I take some one as an authority is a ground

which holds good only is

for

me

as

an individual, so long as

not established and proved as universally valid

ence cannot be binding upon starts from the same data.

me

unless

In this way the distinction has been

it is

;

his credibility

but a process of infer

binding for every one

made between immediate

who

certainty

is

(which

grounded upon perception by ourselves or by others), and mediated certainty which is grounded upon proof though really the certainty grounded upon the perception of others ought rather to be counted as mediated, and immediate certainty is not confined to percep tions alone. The assertorial judgment has been reserved for the former kind of certainty

The -ff,"

distinction

and

"A

;

is

the apodeictical (wpoVao-is ttTroWrt/^) for

borne

must be

JB

out,

n ("

which

is

the

moreover, by the customary formulae,

must

"

latter. "A

is

being taken as the expression of that

merely inferred, as in the proposition it must have rained last But then it becomes to necessary give up the ordinary notion that the apodeictical judgment denotes something higher than the asser "

night.")

torial

there

;

is

and

that in passing from the problematical to the apodeictical an increase cf certainty, and therewith of the value and dignity

POSSIBILITY

AND NECESSITY

183

For every mediated certainty must ultimately

of the judgment.

rest

upon that which is immediate every proof upon premisses which need no proof themselves. It is curiously at variance with the emphasis laid ;

upon apodeictical certainty that in ordinary life the ment must be must have happened "it

so,"

moderate degree of confidence which

apodeictical

;

and

judg

denotes only a very

so,"

because we have good grounds

this

for distrusting the certainty of ordinary inferences,

that

"

"

"it

and

prefer to trust to

But even when the most

is

rigid immediately perceived. presupposed that which is proved can never claim a higher degree of certainty than the data from which it is proved.

proof

is

Other writers seem to have

view rather the difference between

in

propositions which hold good with absolute

universality,

depend upon conditions peculiar to

the individual

necessity of reason

as

is

characterized

and those which

as

;

apodeictical,

in

when,

e.g.,

the

opposition

to

In this way Leibnitz distinguished between necessary truths and truths of matter of fact. 1 Necessary truths are those whose

matter of

fact.

opposite contains a

whose opposite propositions;

is

contradiction

possible.

the latter

rest

formulating the distinction

;

truths

are

of matter of fact

The former may be reduced

to

those

identical

upon immediate sensation. This way of to show that the subjects referred to by

fails

necessary truths, and those referred to by truths of matter of fact, are not of the same kind. Necessary truths of reason set forth comparisons

between concepts, which are assumed of

be the unalterable possession

to

23, p. 145 sq.) only upon (according to can be said of a proposition that it is contradictory, hence that its such truths correspond to Kant s analytical judgments. opposite is true It

all.

that

this presupposition

is

it

;

The

subjects of truths

existence,

existence

and and

of matter of fact are things having a particular

truths of matter of fact, so far as they have reference to to changeable events, certainly tell us

something which

is

not contained in the concept of the thing ; for it is no part of the concept of the thing that it exists, nor yet that it happens to be constituted in one 1

Leibnitz, Princ. phiL, raisonnement et celles de

33 (Erdm.,

p.

707)

:

II

de y a deux sortes de verites, celles

Les verites de raisonnement sont necessaires et leur oppose est impossible, et celles de fait sont contingentes et leur oppose est possible. Quand une verite est necessaire, on peut en trouver la raison par 1 analyse, la resolvant en idees et en verites plus simples jusqu a ce qu on vienne aux primitives 35 ce sont les enontiations identiques, dont 1 oppose contient une contradiction expresse. ce sont Nou-v. Ess., iv. i Erdm., 340 Pour ce qui est des verites primitives de fait, Cf. DC scientia les experiences immediates internes, d une immediation de sentiment. fait.

...

;

-

universali,

Erdm.,

p. 83.

:

:

i

LOGIC

S4

them, therefore, involves no such logical con But because the is not triangular.

To deny

particular way.

tradiction as to say that a triangle

is not a priori impossible, it does opposite of a truth of matter of fact not follow that it is not necessary for me to state the fact after it has

happened

;

or that the opposite statement

knowing the it

for

any one

;

but with them the impossibility

upon the ground of individual experience, not

unalterable concepts from which

ness

would be possible

truths of matter-of-fact are truths only because

impossible to state their opposite

is

rests

Even

fact.

is

I start.

upon the ground of the Even when immediate conscious

translated into a proposition of objective validity,

that the sensation

is

referred to existence

to universally valid principles.

and an

it

is

presupposed

existing thing according

Truths of reason are contained even in

inasmuch as no true judgment can arise out of individual experience except in accordance with general principles (e.g. truths

the

of matter of

principle

which

it

that

fact,

every change presupposes a permanent

takes place).

On

the other hand,

concepts upon which identical matter of

subject in

our possession of general

propositions are

based,

is

in

the

last

something which must be there before the principle of identity can be applied and give rise to a necessary judgment. Thus the necessity of both kinds of truths is, finally, hypothetical. If I instance

fact,

think in definite concepts, I must predicate of them what I think in

and

them

;

have certain perceptions I must predicate of the perceived Even this dissubjects what these perceptions force me to predicate. 1 if

I

1 It may be objected here that the senses deceive us, and that while it is impossible to doubt the proposition A = A, it is possible to doubt the existence of the whole material universe. This is quite true, but in no that judgments way invalidates the

proposition

are true only in so far as For if we assume that our empirical they are necessary. sensations are purely fortuitous, differing for each individual and as inexplicable as dreams in their occurrence, we could make no statement as to an existent, or indeed any universally valid statement at all, but then neither would

any empirical judgment, except such a? referred to our momentary affections, be possible. If, on the other hand, we assume that though sensations are indeed subject to a necessity which is the same for every one, yet both this necessity and its law are unknown to us then again we can form no judgment concerning external existence. This is really the case so far as concerns the question as to the ultimate nature of the existent which we and for feel,

this reason

we

get here only conjecture and hypothesis, not judgments which can be announced as true. But wherever we are persuaded that we recognise necessity, in the processes by which we form judgments from sensations, there we find judgment which is assured and a conviction of its truth. know that we have a accompanied

by

We

sensation of this or that colour, that we are obliged to assign to it a definite position in space and that we must regard it as the colour of some definite phenomenal object ;

whether

this object is

mere phenomenon or the phenomenon of something

existent

and

POSSIBILITY

AND NECESSITY

tinction disappears so far as the nature of the necessity it is

is

185

concerned, and

only the ground of the necessity which differs because the subjects of

the judgments differ.

There

is

no doubt

that our consciousness of the necessity of connecting

a subject with a predicate

may

Many immediate

arise in different ways.

judgments are affirmed by us unhesitatingly and without reflection, without a suspicion that we may be wrong, or that the facts may be otherwise. Absolute certainty and unalloyed confidence in our act of thought is here itself, and with such judgment our thought always

inseparable from that act

The announcements

begins.

statements of what

of immediate self-consciousness,

as well as

immediately evident, whether in intuition or universal are accompanied by no feeling of constraint, such as we might is

judgments expect from the necessity of which we have spoken, nor yet by the thought of the possibility of the opposite ; not until some attempt is made at con tradiction are

we conscious of

strained to certainty because

all

this.

With other judgments we are con

other possibilities are cut off; and in the

consciousness of this constraint the judgment and

themselves together. otherwise, then

If

we may

we

its

certainty

present

define necessity as the impossibility of being

say that only the latter judgments are accompanied

by a consciousness of necessity, not the former.

But

it is

that

immediate security and certainty which

is

the original

and

genuine form which necessity assumes in the sphere of thought in it we And nothing see thought at work in its most active and powerful form. ;

The attempt to can completely replace this immediate self-evidence. maintain a contradiction may indeed serve to confirm the sense of security, and

to

measure the force which

is

exerted in a statement

;

but the validity

of the original proposition must, generally speaking, be presupposed before

we can

see that

tablished that is

not

A

its

B contains a

the proposition,

opposite

;

still it

opposite

is J5, is it

it

is

is

impossible.

Only when

it

has been es

immediately clear to us that the proposition

A

The

twofold negation does not create it circumscribes merely by cutting it off from its in this form that we become expressly aware of the

contradiction.

it and again returning to it. Just as we first conscious of identity through negation of the other, explicitly of affirmation through negation of the negation ; so also we become

truth

by withdrawing from

become

what the nature of this existent may be all this is matter of dispute, and the view which is taken determines the sense in which a judgment concerning matter of fact is true.

LOGIC

186

conscious of necessity through the impossibility that it should be otherwise. But necessity is already contained in the thought which elucidates it ; the affirmation only because this process negation of the negation confirms the is itself

immediately certain in every step is

necessity

and

thought,

that

it

takes.

The

true

and

original

which predominates in all our that reason cannot be brought into consciousness at

unreflecting necessity

just for

every point.

We might distinguish between assertorial and apodeictical judgments by saying that in the case of the latter we are expressly conscious of their necessity, which therefore finds expression in words ; while in the case of the former the necessity

Then we should have

undifferentiated from the act of

is

hit

upon a

really existing difference,

not indeed to the degree, but to the kind of certainty proposition.

But

it

a difference which

is

which shows how that which

is

is

judgment itself. which attaches, belonging to a

entirely psychological,

and

dependent upon conditions peculiar to

may though accompanying the same judgment appear It is a difference, moreover, which one way, now in another. the exact opposite of what we mean by the ordinary expressions,

the individual

now

in

signifies

the apodeictical form

for

"

A

must be

B

"

and of the conceivability of the opposite; spection from

A

to

B>

reminds us of the doubt, it proceeds with circum

while the assertorial judgment makes straight for

when the judgment is an inferred one that the asser torial form expresses more complete confidence than the apodeictical, which seerns to challenge us to test the proof. Thus the former is always mark.

its

the

It is just

more

certainty

;

natural,

because the more direct expression of apodeictical

even logic states the conclusions of

its

syllogisms in the asser

torial form. It

might be objected to

this that

the speaker troubling himself but

This

is

true,

as true as

it

is

many

little

that

refute the proposition that the act

statements are

made

at

random,

as to the necessity of his statement.

many

lies

are told.

But

it

does not

of which the sober statement

is

the

adequate expression involves the declaration of the necessity of the judg ment, and that it is in this way that every one understands the statement. Else would speech be without thought, using words without meaning; or burdened with falsehood and presenting as certain that of which the speaker is not certain. It has nothing to do with logic that many falsehoods are thus spoken in the

strife of interests and party ; for logic presupposes the desire of speaking, as well as of thinking, in accordance with truth.

We

AND NECESSITY

POSSIBILITY grant also that

of

its

it is

only gradually that this desire of speaking and thinking

becomes conscious

the truth

But before

aim.

this

;

at first

;

judgment owes

its

merely an impulse unconscious is clear the speaker knows not

there, but

is

not free and conscious

it is

manifested in the certainty of par-

distinctive character in the last instance

Every particular judgment may be

the unity of self-consciousness.

to

is

it

consciousness

what he is doing judgment is indeed and has not yet come to full maturity. The necessity of thought which 8. ticular acts of

187

repeated with the consciousness of the identity of subject and predicate as well as of the act of judgment ; starting from the same data it is always the

same

exist

synthesis which takes place,

and our self-consciousness cannot

Thus our judging

apart from this invariability.

ego, with

its

un

as a universal,

particular acts of

is opposed to judgment same and the permanent which binds together the different and With the confidence of the move temporally separated acts of thought.

varying activity,

as the

ment

in

connected the consciousness of unvarying same point. In this constancy, which presents

each particular case

repetition, of return to the

a general

judgment

is

we

are conscious of

as something withdrawn from the sphere in

which we have a

law in contrast with the particular

act,

we are conscious subjective choice and are free to bring about alterations of it in the same way as when it maintains itself in some particular act ;

Because

against contradiction. is

this identity

the condition of our consciousness as one

final

and fundamental in

consciousness, there

as in

its

basis

and constancy of our action and undivided,

upon which we can

fall

completeness and comprehensiveness,

immature childhood

is

it

back.

also the

While

this

not

yet

is

so long the psychological conditions of

judgment are not yet fully developed. The case is the same in dreams, where only a few trains of imperfectly coherent ideas are aroused.

From

this

it

follows

meaning, to necessary

that each single act of

and universally valid laws

judgment ;

by its which are

points,

laws, that

is,,

universally valid both for the single subject in his temporally different

moments, and

for the various thinking subjects with

community of thought; laws which, at

first

whom we

stand in one

unconscious, serve only to bring

about the certainty of the judgment, but which, when raised into conscious ness, give us our fundamental intuition of something which is necessary. 9.

The

necessity of thought, which

tainty of the particular act of tion, is

first

becomes apparent

judgment and the

something essentially positive

;

it

is

invariability of

in the cer its

repeti

the immediate expression of

/

1

LOGIC

88

intelligence, the

consciousness

form of self-consciousness

it is

much an immediate

as

For

ego, or of being.

this reason,

it

is

and when brought

itself,

into

intuition as the thought of the

measure of the further

also the

In the sphere of judgment the concepts of possibility and impossibility. possible is that which it is not necessary either to affirm or to deny ; it is the suggestion, the attempt of a judgment, which

never decided and

is

completed, and cannot be taken into the unity of self-consciousness, or

woven

Mere

into the lasting

possibility

two meanings

;

is

fabric

which

The

a privation.

which

that

thought, at the most

it

is

as

impossible to

is

might be spoken thought corresponding to the words "the what Aristotle means when he says that it

same thing

certain as

my own

existence.

impossible, on the other hand, has

it

in

think,

words.

circle is

is

would never be

There can be no square,"

and

this is

impossible to think of the

for it is not same time being and not being On the other hand we have necessary to accept what we say as the possible which must necessarily be denied, the hypothesis which is quite feasible when taken by itself, but the affirmation of which would

as at the

"

true."

conflict with itself.

a valid proposition, and so place thought at variance with is to be found only in the sphere of the mediated

This impossible

judgment; the predicate may be thought of

as compatible with the subject because their incompatibility is not known analytically, and thus the pro position may be temporarily accepted so long as the truth opposed to it escapes consciousness only a thorough comparison between all our judg ;

ments brings about the negation of the possible. It is in this sense only that Leibnitz s distinction is correct, when he says that the negation of necessary truths

is

impossible, that of truths of matter of fact possible.

We may

attempt to state them, but our experience refuses to confirm, and forces us to deny them. 10.

From what we have

negation validity

i.e.

is

said,

a judgment which

it

follows that an actual affirmation or

we

only possible for those to

utter

with a consciousness

whom

it

is

necessary;

of

its

as far as

the

judgment itself is concerned possibility and necessity coincide. On hand the hypothesis is possible if and so long as it is not As the necessary, and therefore impossible, either to affirm or deny it. the other

expression of a subjective state of indetermination it may certainly be said to take a third place beside affirmation and negation ; but just for that reason it is not a

judgment.

AND NECESSITY

POSSIBILITY

189

32.

The

so-called

LAW OF SUFFICIENT REASON,

not a logical law at

is

Leibnitz,

as originally conceived

by

but a metaphysical axiom, which

all,

is

applicable to a part only of our judgments.

Inasmuch

we may has not is

as every

down

lay

judgment presupposes the certainty of

its

validity,

the proposition that no judgment finds utterance which

some psychological ground for its certainty and inasmuch as it only when it is logically necessary, every judgment claims to ;

justified

have a logical ground which makes it necessary for all who think. But it does not do more than raise a claim, the justice of which it falls to logic to investigate.

The nature of necessity in thought is expressed by when the ground is affirmed its consequences are also

the proposition that necessarily affirmed,

when the consequences are denied the ground This principle of Ground and Consequence corresponds to

and

that

also

is

denied.

the principle of

contradiction as a fundamental law of the operation of thought.

The

1.

paragraph seem to find their natural

results of the preceding

expression in the proposition that judgment cannot take place without a

mean

ground, for by the ground we

Thus an

necessary.

just

that

which makes a judgment judgment framed and

analysis of the import of every

spoken would give us the fourth of the so-called laws of thought; it would express the characteristic common to all judgment whatever i.e., that belief in the validity of the

But the law of

2.

to

it,

and

Leibnitz was the

thought.

judgment involves belief in its necessity. Reason has had various meanings assigned

has shared the fate of the other so-called laws

this

in

Sufficient

first

to give

the law of contradiction.

principle with

"

Our

Nos raisonnements

1

Frinc. phi!., 31 sq. ; Erdm. 707: principes, celui de la contradiction

du quel nous considerons qu aucun

it

a co-ordinate place as a

.

.

fait

.

et celui

de

inferences,"

he

of

first 1

says,

sont fondes sur deux grands en vertu

la raison suffisante,

ne saurait se trouver vrai ou existant, aucune

enontiation veritable, sans qu il-y-ait vine raison suffisante pourquoi il en soit ainsi et non pas autrement, quoique ces raisons le plus souvent ne puissent point nous etre connues.

In the de Scientia Universali (Erdm., follows

Omnis

:

veritatis (quse

p.

same principle as reddi posse rationem,

83), Leibnitz formulated the

immediata sive identica non

est)

vel expresse vel implicite proedicati semper notioni sui subjecti evident, therefore, that the principle as he understood it here was a are not identical are true purely logical one, according to which all propositions which On the other hand, there are only in so far as their necessity is syllogistically proved. in the Theod., 44 places in which he emphasizes only the metaphysical aspect, e.g. 1 autre (Erdm., p. 515) principe est celui de la raison determinante, c .est

hoc

est,

inesse.

notionem

It

is

:

.

.

.

i

LOGIC

9o

and based upon two great principles, that of contradiction that of the ratio suffidens, by virtue of which we assume that no fact is .

"are

this

is

it

true, unless there is a sufficient

no proposition

true or actual,

and not something

may be unknown

to

else,

not

It is

us."

although difficult

.

.

reason

why

most cases these reasons

in

here to distinguish the two

sides of the question, and to see that he is speaking partly of the actual existence of real things and events, partly of the truth of propositions. But

we must remember

that Leibnitz intends this principle as the

truths of matter of fact alone,

a

that with

Then

it

him the ultimate

becomes evident

real

world

and the

thing,

;

upon

state facts is

dependent upon

actual event or thing.

regarding

this

But

The

reality of those

that in

truth of

facts, their

the reality of the fact stated

and

this

so that in giving the real ground of a

the cause which has given rise to the

this just

shows how

little

we

are justified in

an absolutely universal logical

as

principle

;

name

I

fact,

and

of every real

must have a cause.

based upon the

the sufficient cause

of matter of

truth

contradiction;

always the Divine Will.

that the existence

is,

reality of every event,

truth being thus

is

no other than the principle of causation

is

the principle, that

propositions which

reality

ratio suffidens

ground for which state

that this distinction signifies nothing,

the principle of Leibnitz the

for the truth of propositions

while necessary truths rest upon the principle of

fact,

and

i.e.

law,

which

should rank beside the law of contradiction as valid in reference to the

same

propositions, or in trying to find in the Leibnitzian proposition a

ground

logical

distinct

from the real cause.

Such an interpretation

indeed excluded by the repeated remark that the ratio suffidens This is true only of real causes. frequently be unknown to us.

is

may

A

ground which we do not know is, strictly speaking, a contradic tion for it only becomes a ground Unless we through our knowing it. believe in the fiction that a judgment can be true apart from any intelli logical ;

gence by which

it is

we cannot

thought,

independent existence of

believe that

its

ground has an

own.

its

que jamais rien n arrive, sans qu il-y-ait une cause ou du moins une raison determinante, c est-a-dire quelque chose qui puisse servir a rendre raison a priori, pourquoi cela est existant plutot que non, et de telle Ce grand principe plutot que de toute autre fa9on. a lieu dans tous les evenements

Pr. de la Nature

et de la Grace, 7 (Erdm., p. a Mr. Clark (Erdm., p. 751). While yet again in the fifth letter to Clark, 125 (Erdm., p. 778) we find the full formula Ce principe est celui du besoin d une raison suffisante, pour qu une chose existe, qu un evenement arrive, qu une verite ait lieu.

716)

:

rienne se

:

fait

.

.

.

sans raison suffisante.

Cf.

Trots, ccrit

AND NECESSITY

POSSIBILITY If therefore

we

it

lay

down as a logical law that nothing should be we must certainly mean something quite

thought

without a ground,

different

from what Leibnitz meant.

3.

we

If

191

distinguish between the Real Cause

and the Ground of the

Judgment, between what makes it necessary for an existing thing or event to be actual in a given way, and that upon which the judgment is based as an act of thought, there still remain two very different meanings in which the word

From one

"

"

ground

may be

taken.

point of view every judgment, as an

actual

psychological

be regarded as something existent, and the conception of the causal relation and its fundamental principle is so far applicable that every event must have its sufficient cause. The cause of an act of judgment must be sought, in the first place, event in a thinking individual,

amongst psychological the

is

sum

gether with

its

total

The

act of judgment.

thus the

is

possible unless certain

psychological cause of a

of the necessary conditions of this particular

principal cause

is

the judging subject

itself,

to

and the laws which govern the manifes further consists in those states and preced

;

and

it

ing acts out of which this given

following conditions

The

;

faculty of thought,

tations of this faculty

a.

itself

no judgment

for

facts,

present to consciousness

ideas are

judgment

may

judgment

arises.

Amongst

these are the

:

ideas both of subject

and predicate must have been present

in

consciousness ; (this presence in consciousness implies causes which are still further removed, and which we may call the causa remotiores of the interest judgment, one of the most important being the will, as led by some in its desire to know and to think about an object). b.

A

must have taken place between the ideas of subject and because of an agreement which has led the activity of

synthesis

predicate, either

thought, in accordance with

its

synthesis was suggested by the

laws, to connect

manner

them, or because their

of their entrance into consciousness,

which gave rise to the thought of their possible connection. In the latter case something must have occurred to bring about a c. decision

either affirmative or negative, and,

includes the consciousness of tion of the certainty as

its

an actual

inasmuch as every judgment

validity, to afford a psychological explana

state of mind.

must be made amongst immediate mere ideas and those which con which connect those between judgments With immediate judgments of the first tain a reference to the existent.

From

this point of view a distinction

,

LOGIC

92

kind the principle of agreement (as expressing a law of motion for thought) sufficient to explain both the synthesis and the certainty attaching to it ;

is

while statements which refer to the existent, as tion

lightens

(it

which in

feelings,

into

a

this iron is hot)

Their occasion

suppositions.

me

;

position in which

ment the sum

a momentary feeling, or complex of number of causes which have brought

is

turn points to a

its

an actual matter of

e.g. judgments of percep depend upon more complicated pre

fact,

senses

my

we must

total of all

may be

thus affected.

But, besides

include amongst the causes of the judg

the psychological forces which are incessantly

re-creating the ideas of actual things and their attributes out of sensations, and bring about in each particular case the certainty that we perceive and

The principle of agreement explains only the way in the existent. which we identify present perception with a former idea ; it can never explain the general conviction of the material reality of things, nor the know

we say at the moment is a true judgment concerning While then the merely explicative judgment is sufficiently explained by the causes which give rise to the ideas and our consciousness conviction that what

matter of

fact.

of them, together with the principle of agreement, the other judgments call for special

explanations of our belief in the reality of things.

see the Kantian distinction between analytical

and

Here we

synthetical judgments

and the meaning of the question how synthetical judgments becomes obvious. It is clear also that

reappear,

(in the Kantian sense) are possible

recognition of the existing causes which give rise to our belief in reality,

and

the actual validity of our judgments of perception, can

in

to the correctness of this

nothing as

existing causes that sun

belief;

and moon appear

it

is

tell

us

due, for instance, to

larger to all of us

when

rising

than when in the meridian.

In mediated judgments, however, the mediation which brings about a decision need not consist solely in premises which can themselves be stated in the

form of judgments;

it

may

also consist in unconscious habits of

combination, and in the influence of authority which

is

rooted in un

analysable impressions. totality of psychological conditions we may now dis the occasion, which brings subject and predicate into con

Amongst the tinguish

i.

:

sciousness,

question

;

thus giving 2.

rise, in

the case of mediated judgments, to the

the ground of decision

which

enables

us

to

affirm

the

judgment, and to state the subjective synthesis as objectively valid, and which is therefore the ground also of the subjective certainty of the judg-

POSSIBILITY The change

ment.

AND NECESSITY

in the objects

193

concerning which we judge depends

occasion, which may, so far as the content of thought

upon the

cerned, be quite a matter of chance, and

come

entirely

con

is

from without

;

but

the ground of the decision always brings us back, in the last instance, to

a psychical force working in accordance with laws, and any particular psychological event can only be called the ground in so far as it introduces

Thus in all immediate the judgment by virtue of a constant connection. analytical judgment the ground upon which we attribute the predicate is the subject-idea, but only inasmuch

as, in

accordance with the principle of

agreement, the presence of subjects and predicates which agree necessitates their synthesis.

Of

5.

this psychological

ground of certainty the law holds good

that

no judgment can be made without a ground, i.e. unless the conscious ness of its validity has in one way or another been produced and thus without

violence to veracity no proposition can be stated which

is

not

accompanied by the consciousness of the validity of the judgment. This is involved in the nature of the judgment itself, as maintaining the validity of a synthesis,

and

in the

fact

that a purely arbitrary act, a sic volo, sic

iubeo; could not produce that consciousness of validity which implies that We do not, however, mean by this that we the synthesis is not arbitrary.

are

always conscious of the ground as

soon as we have uttered the

judgment. But the necessity asserted by every judgment stated with a full 6. understanding of its meaning is not this psychological necessity, but objective

affirmed

truth

with

;

it,

and the ground of is not one peculiar

its

to

certainty,

which

is

implicitly

the individual, but a universal

for every one, and can themselves as such, since these only and not the This alone is the individual frame of mind, etc., can be common to all.

ground which must make the judgment necessary lie

only in the ideas

logical ground, the certainty.

ground of truth as distinguished from the ground of and strife are due in the last instance to a difference

All error

between the psychological ground of certainty and the ground of truth to momentary belief may err, and the temporary feeling ;

the possibility that

of certainty deceive us.

So

far the

law holds good that no proposition

is

ground but just for this reason the investigation of what is a logical ground, and what the conditions are which justify us in affirming The object of our analysis of a proposition, falls beyond our present task. true without a

;

the judgment was only to s. L.

show

that every statement claims

by

its

meaning o

LOGIC

194 to have a logical ground,

and that

also involves the

this

problem of how

the ground may be known.

A

7.

further distinction

in thought

we always

is

start

called for here, which arises from the fact that

from data which have arisen involuntarily and

Absolute necessity would belong only to judgments of judgments as such, both necessarily developed in every being capable itself and the connection connected ideas the being inevitable ; and this is without reflection.

what

is

which is based upon innate ideas (in innate truths. and The ground of these original sense) reason itself, and so far as they are concerned there can be no

presupposed

the older

judgments difference

in every theory

and is

between

logical

and psychological ground.

have only a hypothetical necessity,

i.e.

it

is

But other judgments

logically necessary to maintain

them on the presupposition that something else has preceded in con sciousness. So far, then, as it depends upon external conditions what ideas arise in a subject and come together in thought, the judgment A is B is

B

indeed necessary so soon as we are conscious of A and as agreeing ; but it should come into at all is not thought universally and absolutely

that

Only when we assume an ideal thought, comprehending

necessary.

truth, is the logical necessity

For the individual whose voluntary thought aims is moral and conditioned by his ability.

thought.

all

a material necessity also, giving rise to actual at this ideal,

the necessity

From one

point of view, then,

truest sense only that

another

we can accept

which must

itself

we may look upon every

as a

ground

actual premise as a

that a further

in its fullest

of necessity be thought.

results

from

ground so

and

But from far as

we

with logical necessity.

acknowledge judgment We may indeed go a step further and find a relation of ground and consequence between propositions which we think of only as hypotheses,

and

in reference to

certainty.

To

which therefore there

say that a hypothesis

hypothesis means, that

if

the former

is

it

not

even a psychological

is

a ground with respect to another

is

accepted as

true,

then the

latter

must also be accepted as true. Thus in the first case ground signifies that which compels us to complete a judgment so soon as it has actually

come

into conscious thought ; here it means the hypothesis which, when accepted as valid, forces us to maintain the validity of another hypothesis. It is of the ground in this latter sense that the law holds good which was formulated by Aristotle, 1 and which in later times has ranked only as

1

Aristotle, Anal., ?r. II., 4, 57

b.

I

:

"Orav

5to ?xy OVTU irpfa &\\T)\a wcrre Sartpov

AND NECESSITY

POSSIBILITY

the principle of hypothetical inferences is

ground is is

affirmed the consequence

denied the ground

the negation if

of

is

the law, that

;

also affirmed,

All that

logical

is

that

is,

when

A

is

involves that of

when

the

the consequence

expressed by this formula as the nature of

necessity, just

expressed by the principle of contradiction.

the proposition

A

also denied.

is

and meaning of

nature

the

is

195

It tells

us that

recognised as the ground of B, then the affirmation

B

also, the

negation of

B that of A

This law

also.

alone deserves to rank beside the principle of contradiction, for, like it, it applies to a fundamental form in which thought moves, a progress accord

But

ing to necessary connections.

just as the principle of contradiction

undecided which of the opposed statements holds good, so also law leaves it undecided whether either ground or consequence is

leaves this

it

true.

Material causality must in no way be confused with the

S.

relation of

The

ground and consequence.

logical

proposition that every thing,

or every change, has its cause, stands in just the same relation to the logical necessity of our judgments as every other general proposition which serves as a ground for extending our statements, or enables us to pass with logical necessity "ground"

earth

is

from one proposition to another.

If

we use

the expression

of material causality also, and say that the attraction of the

the ground of the falling of bodies,

all

that

we

are immediately told

one produces the other realiter. But so far as the causal is, by relation when recognised enables and forces us to infer from the fact that the

this

that the cause takes place that the

recognition

effect

also takes

place, so far that

and only by assuming the causal relation of one fact to that of another distinct from

a logical ground

is

;

can we pass from the truth Thus the propositions which state causal relations play an important it. but it is far from being true that every part amongst our logical grounds ;

logical

way in

in

ground is based upon a causal relation, and still which our judgments depend upon each other at

which material causality takes

The

effect.

less true that all

distinction

still

between the ground of knowledge and the material ground, and obvious whenever an effect leads to recognition of the cause. Finally,

9.

probability.

of which &VTOS

e

we must

we have

dvdyKrjs

flvai ddrepov.

eii/cu

it

remains

becomes

and grounds of one of several hypotheses, none affirming ; and this they do by

distinguish between logical grounds

These give the preference sufficient

ground

ddrepov, TOUTOV

fj.rj

to

for

the

resembles that

6Vroj ptv ov5

ddrepov &TTCU, 6vros 5 owe

LOGIC

196

that this intensifying the expectation their value

Thus

one

sometimes a practical significance

when

e.g.,

;

is,

and

prove to be,

will

valid.

only psychological, but they have

in the first instance

is

it is

necessary,

upon

practical

absence of certainty. The have for the growth of knowledge cannot be in which they significance third part of the book. vestigated until the grounds, to

come

to

some decision even

in the

POSSIBLE AND NECESSARY AS PREDICATES OF ACTUAL

II.

JUDGMENTS. 33-

In

"

"

its

objective sense,

dicate of that which

a thing

or that

is,

is

it

expressed

in

This necessity

the nature of the thing, or external

govern the particular ditionally universal

While the

It is

last

instance a pre

necessary either that

is

and due

either internal to causality.

and due

to

In either case

knowable only in the form of general rules, which while, on the other hand, it is the aim of uncon

It is

hypothetical.

i.

always in the

a judgment.

has certain attributes, or exerts certain activities, or

stands in certain relations.

it is

is

necessary

;

judgments

assertorial

to express this necessity.

judgment

is

separated from the apodeictical

by no essential, inherent difference, the statement that something must be or must happen

differs in its

contents from the statement that

it is

or

happens when these statements extend beyond the sphere of our ideas to No doubt, wherever the the existent, and refer to a material necessity. "

must

as

"

"

all

what

and the

"

necessity

"appear

bodies are necessarily is

meant

is

in

merely explicative judgments such and an effect must have a cause

"

"

extended,"

the logical necessity contained in the fixed meanings

of our words which compels us to connect a predicate idea with a subject idea,

and hence

can be applied.

to predicate the former of everything to

The judgment

"

bodies are extended

"

which the

latter

makes the same

statement as the judgment "bodies must be extended"; the only differ ence is that the latter expressly reminds any one who may be in danger of it of the meaning of the words. But when we are speaking of the existent

forgetting

as such, then our statements

necessity refer to something which

is binding upon the and not merely upon our judgment. Necessary then becomes a significant predicate which is affirmed or denied in just the same way as any other predicates of actual judgments.

concerning existent

its

"

itself,

"

POSSIBILITY It is true that

of things as such necessity in

used as a predicate is

a necessary

AND NECESSITY

;

"the

Being,"

proper sense cannot be

not an attributive word.

it is

pression of our thought

its

197

\

world

Such phrases as "God ex necessary," are no adequate

not

is

what we mean

is,

that

God

Just as Set or oportet require a proposition to follow, called auxiliary verb, so also

only what

it is

is

necessarily exists.

and

"

must

"

is

a so-

stated in a proposition

its possession of a quality, its development of an which can be predicated as necessary. Only to abstract nouns which take the place of a proposition can necessary be attributed as a

the existence of a thing, activity

"

"

predicate

;

judgment

the existence of

e.g.,

no exception

is

God

to this

;

is

necessary that

thinking being, should judge thus.) This introduces a new class of statements is

that

which

is

stated in a

attribute

itself,

as in

credible, logically necessary).

false,

can only speak of material necessity in so its

those in which the subject

judgment (not the judgment

case of the predicates true,

the thing with

(The necessity of the I, and that every

necessary.

is

it

and

activity,

far as

the

Thus we

a material unity, that of

corresponds to the synthesis of

the judgment. 2.

What

is

which connects existence with an object of thought, an

it

attribute or activity with a definite existing subject, or different things in

one relation?

assume

If

we

disregard for the present necessity of existence and

that certain things are, there remains for investigation their kind

of being and their

mode

This appears to us primarily as merely

of action.

matter of fact and empirical, and what since

necessary,

thus

The ground

thought.

ment which

alone can

;

to see that

are investigating here

bond

nor do we seek a is

that

is

it

is

also

not the origin of

of necessity in the world,

the knowledge that something

It

is

matter of fact in our knowledge must be found

What we

the attempt to find such a

beyond so it must be

we want

be understood and penetrated by

of the subjective necessity of that part of our judg

refers to the

in material necessity.

it

the

is

and happens,

and

metaphysical justification is

there

to attain,

to the insight that for

this

and governs our

enough attempt popular as well as our scientific thought, so that the problem arises of

assumption.

establishing

its

meaning.

Here we must begin by guides

all

distinguishing between the presupposition which

our thought, that there

is

necessity in the world,

and the ground

of the statement that this or that particular thing necessarily is. Necessity the is knowable only where there is an invariability of connection in

i

LOGIC

98

existent like that

which governs the connection between thoughts in the

when therefore the particular event results in sphere of logic ( 31. 8); infallible certainty from what has preceded it, as the with and variably

when the same data are present judgment always recurs in the same way and when therefore a complete coincidence of material with logical ne In such invariability alone do we find the ground of cessity is possible. ;

That which

the necessity that something

is.

must have the

and universal

invariability

it must be universal as opposed logical ground and invariable as opposed to mutability in time. ;

means

necessary always

which

is

know

to

constant and universal.

see the necessity of that which

parable

with

anything

to the particular case,

To know something as consequence of something reason it is that we can never

as the

it

For is

be a material ground which belongs to the

to

is

validity

this

purely individual,

and

as such

incom

even though we may believe that

else,

it

is

necessary.

We

3,

as

regard the necessity which binds together subject and predicate

sometimes

internal,

sometimes external

of that between analytical

make

in itself sufficient to

necessity as internal rise to It

its

;

for us it is

distinction reminds us

when something we look upon

else it

must supervene

spirit

body moves when

it

is

is

in order to give

is

self-conscious

and

In the

first

pushed.

instance the attribute

and the

alone so soon as

there, in the latter case not until

it is

a subject

as external.

an internal necessity that the

external that a

When

determinations necessary, we look upon the

a determination,

is

thinks

;

and the

;

and synthetical judgments.

activity result of themselves

from the subject

something else

is

there also. 4.

When we

speak of internal necessity, we contrast the unity of the

thing with the plurality of

former as

the

its

which makes the attribute or a fixed order of change.

and

activities,

and regard the distinctions,

activity necessary, either as constant

In so

necessity of certain attributes thing,

attributes

permanent ground, unaffected by temporal

or in

far as the unity of the thing involves the

it is

called the essence (the nature) of the

and everything which proceeds from In no philosophical conception has

its

essence alone

is

essential

thought played a more important part than in the doctrine of Leibnitz that there is none but to

it.

internal necessity, activities

from

its

ticular individual

and

that each particular

own

inner nature alone.

is

this

monad

develops

Here the nature

the sole ground of necessity,

its

series of

of the par

and the whole course of

POSSIBILITY its

existence

AND NECESSITY

only the unfolding of this nature.

is

It is

199

recognisable partly

in immutable attributes and permanent activities, partly in the law of rise to another. development which prescribes that one activity shall give

a

idea of a permanent ground governing the manifestations of the thought of a thing as being identical with itself and yet which thing in If we want activities culminates. having changeable attributes and varying It is this

to establish the full identity of the thing, actuality at

any

Here we

given time.

we must look deeper than

find change;

are not external to the thing, the thing being what

and since it

is

its

attributes

through

its attri

itself seems in danger of disappearing butes, the identity of the thing

there

is

no

basis

permanent

in

change and giving

rise to that

if

very change.

only

the unity and identity implied in a thing can be represented in thought in the same if one and the same ideal content, which recurs always

way,

may be

And

taken as the counterpart of a real existence identical with

itself.

This same thought of the nature of the thing as the permanent, timeless

ground of

its

affords varying, temporal actuality,

an objective

justification

The comprehension of spatially

for our primarily subjective general ideas.

and temporally different things under one general idea, and their denota sub tion by one and the same word, is an arbitrary act guided only by to the grounds of expediency, unless there belongs in all beyond something really common to all and identical

jective caprice or

various things

the similarity which appears to us. the distinguishable ties,

and

particular

and must be found

in

But

this

common

lies

behind

their individual peculiari

phenomena, with

the fact that a

element

common

nature necessitates

and that variations are looked uniformity in attributes and activities, as due to external causes, as accidental, and not essential. 5.

External necessity

is

opposed

to internal,

upon

and determination by

cir

cumstances to the development of nature. Every particular phenomenon takes is this because another is that ; every change in a particular thing because a certain change has taken place in another thing. Things place

of have the power of mutually prescribing each other s action. The order the to one other, from the world consists in this necessity which passes and which is causal necessity in the narrower meaning of cause as causa transient.

The knowledge

that something

is

what

and happens

it is,

as

it

the general

is made up of two elements happens, from external necessity, is neces law and the particular datum to which this law is applicable. It our sun round the knowledge of to move in for the

sary

planets

ellipses

:

LOGIC

200 this rests

on the one hand upon our knowledge of the general principles hand upon our knowledge of the actual mass

of mechanics, on the other

of the sun and the planets and of the relation between tangential velocity

and

attraction

We

a different relation would give rise to different orbits.

;

cannot get rid of

this purely empirical

element, and for this reason our

knowledge of the necessity as such is expressed in hypothetical forms which state that if this or that occurs something else necessarily

only,

The occurrence

occurs.

causes

;

empirical

and so on ad

fact,

Thus the

to be necessary,

causes present, which

The

again necessary from

is

di/ay/o;

e

phenomenon

uTrotfeVetos.

But

if

logical

and

never more than a

is

When

hypothetical necessity of the existent due to

live

may

we look more and causal

willing being

something is said results from the

it

called necessary. 1

cause seems distinct from necessity due to the end. order that he

other further

infinitum.

not the cause, but the fact that

is

it

is

we always come upon some

necessity of each particular

conditioned necessity, an

6.

former

of the

but in explanation of these

;

nature and

its

must breathe

in

its

Man

peace we must be prepared for war. teleological necessity may be analysed into

to maintain

closely, this

Only as the thought of an

necessity.

actual, thinking

the end something actual which can be a ground of

is

something which is thought of as in the future and willed, which is intended, though, according to the causal order of nature, which connects every given result with given causes, it can be realized only by means of given causes. Hence whoever wills the end It is

necessity.

and the

realization of

assuming that we will a definite end, it is neces means. The connection between the thought ot the end and the thought of the means as objects of our will is logical; but the necessity of thought rests upon our knowledge of the causal necessity

must also

will the

sary that

we

The

of being. thai the

end

means

is

facts

infer with logical necessity the

be willed

upon

presupposed in the final cause are on the one hand on the other that efficient causes are present which changed or multiplied. From our knowledge of these

willed,

cannot be arbitrarily

we may

;

will definite

if

the end

results as

is

willed.

But

in

means for a given end, which must our interpretation of nature we look

ends even where there

thinking subject and

its

realization,

is no reference to the will of any because the end here serves as the

point of connection for a plurality of causes

;

and hence

arises the

ance of a special kind of necessity, distinct from that which 1

These concepts

will

be more

fully

explained in Part III.

is

appear

logical or

AND NECESSITY

POSSIBILITY

201

Man must breathe in order that he may live" this expresses nothing more than our recognition of the fact that the order of nature has connected death inevitably with the cessation of breathing, and that breath "

causal.

ing cannot be replaced by any existing contrivance.

must

as an end, breathing

also

be willed

as a

Should

life

be willed

means.

Suppose again that the thought were in itself creative then it would not be an end, needing the means for its realization it would be simply a ;

;

cause having the power to produce a material

would be no

there

The same There

which

so that here again

considerations apply to what has been called moral necessity.

are certain normal laws which a rational being with a will

to recognise as principles valid for his will,

bound

reality,

teleological necessity.

;

and by which he

and the recognition of such obligation

is

forced

is

feels

himself

a necessity of his nature

is

regarded as an essential characteristic of the rational subject.

If

these normal laws are actually willed and accepted as a highest end, then it

becomes

logically necessary to apply

But

the obligation to particular cases.

the light of a necessity because

them

to the particular, to transfer

to regard

the obligation itself in

a feeling of constraint, is to confuse our conceptions and to conceal the cleft which divides the it

brings with

it

recognition of obligation and actual willing. 7.

When

the necessity refers to existence

itself,

then, from the point of

view of external causality, it is obvious that in affirming the existence of any particular thing to be necessary we assume a creative power which produces

We

it

may,

explaining existence

some

either from blind necessity or for the sake of

for instance, it

try to

self-manifestation of

as the

actual end.

understand the existence of the world by

God

;

in so doing,

from a higher cause, and thus attribute to

it

a

we

derive

its

conditional

necessity.

But suppose

it

is

maintained that something has of

existence, as in the ontological proof

the essence of God,

being thus

made

and

to

where existence

necessary

proceed necessarily therefrom, an attempt into absolute necessity ; then

had thrown upon the thought of

necessity,

bond of connection between

thought or of being.

s

own

self-consciousness

and which had shown distinguishable

to

be

data, either

of

it

bond which breaks away as soon as we attempt with a mere concept, a concept, moreover, which

It is a

to connect the existent

belongs to no one

itself

said to belong to

to convert hypothetical

the light leaves us which the experience of our

merely a

is

thought

;

and

if

the idea

is

that something already

LOGIC

2 o2

of

undertakes the superfluous task

existent

itself

making

necessarily

existent (although existence is already presupposed in such necessity), then Just as we cannot speak there is nothing left for the bond to connect.

without presupposing an existing, comprehensibly of logical necessity it is to nature whose think, so also an ultimate and thinking subject is

simple being

always presupposed in necessity of existence.

member

in the first

God

of our series

;

that

we

causa sui and has the grounds of His being in Himself,

is

1

ourselves to be misled by words into stating

and lead

to

formulae,

is

Somewhere

or other

world which

of the

allow

the fictitious

empty nowhere more obvious than when they are taken seriously the metaphysical myth of a ground distinct from God Him

value of which

self.

In the rest

we must have necessity even and when we accept the answer that

we imagine

lessness of our questioning,

we must end

confines

That view

with simple being.

to the cycle of

itself

finite

causes must

whole complex of mutually conditioned beings as something if we would understand the world as necessary,

regard the

simply existent; while,

we make all

it

dependent upon God, where it is even more certain that between being and necessary being absolutely fails us.

distinction

Mathematical necessity

8.

what we

call necessity.

it

often taken as the most perfect type of

Spinoza

s

standing illustration of the material

the production of an effect by

necessity in as

is

follows from

the

nature of the

its

cause

triangle that

"

is

its

in the

same way

angles are equal

two right angles." This is not the place to investigate the nature of mathematical knowledge, or to determine the question whether its necessity is logical or material. It is, however, clear from what has been said that

to

involves that constancy and in which they are always presented in the same way,

the very nature of mathematical objects virtue of

by and because of which every variability

may be repeated material objects we are that

it

in

particular has the significance of a general in

the

forced

same way

in actual intuition

to seek for a constant

;

while in

element and dis

from casual and varying connections. Space and plurality, our and counting, are all no doubt given in the first instance ; but they are given in such a way that we are certain of their absolute engage

it

intuition of space

immutability. 9.

Now

it

is

none other than

universal judgments are

meant

this

objective

necessity which our

to express; the necessity, that

is,

of the

union between the subject and definite attributes, or of the connection 1

Cf.

Arnauld

s

criticism of Descartes in the Objectiones Quartcc.

POSSIBILITY between definite activities,

and

and

attributes, activities,

"

is heavy,"

that which

matter

is

be

to the nature of matter to

judgment

whenever the subject

ject

;

it.

The judgments

is

thing

the universal judgment

;

working according such a judgment

When

said that the subject

is

necessarily all

tells

it

heavy,"

all

belongs

The connection

equivalent.

predicate

is

actually

thrown body describes a

when thrown necessarily describes a forces

"

l(

necessary from the nature of the sub

exists, its

"every

attributes,

this necessity is

The judgments

justified.

are

heavy,"

of the predicate with the subject

203

and other

relations,

Only when we are convinced of

relations.

the unconditionally universal

matter

AND NECESSITY

parabola,"

combined with

parabola,"

again state

"a

the

body same

us nothing but the causal necessity of

to fixed laws.

denied, then the necessity

is

the traditional doctrine by the particular

is

denied

This

might be without the predicate. "

judgment

is

;

and

it is

expressed in

some matter

is

not

heavy."

10.

When

universal judgments express the essential predicates of things,

they coincide with explicative judgments, and the logical necessity of the

judgment with the objective necessity which finds utterance in it. The explicative judgment, while it states the contents of an idea, has also re gard to the things corresponding to the idea, and thus

it

gains an objective

significance whenever the idea comprehends the permanent and invariable

elements necessarily involved in the existence of a given subject or sub

when, therefore, the idea corresponds to the essence of the things. water is fluid explicative judgment expresses only the contents of

jects,

The

"

"

the idea of a thing which has been noticed in certain casual states.

It

does not represent the essential nature or the kind of matter which we

call

water, for this

a part of

its

is

also

oxygen and hydrogen tial

found

in a solid or

essential nature.

nature of water.

"

is

vaporous state ; fluidity is not water is a compound of

The judgment

"

both explicative and an expression of the essen

It is the

attempt to bring the two into perfect har

mony which guides the problem of

definition.

34-

That alone

is

possible

in

the

completely objective sense which

removed from the sphere of necessity

is

as the manifestation of free subjects.

Within the sphere of necessity we can speak of possibility only under two Either we must think of things as removed from the suppositions. temporal course of their actual existence and thus isolated from the con-

LOGIC

204

we may represent as grounded which in their permanent nature predicates really belong to them only must isolate in thought a part of we else when co-existing with others or ditions of their actual being, in order that

;

the conditions

When

depends.

actuality of

upon which the

in the latter case

we

what

is

stated in a proposition

are ignorant of the conditions, the

judgment passes from objective possibility into the subjective conjecture, and thus into the expression of uncertainty.

The judgment

"it

is

possible that

opposition to the judgment

"it

is

A

is

stands in contradictory

B"

A

necessary that

possibility of

not

is

B"

1. In investigating the many meanings of the expression possible," we of will first distinguish between the possibility being something which is "

and the

stated of a subject

in the

finds expression

possibility of its

propositions

the latter in the propositions

"A

is

may be sometimes

judgments, again,

"A

mere

is

possible,

2.

ment

If

meaning

;

such, have the

as

it

and

relations of

are thought as universal.

can or may, we

make

a state

connected with a presupposition from which alone

full

its

JS"

The former

be."

activities,

sometimes of subjects which

;

state of a particular thing that

originally

derives

which,

we

may

former

be

stated of the particular as such, their

subjects being definite things (or attributes, definite things)

A may

possibly B,

A

The

existence.

the

that

presupposition,

power of acting

is,

it

of free subjects

in different ways,

but which

power only at the command of the will and upon the ground of a choice between doing and not doing, doing this and doing something exert this

else.

We

have

which

is

the thought of different activities which the will alone

first

able to realize

which of them

;

when

wanting to the is

cut

off,

is

depends upon a decision

will realize

neither externally necessary, nor yet a necessary consequence

of former activity. inability,

it

Opposed

we have on

to this freedom,

the one

hand

the material causality which could realize the thought will

;

on the other hand there

is

and necessity prescribes the path of

the

"

must,"

action.

however, inability proves to be only another form of necessity of not-doing.

tion,

On "

is

when choice

closer inspec

must

"

;

it is

the

The position of a free subject towards the activities between which has a choice, strikingly resembles the position of the judging subject towards different hypotheses, neither of which it finds itself forced to 3.

it

affirm or deny.

actually realized

In both cases an act ;

in

is planned in thought, but not yet both cases the question arises, what should I do ? "

"

AND NECESSITY

POSSIBILITY

205

But affirmation or negation can enter only when necessity appears, and is removed from the sphere of free action while in the other case it is the undetermined and arbitrary act which realizes one of the the matter

;

We are not dealing thoughts and thereby refuses reality to the other. here with the metaphysical truth of this view, but with the presuppositions which determine the thought of the possible in this direction. While in the one case the different hypotheses cannot become actual judgments,

and so long as the choice remains the judgment is impossible, in the other the power of realization lies in the will, and stands in the same with regard to either alternative, thus causing them to appear Thus we speak of the real possibility of a scheme or

position

as really possible. plan,

when we have convinced

realization lie in our power,

ourselves that

and that

the conditions

all

this realization

of

its

depends upon our

will alone.

The results

therefore,

opposite,

of the

materially

is

necessary,

not without reason that language has combined the ideas of "

can

"

which

that

from freedom; here alone we find the absence of necessity.

in the

meaning of the word

"

It "

will

is

and

"

may."

But the idea of the possible extends even to that which is not This also may be regarded in such a way as to make it comparable free. Even the thing which is not free acts in different ways with the free. 4.

in so far as

same thing

it

is

at

changeable, and all

is

between them. ;

The sun

will

look to

is

a

number of

aroused of a choice

and be concealed by

shine

alternately

future

its

and the thought

different predicates lie before us,

clouds

not constrained to be and to do the

When we

times.

the brook will at one time freeze, at another be dried up

;

our

But thought in picturing the future wavers between different predicates. it does not depend upon the decision of the thing itself which of these predicates shall actually appear at a given time necessity.

The

may be merely

necessity

;

that of

this its

is

own

prescribes a certain development through different stages, it

must become

all

that

it

can become

;

and

it

is

determined by nature, which

and

in

which makes us speak of the future, not as something which

something merely possible.

Or

the necessity

this

case

only a distinction of time

may

is,

but as

appertain to both the

and when we are ignorant of the manifold combinations of circumstances and their changing course,

nature of the thing and

or,

disregarding them,

its

circumstances

comprehend

successive, then the thing

is

to

in

;

one thought that which in time is being of whose future

us like a free

LOGIC

2 o6

we

decisions

arbitrary will

are ignorant,

and

actual states appear to issue from

its

its

caprice.

the former

It is in

and

way

that

we regard

the totality of the universe so far

It contains the whole ground of apart from freedom. will be and happen, but which is not in future the which everything yet This is full possibility, potentia in its most significant mean actual.

as

we

think of

it

ing.

We

regard in the second

way the

particular things or events which take

their place in the order of the world,

and which are both determined and

hindered by circumstances in their natural development. In so far as the contains the of that which will be, there partial ground particular thing belongs to

it

the mere possibility of future states.

Thus

the seed contains

the possibility of becoming a plant.

But

this

when we

"can"

circumstances,

because

of predicates

series

rule

has a perfectly objective and material significance only

are certain that the predicate will actually appear under certain

we

depends upon the nature of the subject what assume under different circumstances. As a

gather our knowledge of that which a thing

experience of the past ledge

it

will

it

when we

;

but

say that the

we mean it moon can be

may be from our know

as a statement of certain eclipsed.

This meaning of can is particularly obvious when we make water may freeze or general statements concerning our subjects "iron can be melted is soluble in water," etc. evaporate cooking-salt Here we have perfectly definite and positive statements, referring to an "

"

5.

"

:

"

"

;

attribute of the subject.

"

;

Indeed, there

is

no way of making general

state-

tTients

concerning changeable attributes except by passing beyond the subject to the conditions and causes which determine its varying states.

When I isolate the idea of a thing and disengage it in thought from the conditions of existence under which the actual always stands, retaining it by itself, then there remains to which cannot be separated from

first nothing but those attributes because they are essential. But as thought surveys the cycle of changes which must and will be introduced it

at

it

by varying relations and refers them merely thing, it makes use of expressions such as

to the general thought of the "can,"

"faculty,"

"capability,"

turn the subject into a permanent ground for the changeable. This ground, however, is not in itself sufficient to bring about actuality; it must be supplemented by circumstances. But in as all knowetc., to

proportion able attributes of things resolve themselves into relations with other things

POSSIBILITY

AND NECESSITY

207

we are able

to express their unchangeable nature only as that which they under be varying circumstances. may Judgments of possibility, which state the further determinations that a

general idea admits

That which in the of, are analogous with these. asunder into the temporal series of successive states here breaks up into the plurality of ideas which contain a common element needing further determination before it can agree with any definite

previous case

falls

A

triangle may be acute, thing or can even be thought as particular. intuitable No contains or obtuse. figure only the properties right-angled,

which

I

think under the

some

one,

word

the general idea presents

colour

definite

Before

and angles

I

is

can form the image of necessary

try different determinations or recall

it I

constructing

No

triangle.

definite relation of sides

me

;

and when

in

them from memory,

with a choice of various closer determinations.

necessarily connected with those attributes of an

is

animal which constitute the contents of the idea horse.

be black, white, brown,

etc.

So

far as

The

concerns the content of

horse can

my

idea,

these judgments are perfectly definite statements concerning the plurality

So

of differences.

far as

existent, they express in

they are intended to apply to the nature of the the

same way a material

which con

possibility

nects variation of colour with the organization of a certain animal.

when applied

to a definite particular thing

itself

the problematical significance of ignorance.

thing

is

that

when

I

know

is

it

is

a horse, I cannot state of

only that something

is

Only

does the judgment take upon

When

that

it

a triangle,

I

it

is

all I

know

of a

black or white

do not know whether

it

right-angled or not.

When we "

judgment

A

are dealing with

can be

B"

subjects thought of as general, then

etc., is

the

the adequate expression of the so-called

particular judgment. It follows

6.

from the meaning of the judgments so

far

considered that

even when they apply to the particular they are intended as universally Possibility and valid, and their validity is not limited to any given time.

when we speak of a particular instance, it what may be and happen here and to-day. When we say, come answer the can be invalid the freeze saved," may may to-night, then our thought does not weigh the future by isolating its sub to-day,"

"

can

and

"

take on another meaning

"

state

;

ject

"

"

on the contrary, it reviews the present circumstances and undertakes But such certain prediction is pro from them the result.

to calculate

hibited by our want of knowledge, whether of

all

the circumstances, or of

LOGIC

208

the exact laws according to which they take effect.

ments mean

is,

man

the sick

be saved

will

if

All that the judg

the right cure

Thus some

etc.

is

applied,

if

of the conditions

no unexpected disturbance appears, are known, and form the ground of upon which the actual result depends known and certain conditions in the in the judgment and estimating we enter upon the calculation uncertain and comparison with the unknown call Still it is our ignorance which we that possible. of the probability of ;

alone that makes

and thus these judgments lead im

possible for us;

it

which merely state the subjective impossibility of a perceptibly to those While they appear to be concerned with things, they are really decision. measure of our knowledge of things ; and they are only concerned with the This is proved the expression of the resignation of our limited knowledge. exists or

is

When

past.

are used of that which already

same expressions

fact that exactly the

by the

the historian attempts to clear up a fact from

the judge in taking evidence fragmentary or contradictory information, or what has happened, then differ clues from endeavours to discover exactly ent combinations offer themselves

then

may

it

also have

may have happened This may or

it

;

happened

expression of subjective indecision

;

and

its

significance

way, but

this

"

"

that way.

"

can

"

is

the

lies in its refusal

be decisively established. When it is in spite of weighty evidence, this innocent be said that the accused may is not sufficient to prove the guilt; that the means only that the evidence to allow the opposite alternative to

judgment "he is guilty there is no question as to

"is

it is

in the objective sense, since objectively

already absolutely determined whether affirmation or negation

But

But

not necessary, nor, therefore, possible.

"can"

the statement that such

and such a thing

is

possible

is

true.

becomes the

more empty and insignificant according as the extent of our ignorance is and we have fewer positive grounds to give as a reason why our

greater,

conjecture should tion

is

come

possible, this

possible.

But

all

is

When we

to pass.

true in so far as

say that spontaneous genera

we cannot prove

that

it

the grounds contained in the order of nature as

to us speak against

it,

and

it is

a possibility which

lies

is

im

known

only in the dark

which our knowledge has not yet penetrated. in this subjective sphere does it hold good that everything is 7. Only which contains no contradiction, nor leads to any. Every hypo possible regions into

thesis

accepted as possible breaks

down

with a proposition recognised as valid

long as we do not find

it

to

;

at

once

hence

if it falls it

into contradiction

can be assumed only so

be contradictory to a valid

truth,

i.e.

so long as

AND NECESSITY

POSSIBILITY

But

opposite remains unproved.

its

209

absence of contradiction has

this

nothing whatever to do with the question as to what may happen in reality.

made

Nevertheless the attempt has been

8.

to find, in the absence of

contradiction, a criterion of possibility in the other sense also, particularly where the question is not as to the possibility of being this or being that,

This

but as to the possibility of being in general. stood by the possible. it

It is

contains no contradiction

;

which

that

and

it

that the proof of the possibility of

But

istence.

established what

one and the same

is

contradictory

and what

thing,

nitz has to secure a relation to

not

is

it.

nothing prevents

1

what Leibnitz under

should precede that of His ex is

meaningless unless

when thought of (

22, p.

demands

127

is

it

to

be that Kant

directed,

which

s

and

will therefore

forced transition from the it is

possible

criticism (Postulate des empir. Denizens iiberhaupt)

by the formal con But Kant himself allows too much scope to the

limits the conception of the possible

ditions of experience.

concept, inasmuch as he would

same sense

first

determination by

merely conceivable to something of which we can state that for

be

Moreover, Leib

sq.).

existence,

It is against this

it

as the determination of

reality for this abstract

postulating that everything possible exist if

God

absence of contradiction

this

is

thinkable (conceivable) because was in this sense that he demanded is

still

use

it

as a predicate of things, in the

Against his view we must here again

as Leibnitz.

insist that

can only be stated of that which finds utterance in the judgment,

possibility

hence that

all possibility,

as well as

all

necessity,

is

hypothetical,

and pre

supposes an existent. The statement that it is possible for something to be has no meaning, if it lays claim to material validity, unless it points out some power which can produce the thing and shows that the existing order of the universe raises no conclusive objection against

it.

This alone

distinguishes the possible thing from the possible idea or possible concept.

A

bare possibility

The

9.

is

possible

self-contradictory.

stands

in a

somewhat

special relation towards the

negation. It

that

would seem to be a matter of course that when we

A

is

B we

include the possibility that

A

is

not

B

state the possibility ;

for the opposition

between the merely possible and the necessary just in the fact that it But on closer inspection it becomes may not be as well as may be. A necessary to impose important limitations on the proposition that every lies

1

S. L.

De

Verit. Primit.,

Erdm.,

p. 99.

Cf. Princ. Phil.,

45,

Erdm.,

p. 708.

P

LOGIC

2IO potest esse

that

is,

B

is

accompanied by an equally valid

we would

A

potest non esse

B

;

if,

deal with significant propositions, and not with empty

formulae.

For instance, our thought,

in its function of

of the different phases of that which

is

comprehension, predicates

changeable, capable of development

Then the or of being determined from without, that they are possible. statement that the negation is also possible either has no meaning, or when to the original

opposed

judgment

an attribute "

it is

proposition

possible that cooking-salt

is

the

alters

may be dissolved What then is of cooking-salt

"cooking-salt

in

meaning of

water

"

is

The

this.

intended to state

the meaning of the proposition

The

"

not dissolved in water

?

proposition

mice may have millions of descendants in a few years is meant as an estimate of their power of increase, and hence as the statement of an

that a pair of

organic law

;

but what about the proposition that the pair

have these descendants its

?

When

may

also not

the positive statement expressly isolates

subject from varying conditions, there

is

no sense

in returning to these

and suddenly resuming the standpoint of the multiplicity of actual events.

When, however, we

are speaking of the particular case in temporally judgments, then the possibility of not-being accompanies that of being, and has the same significance. The answer may come to-day, but it may also not come till to-morrow, or not at all ; it may freeze to-night, but valid

then again the frost

may keep

presupposition that, besides the the result, there first

off. The ground of the negation is the known relations which would bring about

may be others also to counteract or prevent it; in the may be delay on the part of the writer or the messenger,

instance there

in the

second the introduction of a warmer current of

This relation

air.

between causes which bring about a result and causes which counteract and prevent it, is presupposed when the possibilities of being and of notBut its ground is being are opposed as equally justifiable propositions. only our ignorance as to whether the causes actually present and taking effect are favourable or counteracting.

The

case

is

the

same when we

state the

relation

between a generic

concept and its mutually exclusive specific determinations. may be equilateral or not equilateral. If all I know that it "is

I

have no ground

for either affirming or

denying that

it

is

A is

triangle

a triangle,

equilateral

;

the

general idea leaves both possibilities open. 10.

The

negation

necessity to possibility.

of possibility leads to necessity, the negation of

AND NECESSITY

POSSIBILITY a.

b.

It is possible that

B contradicts A is B, and this

is

It is

not possible that

It is

necessary that

A

is

It is

necessary that

A

is

It is

not necessary that

It is possible that

Thus

A

there

arises

the

A

is

equivalent to

is

not B.

B A

contradicts

B, and

is

this

equivalent to

is

not B.

twofold

contradictory

parallel to the contradictory opposition

particular negative,

211

opposition

which runs

of the universal affirmative and

and the universal negative and

particular affirmative

judgments.

But

in

both cases we can only avoid running into absurdities

careful to interpret the formulae always in the

same

These formulae hold good when possible and necessary subjective sense of a hypothesis

;

if

we

are

sense.

are used in the

when necessary necessity of some deter

they hold good also

and possible are uniformly used of the essential minations and of the material possibility of others which are opposed to each other; they hold good, finally, when possibility and necessity are stated of ii.

some

On

particular case in temporally valid judgments.

reviewing

all

the questions to which the concepts of the possible us, we see that the function of judgment has

and the necessary have led

undergone a further development

in

two

directions.

On

the one hand, the

judgment which were traversed by the immediate judgment with one step have been definitely separated by the questionthe mediated judgment. The mere attempt at a judgment

different stages in the formation of the

has appeared upon the scene, and has led us to reflect concerning the relation of the judging subject to this question ; and by means of the

between the question and the decision, NECESSITY, the innermost and essential meaning of all judgment, has been brought to light. On

antithesis

the other hand, judgment has advanced a step further in that particular or a number of these, have been replaced by the statement

simple subjects,

the material unity of subject and predicate, which has become the subject of new predicates, primarily of the necessary and possible. In this way new categories have become manifest which rank above those first discovered, inasmuch as they are founded upon the

of the judgment

itself,

ones and place them in relation to each other, thereby enabling us to know not only particular phenomena, but also their connection.

earlier

Thus they

afford a positive counterpart to the

mere negation, which,

them, has reference to the synthesis of judgment.

like

LOGIC

212

we thus look upon the progress of thought as pressing onward from the mere attempt, the hypothesis, and the possible to the necessary, we If

can give their natural significance to the special forms which are generally co-ordinated with the judgment which states or denies a definite predicate of a subject, that

former

is

is,

to the hypothetical

and disjunctive judgments.

the simple expression of necessity,

pression of mutually exclusive possibilities.

connection between possibility

possibilities,

by necessity

;

the latter

and is

The

the latter the complete ex

The former shows

in this

way

limits

a necessary

the sphere of

the preliminary step towards establish

ing the necessity of one possibility by the denial of certain others.

CHAPTER

VII.

HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS. FROM

the point of view of what

classifies judgments as (if

A

is,

B

is),

called relation,

is

and DISJUNCTIVE (A

is

modern

logic generally

B A not B], HYPOTHETICAL either B or C}. But this not in ac

CATEGORICAL {A

is

;

is

is

nor are there any grounds for regarding 1 it as an exhaustive division of the forms of judgment. It often happens that, so far as concerns the matter of the statement, categorical and hypothetical,

cordance with the Aristotelian

or

hypothetical

logic,

and disjunctive propositions express the same thought

with a difference which

merely grammatical. If, on the other hand, it we look, then the hypothetical and dis with the categorical form of judgment, cannot be co-ordinate forms junctive since this is contained in both of them. If, again, the ground of distinction is

the verbal expression to which

is

and composite judgments, which are ex complex propositions, are opposed to those which are simple,

sought in

is

pressed in

this circumstance,

then we shall find that there are

many other complex propositions besides and disjunctive judgments, and there will be no apparent hypothetical reason for excluding them from logical treatment. As

a matter of

the Stoics

in

fact,

logicians did for a long time follow the

distinguishing

example of from the simple composite judgment

the

judgment which is expressed in a single proposition; and this custom, which had fallen out of use more particularly since Kant s time, has been lately revived

(e.g.

by Ueberweg).

In an investigation of which the chief aim

is

to analyse actual

judgment,

and which must therefore begin by investigating the expression of that judgment in language, we must begin by reconsidering this former custom. This is the more necessary because a number of misconceptions concern ing the hypothetical judgment have arisen owing to insufficient reflection

on the 1

logical significance of the forms of language.

With what follows

cf.

my Programm

:

Beitrage zur Lehre

(Laupp, Tubingen), 1870. 213

vom

hypothetischen Urtheil

LOGIC

2i 4

I.

THE DIFFERENT WAYS

IN WHICH PROPOSITIONS MAY BE COMBINED AND THEIR LOGICAL SIGNIFICANCE.

35-.

There are certain forms of speech

in

which different propositions are

connected by particles, conjunctions, and relative pronouns. This con nection may be such as to express a relation between complete propositions,

which it

judgments and are comprehensible by themselves ; or one proposition is essential to the completion of

state definite

may show

that the

the other.

In the

first

sitions; or

it

case the relation

may

may be merely

verbal, as in relative

propo

express a subjective relation of the propositions peculiar

to the individual speaker

;

or

it

may be

equivalent to another judgment,

between the syntheses expressed by the propositions, or the relation between the facts stated in

having

for its predicate either the logical relation

the propositions (states, events, etc.).

In the second case relational predicates

or

we may

either

make

a statement by

means of modal

concerning the grammatically dependent judgment,

we may make a statement concerning the

fact expressed in that

judg

ment. i.

The

simplest complex propositions, and the most easy to analyse,

are those in which two propositions, each comprehensible

expressing an independently valid judgment, are placed

by in

itself,

and

such a re

more is expressed by the two together than by the The verbal forms simple utterance of the one proposition after the other.

lation to each other that

expressing this relation are the particles, and

we must .

it is

of their significance that

speak.

We

have already seen

(p.

equivalent expressions, can do no are, at the

moment

and since

that the particle

157)

more than

tell

"and,"

and

all

us that the two judgments

of speaking, both present in the consciousness of the

already established by the utter ance of both propositions by the same person, such mere links have in them

speaker

selves

;

this subjective fact is

no objective

indicating

significance, though they may assume the function of a corresponding connection in the objects of thought (e.g.

temporal succession when some event

is

being narrated).

These

particles

therefore are not equivalent to a judgment. b.

Nor can

the adversative particles be taken as the signs of a definite

objective statement.

It is true that in

conversation they are often directed

HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS some spoken

against

proposition, which they confront with an objection,

limitation, or contradiction. it

Still

they have not the force of a negation, for

just as often that they only repudiate

happens

215

what might have been

conjectured or inferred from the proposition by means of some combina

When

tion.

hand

used by one person speaking alone they serve on the one in this way against some looked-for statement, and on the

contend

to

some

other merely to introduce

an affirmative proposition

as

Thus,

while

the

contrasting or unexpected element, such

after a negative, or

denies a definitely

negation

an unexpected predicate. uttered

statement,

the

adversative particles often anticipate tacit combinations merely assumed as possible

;

the negation, therefore, which these express,

is

indefinite,

and

cannot take the form of a proper judgment. It

c.

is

when we come

different

Where

particles of inference.

judgments connected, they

to the so-called causal particles

that the

state

ground (or consequence) of the other

;

but

one judgment is the logical they are meant to express

when

the relation between the facts stated in the judgment, they fact stated in the

one judgment

Thus

fact stated in the other.

the relation they express

of a proper definite judgment.

cold the

;

is

"it

we have

here

;

"It

is

getting cold; the thermometer

is

"it

change d. With the causal

all

is

the force

thermometer

the thermometer

in

the cause of the

us that the

that of a logical,

have

getting cold, for the

therefore

getting cold,

is

to that extent they

;

is

all

and

each case three complete judgments the thermometer is falling the former proposition

latter";

tell

the real ground (or consequence) of the

is

or material, necessary connection

is falling";

and

these express the logical relation of the

is

falling";

"

it

:

is

is

getting

inferred from

falling; the

former

latter."

particles expressing real necessity may be classed determinations which express real relations between the states, events,

spoken of

etc.,

in the propositions, such,

relations in a narrative

tions of place.

These

for instance,

as the temporal

contemporaneousness, succession, etc.

and

rela

also stand in place of definite relational judgments,

by which they might be expressed. e. Under the name of exponible judgments, the older logic has included judgments which, while apparently making only one statement,

really contain several. restrictive

Chief amongst these are the judgments containing

"only,"

man is happy man who is not

wise the

words

"

tells

wise

is

"none

us

first

but,"

etc.

The proposition "only man is happy, then

that the wise

not happy, or that

all

the happy are wise.

the that

LOGIC

2l6

Grammar

2.

corresponds form,

is

it

no

to true,

form

but in this general

;

distinction

essential

seems to

the co-ordinate and subordinate

between

distinguishes

of propositions

connection

in

thought.

signify that the speaker

the

distinction

The grammatical mainly concerned

is

statement of the principal proposition, for the sake of which

with the

alone the dependent propositions are introduced

;

that

is,

the speaker has

in stating the

dependent propositions except for the sake of But language as actually used has not retained the distinction between co-ordinate and subordinate

no object

reminding us that they are accepted truths.

propositions in

all

particles in the

same

its

it

strictness;

sense,

uses conjunctions and

co-ordinating

and the utmost distinction made

difference in the subjective emphasis

laid

is

a slight

the propositions

upon

con

nected by them a difference which has no objective significance with The particles "for "and "because respect to the matter of the statement.

"

are

used to denote one and the same relation "

pressed by

The

same time

at the

significance

manifold gradation. already fully

of

"

may

relative

When

determined as

and the

;

be announced by

connection

relative it

also

is

ex

relation

"

whilst."

especially susceptible

follow a term

pronouns

which

of is

stands, they serve merely to enable us to

make a further statement concerning some portion of The relative pronoun, whilst obviating the express

a given statement. repetition

of

the

gives more prominence to the identity of the two elements than would be attained by mere juxtaposition but the relations definite denotation,

;

between the two propositions thus connected may vary greatly. The most decided subordination takes place when the proposition introduced

by the tion

relative enables us to recognise

more

one element of the main proposi we already know and

easily by reminding us of something

in this case the statement introduced has

but

is

more

There relative

is

in the nature of

an attributive adjective, or an apposition.

complete equality of position, on the other hand, when the

proposition

new and independent statement

introduces a

happens most frequently

But here the

in Latin).

the place of a proper judgment.

It tells

stated in the two propositions connected

verbal

that of establishing the identity

The

proposition

and

A

A

is

;

no independent value whatever,

C";

"A,

all

which

that

it

of the one proposition

is

is

does the

,

is

is

C"

us nothing which

and

A

is

not already

function

is merely by it, between the verbal denotations.

tells

to leave

same

(this

does not take

relative

us no

its

more than

no room

for

"A is B, doubt that the

as that of the other.

HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS

when an element of

Relative propositions have quite another function the proposition

which

subject or predicate, that

they are

sphere

;

live in

cold climates need

is,

receives through

as a part

They then appear and limit a more

determination.

first

in itself indefinite

is

217

them

its

of the denotation of

general denotation to a definite

In the proposition

determining.

more nourishment than

"

men who

the subject

others,"

is

incomplete without the relative proposition, which plays the same part as elastic bodies are resilient." a determining adjective in other cases e.g. "

In this way simple denotation by a definite word may be paraphrased by a relative proposition; the phrase "parallelograms, which are right-angled

and

"

synonym for squares." Here we must also add the indefinite relatives equilateral,"

thing

is

a

6 crris av,

that,"

quisquis),

of which the one predicate

is

which

tell

("

any one

who,"

"any

us nothing but that subjects

The

true have the other predicate also.

then equivalent to a universal judgment, and, like it, may expression have either an empirical or an unconditional universality; while, again, is

is mortal";

mean

all

mortal,"

"all

men

are

mortal";

absolutely the

The

in this form.

any universal judgment may be expressed "man

"anything

which

propositions is

a

man

is

the necessary connection

same thing

between humanity and mortality. The only difference is that in the form of naming, which has already anything which is a man is mortal the act and it is left, all men," now takes place before our eyes in taken "

"

"

place

;

moreover, an open question as to what particular thing, if any, can be so men are mortal," on the contrary, although it named. The formula "all

does not actually state that subjects are forthcoming,

them

if

we understand the words

Much

same may be said of when (wenn) and "where" (wo) as The use of when to denote one definite time and place. "

"

relatives of

point of time in the past, while

there

presupposes

the

"

"

German

still

in their ordinary sense.

Here

language.

often

attaches to

it it

still

retained in English,

is

lost to

the

used principally of the future, and hence a kind of indefiniteness and uncertainty as is

come to pass and this may be, although intention of ex perhaps in a very slight degree, even where there is no will happen at the same time pressing anything more than that one event

to

whether the future

as another

(when

it

will really

;

year will begin ; when Where, again, it stands as a general

strikes twelve o clock,

the

new

is ended, we shall return). (whenever = as often as), its only direct meaning is the universality of the co-existence of two states or events ; this universality being either

the war

relative

LOGIC

218

merely empirical, as expressing a perception to which there has been no

(when it grows dusk, the bats begin to two events will happen together in the

exception, or absolutely universal

But we cannot

fly).

future,

nor that they

state that will

always and unconditionally take place together,

some necessary connection between them. To this extent, therefore, the meaning of what was originally no more than a temporal particle comes to include this necessary connection, and thus to serve as unless there

is

we

the conditional conjunction in the hypothetical judgment, of which shall

have to speak

later.

"

Where

"

(wo) in

its

general significance passes

through the same process. From connections such as these we must distinguish others in which 3. a proposition as such forms part of another proposition, either as subject,

The

or as part of a relative predicate (object).

may

proposition

then

represent either the judgment as a subjective thought or utterance, or the fact expressed in the judgment ; and this again may be sometimes merely thought or assumed, sometimes objectively valid as matter of fact.

Those statements

a.

in

judgments have propositions that a

judgment

is

which modal relational predicates for their

component

true, false, credible, doubtful,

parts.

The

refer

or necessary

possible,

the statements that I believe, repudiate, dispute, or doubt something

these have reference to a hypothesis which

and they in

state

how

the hypothesis

All final

general.

is

propositions

is

anything in order that something else

;

all

expressed in a proposition,

my

related to

belong

to

statements

to

thought or to thought

this

may happen,

class.

When

the purpose

I

do

makes

appearance as rny thought and the statement refers to the relation between a result as expressed in the form of judgment and my thought and will, with the action to which it leads. its first

;

Since every judgment as such must stand in definite modal relations, these

may

always be predicated.

or necessary

say that

I

To

say that the judgment

means no more than the simple statement

maintain, I know, I

am

certain that

A

is

"

"

A is B A is

"

is

B"

true

To

B, only gives special

emphasis to the certainty already contained in the fact of the statement "A is But in such a rendering the proposition "A is B" becomes the expression of a merely conceived judgment or hypothesis; the com ."

pletion of the

judgment

is

transferred to the

modal predicate.

Statements of which the component parts are states or events ex pressed in the form of propositions differ only verbally from those which b.

contain adjectival or verbal abstract substantives amongst their elements.

HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS The thought remains the same whether I say, summer is due to the higher position of the summer

is

warmer

is

due

"

219

the greater warmth of the "

or,

sun,"

the fact that the

sun stands higher ; all that that fresh predications can be made

to the fact that the

is necessary to such a statement is concerning what is originally expressed

in a

"

judgment.

survey lays no claim to completeness, it may at least suffice to show that the manifold grammatical forms in which propositions are connected together are no ground for special kinds of function 4.

in

Although

this brief

judgment, which are not forthcoming

in

simple judgments.

y

The mean

ing of such forms can always be expressed by the predicates of simple

statements, and logical theory has therefore been fully justified in leaving such connections as those of time and place to grammar, which treats of the

expression of thought in language.

The

"

expression

"

compound judgment

misleading and inappropriate; that which is composed of judgments may be a combination of judgments, but we cannot therefore say that this

is

The fact is that when the component is itself a judgment. judgment are propositions these propositions are not themselves

combination parts of a

judgments

;

that

is,

they are not at the

moment

intended as statements

:

new judgments, either as hypotheses, or as the results of of what is meant in the previous judgment, and therefore as an indication

they enter into

judgment. 5.

Amongst

all

the different combinations of propositions conventional

logic has distinguished only

what are called hypothetical and disjunctive

that judgments, and in so doing has rightly judged

varied only with definite statements, however

of definite predicates to definite subjects.

have to deal with such statements direct

importance

for

;

that

But

concerning

the final aim of

all

other forms deal

all

is,

in these

two forms we

hypotheses

thought

\J

with the attribution

as

are of

progress from the

and there to the necessary subjective to the objective, from the possible con Reflection statement. of kinds fore of universal importance for all is always necessary where cerning the value and significance of hypotheses we cannot straightway form a definite judgment, but must endeavour to

Thus hypothetical by way of a preliminary experiment. is a the with and disjunctive judgments rank negation, which, like them, that to both stage apply judgment concerning a tentative judgment ; they arrive at truth

of thought

which

lies

between the question and decision.

\.

LOGIC

220

THE HYPOTHETICAL JUDGMENT.

II.

36.

The HYPOTHETICAL JUDGMENT states that two hypotheses are related NECESSARY its predicate is to each other as GROUND and CONSEQUENCE "

;

"

CONSEQUENCE."

A

If

is

the necessary consequence of

is

The

r.

which form

its

"if

"

is

true,"

means, therefore,

B

A."

ordinary expression of the hypothetical judgment, and that in

is

most obvious,

is

meaning

A

B

then

true,

C is

B, then

of propositions,

"

if

A

is

D"

true,

is

a combination of propositions of the

More

then

B

briefly,

is

A and B as

and taking

signs

true."

In grammar such propositions are generally called conditional, and them this name we take what seems to be the most natural view,

2.

in giving

that the point in question

is the validity of the This consequent. cannot be directly stated, but presupposes the validity of the ante cedent, the whole being thus a conditional statement of the consequent, hence a statement concerning the subject of the consequent. 1 But the i.e.

validity

consequent

not to be stated until the antecedent has been confirmed,

is

and a conditional proposition

is

therefore an expression of uncertainty with

and consequent. Both, as the expression goes, are problematically stated, or, as we should say, express mere hypo theses. So far as concerns the two propositions themselves, therefore, there reference to both antecedent

really

that

seems which

is,

to is

be no judgment at

all

in

the proper sense, no utterance,

and necessary

stated as true

;

and

this

view

is

confirmed by

the fact that conditional propositions are sometimes stated with the falsity of both antecedent

consciousness of the

and consequent

avowed

(si tacuisses,

philosophus mansisses). 3.

Nevertheless such a combination of propositions does contain a state is a judgment in the proper sense of the word, and this the

ment which

Stoics 2 were the

first

that antecedent

consequence

to recognise definitely.

and consequent are related

(p. 195), that to

accept the consequent,

and

accept the antecedent makes

1

This

is

Cf.

p.

It

is

this relation

the hypothetical judgment in his Logik.

See

is infallibly

of necessary

p. 12.

3

J. S. Mill, Logic, bk.

I,

and

my Programm

23 sq.

my Programs,

us

necessary to

the true predicate of the hypothetical judgment, 3

how Wolff defines

mentioned above, 2

is

it

tells

ground and

to each other as

that the validity of the consequent

connected with that of the antecedent.

consequence which

Such a combination

ch. 4,

3.

HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS

221

the two points of reference for the relation are antecedent and consequent. So far as concerns the statement of this necessary connection, the question as to the validity of the antecedent

probability, improbability,

or

and our conjectures as are of no importance,

falsity,

to its

truth,

just as in a

simple judgment concerning some object of thought it is quite immaterial whether we regard the object as existing, as possible, or as merely fictitious. In this way we may explain how it is that judgments beginning with (wemi) seem sometimes to express uncertainty alone, and at other times 1 to be the expression of sequence amongst actual phenomena. This necessity, which in hypothetical judgments refers to propositions "if"

which are merely assumed, is also stated with reference to valid judgments is true because A is by the so-called causal connection of propositions.

B

true,

a

judgment which may

or to the material ground.

the thermometer 4.

The

is

rising

ground of our knowledge warmer because the thermometer is rising

refer either to the

(It is

because

;

it is

warmer.)

nature of the statement remains, of course, the same whether the

judgments which appear as antecedent and consequent be affirmative or or explicative. negative, universal or particular, narrative

The attempts

to

are based

find differences of quantity, etc., in the hypothetical

judgment upon a confusion between hypothetical judgments and statements concern and casual coincidence. ing mere time-relations or some purely empirical

No twelve

one would maintain that judgments such as

some one

dies"

The

are hypothetical.

"whenever it

confusion

is

strikes

especially

apparent in the judgments which have been called particular hypothetical If the connection "when it is fine the barometer generally stands high." :

cannot be necessary, and such judgments can never casual coincidence in a relatively greater or express more than empirical or sometimes when a triangle The instances. of smaller number proposition

is

not invariable,

it

"

is

right-angled

it

has two equal angles

"

tells

us only that the

attribute

be found together with, and does not exclude, right-angled sometimes when two of the remaining angles. The phrase equality does not connect ground and consequence it only states the coincidence of attributes or events in the same or different things, the statement being is

occasionally to

"

"

;

as to the ground of the coincidence. merely empirical, and saying nothing v. i, p. 109 sq.) and Vierteljahrsschr.f. unss. Phil. (Cf. my Programm^ p. 45, 5.

The

co-ordination

of the

hypothetical

with the categorical as a

the difference of special kind of judgment, distinguished by 1

See Appendix B.

its

logical

LOGIC

222

may be

function,

In the categorical judgment, he

said to date from Kant.

are subordinated to each other as predicate to subject, in the says, ideas

hypothetical 1

as

The

06).

consequence to ground (Krit. der of in

necessary sequence thought

r.

V.,

corresponds to the copula in categorical judgments

:

function of the hypothetical

judgment

Hart., p.

;

that which unifies

it is

Thus the category which corresponds

the different ideas.

3

9.

hypothetical judgments,

to the logical

that of causality.

is

But the classification is throughout superficial and inadequate, because the ideas which are related as subject and predicate are,

if

only

in the

Kantian phraseology, concepts, while the ideas which are related as Kant s distinction gave rise to ground and consequence are judgments.

which

the further doctrine

he, however, did not himself teach

that cate

are the expression of the relation of inherence, hypo gorical judgments thetical judgments of the relation of causality, a doctrine which is quite

untenable

the expressions hypothetical

if

their ordinary is

certainly categorical

causal relation

it

relational

and categorical

God

"if

the soul

is

But

judgments

included at

in all,

are taken

in

the cause of the world

is

it

material,

it

"

expresses

extended," is

(as,

When, again, and distinguish between judgments of quality we may find some justifi e.g., Drobisch does),

cation for the division, so far as concerns the

ments.

is

treats entirely of relations of inherence.

disregard the verbal form

and

"

the ordinary sense, nevertheless

in

the judgment

;

hypothetical, yet

we

The judgment

meaning.

classification the

this

and only by

meaning of

definite state

judgment is not be subsumed under

true hypothetical

straining a point can

it

those relational judgments which are statements of real relations between things.

The

6.

exact meaning of the hypothetical judgment differs according

by it as ground and consequence. two propositions, which standing alone would express unconditional if the statement is merely that if we then," validity, are connected by

to the nature of the propositions related

When

"

accept the one,

then "

if

it is

God

we must

extended is

propositions

"

"

;

also accept the other. if

the soul

almighty and good to

make

is

If the soul

"

simple, then

all,

it

then the world

the truth of the consequent

depend

is

corporeal,

indestructible

is is

"

;

such

"

perfect

as necessary

con

sequence upon the truth of the antecedent, and state that whoever accepts the one must also accept the other. The ground of this necessity is not apparent in the hypothetical judgment. relations of the ideas (corporeal

It

may

and extended) by

consist in

the

simple

virtue of which predica-

HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS one involves predication of the other

tion of the

or

;

assumptions concerning the nature of things, such as of certain causes

view we

may draw

such a way

in

But

us which.

tell

that the generally recognised

contained in the

is

meanings of the words

enable us to infer the one from the other, then the judgment if

in

is

of action

the distinction between analytical

second proposition

If the

and synthetical judgments. first

mode

the hypothetical judgment does not

;

this point of

consist in

the simple

or in assumptions concerning the necessary

destructible,"

From

may

it

"

223

is

analytical.

the connection must be mediated by a ground of necessity derived

from some other source, then tinction

it

is

This, however,

synthetical.

which cannot be more exactly denned

We

doctrine of inferences.

a dis the

to

find instances of a similar nature in applica

tions of a general rule to a particular case

death be the penalty of

"

if

:

murder, then this murderer must be punished by the logical necessity by which

tions express

is

we come

until

Such proposi

death."

the particular

instance

is

contained in the general rule. When antecedent and consequent refer to the particular and are 7. statements having a temporal validity only, there are two cases

Here, again,

distinguished.

contained in the

we may

and follows from

first,

it

by virtue of the

predicates, these being invariably connected

Or

irresponsible."

;

necessity of connection

are not contained in the antecedent. will freeze

to-night,"

if

this

meaning

man

drunk, he

is

is

of the is

may be due to the special and inferable from it according to

the necessary sequence

circumstances of the case before us, certain laws

"

:

be

to

second synthesis

the

that

find

we presuppose

sary sequence depends

is

found here

When we

but

also, "

say,

if

the given temperature,

upon the laws of the

its

conditions

the sky clears, etc.

;

it

the neces

radiation of heat, but these

not produce the result except at the given temperature.

will 8.

There

is

a special application of the hypothetical judgment in which

the propositions connected by

themselves are

left

it

The subjects when they are indefinite, when

have no definite subjects.

indefinite; either absolutely indefinite,

denoted by some such word as "something," or partially If anything is corporeal, they are denoted only by a general term. is he to one extended"; every one his due"; gives just, any "

triangle

of

is

equilateral,

it is equiangular,"

a given statement

being given

;

we

it is

"if

"if

left

are also

in suspenso,

left

etc. its

Here not only

it

a

the validity

necessary consequence alone

uncertain whether there

longing to the predicates, or where

is

may be

found.

any subject be But as it is stated

is

LOGIC

224 that any subject in

other as well,

it is

which the one predicate

essential that

is

found must contain the

and

these judgments the antecedent

in

in meaning, if not in words. the same subject consequent should have u if a triangle has equal angles, its sides are equal," there In the judgment no doubt, two grammatical subjects ; but the second refers by means of are,

the possessive

ment "

is

really

pronoun to the made.

and

first,

They are then precisely equivalent he who is just gives to every one his

it

the

is

of which the state

first

to universal relatival propositions due";

"every

triangle

which

is

:

equi

Propositions such as these state the identity

lateral is also equiangular."

of the subjects to which the two predicates belong, but they can do so is necessarily connected with the first ; only because the second predicate this necessity shows itself in the fact that the two predicates are always

and without exception found

The clear.

same

in the

subject.

course of thought presupposed by these

We

find

them where

particular things,

time assumed, are being characterized. the antecedent in our minds,

modes

With the

we look abroad

of expression

whose existence

definite predicate of

into the manifold;

expectation that the predicate will be somewhere applicable, if it is,

9.

we

and

tell

us absolutely nothing which

is

in the

state that

then the other predicate must be necessarily connected with

But these judgments

is

for the

is

it.

not contained

"All bodies are judgment. does not refer to any limited and definite number; it merely if anything is a whatever is a body is extended," or that states that

in the unconditionally universal categorical extended"

"

"

it is extended." The word by which the subject of the statement denoted contains by implication the antecedent of a hypothetical

body is

Such a proposition,

judgment. of himself

duced

as

is

last"

"

a

therefore,

as truly hypothetical as

good man

"

as if

"the

the

with a view to leaving

good man

thinks

subject were it

intro

an open question

whether and where such a subject is to be found though not when it is merely the incomplete denotation of a definite subject. (The distinction

may be seen from emperor was a

the examples,

"an

emperor must die standing

"an ";

Stoic.")

is the answer to the much-disputed question as to the rela between hypothetical and categorical judgments. All categorical judgments which are unconditionally universal are exactly equivalent in

This, then,

tion

meaning

to hypothetical judgments, for (see

nothing whatever but that subject

27, p.

162 sq.) they state

and predicate necessarily belong

to

HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS

225

each other, so that to predicate the subject of a particular thing neces sarily involves the predication of the predicate.

Inasmuch, indeed, as the ambiguous, and may introduce either a judgment which is em universal, or one which is unconditionally universal, the hypo

is

"all"

pirically

thetical

form

the

is

more accurate and adequate

in

hand, judgments

which

definite

On

expression.

them

particular subjects naturally resist the attempt to convert

The

hypothetical form.

the other

predicates are attributed to definite into the

moreover, has a wider

hypothetical judgment,

meaning and application than can be naturally expressed

in the categorical

form. It is different

10.

activities, "

"

When when

and the

when

the antecedent predicates changeable attributes,

which

relations of a subject

temperature of water

only indefinitely denoted.

is

below

falls

a body projected with a given velocity

becomes

it

zero,

"

"

;

illumination

is

strongest

when

:

subject to the action of

is

a force which varies as the inverse square of the distance,

conic section

"

solid

describes a

it

the rays of light

fall

per

such statements may refer either to repeated pendicularly on a surface instances in which the subject remains the same, or to instances where the "

subjects are different

;

and

for this reason they

would be inadequately ex

pressed by a universal categorical judgment. necessity as unconditional universality,

here the

that

every time

"

relatival phrases

that,"

"as

hypothetical judgment

Changes must take place

at

definite

definite time for the validity of the

are,

we

are to

often is

as";

also

moment immediately

before or

express the

of the general

and from to

subject

this

follows

it

time-relations.

points of time, and to limit the

antecedent to a definite period of time

validity of the

the

If

we must make use

after.

It

is

either the

consequent is

to

appoint a

same

time, or

these judgments which

from the nature of the case, based upon causal relations whenever be found amongst real things; for when change in

their subjects are to

one thing involves a second change be due to causal connection. 11.

must

Amongst

variables.

The

equation in the ordinary sense or figures are equal states only that

belonging to s. L.

it

same

(or another) thing,

it

must

hypothetical propositions having indefinite subjects

also include those equations

which contain

in the

if

of analytical geometry

equation of the parabola i.e.

2

y =px

is

not an

a judgment that two lines, numbers,

because of the indefinite value of the variable. the abscissa has any definite value,

has a value which

we

and mechanics

is

determined by

its

It

then the ordinate arithmetical rela-

Q

LOGIC

226

In the same way

tion to the constant.

ing general symbols a(b

may be

algebraical formulae contain

all

translated into hypothetical judgments,

e.g.

+ c} = ab + be.

Passing to hypothetical judgments containing negations, we find A is, is not," represents the negation of a proposition that the form 12.

B

"if

consequence of an affirmation, thus affirming that the This incompatibility may be due are incompatible. and

as the necessary

hypotheses

A

B

either to the incompatibility of certain predicates, or to the real relations of

The relation is always mutual. If the from the affirmation of A, then (according necessarily follows

hindering or counteracting causes.

negation Q{

B

ground and consequence) the negation of A follows necessarily from the affirmation (i.e. the denial of the negation) of B and this is true to the law of

;

A

whether

B

and

represent universally and unconditionally valid judg

ments or temporally valid judgments concerning the particular, or whether their subjects are indefinite (when the sky is clouded no dew falls; when

dew

the sky

falls

To

not clouded).

is

such a hypothetical judgment there

corresponds the categorical judgment, which

The

"

proposition

no right-angled

statement as the proposition

if

;

universal

a triangle

is

and negative.

makes the same

equilateral

right-angled,

the negation of the predicate equilateral

"

lateral

"

is

"

is

triangle

it

is

not equi

stated as the neces

is

1 sary consequence of the determination right-angled.

When tion

(if

a negation appears as the necessary consequence of another nega

A

is

not,

B

is

connection between

not) the

ground of the relation must be the necessary This is the sole

the corresponding affirmatives.

condition upon which the negation of the one can have the negation of

the other for

its

from which to sequence of B. unless I

am

consequence.

The

I

A is when A

invalidity of

infer the invalidity of

B only

is

cannot say that when the sky

certain that

when dew

falls

is

an

infallible

ground

the necessary con

not clear no

the sky must be clear

;

dew only

falls if it

1 The difficulty raised by Twesten (Logic, 64) against the view that the hypothetical judgment with a negative consequent is affirmative is easily removed. If the categorical no equilateral triangle is right-angled is negative, how, he asks, can the judgment "

"

corresponding hypothetical tive? It certainly could not

a triangle is equilateral, it is not right-angled," be affirma if the hypothetical judgment were a statement about the

"if

equilateral triangle, and not about the necessity of a consequence ; but why should we be unable to affirm that a negative proposition is a necessary consequence ? The very possibility of the unconditional negative "no A is B depends upon our knowing that "

A

B

and the determinations contained in the thought of necessitate the negation of ; this, which is the meaning of a universal negation, the hypothetical judgment expresses by affirmation of

this necessity.

HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS is

true that every equiangular triangle

triangle

A A

B

is,

is

not equilateral,

is

we may always deduce

is,"

From

not,"

of the

meaning

it

be said that

the principle, that

B

"

if

is

not,

not,

is,

which expresses

consequence stated by the hypothetical

necessary

the judgment

is

a

"if

of the consequent

judgment. When an affirmation appears as the consequence of a negation

B

if

the proposition

the other proposition

according to the principle that the denial

involves the denial of the ground

the

equilateral can

is

not equiangular.

it is

227

if

A

is

always immediately or mediately grounded

is

upon the position that of different possible hypotheses which are mutually exclusive one must necessarily be valid the position, that is, which finds ;

utterance in the disjunctive

ment

A

"if

A

"either

is

not,

or

is

B

B

is"

But

judgment is,

as

it

is

it

not true that the judg the disjunctive

stands, equivalent to

1 is."

The negation of a hypothetical judgment can take place only 13. through the denial of its predicate that is, of the necessary consequence stated by is

The

it.

the proposition

A

B

i.e.

;

is

contradictory opposite of the judgment "

B

not true because

A

is

(even

if

A

is,

In the same way the negation of the statement

A

because

B

"

is

A

B

is,

is,"

leads to the

"

judgment

if

A

nevertheless "

it

is,

B

is

a not)."

does not follow that

B

is."

A is, and B is, and C is, Hypothetical judgments of the form should not be called copulative hypothetical judgments; they "if

14.

D

then

is,

"if

not the necessary consequence of the proposition

is

do not

is"

state of different relations that they are all necessary

as in the

"

judgment

judgment of several

is

both when

A

is

and when

B

is,

copulative, but the former gives only one

conditions,

and therefore

it

C

consequences,

is."

The

latter

ground consisting

cannot be resolved into several

hypothetical judgments. 15.

The

possibility of the

of the ground, but only

consequence can be connected with each part this possibility as having

when we understand

reference to the partial ground

"

(

34, p. 208).

When

the

moon

is

moon

in

The proposition "when the centre of Vide my Programm, p. 54 sq. not in the plane of the ecliptic it forms a triangle with the centres of the sun and the earth does not mean the same as the proposition "either the centre of the moon is in the plane of the ecliptic or it forms a triangle with the two other central points." For i may also form a triangle when it is in the plane of the ecliptic, but the node does not fall upon the straight line passing through the centres of the sun and the earth. the

1

is

"

2

This shows also the logical position of the so-called concessive propositions, their consists in their rejection of some immediate or mediate consequence which

meaning

might be inferred from the antecedent.

LOGIC

228

same time the lunar node is in a conjunction or opposition, and at the line with the sun and earth, then there must be eclipses," the proposition

may be

resolved into the two judgments

may be

tion or opposition there in a line with the

same

"may"

"when

and

eclipses,"

"

sun and the earth there may be

when the antecedent expresses the

which would annul the consequent does not diminish, organic

"

if

;

moon

when

in

is

conjunc

the lunar node

eclipses."

We

invalidity of a

is

find the

judgment

the radiation of heat from the sun

may have an

life

the

unlimited duration upon the

earth."

THE DISJUNCTIVE JUDGMENT.

III.

37-

The DISJUNCTIVE JUDGMENT exclusive hypotheses one the two it

members

necessarily true.

is

number of mutually

states that of a definite

When

it

does not refer to

of an antiphasis as in the principle of excluded middle,

a simple judgment upon which the different and which, by its contents, determines and limits Most frequently it happens that either the possibilities.

presupposes

always

hypotheses are based, the range of

subject or the predicate admits of a closed series of mutually exclusive

determinations, and these are enumerated by the divisive judgment.

The

i.

is

way of expressing

simplest

to say that neither

its

that a hypothesis

affirmation nor

confronted by an undecided alternative. is

true the negation

false the

But

negation

it is

is

false,

true

is

and

and

A

is

B

is

uncertain

negation can be asserted ; I am But I know that if the affirmation

its

vice versa

;

and

that

if

the affirmation

is

vice versa.

not only between affirmation and negation that such a choice

different hypotheses

amongst be possible

may be

in reference to the

perhaps D.

Where

presented.

same subject

A

Various hypotheses is

perhaps

B>

may

perhaps C,

D, are quite independent of between the hypotheses (thus I might say of Queen Semiramis that she was perhaps tall, perhaps blackeyed, etc.) but if the one predicate necessarily involves the other, then each other there

is

these predicates B^ C,

no

further relation

;

there arises the hypothetical judgment. to accept the

by

one predicate

irreconcilable

is

If again they are incompatible,

to exclude the others,

propositions,

each of which by

and

I

itself

am

confronted

is

a possible

hypothesis.

When

irreconcilable

propositions such as these are both equally un-

HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS

229

V

Such hypotheses are they are connected by the particle not necessarily predicates of one and the same subject, but may be any "

)

or."

certain,

assumptions whatever which for some reason are mutually exclusive, and the relation between which can therefore be expressed in a hypothetical

judgment connecting the affirmation of one with the negation of the other. Thus the particle or contains two statements that the propositions are "

"

uncertain, that

A

2.

is

A

and

that they are mutually exclusive.

perhaps B, perhaps

C

;

if it is

B,

is

"A

C

not

it is

similar juxtaposition of predicates occurs in

;

B or

if it is

C,

C"

means

it is

not B.

judgments which state solid and vaporous

The judgments water can be liquid, a possibility. man can wake and sleep may also be expressed, when any one point of water is liquid, solid or vaporous man time is referred to, in the form "

"

"

sleeps or

We

wakes."

further determinations

"

find the "

:

or"

again

the triangle

when

rectilinear figure has three, or four, or five angles, is

denoted only by a general term there

by means of mutually exclusive thing

is

that

it

is

determinations, any of which 3.

When we

say of a

to

true, the statement implies that

know and

all I

it.

of such hypotheses that one

all

say of a

and incompatible

different

many

may belong

number

further determination

for

When

a plane

Whenever anything

etc."

room

is

predicates.

a triangle, there are

a general idea admits of

plain or spherical, etc.

is

is

necessarily

the mutually exclusive predicates which

are subjectively or objectively possible are included in the enumeration. or C is is Then we have the disjunctive proposition: either either

B or C or

D.

Thus

in stating a disjunctive

in view the necessary validity of

D A

B

A

is

;

judgment we have

one out of a given number of possible

and incompatible hypotheses. 4.

The

simplest case of such a disjunction

far as tradictory opposition of judgments, so

excluded middle.

Of

is

the other false.

necessarily true,

the two propositions

But

A

is

to be

is

is

B, and

just

found

in

con

subject to the law of

it

because

A

is

not B, one

this disjunction

is

The so self-evident it is of little value (see 25, p. 154). with junctions are those which limit our choice amongst positive judgments important dis

definite predicates. state the limited amongst these are the disjunctions which be a number of mutually exclusive attributes by which general idea may is either a crooked triangle A line is either straight or further determined. 5.

First

;

right-angled or oblique-angled

water

is

;

a

human

either fluid, solid or vaporous.

being

The

is

either

male or female

;

kind of possibility possessed

LOGIC

23o

by the single members of the disjunction

The meaning

206-7.

of the disjunction

as falling under the general idea

A

the various attributes possible in

A.

these

if

;

Here then

anything

there

is

a

to

me

only

must have some one or another of This meaning full

is

most obvious

in

force of disjunctions such

either a straight line or a crooked.

is

it

line,

34, 5, p.

known

that a thing

the hypothetical expression, which gives the as

that discussed in

is

is

presupposed both a judgment ascribing a general

is

and the knowledge of a closed series of mutually exclusive determinations which are possible to that predicate. predicate to the subject,

When we

6.

be

have in our minds

all

the particular subjects which

this relation

may be

expressed also in what

JUDGMENT.

"Lines

are

"

human

beings are

some

them

of

some of them

"

is

water

is

sometimes

called the DIVISIVE

straight, the

in the

others

crooked";

female."

When we

same thing the corresponding

sometimes

liquid,

may be

male, the others

review a complete series of changes

form

may

A, thus thinking of the different determinations as actual,

included in

solid,

sometimes

vaporous."

Here we must notice that the relation between divisive and disjunctive

When our knowledge judgments varies according to circumstances. is derived from experience alone, the disjunctive judgment is grounded upon the

divisive

;

since

is

it

a matter of fact that

all

human

beings

be divided into males and females, we infer that a third kind sible;

and upon

human being

this inference

is

we ground

man

either a

or a

woman."

comes

other hand, the disjunctive judgment that a triangle

we is

is

the disjunctive

first;

either parallel to

"

only after the judgment

or not

one generating

when we know

that

it

line or

is

It

complete.

a plane which intersects a right cone

the base, or not

the generating lines,

only

"every

In mathematics, on the

certain that our enumeration of the kinds of triangle

parallel to

judgment

may

impos

either right-angled, or acute-angled, or obtuse-angled, are

the same with the judgment

all

is

all

;

;

if

and

not."

exhausts

not parallel,

all

it

is

either intersects

in the latter case

it

This judgment comes the possibilities do

we

is

either

first,

and

obtain the

division of conic sections into circles, ellipses, parabolas, and hyperbolas. The divisive judgment may also be in the form of a "

judgment tions,"

and

expressed copulative the circle, ellipse, parabola and hyperbola are the conic sec

the definite article indicating the identity of extension of subject

predicate.

The need

of expressing the completeness of the enumeration more than some has led to the divisive judgment definitely by the use of 7.

"

"

HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS being expressed in the form of a disjunction or crooked

"

"

;

of expression "all

lines are

is

human

ambiguous. straight

"all

:

beings are either male or

all

The judgments

231

lines are either straight

But

female."

mode

this

said to be disjunct are not

lines are crooked"; as,

the

for instance, in

judgment "the human race is descended from one pair or from several," where the disjunction is between the propositions "the human race is descended

from one

pair,"

and

"

the

human

race

is

descended from

In the former instance the disjunction applies to each particular line; so that here again, if we would avoid ambiguity, we must make use of the hypothetical form "anything which is a line, is

several

pairs."

either straight or

crooked."

These disjunctions have for their members the more exact determin ations of the subject, and may therefore be reduced to divisive judgments which divide the subject-concept into its species. From them we must 8.

distinguish judgments which unfold the different possibilities in the predi cate of a given subject. 1 When we say that the planets either shine by their

own

light or derive their light

from the sun, we do not mean that

the fact of being a planet includes both possibilities, and that

by their own really

do

is

light,

to start

some shine

while others are illuminated by the sun.

from the judgment

tigate the exact nature of their light

planets

"the

shine,"

What we

and

to inves

the possibility of finding an

and

Take

explanation amongst the given circumstances.

the proposition

world has either existed from eternity, or has had a beginning

;

"the

and

its

In the

beginning was due either to a free cause or to blind necessity." disjunction we start from the existence of the world as datum, and

first

enquire as to the duration of this existence

;

in the second, our

datum

is

the beginning of the world from a cause, and our enquiry concerns the different kinds of causes. When we say he is either a hypocrite or a "

presupposed that he behaves unreasonably, and the question is, as to the source of this behaviour. A further distinction may be made

fool,"

it is

according as the closer determinations of the predicate form a part of its meaning, or are gained from a consideration of the concrete possibilities of the particular instance.

1 Trendelenburg s doctrine that the disjunctive judgment is a statement of the exten sion of the subject concept applies only to those disjunctive judgments which are based upon a division of the subject concept. It is not applicable when the disjunction refers to changeable states, and it is not applicable in this sense when the concept of which the

possible determinations are developed

is

predicate.

Cf.

my

Prograrnrn, pp. 60, 61.

LOGIC

232

Judgments such as

9.

no divine

justice,"

"

either the

wicked

will

be punished, or there

upon hypothetical judgments, and

are grounded

is

are

denial of the consequent involves the governed by the principle that the denial of the ground, taken together with the principle of excluded If there

middle.

is

a divine justice the wicked will be punished

the wicked will be punished or not

either

supposed ground of

not, the

if

their

punishment cannot exist. It is of course true that the disjunctive judgment "A is either,/? 10. or may be resolved into two hypothetical if A is not J3, it is C" "

C,"

and

"if

A

disjunctive

is

B,

it

is

not

but

C";

it

does not follow from

judgment has no importance of

this that the

own independently

its

of the

We

cannot state a negation as the ground of an The affirmation, unless the disjunction has already been established. judgment that if light is not matter it is motion, cannot precede the know hypothetical judgment.

ledge that light 11.

It

disjunctive

A may

is

follows

either matter or motion.

from the nature of the statement contained in the

judgment that the

be either

B

or

C A

propositions

"A

must be either

is

B or

either C,"

are

B

or

all

C

exactly

equivalent.

38.

RESULTS.

THE FUNCTION OF JUDGMENT

is

always the same in so far as

states categorically that a predicate belongs to a subject.

The

it

always

differences

which we find depend partly upon whether the synthesis between subject is simple, as in the denominative judgment; or complex as

and predicate in ju.lgments

Partly,

or

is

governed by the categories of attribute, activity and relation. again, upon whether the subject of a judgment is a simple idea,

itself

a synthesis of the nature of judgment, or a combination of

such syntheses of which we

may

predicate that

it

is

false,

possible,

necessary, etc.

The and real

made are based upon differences of predicates and not upon differences in the function of judgment ; any variations in function are to be found in one class alone, that of distinctions generally

subjects,

categorical judgments.

For

this

reason the importance of the predicates presupposed in

judgment becomes more evident;

to recognise

these

as

all

remaining the

HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS same throughout

changing subjects

the

is

essential

233

characteristic

of

judgment.

So

1.

far

our investigation has shown that the customary classification which has been established mainly by the authority of

of judgments,

Kant,

is

The is

inadequate.

and presupposition of all judgment is the judgment which immediate, simple and positive; and this consists in the synthesis of basis

a subject and predicate accompanied by the consciousness of objective The meaning of this synthesis and of its objective validity validity.

depends upon the nature of the ideas connected in the judgment ; it is simple when the act is merely one of denomination, complex when it is That grounded upon the categories of attribute, activity and relation. which takes place in judgment is always the recognition of the agreement between an idea previously known and one element of the subject and, ;

meaning of

according to the original

"

to

know,"

every judgment

is

the

is already cognition and recognition of something in the subject which known. But it does not follow that every judgment consists only in this knowledge, and is nothing more than the statement of a subsumption.

one

In

class of

judgments

it

is

just as indispensable that there

between attribute or

also be present the consciousness of unity

and

thing, or the consciousness of relation

between two things

;

should activity

and sub-

sumption cannot take place in judgments concerning attributes, activities, and relations without the differentiation and synthesis of different elements in a presentation.

Even

the judgments which have numerical

predicates show no

the numerical judgment that

ments

;

determinations

essentially different function. it

every judgment which

It

is

for

their

not peculiar to

must have been preceded by other judg and names it by

refers to the particular,

All that is peculiar the subject-term presupposes a previous judgment. to numerical predicates is the nature of the preliminary operations which necessitate preliminary they necessitate, just as other relational predicates nature to their equality and inequality e.g. peculiar operations appropriate

presuppose measurement

;

the

number given

is

compared with a number

previously known. 2.

But the course of thought extends beyond immediate knowledge, from to think of judgments which might take place as distinct

and leads us

actual judgments.

Then new judgments

arise

having reference to these

ideas of judgments or to the relations between them.

LOGIC

234

Every statement contains the judgment that the synthesis expressed by necessary or true, and in the negation this judgment is contradicted by the statement that the synthesis is false. Besides this affirmative or negative decision, we find on the one hand the judgment that a hypothesis it is

is

deny

it

;

that

i.e.

possible

on the

is

it

not subjectively necessary either to affirm or to

other, the judgment that

it is

the necessary consequence of

another hypothesis, or that amongst a number of given hypotheses one

must necessarily be true. These judgments all resemble simple judgments in that they state simple modal predicates concerning a subject; their peculiarity lies, therefore, not in the synthesis, but in the nature of their subjects and predicates. Since, however, these subjects form an essential element of the function of

judgment, and since the predicates refer to just that characteristic of the function which expresses its relation to the final aim of all serious thought, such judgments are in an eminent degree logical. Indeed, there could be no conscious judgment at all unless some account were taken of this re

between the originally subjective combination of subject and predi

lation

cate

We

and these modal determinations.

special attention to negative, hypothetical

are therefore justified in giving

and disjunctive judgments; not

because they are special kinds of the judgment, but because they have reference to hypotheses

Thus

there

is

and

really only

to their logical value

one

sort of

and

significance.

judgment, the categorical statement

If any distinction at all is made and FORM the MATTER of the judgment, then by form we must mean that mode of activity in thought through which a judgment as that a predicate belongs to a subject.

between the

such

formed

is

same.

The

;

and

this

diversity

forms of judgment

is

mode

which

is

of activity

is

in all cases essentially the

generally represented as attaching to the

really a diversity of matter,

nature of subjects or predicates.

As

this

and depends upon the

nature varies, we certainly find a

modification, sometimes in the movement of thought which precedes the judgment, sometimes in the meaning of the predication that is, in the meaning of that unity between subject and predicate which is the thought

present in "

forms

"

all

to the verbal

reason

judgments.

The conventional

doctrine

of the

different

of judgment (due in part to the importance generally attached

why we

expression) loses sight of the one idea which give the

All judgment,

number of

name

therefore,

of judgment to

presupposes

predicate-ideas which

may be

all

first

is

the sole

the different kinds.

of

all

the

presence of a

recognised in the subjects.

It

HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS requires, moreover, that

we should have

235

ideas of different kinds of synthesis

between subject and predicate these differences being determined by the nature of the subjects and predicates, and constituting the meaning of the ;

simple statement that the predicate belongs to the subject. to denote the resulting kinds of synthesis If, however, we still continue "

as

"forms

of judgment,

it is

after all a question as to the use of language.

doing we must guard against thinking that the name "judgment" denotes a number of originally different and co-ordinate acts of thought, a mistake which is constantly made when affirmative and negative judg

But

in so

ments are distinguished as opposite forms. Unless we do so we are in danger of losing sight of the one concept which should correspond to the term,

and the term

itself

becomes a mere homonym.

PART

II.

REGULATIVE.

INTRODUCTION. 39-

IN order that the function of judgment may actually succeed to certain

and universally

valid judgments,

before

is

it

all

in attaining

necessary that

the certainty of the particular judgment in question should be invariable, and accompanied by the consciousness of its universal validity. Two

conditions are essential to

this.

In the

place the person judging must

first

be conscious of the logical ground of his judgment and secondly, the elements of the judgment itself must be completely determined and con ;

stant,

and thought by every one

For the

latter

of our iudgments, perfect concepts

be grounded

in

in the

same way.

condition to be fulfilled

;

and more

it is

necessary that the elements

be logically especially their predicates, should

for the former, that the judgments themselves should accordance with universally valid and necessary laws of

thought. 1.

In Part

we have taken thought

I.

analyzed the function of judgment in which

aiming

at

and universal

truth

validity.

we

as it

actually find

We

necessary and therefore valid for

We

must now

which judgment

test

attains

this its

claim,

end.

all

and have

itself

when

have sought to show the its relations, and we have

meaning and significance of the judgment in all found that one essential element of every statement i.e.

it,

always manifests

is its

claim to be true,

thinking beings.

and investigate the conditions under The conditions, that is, under which the

involves momentary certainty which accompanies every actual judgment which under and no delusion, but is the expression of objective necessity ;

the universal validity of the individual act of 2.

In order that a judgment

place that

it

may be

judgment

perfect,

it is

should remain unaltered for the person

should always repeat

it

in just the

is

guaranteed. necessary in the

who judges;

same way whenever

the

first

that

he

same subjects

and predicates recur and that its certainty should therefore If the same synthesis were for him at one time variable.

also be in

;

certain,

at

LOGIC

24 o

same way within the

in the

connected

same subjects and predicates were not always limits of one and the same con

the

if

anothei uncertain;

thought it possible that, starting from the same data I then the act of judg in the future than I now do otherwise might judge success its involves confidence in the irre for have must ment failed,

sciousness

if I

;

the judgment. fragable validity of But the certainty that a judgment

permanent, that the synthesis is this certainty can only be

is

irrevocable, that I shall always say the same,

it is known to depend, not upon momentary psycho, which vary as time goes on, but upon something which is logical motives, immutably the same every time I think and is unaffected by any change.

forthcoming when

This something

is,

on the one hand,

am

my

self-consciousness

the cer

itself,

same person who now thinks and who thought I, who thinks both one thing and another. On the other hand, it is

tainty that

before,

that about

I

which

content, which

the

I

dependent of the state of

The

my

judge,

itself as far as

thought

recognise as identical each time,

I

certainty that

mind

its

un variable is

quite in

of the individual thinker.

am and

I

regards

and which

think

is

final

and fundamental, the con

Here there can be none thought and all certainty whatever. but immediate and self-evident certainty we cannot even say that it is In the same way the certainty necessary, for it is prior to all necessity.

dition of

all

;

of my consciousness that it is

I

think this or that

inextricably interwoven with

my

is

immediate and self-evident; the one involves ;

self-consciousness

the other.

now we can

say that there is a necessity which obliges me to judge of one particular way so soon as I am aware of it if I can know that as surely as I am I, I must connect subject and predicate in this way, for no other reason than that I have thought of them, then my discernment If

an idea

in

;

of this necessity stitutes

is

the ground of certainty for every judgment.

consciousness of

my

its

logical

established between the judgment and

my

that so surely as I myself continue the

same

ment

in the

judging must

What

A

I

consciousness

is

itself; I

thus

know

must always repeat the judg

is

the

first

condition

:

for a judgment

to be perfect the

person

be conscious of its logical ground.

conditions must be fulfilled in order that

consciousness If an

self

same way.

This then

3.

This con

ground, and a connection

we may

attain to this

?

of which I

am

conscious

is

to

be the ground which makes a

INTRODUCTION judgment

B logically

necessary, then this necessity must rest

is

in so far is

upon a con

B

A

always and invariably follows from the necessity knowable; the presence of however

stant law, according to

and only

241

which

A

pure matter of fact, without which the necessity cannot take effect. the consciousness of the ground resolves itself into consciousness of

Thus

the law according to which

B

follows from

premises, and consciousness

its

of these premises.

may be

It

that these premises are not themselves judgments, but objects

which nothing more is known than such as sensations, reproduced ideas

of consciousness of another kind, of that they are at the

of

all

moment

present

;

which are present to consciousness. Thus so far necessity we have arrived at an ultimate fact which

kinds, or concepts

as concerns logical

must be regarded as pure matter of necessary consequence?

equal

is

intuition

based upon our concept of a

which gave

rise to

it,

in

my

consciousness at

;

circle

and

its

to

is

:

what

all,

is its

concept however, or the

this geometrical

No

image should

either from intuition of external objects,

Every judgment of perception

premises the immediate consciousness of a sensation,

this again is purely

be raised as

this

;

shown why

or as the result of inventive construction.

includes amongst

we can ask

all

that the diameters of a circle are

in the last instance matter of fact.

is

universal logical necessity can be

appear

fact

The judgment

whether

matter of its

fact.

It

true that the question

is

may

conditions are normal, and whether, therefore,

judgment concerning the existent i.e. it maybe asked what and universally valid inference can be drawn from the simple necessary But that the sensation is there has nothing act of a subjective sensation.

it

to

justifies a

do with

a simple

logical necessity,

we know

it

by our immediate consciousness of

fact.

When, on the other hand,

the premises are themselves judgments, then itself into the consciousness of the

the consciousness of necessity resolves

laws according to which from certain judgments other judgments follow the rules of inference), and the consciousness of the validity of the (i.e. premises.

Here again the same conditions apply

of the grounds of these judgments.

conditions unless their certainty as

immediate matter of

fact,

no

is

;

we must be conscious

No

judgments are exempt from these so self-evident that it must be regarded

less

than the

"

I

think,"

or the presence of

definite ideas; the certainty of these judgments cannot be further analysed by a consciousness of their necessity. To them we must add the judg

ments whose contents constitute the fundamental laws of s. L.

all

necessity,

R

LOGIC

242

the validity of which there according to which anything is necessary, and from some other judgment, but follow fore cannot be seen to necessarily

judgments, that is, which are as necessary as the a certainty which itself, or which can be shown to have

can only be recognised "

proposition is

am

I

"

of this proposition. necessarily involved in the certainty rules for thought is possible unless down is to which Thus no logic lay

such ultimate laws can be known by tain

and

Our

self-evident.

us,

task

first

and shown to be absolutely cer is

not to trace the inexhaustible

phenomena of matter of fact and of individual experience which constitute the given premises of our judgments in particular cases, but to lay

down

the laws according to which certain ideas necessary, and

and judgments make other

constitute a

ground for their certainty. judgments logically This involves what we have already claimed as a postulate in the Intro duction,

3

:

that

we

are able to distinguish objectively necessary thought

by the evident certainty with which

it

manifests

itself,

and by analysing the

Our success

conditions of this certainty to discover such universal laws.

out this task must show whether or not there

in carrying

is

any ground

for the postulate. 4.

In order that a judgment

may be always

and immutably cer

valid

tain, other conditions must be fulfilled which apply to an earlier stage in

and are not fulfilled in its natural course. The ideas denoted by and predicate terms must be constant and completely determined. subject thought,

The

of the identity of a judgment attaches in the

consciousness

verbal expression, to the fact that the

first

same statement

instance to

its

made about

the same thing in words, and the predicate must always have

this verbal

expression, the subject

at least

in explicative

is

and universal

Unless every word always keeps exactly the same meaning, judgments. the meaning being thus perfectly definite and fixed, we cannot possibly be certain that the repetition of the

the

same proposition

is

also the repetition of

same judgment, and the meaning of the judgment

uncertain.

Indeed, the very act of

itself

becomes

judgment tends to bring about this

confusion by a sort of shifting amongst our predicate ideas, for on ordinary

we are often guided by what is no more than a vague similarity between the new and the familiar (see 7, 8, p. 44). When the Marco-

occasions

manni mistook the

lions

which were

let

loose

upon them by Marcus

Aurelius for dogs, and slew them without ceremony, their judgment are dogs

animals

"

meant only

known

to

that the lions were

them.

more

Even while they were

like

"

these

dogs than any other

judging, their idea of the

INTRODUCTION

243

dog and the meaning of the word was changed, and a new image com prised in

it.

Again, although the necessity of judgments their universal validity, this only

same premises must synthesize

means

in the

a sufficient guarantee for

is

one who

that every

same way.

But

if

starts

from the

the primary data,

the ideal elements between which the synthesis takes place, were different

and absolutely incommensurable, so that every one connected a different meaning with a given word, then, however small the difference, our judgments would never actually attain to universal validity, for every individual

they would at the most approximate thereto.

That community of thought which, we endeavour to reach by means of language, and which is the condition of higher mental development, more especially of all science, would never be

We

saw, in

fully realized. 7,

that in the natural course of thought the ideas of the

individual are not constant nor completely determined,

do

individuals

On

words. of

and

that different

same ideas nor denote them by the same

not have the

the contrary, the very laws which govern the natural formation

both their variability in the individual and their different individuals, thus prohibiting a completely fixed

necessitate

ideas

difference

in

verbal signification.

Hence we cannot speak nor of

seems

its

to

be the same

really the

is

And

subject.

valid

in

of the complete logical certainty of a judgment we assume that whenever a judgment

invariable validity unless

same

;

before

concrete*,

as another,

that the

we can

therefore,

because clothed in the same language,

same statement

is

say that any given judgment

is

comprehensible and convincing

must assume that the ideas contained

in

it

common

are

it

the same

made about

universally

we

for all

to all

and the

of natural thought

is

completely excluded by

the ideal of perfect thought, and a logic which

is

to contain the rules of

same

for

all.

The anarchy

are the conditions perfect thought must begin by determining what fulfilled 5.

to

be

by ideas themselves as elements of the judgment.

This brings us to the two main problems of

this

part of our

work. that

are possible are, (a) The conditions upon which perfect judgments the ideas which enter into the judgment as subject or predicate should be

absolutely constant, completely determined, the

denoted by unambiguous terms.

we

call a

An

same

idea which

concept in the logical sense of the word.

for every one,

fulfils

One

and

these conditions part of our task,

LOGIC

244 therefore, will

ideas (b)

may The

ments

is

therefore

be to investigate the conditions necessary

condition of the logical necessity and universal validity of judg have a ground. second investigation must

A

that they should

discover the

necessarily from

One

its

rules

according

to

which a

judgment follows

premises.

part of this investigation will be concerned with the laws according immediate judgments find their ground in the ideas of which

to which

are

in order that our

be logical concepts.

composed

they

;

the other part with the laws according to which mediated

judgments are grounded upon other judgments.

CHAPTER

I.

THE CONCEPT. 40.

THE

LOGICAL CONCEPT

differs

from the general idea which has developed and is denoted by a word, in its constancy,

in the natural course of thought, in

and immutability of its determination, and in the It differs will employ the same term to denote it.

the completeness

certainty that every from"

one

the concept in

metaphysical meaning as the adequate thought its only aim is the complete determina

its

of the essence of an object in that tion of our predicate ideas,

and

this

aim has no

direct connection with

the question as to whether the concept corresponds to any real object, The quality of or whether it adequately represents such an object. It is the fact that it is with every idea. generality it has in common which defined, and clearly distinguished from all other ideas, strictly

forms the distinguishing characteristic of the concept, and in the construc tion of logical concepts our aim is to establish one mode of arranging thinking beings, and so to com without conscious purpose plete systematically the process which begins their

manifold ideal contents for

all

in language,

we must distinguish three meanings of In speaking of concepts," It may denote a natural psychological production, and here the word. "

i.

as used in ordinary natural term the simple correlative of the it has become a mental where It is the idea at the stage language. "

"

it

is

possession,

and has gained the generality explained

to every idea as such.

It

is

now

judgment, more especially a predicate. seen,

in

7,

which belongs

become an element of the Such ideas, as we have already

qualified to

are different for different people,

and are

still

in the process of

so that a word formation; even for the individual himself they change, same person. the for even same the does not always keep meaning Strictly

speaking,

it

is

only by

a

fiction

which

neglects

individual

LOGIC

246 peculiarities that

we can speak

of the concepts denoted by the terms

used in ordinary language. In contrast with this empirical meaning the concept may be 2. viewed as an ideal it is then the mark at which we aim in our endeavour :

we seek to find in it an adequate The concept in this sense must enable us

to attain knowledge, for

copy of the essence

of things.

to penetrate into

the very heart of the thing, to understand it ; i.e., to see that its particular determinations as connected in it are the necessary consequence of its

The concept

nature as a unity.

stone to physiology

;

of

life,

in this sense,

would be the key

and physics that of this direction would be

that of matter, to chemistry

;

psychology ; and all knowledge in complete when we could exhibit a system of concepts comprising the true When we try to think of an absolute counterpart of every existing thing. mind,

to

and divine knowledge, we define it by saying that in the absolute intelli In this sense we may indeed speak gence, concept and being are one. of the truth of our concepts

they are true

;

when they are in themselves The true concept of

the exhaustive expression of the nature of things.

God would comprise in its of God in all its aspects. 3.

determinations the thought of the real nature

Between these two meanings of the word, which may be called the

empirical and the metaphysical, there lies the logical^ which alone concerns

us here.

This has

its

origin in

the

universal validity in our judgments.

logical

All that

demand is

for

required

should be absolutely fixed and determined, and that

certainty

all

and

that our ideas

is,

who make

use

same system of denotation should have the same ideas. In what relation our thought stands to the existent, and whether there is absolute of the

agreement or not, is not determined here must indeed suppose that as knowledge

or at least not directly. is

always growing, less

tained in our ideas at any given time than in the existent

;

is

We con

at the best

our ideas are representations which correspond to the existent so far as If our judgments could never be they go, they are never exhaustive. universally

valid

unless

metaphysical sense, and differences

it

and indefiniteness

inadequacy to the

elements were perfect concepts

their if

existent,

were as in

difficult to

our ideas as

then

it

in

the

get rid of individual is

to

overcome

their

we should be debarred even from

approximating to the goal of knowledge by the gradual progress of science, for science always It

is

presupposes uniformity in the construction of concepts. the formal sufficiency

necessary, therefore, to distinguish between

THE CONCEPT of concepts

adequacy

;

for

former before the 4.

the

of

purpose

and we must assume

Finally,

latter

we must

judgment,

that

it

is

247

and

their

metaphysical

at least possible to attain the

has been reached. distinguish

between the

logical perfection of the

concept and the appropriateness of its construction to some end, the latter being connected with the problems of classification within some given sphere of things (objects, actions, crimes,

A

etc.).

concept

may be

completely determined, and hence logically perfect, and yet not so well For the adapted as some other to meet the requirements of science. is to attain, by means of concepts and the terms which denote them, the greatest possible simplicity and brevity in our know How must our concepts be formed to and it therefore asks, ledge

aim of science

"

;

most important and

to the

enable us to give the simplest expression

By this aim we must be guided comprehensive universal judgments ? in methodology, which has its origin in the problems arising out of the "

nature of the conditions of our knowledge.

On

the other hand,

we

if

are really to attain logical perfection in our

judgments, it is necessary that we should always have a sufficient supply of logically perfect concepts to enable us to express and determine every In judging we do not thing which becomes subject to our judgment.

merely repeat what is already known ; we are constantly appropriating something new. In this sense the possibility of perfect judgments is determined by the extent to which the raw material of all human ideas

We must always be prepared has taken permanent form in concepts. with concepts in which to express our knowledge ; or we must at least be sure of

being able to create

conceptually determined.

them from elements which are already

We may

compare

this

ideal with that of a

universal alphabet which comprises generally accepted signs for all the of speech. distinguishable simple sounds possible to the human organs universalis the characteristica of s idea of view Leibnitz From this point for that at which we should aim in the was a most

appropriate expression

1 logical construction of concepts. 1

Cf.

Histor.

Ueber Leibnizens Entwurf einer allgemeinen Charakteristik." Trendelenburg B eitrage zur Phil, iii. p. i sq. And Descartes, Ep., I, in, where a similar "

:

is developed Ejusmodi linguse inventio a vera Fhilosophia pendet. Absque enim impossibile est omnes hominum cogitationes enumerare, aut ordine digerere Et si quis clare imo neque illas distinguere, ita ut perspicuse sint et simplices "

thought

:

ilia

;

.

explicuisset, quales sint et

ideas

illoe

simplices,

ex quibus componitur quidquid

receptum, auderem

demum

illi

quae in

cogitant,

sperare linguam aliquam

hominum

essetque

.

.

imaginatione versantur,

hoc per universum orbem

universalem," etc.

LOGIC

248

The

5.

essential characteristic of the concept

generality 1

by

abstraction,

i.e.,

is

generally said to be

this is the doctrine that

Connected with

by a process which separates the

its

concepts are gained

common

characteris

of particular objects from those by which they are distinguished from each other, and gathers together the former into a unity. But the sup tics

porters of this view forget that, in order to resolve an object of thought into

its

particular characteristics,

judgments are necessary which have

their predicates general ideas (or, as they are

and

as these concepts

make

commonly

for

called, concepts),

the process of abstraction possible, they must

have been originally obtained in some other way.

They

moreover,

forget,

that the process presupposes that the series of objects to be

compared is made of some

some way determined, and a tacit assumption is motive by reason of which we group together just these objects, and seek their common elements. If we are guided by any motive, and not by already in

mere

2

caprice,

from the

common

it

must be found ultimately

in the fact that the objects are

recognised as similar, because containing certain elements to all ; that is, a general idea is already there, by means of which first

these objects are selected from amongst all others. There is only one connection in which the doctrine of the construction of concepts by com

parison and abstraction

is

at all appropriate,

and

that

is

when we

elucidate

meaning of a word by enumerating the common characteristics of the things which, as a matter of fact, are always denoted by the

the actual

word. 1

In explaining the concept of animal, gas,

See Kant in the Transcendental Aesthetic,

of as an idea which

contained in an infinite

2, 4.

theft,

etc.,

we might

Every concept must be thought

number

of different possible ideas (as the element common to all), and therefore as comprising these ideas under it. 2 Drobisch is quite consistent in admitting that this selection is arbitrary (Logik, edn. It is in itself a 18, p. 20). 3, completely arbitrary matter what objects we choose to is

compare with each other we may compare a raspberry cane with a bramble, but we may compare it with a penknife or a turtle. When, however, the Linnean system, which classifies together widely different plants, is cited as an example of this "far-fetched comparisons," it is overlooked that the concepts by which the Linnean classes are deter mined are not due to this simple and direct method of In this method it is comparison. the common element of objects which are chosen at random which is selected, while the Linnean classes, on the contrary, are the result of an endeavour to find simple distin ;

also

guishing characteristics whereby to divide into definite groups the incalculable varieties of plants. First it was seen that plants differ in the number of stamens, etc. ; then followed the methodical grouping Of together of those which agree on these points. course, this distinction was itself based upon a comparison in the wider sense, but it was first employed to discover differences, and not the common element, of the com objects

pared. (The last edn. 5, p. 21.)

two sentences

refer to the contrary

view expressed by Drobisch,

THE CONCEPT attempt to select the rally

called

"animals,"

of

characteristics

the

all

all

bodies called

the

gene

things or of

"gas,"

all

the

Whether or not we should succeed, whether

theft."

it

a recipe for the construction of a concept possible to carry out such that

if

of

or

l

"

actions called is

common

249

is

another question.

we could assume

to

call

animal, gas,

concept we

way

is

that there

There might be some chance of success is never any do.ubt as to what we ought

etc.

theft,

But

are seeking.

we

possessed

the this

we

to look for the spectacles

that

form a concept by abstraction in

if,

;

to

is,

already

are wearing by the aid of the spec

tacles themselves. 6.

Nevertheless, there

is

some

truth in this doctrine.

cerns the generality of the concept,

we may

find

it first

So

far as

con

in the fact that as

a rule logical concepts merely complete ideas which have arisen naturally;

they do not supersede them ; we cannot change the nature of ideation, and the concept as a work of art must always be preceded by the idea as

Now

a natural development.

every idea naturally possesses generality,

detached from the original particular intuition or par ticular function, and has been made our own as a reproducible object nor can any arbitrary action on our part deprive the idea of this natural

inasmuch as

it

is

;

But

generality.

no way depends upon whether an idea

this generality in

has been formed from one intuition, or from intuitions

(

7)

;

all

guardedly expresses

it

we

that is

learn from

contained in an

it

many

is,

infinite

similar or dissimilar

that the idea

number

as

Kant

of possible ideas.

The Socratic method of determining concepts is in the main the same as this. It always starts by assuming that definite concepts correspond to the current meanings of words, and it proceeds to find the right explanation of the word by comparing particular examples of that which it denotes, and contrasting with these examples of that which it 1

does not denote.

The

only difference

is

that Socrates does not

aim

at

surveying every

To the present day the particular thing, but contents himself with a few examples. doctrine of the concept is really based upon this Socratic method of always presupposing must be concepts corresponding to words ; and to this method is due the of general failure to distinguish between the concept of psychology and the concept The method finds its justification and importance in the fact that in language as logic. learnt tradition we find it already established what concrete things and events are that there

by

a word, customarily named by certain words, and as we come gradually to understand the idea of a number of particular objects is connected with it before we are conscious of answer of its general meaning as such. typical instance of this is to be found in the Children and Theaetetus to the question: What is eTrto-r??/*?? ? it is mathematics, etc. those without scientific training will always answer by giving an instance instead of a the Socratic method was that it pointed out service rendered definition. The

A

by

primary

the meaning of the are based.

word

as such, that

meaning upon which

particular acts of

naming

LOGIC

25o

Whether or not

it is

contained in

many

nature of the idea or concept, and

actual ideas,

makes no

it

been derived from one or from many. But we may find a further justification

for the

the generality of the concept in the fact that separation

of the

immaterial to the it

has

importance attached to necessitates a complete

it

meaning of the word from

is

difference whether

particular intuitions, thus

securing for the judgment a clear and definite meaning, and substituting for a vague comparison a real statement of unity between subject and predicate.

When we

see a

palm

for the first time,

and

call

it

a tree,

we

do so

are led to

and beeches, which we know, and the images of which are connected with the word although we may not by

its

general similarity to the

firs

"

tree,"

have noticed exactly wherein the similarity consists. "The palm is a tree is not strictly justified as a proper judgment unless the word "tree raeans nothing but what the palm has in common with firs, beeches, etc., "

"

then only can

we

take the judgment in

its

strict

palm everything which is contained instead of the vague and inaccurate meaning, in the

in "

and proper

common

the selection

which

to the objects is

I

call

all

which

tree,"

tree."

the characteris

But the chief object of

trees.

not to find a general idea comprising the particular

to obtain a firm grasp of the general idea

I find

thought of the The palm is like a

my

This process certainly involves a conscious selection of tics

"

sense,

is

;

it

is

already indefinitely and

confusedly contained in the thought of the particular, and, by sharply it, to give a definite meaning to the judgment, thus completing a

defining

The involuntary action of process which always begins unconsciously. psychological laws is sufficient to give rise to generic images formed from manifold similar intuitions, the differences of the particular images being lost sight of,

Thus we

do,

and leaving shifting schemata to correspond to our words. no doubt, drop the distinguishing elements, and retain those

which are common, but the process

is

incomplete because

it

is

not

grounded upon any conscious comparison and distinction of the parti cular characteristics. To supplement this process is the aim of conscious comparisons

(7, n,

p. 47).

formation of our ideas

we

It is

find

the abstraction which separates.

true again

that

in

the

involuntary

what alone should be called abstraction, It is

by means of

this that

we break up

the undivided whole of intuition into thing, attribute, and activity, and that by detaching them from this unity we form those abstract ideas

which enable us to compare different things, finding them alike in some respects, different in others, and which alone can supply predicates for the

THE CONCEPT

251

judgments in which conscious comparison and distinction take place. is true, also,

It

that a comparison of partially resembling objects taking place

may become new concepts.

more

under these conditions

the

for the formation of

If visible objects always presented the

or less fortuitous occasion

same combination of colour and form, we should have much more that is, in difficulty in constructing separate ideas of colour and form abstracting

them from the given whole

;

but a conscious comparison of red

only possible after such an abstraction has

things as to their colour

is

taken place,

simultaneously with

or,

horse, the dog,

at

least,

and the

of four-footed animal,

lizard,

may perchance

we happen

if

to

A

it.

comparison of the

lead us to form the concept

be struck by their

similarity in

having four feet (though more probably we should proceed by differentia

quadrupeds differed from men and birds, beetles and on the one hand, and from snakes and snails on the other) and many generalizations arise in this way. But the processes, when thus

tion, finding that flies,

;

carried out, are not the result of intentional

skill,

nor

is

their

product such

The characteristics found upon com always subject, when selected in this casual way, to

as to satisfy logical requirements.

parison to agree are

that natural indefiniteness elasticity of

selves

and absence of

limitation which arises from the

our ideas and their tendency to annex what

and place

it

lacks a solid basis

under the same denotation

;

is

similar to

them

and the whole process

the characteristics which form the predicates of

when

judgments of comparison are not themselves perfectly definite and deter mined by every one in the same way. It is one of the chief failures of the

ordinary

doctrine

of the

concept

that

it

proceeds

as

if

these

characteristics were given ready made, and such as to need no further elaboration. Really, the enormous difficulty of passing beyond the in natural state which every one speaks his own language consists much less

the processes of comparison

in

itself

than in establishing accurate

the difficulty is to and generally accepted standards of comparison ; determine conceptually the attributes which are to be used as charac />.,

teristics. 7.

The

developed naturally and in

it

is distinguished from the idea which has the basis of ordinary speech by the fact that of ideas to expand in the process of formation

logically perfect idea is

the natural tendency

has been counteracted by an activity which negates and limits, and thus form and consistency. If we disregard for the moment the demand gives

that ideas should be the

same

for all,

we may

charsay that the essential

LOGIC

252

concept is the constancy and complete distinction of the which is denoted by any given term.

acteristic of the

ideal content

This constancy presupposes that a definite ideal content and its appro priate verbal sign have been consciously fixed by us in order that we may always be able to reproduce of

its

strict

identity.

it

as the same,

Complete

survey, in the first place, of those objects

and are most

liable to confusion,

possible objects of our ideas.

and be conscious every time

requires a comprehensive which most resemble each other

distinction

and

further of the whole range of the

depends also upon conscious acts by which we become aware of the differences between the ideas A, C, D, etc., retaining as clear an idea of the intervals between them as of the It

B>

determinations

conscious

of

This

themselves.

act,

which

first

makes us expressly

same content by

identity of the

the

its

negation

of a

and completes the determination of our ideas, 1 while same time we are enabled to arrange them according to the degrees

different one, aids at the

of difference. 8.

Suppose that

all

become elements

the ideas which

and manipulate

thought to consider

we have occasion

as units,

of judgments, were capable of being produced

indivisible act, either of intuition or of relating

that the objects of

in the course ot

and which are destined

to

by an

thought suppose, further, which we form ideas were limited in number and easily

surveyed, with such

marked

differences between

;

them

we should be

that

as

conscious of the transition in passing from one to the other as in passing 1

The view

that an idea

owes

its

first

determination to distinction overlooks the fact

only possible when different ideas are present, and that dis tinction does not therefore create the contents which are different. Ulrici, for instance Red is the particular colour we call red (Compendium der Logik, edn. 2, p. 60), says,

that distinction itself

is

"

without only because, being red, it cannot also be blue, yellow, etc. in general, an blue, etc., it would be quite indefinite, mere colour

its

difference from

absolutely indeter have shown, we are

minate quality of which we should know nothing because, as we aware of colour as colour only by means of distinctions in colour." This I cannot allow. The sensation of red more accurately, of a particular shade of red is a positive datum with a content peculiar to itself, and it would continue to be so even though it should be

accompanied by the sensations of fewer colours than are perceived by all normal eyes. Colour sensations are not less definitely determined for any one because it may happen that many colours have never been seen by him at all, The variety of his colour sen sations would be the smaller, and he would have a poorer supply of ideas, but that would be all no doubt to any one feeling red only, red would mean the same as colour in general, but this is only equivalent to saying that the idea colour would comprise no plurality of distinguishable qualities, not that it would be absolutely indefinite. The con ditions which enable us to retain a plurality of sensations in consciousness are not those upon which the definiteness of particular sensations depends on the contrary, this de;

;

finiteness

is

rather presupposed

by such

ability.

Cf. Lotze, Logik, edn. 2, p. 26.

THE CONCEPT

253

from one to two, from two to three, then the logical task of constructing concepts would come to an end with the functions we have mentioned

and with the establishment of a generally accepted system of names no more would be needed but a memory able to retain what had been gained ;

from the general survey.

If,

for instance, our

world of ideas were limited

to the twelve simple notes of the octave, then everything necessary to give

the definiteness of concepts to our ideas would be that

member each

particular

sufficient certainty to

note and distinguish

it

The

guard against confusion.

we should

re

from the others with ideas of the particular

notes and the consciousness of their differences would yield us the whole material for our concepts arranged in a fixed order.

But both assumptions are incorrect. The first, because the ideas which treat as units and denote by one term can generally be resolved into a plurality of distinguishable elements they prove to be products com

we

;

pounded from simpler ideas which the mind can grasp by themselves. This makes them more difficult to retain in thought, for in a compound idea both the particular elements and the

must be retained

manner of

their

composition

on the other hand, the difficulties of distinguishing are greater and more special in nature, inasmuch as a compound idea may resemble another in some of its elements and differ from it in others.

When, can do

;

while,

for instance, I try to it

keep before

it

the idea of a horse, I

manner when, again, I wish to distinguish from some other idea, such as that of the donkey, I find that while agrees with it in most respects it is distinctly different only in a

parts of the figure in a given it

my mind

only by a process of mental construction, piecing together the ;

few.

The second assumption is also incorrect. memory we come upon numbers

collected in

which obliterate the marked intervals give definite form to

our ideas.

for

Throughout the materials of imperceptible differences

which we look when trying

to

This continuity, moreover, applies to

the simpler elements of our ideas as well as to

compound

images.

In the

sphere of colours, red passes by imperceptible degrees through violet into blue, through orange into yellow, through pink into white, through dark

red into brown.

A

similar continuity

magnitudes and forms, and hence there of scarcely distinguishable objects that

and

to retain

them

things themselves.

is

it is

in their differences.

in the sphere of spatial such an unlimited number

found

arises

impossible to differentiate them It is the same with intuitable

Intermediate terms intervene everywhere as know-

LOGIC

254

ledge extends between objects which were at first sharply distinguished ; snow and hail, tree and shrub, horse and ass, negro and

between

European.

41-

Since the greater number of our ideas are composite origin in

we cannot determine

distinguishable acts

by a conscious determination of

and of

ponent ideas)

their

their

manner of

have their

elements (characteristics, or com Thus the conceptual synthesis.

determination of the content of an idea presupposes into simpler

i.e.,

their content except

first

of

all its

analysis

and unanalysable elements, the same analysis determining

also the form of their synthesis.

This analysis could not be completely carried out unless based upon a perfect knowledge of the laws which govern the formation of ideas^ and such a knowledge alone could assure us that the elements were the same But our analysis can never arrive at elements all thinking beings.

for

which are completely isolated as products of independent functions ; it always ends in a system of connected functions which are related to each other, and which comprise the various forms in which the manifold The functions by which we think the logical categories synthesized.

is

difference) are connected with the spatial

(unity, identity,

forms of intuition

and when

;

referring to

existing both are connected with activity, relation)

;

and

all

which

that

the real categories

is

and temporal thought of as

(thing,

attribute,

are again connected with the intuitively given

contents of immediate inner or sense perception.

The

perfection of our

ideas as concepts presupposes a complete system of these elements.

As we have

an unlimited multiplicity of ideas which are separated by imperceptible differences, our conceptual determination of them must be limited to establishing definite boundaries within the gradual in intuition

fusion of differences. i.

The problem

to

which the

first

the composite nature of ideal objects

of the facts mentioned in gives rise

was

40, 8

familiar to the tradi

tional logic.

Here we

a single idea

and denoted by one term must be defined by its charac a concept must be resolved into its component ideas or

teristics,

concepts.

that

are taught that the thought which

These are thought

in the

concept and form

the characteristics heavy, yellow, bright, metallic,

its

is

contained in

content.

Thus

etc., are thought in the

THE CONCEPT concept gold

the attributes bounded, four-sided, equilateral, rectangular,

;

plane surface in the concept illegal,,

255

square

and

;

intentional, deliberate slaughter of a

represented as the

sum

the

in

human

concept murder the This content is

being.

or product of the particular characteristics.

It is

generally held, moreover, that this analysis into characteristics solves also

the further problem of distinction, these characteristics constituting just that

whereby

The

different ideas are distinguished. 1

how

question as to

teristics in

is

it

the totality of an idea

possible to distinguish different charac is

generally treated as

and were evident from the examples

settled,

repeatedly called

by Trendelenburg

especially

if it

were already

Attention has been

cited.

the need of a

to

exact determination of the relation between the characteristics.

homogeneous? and

all

if

how do

not,

more

Are they

they differ? are they indifferent to

each other, or are they mutually dependent ? and finally, in what relation do the component parts stand to the whole ? For in borrowing terms

from spatial or temporal relations, and speaking of concepts or ideas as

component that the

parts,

we

component

are only using figurative language.

We

do not mean

ideas are ideas of the parts of a whole (as head, neck,

trunk, are ideas of parts of

an animal), standing in the same relation to to the whole we mean that they

the idea of the whole as the parts do are elements of the idea in the

;

same way

that the particular attributes are

of a thing.

We

2.

unless

it

cannot analyse a given idea into

has been in the

first

its

parts

or characteristics

instance developed by means of distinguish

able functions out of different elements.

If the idea

was originally simple

and produced without a succession of acts, it would show no joints into which the analysis could penetrate, nor would there be any justification for such an analysis

;

it

would

at best

be no more than an arbitrary breaking

up of the idea.

As

a matter of fact the ideas which most naturally occur to us in this

connection, the ideas of intuitable things, have

conscious synthesis. plete as wholes

;

When we become

arisen

through

an un

conscious of them they are

com

but psychological analysis gives irresistible evidence of

by which the whole has been developed from particular The image of an apple does not penetrate through the doors of

the processes

elements.

the senses to the tablet 1

Ueberweg,

such of

its

e.g., writes,

upon which our ideas are depicted 49, p. 103:

elements as distinguish

it

"The

from other

characteristics of "

objects.

at

one

flash, as

an object consist

in

LOGIC

256

conveyed by a kind of enchantment, or by the mechanism of a psychical photography. Analysis of sense-perception shows how the sensation of

if

movements of the eye in following the must be combined with others, and view outline; how one perspective

colour must be connected with the

these again with particular tactile sensations of the hand, mentally grouped into the form of a stereometrical

image

;

how one

psychical function must

construct from the sensations the idea of an external object, assign to this object

of the visible taste,

its

position

and tangible thing

in space. is

It

shows, again,

and another

how

the idea

enriched by sensations of smell and

the reference of these to the visible

and tangible object presuppos

ing fresh functions appropriate to the combinations of the impressions of different senses.

Finally,

shows how such impressions when

it

partially

repeated are continually supplemented by reproductive imagination,

become

associated with the

word

apple, in connection with

which we

reproduce a kind of mental abbreviation of these processes takes place so rapidly

and unhesitatingly

and

;

and

easily

all this

that the result appears in the

mind without our being conscious of the

steps

by which

has been

it

formed. 3.

That which

is

true of ideas of things applies also to the ideas of at

tributes, activities,

and

presupposes,

the apprehension of the particular sides

first,

relations.

recognition of a line as a side

is

Equilateral

we need

a composite idea, for

and

a relational idea

it

for the

and then a

measurement of the

In the sides and the judgment that they are equal. same way the idea of movement, the simplest activity, requires the ap prehension of different positions and of the transition from one to the other.

The

idea of murder

is

a relational idea, and includes in addition

two points of reference the murderer and his victim a whole series of determinations, such as the conscious and deliberate intention of the

to

its

one, his action, and its effect in destroying the life of the other ; so that the idea as a whole can only be produced by a series of acts. This is doubly true of ideas which contain the thought of a plurality of independent objects connected by one or in the widest sense 4.

So

far as

:

an idea

sciously attending to

more relations, the

so-called collective concepts

people, family, etc.

its

is

composite we can only determine

particular elements

and

their

it

manner of

by con

synthesis.

Thus the formation of concepts always presupposes, on the one hand, analysis into

simple, indecomposable elements

constructive synthesis of these elements.

;

and, on the other, a re

Here the form of the

synthesis

THE CONCEPT may

itself

257

be called an element and characteristic of the concept in the

wider sense of the term, and we shall in future denote

The concept conscious

thus

related

is

construction of an

involuntary formation

;

it

to

the

object

presupposes

is

it

as such.

naturally developed idea as the

related

to

we

that

unconscious and

its

are

able to bring

consciousness the complete process of the formation of the idea. takes place by

into

This

means of judgments, which assign particular characteristics its predicates, and the concept therefore presupposes these

to the object as

predicates

the ideas of the characteristics

i.e.

which must themselves be

We thus find conceptually determined if the composite idea is to be so. that we need a number of simple characteristics, i.e. of ideal elements which cannot be further analysed, but which are nevertheless perfectly definite, fixed,

and

distinct.

But the concept must

5.

fulfil

yet another condition

as to serve for universally valid judgments.

That

is,

;

it

must be such

every one who shares

community of thought must connect the same ideas with the same words, and be able therefore to analyse them in the same way, and reduce them to the same simple elements. We can communicate a composite concept by enumerating its elements, and the manner of their synthesis in the

;

but these elements must be the same for every one, and be combined in the same way if our concepts are to agree. There is presupposed, there fore,

laws

a store of ideas formed by every one according to exactly the same and we can be certain that our concepts agree only to the extent in

;

which we are certain that our ideas are formed according to laws which are the same for all. Thus completeness and perfection in the formation of our concepts depends

upon our having complete

insight into the pro

cesses by which our ideas are formed,

and upon our consequent ability to arouse the same idea in every one else. If we could assume that all our ideas are innate and possessed by every one alike, as was assumed by a former theory of knowledge, at any rate with reference to a part of our concepts ; or if we could assume that the same world when presented always produced the same system of ideas, with a mechanical certainty like that with which equally tense strings give out the same note when struck

then the assumption of the traditional logic that the char ; concepts present themselves, as it were, spontaneously might But in proportion as the process by which our ideas are formed

with equal force acteristics of

be is

justified.

complicated and dependent both upon external conditions which must

differ

with the individual, and upon internal laws,

s. L.

it

becomes more

difficult s

LOGIC

258

and

to recognise

same

exactly the

down

lay

ideas,

the conditions

and

upon which every one

will

form

what elements agree or differ in The difficulty, which is often great, of as

to recognise

the ideas of different people.

same thing by the same word, is due to the difficulty of finding ideas which are the same for every one and are called by the same name. the certaining whether two people understand exactly

we

Since

6.

are only laying

down

in the logical formation of concepts,

the conditions of an ideal perfection

we cannot undertake

to present a

com

Such a theory belongs to the of our investigation so far show that

plete theory of the formation of our ideas.

work of the

future. 1

But the

results

the problem of resolving a given idea into simple characteristics which are the

same

every one

for

istics

a b

c d,

much more complicated than would appear

is

from the formulae which

tell

us that a concept

and that these are

its

A

kind of mechanical or chemical compound of isolated,

different,

and of equal importance,

syllable, to take the

example given

contains the character

As

constituent ideas.

in

familiar

the

in the Thesetetus,

if

A

elements,

same way a

is

were a all

that a

compound

of

letters.

The

7.

first

question which arises, then,

is

whether we may assume

any such simple ideas as isolated elements, which, like the letters of the If we return to alphabet, might each be expressed and retained by itself. our fiction of a world of ideas consisting solely of twelve notes, which only

need

to

be

fixed, distinguished

determined, then

But

various chords.

simple note

is

it

really simple,

it

no other way can is

in order to

as one, it

homogeneous and incapable of being

A

with self;

therefore

have the idea of any given note as such, we identical with itself and differing from others ; in

enter into consciousness at

it

is

further

To

all,

for consciousness itself

inconceivable without a plurality of distinct objects.

the note

be conceptually

say that composite ideas correspond to the was a fiction even to assume that the idea of a

resolved or differentiated.

must think of

and named

we might

The thought

of

inseparable from the idea of unity and of identity

involves moreover the idea of difference from others, and hence

of a plurality of these others.

All this points to functions

by which we

think of something as one, identical with itself and different from others

thus thinking also of plurality as distinct from and related to unity. clear consciousness, therefore, of all that 1

is

involved in forming the idea of

Here our views coincide with those enunciated by E.

Antrittsrede.

;

A

Zeller

in

his

Berliner

THE CONCEPT A

shows us

addition to the audible note,

that, in

determinations

;

and the idea proves

259 it

comprises these various

to be already

complex as

it

comes

into consciousness. 1

We

cannot, however, regard these determinations

difference cannot be thought in absolute independence.

and

impossible to think of identity without unity

it

are inseparably interwoven

terminations

and negation

we attempt

as the

identity

Not only for these

is

de

but they necessitate also the

thought of a something to which the unity, identity

Nay, so soon as

and

unity, identity

difference, on the one hand, and the sense-given note on the other ultimate and isolated elements for which we are looking. Unity,

and

difference belong,

to think of these determinations each

by itself can these themselves we only keep concepts story repeats before the mind by placing them under the determinations of unity, identity and difference. Thus our analysis never arrives at the absolutely simple,

same

the

itself

inasmuch simplest,

as

it

finds

certain elements included in

which are due

any judgment

is

to

be

;

to the

mere

fact

made concerning

that it.

it is

every idea, even the

thought at

all,

and

that

These elements are therefore

the necessary and constantly recurring products of the various functions means of which we are able to grasp an idea and to turn it to account

by

as the subject or predicate of a judgment.

Thus, instead of the isolated

complex of functions, dependent upon, and and manifesting their activity in what each other, conditioning, mutually we may briefly call the FORMAL LOGICAL CATEGORIES. They are related

we sought, we

letters

in the

same way

find a

to all objects of thought, being the conditions

upon which

2

any idea can be consciously retained in the mind. 8. But more yet lies hidden in the note of our hypothesis. 1

We

can-

Cf. Lotze, Logik, ed. 2, p. 26.

these formal categories, without which nothing whatever can be retained in include also member, in the sense that these most general conditions of That is, they involve is based. thought involve the functions upon which all counting to the positing and distinguishing of unities, the consciousness of progress from one unity these steps. another, and from that to a third, and the unity of the consciousness of allow that further development of counting, and the more complicated operations of arithmetic are due to the relations of intuitable things in space and time, and that frac of a whole which is originally found in space that tions 2

Amongst

thought,

we

We

divisibility especially presuppose or time only ; but it does not follow from this that number is altogether dependent upon stands in no other relation to time than that the conditions of intuition. Counting 1 which all our activities stand, that is, a succession of them can take place only in time ; we should be aware of time. The idea of essential that in but is in no

m

it

time Cf.

is

counting way even dependent upon the idea of number, of a plurality of distinguishable

6, 3

/,,

p.

36.

acts.

\/

LOGIC

2 6o

not have an idea of a note or of a number of notes, except as in time just as

we cannot have an

sciousness,

therefore, of

idea of a colour except as in space.

what

is

present to our minds

idea of a note includes the idea of time.

And,

again,

when we form

try to set

we

find that

We

must combine

with the idea of something in time, something, moreover, which

and manifold

\

we must

just as

and

isolated

;

we can indeed find More

distinct, but they always involve each other.

elements which are

is

it

various

the nature of our ideas will not admit

of our finding the absolutely simple

over, the relation in

is

think of space in connection with different

Thus here again

things in space.

the

when we

aside time as a simple element, not to be further analysed,

we can form no idea of time as absolutely isolated.

;

Full con

which time and space stand to their intuitable contents from that in which identity, etc., stand to their

essentially different

objects.

Hence we

get fundamentally different syntheses of the different

we may express this difference, and time as FORMS OF INTUITION, in

Kant

elements of an idea, and

as

speaking of space

contrast with the

did,

by

formal categories.

When

9.

far as

the concepts

we think

of

it

we

are forming refer to the existing, then, in so

as actually or

new

possibly existing, there appear

elements again. Our only idea of the existent is of a thing with attributes and and activities, we can have no idea of particular existence which is not at the very least it must be related to us as our ; our ideas of the existent, or possibly existent, include

related to something else object.

Thus

all

this cycle of inseparable determinations,

isolated characteristics,

manifold, that of the thing with

elements the

which refuse

and which involve a its

attributes

be resolved into

and

activities.

We

call these

REAL CATEGORIES.

Traditional Logic generally chooses for things,

to

third kind of synthesis of the

and then the

characteristics

examples the concepts of

characteristics of the concepts are attributes

of the concept

But in addition to these, there characteristics

its

(e.g.

the

are heavy, yellow, shining, etc.). a distinct kind of synthesis among the

"gold"

is

that of attributes in a thing.

This synthesis

is

essentially

meaning from that between the characteristics of a compo concept of attributes or activities, and it differs again from the syn

different in site

thesis

whole by means of the definite relations can only lead to confusion if we express everything dark red, rotatory motion, yellow body, a kernel sur

of particular things to a

connecting them.

It

three-sided figure,

rounded by a

shell, etc.

all

without distinction by the same formula

A=

THE CONCEPT if this

abcd;w?>

nection which If

is

261

juxtaposition were the expression of a

mode

of con

always the same.

these real categories are indubitably elements of our ideas of the

then it follows that in conceptual determination we must, first determine these categories themselves as concepts. The popular

existent,

of

all,

between thing, attribute and

distinctions

the forms of words, and vaguely

veloped into clearness. refers

the

to

existent

activity,

guided as they are by applied, must be de

and waveringly

Thus the determination

of any concept which a recognised theory concerning the presupposes

nature of these categories.

It

is

logically

in so far as this

complete only

hold good only to the extent in which logically theory And the possibility of such a theory depends it is generally accepted. of the again upon the possibility of producing generally accepted concepts It depends, therefore, upon an analysis of our themselves. complete, and

is

will

categories

mental processes which shall make us conscious of what it is which every one must think in accordance with necessary laws, when thinking of any thing as existent.

The

10.

as universality of such elements of our ideas

we have noticed

functions which always ultimately due to their derivation from recur in the same manner, however varied the matter of thought or in The nature of our spatial and temporal tuition to which they refer.

so far

ideas

is

is

or time

the same, whatever the particular objects thought of as in space No matter how varied the ways in which our senses are be.

may

affected,

and the

particular affections

combined amongst themselves, the activities things with attributes and

to process of referring the sense-given remains the same. The possibility of presenting a complete system of

these elements depends entirely a priori, as

forms which

lie

discoverable by a complete analysis affections

Kant assumes, they are given ready in the mind, and are therefore

upon whether,

;

as

or whether the nature of our sensuous

themselves determines what formal elements

are developed.

affec In the former case an organized and unalterable system meets the

tions of the senses as they successively appear

;

in the latter, the categories

kind would be the result of a development determined by the particular alter these mention possible and order of our sensations. We need only natives to

show

that the final determination of our concepts depends

upon

a clear insight into the genesis of our ideas themselves. elements which Different from these elements of our ideas are the ii.

are given in intuition by immediate sensation or inner perception.

From

LOGIC

262

the subjective psychological point of view there

is

no doubt that we have

something simple and ultimate, really elementary, in particular colours, notes, odours; and again in the immediate consciousness of inner events

The

of pleasure, pain, desire.

white of this paper, the black of these

cannot be further analysed

letters,

of our sense-organs.

forms

spatial

recurs

It

;

given immediately by the affection

it is

in

the

most varied combinations and

always the same and cannot be resolved into sim Here, then, it seems easy to set forth elementary charac

but

;

pler elements.

it is

which cannot indeed be thought of as isolated colour is never but can at least be easily retained in the mind as

teristics,

without space, and so on distinct

from

their

from notes.

named and not alphabet

;

form and from each other if

Here,

and

;

odours from colours, colours

anywhere, we have something which can only be

something analogous to the letters of the could be shown that all our ideas were formed from

explained,

if it

these elements given in immediate intuition, from the forms of intuition,

and from the

and formal

real

then

categories,

would be complete. But here we come upon the second of the

the circle

of ultimate

characteristics

simple and elementary sensations

is

difficulties

noticed in

sensation, every particular feeling of pain,

definite

Every

;

infinite.

but the

It

is

number of

is

40, 8.

something

these distinguishable simple

absolutely impossible that every particular

degree of light and warmth, each of which comes into consciousness as a simple presentation, should be fixed in others

;

memory and kept

by no expedient could language be made

multiplicity.

Language takes advantage of the

distinct

from

all

to suffice for all this

fact that similar sensa

by imperceptible differences, and denotes a whole of approximating degrees by one word. But similarity by itself is

tions are separated series

of no use for conceptual determination, for

indefinite,

it

difference

without

is

stating

its

degree.

The

it

implies

only way of attaining the

is to start from a comprehensive survey of by these imperceptible differences, and in this continuum to draw boundaries within which a given name shall hold good.

definiteness of a concept here

the whole series formed

Thus we

get what

we have

called the generality of the

word

in distinction

from the generality of the idea ( 7). The names of the colours, for example, are not conceptually determined until the whole series of shades has been exhibited, and green, red,

must be

etc., shall

left for

it

apply.

Part III.

has been settled within what limits the names

Our means

Here

it is

of carrying out this determination

sufficient to point out that

"

red

"

is

THE CONCEPT

263

not general in respect to dark-red and rose-red, in the same sense as "

extended

"

is

red in different

general in respect to different bodies.

each sensation

element which

From

this

odour,

note,

general idea

It

not the same

is

combinations which we think of in dark-red and rose-red is is

absolutely simple, and

the same in

we may

all

and one which

learn also what

is

;

cannot be resolved into one is

different. 1

the import of such words as colour,

According to the ordinary theory, as colour is the corresponding to red, blue, and yellow, the concept of

etc.

colour should be one element of the concepts red,

But

etc.

red, blue,

and we cannot say what colour is except by an enumera If the word colour is to have over and of the particular colours.

yellow, are simple, tion

enumeration any definite conceptual meaning, it must be in the by grouping together a whole series of ideas it presents them as marked off from others which are incomparable with them, such as clearly But if we try to express the common element of these notes and odour.

above

this

fact that

we can do so only by means of a relation, which does not directly denote the ideal content, but only a reference which red, blue, yellow, all contain, and by which they are distinguished from other simple sensations

ideas,

reference, that

is,

and

to sight

to the eye.

In such relations alone

is

a

common

element to be found, but these relations are not elements of the This distinction between words which are merely ideas themselves. common names of simple characteristics, and words which really denote simple ideal elements, must be constantly borne in 1

Cf.

Werner Luthe, Beitrdge zur Logik,

shade of red that element which sq.) there

is

common

is

p.

2

"

:

to all

mind

;

otherwise, the

We

cannot distinguish in any given In Lotze (Logik, ed. 2, p. 27 said above. True, he says at first

red."

only apparent contradiction to what is distinct impressions there is something

(p. 28), that in several

common

to all

which

is

conceivable apart from their differences, and to which (p. 29) the differences peculiar to the But he recognises that particular members of a series attach (light-blue, dark-blue, etc.). the general blue cannot be realized in the same way as the elements of other concepts and he adds that the presence of a from known

which we compound

particular ideas, or experienced, that the

common element does not form the content of a third idea of a like nature and species with those compared, and that it cannot be independently intuited. of This is what we wished to express above, and it would be more correct not to speak This im a common element at all, but only of an unanalysable impression of similarity. and guided by it, we arrange our simple pression is present in very different degrees,

common

element can only be

felt

limits in the series sensations in a series of diminishing similarity, so that we may fix It is different with differ within which to apply a definite denotation (red, yellow, etc. ). we can form an ences of intensity, e.g., of warmth, or of notes of the same pitch; here the excitation of idea of the common element, because the differences are based upon feeling,

and are not differences of an

ideal content.

LOGIC

264

doctrine of the characteristics of concepts, together with the

ing doctrine of their subordination to each other, will Nevertheless, even

common names

such as these

fall

may be looked upon

common

the signs of characteristics inasmuch as they indicate a

which

the ground of the reference which they

is

and

Intensity of sensation

concepts

;

in

contain.

which accompanies the

same way, although the objective

the

differ.

What we have

12.

all

as

element

however, are true general

differences,

for they refer to the excitation of feeling

and which changes

sensation,

elements

its

accompany

into confusion.

said of sensuous qualities

seems

to

be true also

of forms and movements, since these, too, appear as immediately intuit-

Here again we have infinite here again we seem to

able.

of difference

;

multiplicity start

and imperceptible degrees

from the particular sense-intuition,

and the general idea (form or motion) appears to possess a generality of the alone. But it only appears to be so. The idea of a given form

word

a triangle, square or circle directly as the

necessitates

is

far

from being given so immediately and Perception of form

sensation of a sound or a smell.

movement of

the eye or of the

returning into itself and thus limiting a is

really

body

hand

in

;

space

and in

this

movement,

a definite manner,

from one point of view, as this kind of action, the same in every from another point of view it is differently modified ;

perception of form

according to the course

movement.

The

it

takes.

It is the

process by which

it is

positions, recognition of their difference sition

from one to the other,

are variously modified.

is

same with the idea of objective

perceived, the comparison of two

and the idea of continuous tran

always the same

Movement and form

;

but the path, velocity,

etc.,

are true general concepts

;

colour and sound (as the expressions of something immediately given, not in the physical sense) are general words or common names. For this

reason one example suffices to show what

movement

is,

but not so with

This explains also why every theory which starts from sensations as the only primitive elements of our ideas must tend to regard all gene rality as only that of common names ; and why it extends this view to all colour.

things which

it

regards as sense-given, ignoring the processes by which

form ideas of them. each other.

we

Sensationalism and nominalism always accompany

THE CONCEPT

265

42.

The

analysis of objects into their final elements gives rise to series of

concepts in which each successive member is determined by a new distin guishing characteristic, and thus has a fuller intension than the preceding

The

member.

analysis of a single object

may form

as

good a ground

for

such a series as comparison between different analysed objects. The poorer concept with fewer determinations, which is included in the thought of the subsequent concept,

concept

;

is

called the super-ordinate, higher, or generic

the richer concept, with more determinations,

dinate, lower, or specific concept

The

;

their relation

is

is

that of

called the subor

SUBORDINATION.

between concepts of the same which determines the sense in which category ; for it is the category and their characteristics are synthesized, through it alone they are com relation of subordination exists only

parable.

The

extension of a concept

subordinated to extension

is

it.

is

the sum-total of lower concepts which are

Within the same

greater as

the intension

series of is

less,

subordinated concepts the

and

vice versa.

We

must

distinguish between the logical extension of a concept and its empirical extension ; and again between the empirical extension of the concept and

the extension of the name.

We can speak of essential and unessential characteristics only

in reference

to objects in their relation to a given concept. i

.

nation

Let us suppose that the most important part of conceptual determi has been of characteristics in their different classes the

survey carried out in accordance with a complete and universally valid theory of the formation of ideas ; let us suppose further that we have thus discovered

and are dependent upon others (e.g. colour and that a extended surface, point which is generally overlooked), upon we are also clear as to which terms denote definite ideal contents, and

what

characteristics presuppose

which are only

common

Then

names.

the question arises

how our

uni

verse of concepts will shape itself under these conditions. ideas which are conceptual determination we have to work upon first task is to reconstruct and determine our and as material, already given and these. Moreover, the constant supply of ideas which arise naturally

In

all

without reflection always constantly called predicates.

For

its

origin in the

particular,

and we are

to form judgments determining the particular by reason our explanation of the further relations of our

upon this

has

LOGIC

266 concepts

some

will

be

facilitated if

we begin by the conceptual determination of

idea excited by a particular thing.

When we

2.

wish to retain the idea gained from any particular thing

committed to memory, and recog is, when we wish it to be securely the merely involuntary function of nised as the same when reproduced This function, which we find aimlessly reproduction is not sufficient. that

active in,

dreams, and upon which, in the earlier stages of judgment,

e.g.,

our denominative judgments are generally based, simply repeats an image as a whole ; this involves no consciousness of the particular elements of the idea, and, therefore, no consciousness of

nected with its

it,

and

it is

its

identity

is

necessarily con

danger of being confused with others.

in

exactly identical repetition,

necessary above

it is

all

To

secure

that the idea should

be decomposed into its particular elements, and this decomposition is again the condition which enables us to distinguish a thing from all others. It consists in going back to absolutely simple and perfectly definite char

and the condition most

acteristics,

differences should be fixed

;

essential

to this

differences of colour

e.g.,

is

that fluctuating

must be

fixed by a

generally accepted denotation, of magnitude by a fixed standard.

The

result of

such an attempt

junctive judgment.

I

orbicular, circular thing,

and smooth

red, light,

is

a description as

it

might describe the wafer before

;

two centimetres that

is,

in diameter,

should describe

I

predicates perceived through the different senses,

bining them into one whole

;

takes place in a con

me by saying it is an one millimetre thick,

by enumerating all the and consciously recom-

it

the import of the synthesis

is

stated by the

category of the thing, and the nature of the characteristics red, smooth, etc.,

determines their dependence upon the spatial characteristics.

Any

one hearing such a description is called upon to carry out, step by step, the synthesis which in intuition was involuntary and, until completed, uncon scious

;

it is

supposed that the hearer thus obtains the same idea from the I had myself, always assuming that he thinks each

description which

characteristic in just the

But

it is

not what

same way.

obvious that when

I

intended

;

it is

I describe something in this way the result is seldom that the description is equivalent to the

an cannot replace intuition itself. The words constitute a formula in general expres orbicular, circular, smooth thing sions j to the hearer it is like a riddle to be guessed, a problem for his particular image,

and

"

it

"

imagination

;

how may he form an image

conditions of the problem?

of a thing which shall satisfy the

It is true that

every additional characteristic

THE CONCEPT istinguishes

my

idea from others which share the remaining characteristics,

by the nature of the predicates

at

form the idea

267

left

it is

open

to each individual to

Predicates such as red,

in different ways.

light,

smooth,

etc.,

even when accurately limited in meaning (e.g. light denned as of less of difference, amongst specific gravity than water), admit of many degrees which the hearer must choose before he can form his intuitable image. description gives us a sketch which fits not only an indefinite number of things which are exactly alike, but also many distinguishable things ; it is. therefore, a formula having a generality which is not merely numerical,

The

but also generic.

We

see further that this generality does not result merely from the

breadth

of particular

of meaning

frequently happens

that the

determinations, such as red,

enumerated

characteristics

the attributes either directly perceived or inferable of

my

object.

it

etc.,

do not exhaust

all

As the

nor the attributes dependent upon well a round as to it would piece of cardboard or a red it, apply just In this case the incompleteness of the description is easily counter.

above formula does not

corrected

state the material

but the same deficiency

;

may occur where differences

are present

which are unrevealed to our knowledge, or such as we cannot recognise. The most exact description of the germinal cell of a mammal would apply without further modification to those of are

bound

to

selves in the

any

many

other animals, although

we

assume that there are hidden differences which manifest them

Xor again can the description of it may not possibly apply in which nevertheless differs in some way

course of development. 1

real thing claim to

every respect to

be so exhaustive that

some other

thing,

not known.

In a formula thus reduced to characteristics we have, then, not the expression of a thing, but what expressing the idea

is

full

in the first place a subjective creation,

we have formed from

the intuition of a thing so far as

which every one determines in the same but It is a rule for the formation of the idea which we must observe, way. wide the to Its generality is due partly observe in various ways.

we can

retain

it

in characteristics

may

to the possibility of adding particular characteristics, partly new characteristics to those already given. It matters little for the present n it whether or not ordinary language has a special term for such ar idea ;

meaning of the

were worth while, one could be made. 1 We shall speak in Tart III. of the necessity to which this gives our determination of concepts characteristics based upon relations.

rise of

employing

in

LOGIC

268 If our description

were

less

complete

if,

for instance,

it

omitted to state

a difference would be neglected which distinguishes this object

the size

from others which are larger and smaller ; the formula would be applicable to many other objects, inasmuch as we could complete it by supplying any If

possible magnitude.

it

were more

definite,

if,

e.g.,

rose-red were sub

then a number of distinguishable objects which were We should, however, previously comprehended would now be excluded. still have a formula expressing a synthesis of characteristics to which others stituted

for

red,

may be added a formula which the hearer can supplement in many ways. It may thus happen that even the analysis of the idea of a single 3. object may give rise to a series of formulas, including successively more and more

As each

characteristics.

becomes more

definite,

characteristic

is

added the idea

and by each additional

to be

formed

characteristic objects are

excluded to which the previous ones by themselves applied. From each we may obtain the preceding one by omitting, the subse

of these formulae

The

quent one by adding, a characteristic.

fewer the characteristics

com

prehended, the greater the number of different objects of which the formula can be predicated if we assume the possible differences to be actual, and vice versa.

The

concepts.

Even

more and

less

general in so

far

formulae are related to each other as the

most specialized

is

still

general as

its

admit of a certain width of interpretation; only if all the characteristics were perfectly definite would the generality of the concept characteristics

be merely numerical centimetre

"

"

(e.g.,

a cube of pure gold having sides measuring one

a perfectly definite concept).

is

is expressed by saying that we ascend from a given concept one more general by abstraction, i.e., by omission of characteristics and that we descend to one more special by determination, i.e., by the addition

This process

to

;

of characteristics.

tension

Abstraction diminishes the intension, but widens the ex

determination increases the intension, but narrows the extension. Intension and extension stand in inverse relation. The more general ;

concept is called the higher or wider ; the more special the lower or narrower ; the relation between them is that of subordination.

We object,

are

should reach the same result but from several

common

;

if

we were

to start, not

from one single

the problem being to state what characteristics

to various objects.

The

greater the

number of

different

objects to be comprehended, the fewer will be the characteristics they have in

common, and

the smaller the intension of the concept

objects, the greater the intension.

;

the fewer the

THE CONCEPT

269

These propositions, simple and obvious as they appear, nevertheless 4. conceal several questions and difficulties which do not generally receive

These

sufficient attention.

and

refer partly to the processes of abstraction

determination, partly to the relation between intension and extension.

In the

place, the omission

and addition of

characteristics is by no would appear from these propositions. Amongst the characteristics there is always one which determines the nature of the synthesis by giving the category should this be omitted, the first

means so much a matter of choice

as

;

remaining characteristics would lose their ing of their synthesis would be uncertain.

common It is

and the mean

support,

only concepts within the

and to speak of ; such a concept as red as super-ordinate to rose, or reasonable as the superordinate concept to man, or intentional as the super-ordinate concept to same category which can be subordinated

murder,

is

to each other

only confusing.

Moreover, the characteristics are not

all

independent of one another

;

to

some extent they presuppose each other. It would be useless to omit the the latter presupposes the former. characteristic extended and retain red ;

Thus the course of generalizing abstraction

is

prescribed to

it

within certain

limits. It is

the

same with determination.

In the

first

place,

it

a matter of

is

course that incompatible characteristics cannot be added without giving rise to contradiction.

But by what

is

the determination to be guided

twofold ground for the determination here presents

itself.

If the

?

A

given

concept-formula contains characteristics which naturally admit of a further series of distinctions as red admits of a series of shades, circular of all possible magnitudes of the diameter, etc.

then the addition of one of these

distinctions naturally presents itself as the next step in determination, finds

its

justification in the given

concept

itself.

some of

take care that other characteristics do not exclude characteristics

and thus

bounded by three

figure

limit the determination.

and

But even here we must these possible

The concept

straight lines contains nothing

of a plane

about the magnitude

of the figure, nor about the magnitude of the straight lines and their relation to each other.

Some magnitude

in the concept, but not,

however,

fix

it is

left for

of the straight lines

is

necessarily implied

the determination to settle which.

upon any determination

I like for

each

can

I

straight line

;

my

limited by the law that any two sides taken together must be character greater than the third, this law being prescribed by the remaining

choice

istics

is

and the nature of the synthesis demanded.

Thus determination

2

LOGIC

yo

cannot proceed from one characteristic alone, but only from the whole complex. But determination of this kind

new and independent

is

accompanied by another, which adds no special connection with

characteristics having

Matter, for instance, may be determined anything in the given concept. and heavy substance ; but at our present stage of knowledge we cannot regard the specific attributes of particular materials as in any as extended

way modifications of extension and

In such cases, however, we weight. guided by our purely empirical knowledge of under the concept of matter ; we add those characteristics

find that determination

objects which

fall

is

which, in our experience,

Only

if

we had

full

we

find

combined with the more general

ones.

insight into the nature of things could this determina

by the contents of our ideas. Because there are these two modes of determination

tion be guided 5.

it

is

uncertain

what we are to understand by the extension of a concept. The logical point of view, where the first demand is for conceptually determined predicates,

is

concerned only with the ideas with which we approach actual the relation of subordination can never be found except

Hence

things.

between concepts, and the generality of the concept consists in its being contained in the thought of a number of ideas distinguished conceptually,

by different characteristics according to their intension. The mere numerical generality, through which the same idea is found in an indefi nite number of particular intuited things, has nothing to do with the i.e.,

nature of the concept in

all

the instances,

hundred

;

it

is

one and the same concept which is thought it can be predicated of one or of a

and whether

things, its nature is the same.

Hence

the

extension of a concept can never

empirical number

of similar things which

fall

to the principium idenlitatis indiscernibilium,

under

be measured by the it,

if,

we recognise

in

opposition

the possibility

of objects which for our knowledge are not distinguished by their attri butes, but only by difference in time or space. On the contrary, it must be laid down that a concept which does not

admit of further determination has no longer any extension ; it represents the point, even though that which cor responds to it may be empirically forthcoming in millions of instances. the final limitation of extension

be the same, then a cast-iron

ball having a such a concept. There are certain characteristics which can be conceptually determined

Assuming

all

cast-iron

to

diameter of 10 centimetres

is

THE CONCEPT

271

only by fixing limits within a continuum of imperceptibly small differences. is it true that even the lowest conceptually has an extension, which, however, cannot be

In connection with these alone determined formula further

still

broken up into discrete concepts.

question of singular concepts partakes of this difficulty. A concept can never be called singular because there happens to be only one thing

The

corresponding to

it

in empirical reality

of the concept would be affected

if

;

any more than the

there were

logical nature

no object whatever cor

Only concepts whose characteristics involve the unique ness of the corresponding object can be called singular; in this sense the The question, on centre of the material universe is a singular concept.

responding to

it.

the other hand, as to whether

all

individuals which actually

fall

under a

given concept are distinguished otherwise than spatially and temporally,

and whether only one, or whether prehended logic,

in a

but belongs to the science of

For

this

particular things can be

several,

com

concept of the smallest extension, has nothing to do with

reason also

it

is

reality.

when

purely a matter of chance

the

same

under two concepts of different intension. Hence as concepts they must not be called equivalent or interchangeable ideas, but only in so far as, when used as names, they denote things which are

number

the

of things

fall

same within the range of our knowledge.

They

are really different,

logically considered they have a different extension. feathered animal is a different concept from that of man

Two-footed un-

and

as

names do they denote the same

between the

logical extension

We

beings.

;

only

when used

must, then, distinguish

of the concept and the empirical extension of

the name.

At most there "equilateral

ferent.

room

is

triangle"

They

for

and

differ in the

doubt as

"equiangular

formula

;

to

whether such concepts as

triangle"

are identical or dif

but as the characteristic equilateral,

taken together with those comprehended by the word contains the characteristic equiangular, and equivalent. tain that

Only by

triangle, necessarily

versa, they are absolutely

upon the verbal expression can we main and in that case we must also say that an

insisting

they are different

equilateral rectangle

-vice

;

and a rectangular rhombus are

different concepts.

which are only the extensions of subordinated concepts We cannot compare the extensions of concepts which directly comparable. Again,

it

is

are independent of each other, except in so far as every concept which admits of many additional determinations may be generally called wider,

LOGIC

272

while those which admit of few

may be

There can, how

called narrower.

ever, be no definite and universal standard of measurement for the exten

sion of concepts.

There

is

a further distinction

The

extension of a concept.

between the

logical

and the empirical

logical extension consists in

all

the concepts

which are gained by the further determination of its characteristics when But we this determination is involved in the characteristics themselves. merely by our knowledge of actually existing work out any series of determinations or com things, binations of characteristics because no empirical occasion presents itself When this is the case, because we do not see any necessity for so doing. in our task

may be guided

and thus

fail

for selecting these,

to

and only these determinations, we can only speak of No one could infer from the concept of metal

an empirical extension.

many and no more

that there are just so

even discover the number by attempting characteristics

concepts

;

different metals, nor

for us the extension of the

of the metals

we know.

Just

could we

the possible combinations of

all

in the

concept metal consists for

this

the

reason, however,

empirical extension of a concept can never be regarded as complete. 6.

The

expressions

Genus and Species

are often used with reference to

the relation of subordination between ideas lower, species to a higher concept.

Of

;

each concept

these terms

it

is

is

genus to a

again true that

Red

they have no fixed meaning except within the same category.

the generic concept of rose, but only of the various shades of red. highest genera, the Trpomx

common

element

is

highest

are therefore the categories;

and

not

The their

again nothing but the relation which consists in being

objects of thought.

many

yeV?/,

is

Unless we accept

genera

as

this limitation, there

there are independent

would be as

characteristics

of any

kind.

We

must of course distinguish between the generic concept and the its concrete sense as the sum-total of all the things falling under genus a generic concept, between the generic concept human being and the in

"

human

"

race or genus.

When

a concept contains different characteristics which are inde pendent of each other, the higher concepts to which we may pass are various. From the concept of the square we may ascend to that of the 7.

equilateral quadrangle, or the equiangular quadrangle or the regular figure,

according as we omit one or the other of the independent characteristics equiangular, equilateral, four-sided.

All these higher concepts are equally

THE CONCEPT related as generic concepts to that

273

of the square.

In like manner the

may take place in different order, according as one or the other of a number of independent characteristics is first to be added. We determination

may proceed from

the concept plane figure

order figura plana

the

aquiangula rectilinea

;

bounded by

quadrilatera

we may

cequiangula

rectilinea

-figura

:

rectilinea

plana

cequian^ula,

figura plana rectilinea aquiangula, aquilatera, quadrilatera, every concept containing characteristics find a place in different series all

lines in

straight

figura plana

figura plana rectilinea quadrilatera, czquilatera, also proceed in this order figura plana

quadrilatera aquilatera

but

rectilinea

aquilatera etc.

Thus

independent of each other

may

of subordinated concepts, and to exhaust

would need an arithmetical calculation of combina

possible variations

tions.

There

is

no order of succession

therefore

sarily given by the nature of the concepts

which

in ;

the subordination neces

there

is

no

settled order of

precedence according concepts which have a logical possibility and justification may be arranged in one way. Just because concepts, as we understand them, are subjective creations, formulae whose chief pur to

pose

is

merely to

fix

all

our ideas and mould them into

commonly accepted

and unambiguous predicates, they are capable of unlimited 1 many ways in which they may be combined.

As

8.

the primary function of concepts

we cannot regard

is

variation by the

to serve as predicates in

our

an imperfection that, generally in than the concrete and fully determinations are they poorer speaking, determined subjects of which they are predicated, and that they are more manifold judgments,

or less deficient things and

own

as

when compared with the intuitable The fact that no one can eat

events.

only apples, pears, its

it

reality of particular

"fruit"

etc.,

individual size

Nor

in general, but

each, moreover, of an absolutely definite kind, with

and shape,

in

no way diminishes the value of the

any the less because no one can have a clock in general, but only a clock with a pen-

concept

1

The

branch

"fruit."

is

the value of the concept

"

clock

"

idea of an arrangement of concepts such that the more specialized concepts numbers from one point, the concept of the 6v or something, is vicious. It that there must be a much smaller number of higher

off in increasing

thoroughly

presupposes

but if we regard concepts as being com generic concepts than of the more specialized binations of a limited number of characteristics it depends entirely upon their inter 1 lie relations whether combinations of greater or less generality are the most numerous. necessity of any fixed order, and hence this imaginary pyramid of concepts, can be the view which regards the higher concept as the real grounded only ;

upon metaphysical cause of producing the lower. S. L.

T

LOGIC

274

It is a necessary part of the purpose and dulum, or a clock with a spring. For it should thus differ from the real thing.

function of the concept that this reason,

when

logical theory

aims at supplying a supposed deficiency

by making the statement or condition that the concept of a thing should contain its essential characteristics, it fails to understand the most impor

and universal purpose of the formation of concepts. Moreover, ac cording to this theory, that which is left undetermined by the concept is Now, apart from the fact that represented as unessential, as accidental. tant

a complete knowledge of the whole universe would be necessary before*we know what are the essential characteristics of a thing and what not,

could

this view,

when taken

would lead nature of

in

connection with the subordination of concepts, only one essential

to the pantheistic conclusion that there is

all things,

their ultimate

and

that all differences are merely accidental, having

ground only

in the subjective

view of things.

There

no

is

absolute and fixed line to be drawn between differences which must be

neglected in our determination of concepts, unless these are to be multi plied to an indefinite extent,

and the differences which are fixed and

for

mulated in concepts. Hence there is as much reason for saying that the differences between the last species are accidental in respect to the genus as for saying that the merely individual differences of a thing

under a lowest concept are accidental always related to

its

species in the

which

falls

and, finally, since a higher genus

;

same way as the most

specialized idea

is is

related to distinguishable individuals, the essential nature, properly speak

can only be expressed by the highest concept. This is, in fact, the origin of Spinoza s doctrine, that there is only one substance, and that all ing,

differences are merely modifications of this.

The

between essential and unessential characteristics

distinction

first

:

obtains a meaning

When we

and

justification

when we come

desire something actual as

means

generally so constituted as to possess also a

to

to concepts of purpose.

an end, these means are of attributes which are

number

not desired, and therefore not determined by the end they are accidental.

The

;

with reference to

it

necessity of guarding against the cold gives rise

concept of a covering which will prevent the loss of heat ; and which is to serve the purpose shall be

to the

this necessitates that the material

flexible

many

and a bad conductor of

heat.

But any available material has

other attributes besides those of being flexible and a bad conductor

of heat, and these other attributes contribute nothing towards the. purpose.

With reference

to

the concept of clothing, they are accidental.

In the

THE CONCEPT

275

same way the concept of a clock is originally a concept of purpose the So far concept of an apparatus which measures time by spatial changes. as concerns the concept of the clock,

accidental so long as

it

fulfils

its

the

mode

purpose.

of

construction

its

is

Here then the subjective

It concept with its characteristics does actually precede the reality. follows from the nature of the things which must be used as means that

we cannot concept

realize those determinations alone

;

when nature

which are included

in

species are determined by the variety of the means.

its

the

Only

placed under the concept of purpose, and regarded as of certain ideas or forms which, like human at the realization aiming itself is

purposes, take the shape of indeterminate and varying thoughts, in

any meaning

distinguishing

characteristics in the idea of an

between the

essential

existing thing.

there

is

and unessential

If nature

is

concerned

merely with creating the form, structure, an organization of a horse, and if colour has nothing to do with her purpose, then it is an unessential characteristic

which

The

colour.

similar

is

from the

is

fact that

only present because the horse must have some such characteristics vary in individuals otherwise

then taken as a sign that they are immaterial.

Nevertheless,

view the colour of the white or of the black

scientific point of

horse follows as necessarily from the constitution of the particular indi vidual as the structure of

Thus

we compare an tained,

its

skeleton and muscles.

the distinction of essential and unessential

and

is

always found when

idea with a previously given concept in which

try to find in

sets forth certain

it

it

is

con

The penal law

the realization of the concept.

concepts of crimes, and the judge endeavours to find in by the law ; for

particular concrete actions the characteristics determined

the subsumption of the crime, and the meting out of punishment, these are essential, while the special circumstances of the deed which are un

provided for are unessential.

If

one

man

has killed another,

it is

essential

to know whether he did it intentionally or unintentionally, with or without deliberation ; it is unessential whether he did it with a round or a conical bullet.

The

distinction recurs again

when

the problem before us

ceptual determination to the meaning of

some word

is

to give

in ordinary use

;

con here

the unessential characteristics are those which belong, not to the general

meaning, but only to the particular things included by specialized ideas.

house whether

it

is

In this sense

it

roofed with

tiles

is

it,

or to the

more

unessential to the concept of the or straw, but

it

is

essential

that

it

LOGIC

27 6

The

should have some roof.

meaning of the word

actual

"

house

"

includes the characteristic of having a roof, but does not specify the material.

This logical treatment of the difference between the essential and unessential characteristics of a thing must be carefully distinguished from 9.

the question as to what belongs to the real nature of a thing, what is essen tial to it or not (cf. may be called upon to form our 33, 4, p. 198).

We

concepts of things in such a

way

shall express the

that they

essential

nature of things, i.e. those determinations which belong to them indepen dently of all other things, and proceed entirely from their own nature. Then the characteristics of the concept must include the essential deter

minations of the things, and

must

fall

all

same

things having the

But

under the same concept.

is

it

essential nature

clear that unless

we

are to

condition can only be

fulfilled

it is inapplicable to any higher concept. by the infinite species same way it is clear that these essential concepts, if attainable at

In the

in with the pantheistic tendency,

fall

this

;

all,

can

form but a small part of the concepts of which we have need. Knowledge is concerned not only with the essential nature of. things, which always remains one and the same, but also with the

mena and

effects

due

to this nature

;

and

many for

manifestations, also

this

pheno

judgments are

needed which have concepts for their predicates. From one point of view there is certainly a difference between the per manent and lasting states or attributes of a thing and those which change

and

tinction

meant

the difference which Descartes

vary,

between attributa and modi.

to denote

by his dis must be a constant As the concept

and the concept of a thing means something enduring in time, only that which belongs permanently to the thing can be contained in the

idea,

conc ept of

Thus

it.

its

changing aspects are unessential with respect to

the thing, but only because they cannot be included in the concept, not as having

no reference

to the real nature of the thing.

these changes that the real nature unfolds

the real nature of a thing,

ground of

its

itself,

we must include

and

if

For

it

we wish

is

just

in

to express

concept the permanent changeable aspects, under some such name as faculty, or in the

power.

The

10.

which

distinction

in reference to

between

essential

and unessential

the concept as such

is

characteristics,

meaningless, must not be

confused with the distinction between fundamental and derivative charac teristics.

When

from a combination of elementary characteristics other

THE CONCEPT

277

predicates necessarily follow, then the former are called fundamental, the latter derivative. 1

parallel sides

and

It is a

diagonals.

It is

a fundamental attribute of the rectangle to have

right angles,

it

is

a derivative attribute to have equal

fundamental characteristic of an odd number that when

divided by two there

is

a remainder one

;

derivative, that

it is

not divisible

by even numbers, and so on. But here again we must guard against We must not look upon the confusing the logical and the metaphysical. fundamental characteristics as constituting the real essence of a thing in many cases nothing is known about this. All we can say is, that accord ;

ing to the way in which we consider the attributes to be dependent upon each other, these fundamental characteristics constitute the concept as a fully determined idea. ii. It follows from our doctrine of the negation that negative deter minations can never be original elements in the idea, and therefore that they cannot be characteristics in the proper sense. Every negative deter

mination presupposes a negative judgment, and the subject of this judg ment must be capable of being distinctly thought before the negation which is founded upon it. How far negative determinations may nevertheless be necessary to enable us to arrange our concepts will appear from what follows.

43-

We

must not confuse the distinction of simple characteristics and the

resulting

distinction of composite concepts

with

the difference of

the

which the concept is contained. Different concepts which are contained in, and can be predicated of, the same object, are called com Different concepts which are patible ; they are generally cross concepts. objects in

incompatible cannot be contained in the same things

;

their extensions are

mutually exclusive.

The

determination of a generic concept by incompatible characteristics its differentiation into disjunct co-ordinate concepts, and a

gives rise to

a DIVI complete enumeration of disjunct co-ordinate concepts constitutes

SION.

Division

may proceed

either

by a development of

characteristics already

A

characteristic is depen Derivative are not the same as dependent characteristics. we cannot think of it without presupposing another, as colour presupposes of other extension; it is derivative when it is also the necessary consequence 1

dent when

characteristics.

LOGIC

278

given in the concept, or by the addition of new ones ; in the latter case sometimes by negative determinations. In division we are justified in in

cluding negative characteristics of the form regarding non-^

non-^

in a concept, but not in

an independent concept. so-called contradictory and contrary opposi between distinction The when tion, rightly understood, coincides with the distinction between a itself as

division having two terms

The members

and one which has more than two.

of a division

may be complete

either in a merely empirical,

or in a logical sense.

The

i.

between the various characteristics must find

distinction

which

expression in the negation,

(21,

i

us that

A

is

not B, not C,

its

etc.

Conceptual determination can only be complete so and indisputable, and is not made

22, 6).

;

tells

long as this negation remains obvious

uncertain by the indefiniteness of ordinary language

when

dealing with

gradual transitions.

The same identical,

i.e.,

is

true of all composite concepts,

equivalent syntheses of the

sarily differ in their contents, istics,

and

this difference is

tells

us that

which tion

is

A

is

same

which are not absolutely

They neces

characteristics.

according to the difference of their character

again expressed by the negation of identity, The only object of the nega not the same as B.

to confirm the fixed

and immutable

which

rule according to

ent words signify different things, and which,

if

we

differ

are concerned merely

with the contents of concepts denoted by different words, holds good even

when

the predicate denotes a concept to which the subject

square

is

is

subordinated

The attempt

has been

made

to

express a

maximum

of difference

speaking of disparate or incomparable concepts, which have istic

:

not parallelogram.

whatever in

common

(such are understanding and table,

various simple characteristics themselves, red and sweet, distinguished from concepts

more characteristics

in

by no character

etc.).

and the These are

which are comparable, which have one or

common

(hence, according to the ordinary doctrine,

same higher concept) and differ only in the remaining But this distinction is only relative. Nothing whatever is

are included in the characteristics.

absolutely incomparable, to the

extent at least

that the formal

determinations apply to everything which enters into thought. disregard

this

fact

amongst concepts

is

then the most fundamental that

which causes

difference

to

their characteristics to

sized in a different way, the difference of their categories.

To

logical

But

if

we

be found

be synthe this extent

THE CONCEPT it is

279

correct to speak of concepts which belong to different categories as

fundamentally different (e.g. man and virtue, man and movement) of those which stand within the same category as relatively different. But funda ;

mentally different ideas

though they have them

and

living,

and yet not

may

still

fall

We

must be careful

iron

and

under the same higher concept

sense, since subordination has 2.

have many characteristics

in a different way, as with

in

common,

man

metallic,

in the ordinary

no meaning except within the same category. between the difference of concepts

to distinguish

themselves according to their content, and difference of the objects in which they are contained, and of which they can therefore be predicated.

Composite concepts would be impossible unless we could think of different of one and the same idea, whatever the

characteristics as determinations

form of their synthesis

may be

;

and our

form ideas of the incal

ability to

culable

number

sibility

of combining

thing.

Every concept which admits of further determination by

characteristics

cepts

;

of different things

is

is

especially

dependent upon the pos

different attributes as determinations of the

same

different

included by the addition of these in various other con hand many higher concepts may be included in

while on the other

one and the same lower concept. Characteristics which can be combined

in

one concept, and concepts

which can be thought as parts of one concept, are called compatible. When one species is comprehended under different generic concepts, these are called cross concepts, inasmuch as they have at least a part of their

common ; when they are represented figuratively (say, as boundaries of their extensions intersect and include a portion

extensions in circles) the

which

is

overlap. arises

common

to

all.

It is clear that

Thus

in the square,

from the combination of characteristics

which thus appear

as

quadrangle and regular figure

the concept in which two higher concepts overlap in

mutual determinations.

a bg overlap in the concept a beg, and mination of a b c by g, or of a b g by c.

this

which these two

The

may be

differ,

two concepts a b

c

and and

regarded as the deter

compatible characteristics are those which are irrecon These cannot be cilable or incompatible (cf. 22, 8-13, p. 131 sq.). 3.

Opposed

to

as deter thought together in the same concept, but are mutually exclusive would be which characteristic is no There minations of the same thing.

incompatible with

all

others;

formal logical determinations.

all

must

at

least

be compatible with the

But incompatibility

involved in the nature of our ideas

(cf.

itself,

22, 8, p. 131 sq.).

when

logical, is

LOGIC

2 8o

Upon the fact that may yet be all

4.

entiation of concepts,

When and

a concept

A

and is

which are incompatible among is based the differ

characteristics

themselves

compatible with another,

l

their

complete development (Division). determined by two incompatible characteristics b

these are called specific differences,

and the

resulting concepts are they cannot both be thought as parts of the same lower concept, nor both be predicated of it (no Ab is Ac, no Ac is Ab). Hence their extensions are absolutely distinct, and all the more specialized c,

themselves incompatible;

i.e.,

concepts which are developed out of them are also incompatible, each of these extensions, meanwhile, forming a part of the extension of the higher concept (right-angled and acute-angled quadrangle, red and yellow rose, Such concepts are called disjunct, and when their relation of subor etc.). dination to a higher concept

When

a concept

sive determinations

A

is

the same, disjunct-co-ordinate concepts.

admits of only a limited number of mutually exclu

bed, there

concepts, whose

arises a series of disjunct

when

extension covers the extension of the concept A, so that

loped into

all

the differences possible to

it,

A

is

deve

each lower concept must

The concept A is said be divided into the concepts Ab, Ac, Ad, and these are called the

possess one or the other of these determinations. to

members of the

The

division.

division itself

is

represented by a divisive judgment

Of every

Ab, partly Ac, partly Ad. the disjunctive 37>

judgment

is

particular thing

true that

it

is

either

Ab

which

Ac

or

:

A

falls

is

partly

under

or Ad.

A

(See

6, 7.)

5.

mined

Every differentiation presupposes that a concept is still undeter in one or more of its characteristics and admits of additional and

mutually exclusive differences

;

or that the synthesis of

its

characteristics

incomplete and leaves room for more characteristics.

is

presupposes that the total

Every division number of possible determinations is limited and

The prevailing logical terminology is inconvenient in that it employs the same ex pressions to denote two processes so different as the analysis of a concept into its cha racteristics and the development of opposed concepts from one higher concept ; these 1

expressions being derived from the act of dividing and signifying sometimes the division of the content into its elements, at others the division of its extension into mutually ex clusive extensions. To this is due the paradox that by dividing a concept we do not get parts of the concept, but concepts which each contain the whole divided concept as a If we keep consistently to the content of the part. concept we are concerned with nothing but a development of the characteristics contained in it. The term division (Aristotelian Sicu peo-ij) is

cept

;

this

more applicable

sum

is

to the

sum

of the particular objects which

fall

under the con

regarded as a whole to be broken up into different groups.

THE CONCEPT The concept

completely known.

mined

of the rectilineal plane figure

several points, both as to the

in

281

number

is

undeter

of the sides and their

magnitude, and as to their relative as well as their absolute magnitude

and again

as to the relative

tude of these

is

;

magnitudes of the angles (the absolute magni

not a completely independent characteristic, but depends upon the number of sides). According as determina

within certain limits tions

added on one or the other of such

are

developed

concept of

fluidity is as yet

the concept is In the same way the

points,

in different directions into its differences.

undetermined with respect

to

its

transparency

or capacity of reflecting light, with respect to its smell, taste, etc. Smell, taste, and colour are not differences in one of the characteristics forming the concept of fluidity

because concept

;

but they can be added to the other characteristics

their general possibility

involved in the characteristics of the

is

fluidity.

Strictly speaking, only the

development

or explication.

form of differentiation can be called

first

If

we

call that characteristic

which

differ

is

entiated the ground of division (fundamentum divisionis), then the ground

of division here

in the given concept

is

itself,

and

consists in the fact that

a characteristic admits of mutually exclusive determinations.

concept of the line lines.

The

is

developed

into the concepts of straight

Thus

the

and curved

idea of the line involves movement, and this cannot be thought

\yithout direction; direction

direction which

is

which remains the same forms the

constantly changing the curved.

straight line,

The concept

of the

curved line develops into the concepts of those which return into them selves and are thus closed, and those which may be continued to infinity, for

constant change of direction includes both possibilities.

The second form of differentiation adds determinations from without. The ground of division is in the first place nothing but the indefinite possibility of a further characteristic

present,

or

which

is

independent of those already

the possibility of various irreconcilable

characteristics

;

the

asked whether there are any more characteristics which are recon The cilable with Ab, and such determination might be called synthetic.

question

is

concept of

fluidity

upon sensations of

contains no characteristics but those which are founded sight

and touch, only the mere possibility of taste and of it they must be added as new elements.

differences of taste are given with

;

here then that there arises the possibility of negative distinguishing We divide the concept of characteristics, which express mere privation. It is

organic being into feeling and

not feeling, of flowers into scented and

LOGIC

282 scentless, of fluids into colourless

which

and coloured

;

the absence of a character

compatible with the remaining characteristics, but is not In necessarily connected with them, forms here a specific difference. such cases the negative formula loses its indefiniteness it has for its istic

is

;

content the possibility of the positive characteristic which

is

the general concept and realized in one of

Its

its

species.

not the independent expression of some content ; a distinction and to fix the order of the concepts.

We must carefully means of tained

in

is

the

and those in which the negative expression ot only an indirect statement of the positive differences con straight, or

a

definite

When

characteristic.

men

into white

positive

I

divide lines

into

and not white, the negative

meaning

it

signifies

those character

which are excluded from the negated difference on the ground of the

same fundamentum is

is

mark

distinguish between these privative characteristics as

same general

and not

expression has istics

function

serves merely to

differentiation,

characteristics

straight

it

included in

The negation

divisionis.

limited to a definite area

grounded upon a disjunction

and thus

of the possible determination

states

something positive;

(straight or crooked, white or coloured,

again white or yellow or red or brown or black).

member

The

it

is

and

negation of one

of the disjunction contains the assertion of the others.

This negative formula finds a double application. In the first place it comprehend a number of co-ordinate disjunct members into one

serves to

expression,

because they are alike in some other respect in which they

from the concept excluded by the formula. The meaning of divid ing men into white and coloured (i.e., not white) lies in the fact that in all coloured people the capacity for higher culture possessed by the white is differ

wanting.

Otherwise,

if

colour alone were taken into consideration, the

between black and red, or red and yellow, is as great as that between yellow and white ; there would be no ground for expressing this series of equivalent differences by the negation of one alone. difference

The second

application

is

where one amongst an

infinite

series

of

possible differences can be conceptually determined, this being impossible

or less easy with the others because of their endless

number

;

they can be

conceptually determined only by limiting them with reference to the one. Each of the latter has This is the case with regular and irregular figures. itself

a definite relation between sides and angles, but opposed to the

simple characteristic of having equal sides and equal angles there is an endless number of other relations, none of which can be reduced to so

THE CONCEPT simple an expression, and which

it

is

283

absolutely impossible to determine

one by one. Here, then, in connection with the division of concepts, we find the

6.

value and significance of negative expressions, to which we were obliged 22, n, p. 134 sq.) to deny any justification when put forward as in dependent symbols of ideas, by themselves and without reference to the We can see now also in what sense the distinction question before us. (

between the so-called contrary and contradictory oppositions is justified. to the relation between disjunct If we limit the expression opposition "

"

co-ordinate concepts, then disjunct

members

we

between the

find contradictory opposition

of a division having two members, contrary opposition

between the disjunct members of a division having more than two. In the former case, one member can always be quite definitely and unam which consti biguously denoted by the negation of the determination the former case, In case. tutes the other member ; not so in the latter if

Ab and Ac

Ac

is

same

the

members, Ac formula

A

non-, 7.

speak

are the disjunct members, as

A

non-

;

in the

Ab

latter

is

the

case,

indeed included in the formula

is

comprehends

both Ac and Ad,

it

same if

A

as

Ab, Ac,

A

non-r,

Ad

non-, but

should

be

and

are the as this

expressed

as

c.

When

the

number

of differences

is

by nature unlimited, we cannot

but only of the development of ; Thus series of disjunct lower concepts.

of a division in the proper sense

a higher concept into an infinite

the concept of the polygon

may be developed

quadrangle, pentagon, and so on in infinitum. 8. Our attention is drawn by this example a characteristic taken by as the characteristic

itself

into the species triangle,

to another point.

When

implies a series of disjunct differences, numbers, and colour the particular

plurality implies

characteristics depends upon the nature of the remaining with the combined be can determinations different of these whether any All numbers occur as disjunct charac concept, or only certain of them.

colours,

teristics

then

it

of the concept of the spherical polygon ; but the characteristics the number 2, and those of a figure exclude

of the rectilineal

plane

the numbers body bounded by plane surfaces exclude

2

and

3.

characteristic This choice amongst the various determinations of a does not becomes of special importance when the process of division

thus take place by the development of the contents of a given concept, extension. starts from its empirical circumscribing its logical extension, but

LOGIC

284

Then

manner

the problem arises of dividing a concept in such a

the different

that all

The

determinations may be empirically forthcoming.

fact

that the human body is not transparent involves its having some colour ; and if we were to develop the concept from this characteristic alone, we

should have to introduce

all

the colours as

members

the division.

of

and leaving other considerations out of much bound to assume a species of blue or green

Starting from this characteristic

the question,

men

we

are as

as of black

In reality

or white.

many

of the colours are wanting,

and when we divide the concept man on the ground of colour, we enumerate only those colours which are actually forthcoming, regarding the division as complete

But there quite

distinct

number of closely,

when

no doubt

is

problems

is

includes

there

:

particular beings,

and there

it

these actual variations.

all

that in this limitation

and

this

we

generally confuse two

problem of

the

is

we

classifying

shall afterwards

a

given

examine more

the problem of presenting a system of concepts to

serve for our knowledge of the particular by

means of Predicates which

have a perfect logical determination. If it were merely a matter of chance that only some colours are actually found within the range of our

human skin, men would be no division of the concept, we could never say actually given men

experience as the colour of the

then the so-called division

of

but merely a classification

of

;

exhaustively divided the concept. disjunct species

meaning If,

;

just as

to say that

indeed,

in

It

chemistry

that

we had

in

this

way

would be a mere enumeration of

we enumerate

the metals without

no more new kinds can be discovered.

we can regard

the fact that

as a sign that a blue or green

no other complexions are

forth

excluded by the other characteristics of the human being, then, and then only, would it be possible to accept the empirical classification of men as an exhaustive

coming

division of the concept in experience

is

man.

complexion

That a mere

frequently substituted

is

classification of

what

for the division of the

the logical extension being thus confused with the empirical

is

given

concept is

quite in

accordance with the habit of neglecting to consider the concept according to its intension, and with the more popular and intuitable method of always starting from the empirical extension.

must always be remembered that

logical

In consideration of

completeness of division

is

this

it

never

guaranteed by the fact that the extensions of certain members of a division are together equal to the empirical extension of the concept divided. 9.

When

the division has been carried out,

it

brings to light a dis-

THE CONCEPT

285

amongst the characteristics which has not yet been noticed the Some of distinction between the notes communes and the notce prop rice.

tinction

;

the characteristics, that

which are otherwise

is,

may be common

different

;

and thus

bination of other characteristics,

from

its

all

higher

or

co-ordinate

number

of concepts

Thus the

can occur only

possessing only plane right angles is a nota propria of the right-angled quadrangle. also belong to a generic concept,

characteristic

the quadrangle

in

hence characteristics which

may

belong

notes propricz. only to an infima species are called specific

found they distinguish one concept from

and they are then called distinguishing characteristics. The same concept may be divided according to 10.

and because the

all

Where others,

different grounds,

are called cross resulting concepts generally overlap, these

Thus

divisions.

;

But such a nota

propria

such characteristics are

com

distinguish a given concept

concepts. "

it

to a great

while others presuppose a definite

the

division

oblique-angled crosses their

of

parallelograms

into

division into equilateral

rectangular

and

and unequilateral

;

phanerogams and cryptogams crosses their land and water plants. Such a combination of grounds is & of plants into

the division division into

means of breaking up a concept subordinated. 1

immediately

into a

number

The number

of

of others which are not

members

resulting

fron

which by itself would yield a, b, c\\ these numbers. of the to is product equal etc., members, We can imagine a logical system containing all the most simple 11. combinations of characteristics which can be thought as independent and several independent divisions, each of

isolated concepts, in

by division

on

which these combinations should again be developed and according to all grounds into the most specific

sides

all

We should then have a systematic synopsis of all the concepts possible. their relations of subordination could we possibly construct; both concepts and their differences would be fully determined, and we should be able to The

others.

and opposed to all given idea was subordinated ideal of a perfect analysis of our ideas would then be

how any

see at once

logical

and we should have moreover a system of Predicates appropriate in the most to all particular objects, and a means of classifying them under fall only one For though every object would then varied ways. other all from objects lowest concept, so that it would be distinguished

attained,

which did 1

There

process

is

is

not

agree

with

it

in

every

characteristic,

still

its

various

for the no ground for any special treatment of what is called sub-division, same whether we divide a higher or a lower generic concept.

exactly the

LOGIC

286

subsume

aspects would enable us to

under

it

different series of

higher

concepts. 44-

A

DEFINITION

is

a judgment which states the meaning of a term denot

This

ing a concept.

it

concept broken up into its

do, either by an expression which exhibits the

may its

and gives a complete account of it, and the specific differ

characteristics,

content, or by stating the genus next above

ence, thus indicating

position in the ordered system of concepts.

its

All logical definitions are nominal definitions.

The demand

for a real

from the confusion between metaphysical and logical

arises

definition

problems. Definitions are analytical or explicative

which

when they

refer to

already formed and denoted by a recognised term

is

synthetical or determinative

when by

new

they present us with a

a concept ;

they are

synthesizing determinate characteristics

concept, and introduce a term for

it.

We

must distinguish between definition proper and the attempt to dis cover the concepts upon which our ordinary use of language is grounded. i. (

Suppose our

moreover,

its

logical ideal to

be attained, and every concept

:

the problem of stating mere repetition of the analysis and synthesis through which

we should only have

a concept, and

moment

realize the

its

make

to

sure that

became

it first

we could

at

any

word by unfolding the elementary the concept denoted by it, and that we could

meaning

characteristics contained in

recognise

to have,

and unambiguous denotation in language then the contents of a concept would be solved by the

established

of such a

position as subordinate

and

disjunct.

The

first is

done by a

formula stating the particular characteristics, from the synthesis of which the concept arises ; the second by a formula naming the genus proximum

and the

differentia specifica,

division.

(Since the

order of determination

The

second answer. rectangle, etc.

when

;

i.e.,

exhibiting the concept as

same concept may have

may

square

vary, there is

may be

member

different genera,

of a

and the

different formulae for the

a quadrilateral regular figure, an equilateral

differ only apparently, and cease to differ continued, and these higher concepts are also resolved

such formulae

the analysis

is

into their characteristics.)

We may

call the

statement of

all

the characteristics of a concept, or of

its

genus proximum and differentia

in

such definition we cannot be concerned with the explanation of a con-

specifica, definition,

and

it is

evident that

THE CONCEPT cept, but that, so far as there is

idea

is

what itself,

not a concept unless

any explanation,

it is

clear,

contained in our thought of

is

not something different.

with the concept

is

external

It

and

is

i.e.,

it

;

unless

287 it is

we

that of a term.

An

are fully conscious of

thus the definition

is

the concept

only the term, which in comparison

fortuitous,

which secretes the wealth of a

one sound, and which, indeed, is frequently used like x and y thought in algebra, as a mere symbol of which we fail to realize the meaning at every step it is the word which, because its external form fails to show in

;

relation to the

its

words which stand

for

higher or lower concepts, as a

chemical formula shows composition from elements, needs to be explained and to have its content constantly brought to mind. Such explanation is

taken from popular language with when we have formed, or wish to form, a fluctuating boundaries, and

especially

its

needed when the word

is

constant and unambiguous symbol, from one which was uncertain and If we were to carry out Leibniz ideal of a characteristica

ambiguous.

with every

symbol indissolubly connected in thought and would enable us to see concept would also be its definition, universalis, then the

tion to

all

its

rela

others.

Definition in this sense, then, can never be anything definition, stating the

meaning

of the

word

;

it

more than nominal

can be a

l

real definition

to confuse different

a definition should be real in any other sense is cannot say whether any actual object corresponds to a concept of com until we have our concept and can subsume under it the objects plete logical definition We cannot say whether the characteristics of a concept represent the essential given. the real causes of these nature of the things which fall under it, or whether they include but this knowledge itself of the objects a have we until knowledge perfect things, Lotze (Logik, cannot be called a definition. This applies also to the example given by 1

To

insist that

problems.

We

;

2nd

"

ed., p. 202)

:

When we

of call the soul the subject of consciousness, of ideation,

be appropriately called a nominal definition. The real defini feeling and will, this may either that the subject of conscious tion of the soul could be established only by proving and indivisib but a be ness and

its

manifold phenomena could

nothing

supersensuous

be nothing but a complete system of material elements, being, or that it could in our concept of the being which we have first determined nature the of knowledge 01 it merely establishes the dependence no is definition, the subject of consciousness others which are not yet included in the concept. of <

characteristics first thought

upon

is enriched ; we now understand by the knowledge of this dependence the concept of consciousness, an immaterial, indivisible being, which is the subject "soul" that the first was, and in the same sense that this definition is nominal in the same sense name the conditions which any thing n the first was it is also real ; here again we the only difference is that we name them ; the name of soul

By

"

"

must

fulfil, if it is

to claim

towards The two concepts merely denote two stages on our way fully. which fall under th will teach us how the beings knowledge; further investigation sirelated to other beings, and from enriched concept must, by their nature, be Knowledge always presuppos creased knowledge will result still richer definitions.

more

LOGIC

288 only in the sense that thought,

it

must analyse the contents of the concept

Merely verbal explanations, such as "

democracy

tions,

is

such as

"

the rule of the

Thus a

all (cf.

definition

representing a concept ;

and

is is

"

people,"

a perpendicular

called definitions at

sion

in

and distinguish them from the contents of other concepts.

is

logic

is

the science of

thought,"

or explanations of verbal abbrevia

a perpendicular straight

line,"

cannot be

5, 3, p. 27).

a judgment, in which

the

meaning of a word

equated to the meaning of a composite expres

con

this expression states the particular characteristics of the

and the manner

which they are synthesized, by means of the the expression, and the way in which they are particular words forming We have an equation between two symbols of grammatically connected. cept,

in

same concept, and the symbols may therefore be substituted for each It follows, as a matter of course, that anything which is covered other. the

by the one word is also covered by the expression, i.e., that the extensions The existence or of subject and predicate are absolutely the same. material possibility of something corresponding to the concept may indeed be presupposed by the definition, but can never be stated by 16. definition is an explicative judgment, such as we dealt with in

it;

the

From this it follows directly that the definition (definiens) must not repeat word to be defined (the definiendum). We must not define idem per idem,

the

for in so doing we fail to fulfil the condition that analysis must always break up the thought, which, when it appears in one word, is a unit, into This is the elements which are necessarily denoted by different words.

source also of the objection to repeating in the definiens even a word of the

same derivation

which

is

(e.g.,

justified only

freedom

when

is

the ability to act freely), an objection

the etymological relation of the two words

unequivocal, and both are used in exactly the same sense

(e.g.,

redness

is is

The explanation of freedom given above may the quality of being red). serve as it stands for a definition, because the meaning of "free" is limited word which it employs, to give clear determination to its object the which are thus established may be found to be necessarily connected with others, and then these are taken into the definition and the same process repeated with a definition of the

;

characteristics

The demand for a real definition, containing the essential the concept thus enriched. is a return to the Aristotelian demand, that the concept should state the

characteristics,

Now

essence of the thing, according to his metaphysical theoiy. that we have left the Aristotelian metaphysics far behind, and confess our ignorance in most departments of knowledge of the ri eo-ri, in the Aristotelian sense, it would be well also if logic were to It has ceased to have any relinquish the concept of the real definition. logic, and represents only a one-sided ideal of knowledge.

meaning

in

THE CONCEPT by the expression, free from pain,

"to

is

e.g.,

act

and not every instance of being

freely,"

be called freedom.

to

ing of the derivative syllable which

and there

as

is

of a

portion

much

(e.g.,

In such cases

the

it is

free,

mean

the chief object of the definition

is

justification

composite term

289

for this vital

as for explaining

force

is

;

only one

the inner ground of

vitality).

further from the nature of the analysis demanded that in we must defining go back to simpler elements, and that a correct definition must not move in a circle, so as to reintroduce the definiendum itself in its It follows

enumeration of characteristics.

On

the other hand, the rule

hold good under

all

"

definitio

circumstances.

ne fiat per

negationem"

does not

that the statement of what

It is true

tell us what it is but as a concept is often dis from co-ordinate tinguished concepts only by the privation of a char

a thing

not does not

is

acteristic,

and

;

as this task of distinguishing

included in definition, we

is

cannot always avoid negative determinations. That an enumeration of the species of a concept cannot be a definition is

evident from the fact that the species contain the concept, and their

enumeration would involve a

The

rule

that

characteristics,

circle.

definitions

must be

precise prohibits the statement

which are already contained

in,

of

or necessarily connected

with others (derivative characteristics), e.g., to include in the definition of a parallelogram the statement that the opposite sides are equal as well as parallel.

wrong, and

Still,

a so-called

"superfluity

even preferable where there the connection between the characteristics. is

in definition is

For the names of ultimate elements there

assume

that every

1

is

no

Where

not positively

definition

one attaches the same meaning to

be named, but not explained.

is

not absolute certainty as to

they are not yet

;

we must They can

these.

known

they can

only be shown by bringing about the conditions under which the idea will be aroused. This is possible in the case of colours, smells, and tastes, if

we assume that different people are similarly constituted. The which we find something analogous to definition is with a

in

concepts bearing a

common name,

the statement of which

only case series of

recalls the

members of the series e.g., when we say "red is a colour." Here we can give something which corresponds to the genus proximum, but we

various

cannot give the differentia negatively, s.

L.

by denial of

all

specifica

;

this

could be replaced at best only

other varieties.

u

LOGIC

290

then, in constructing our concepts

If,

the laws of our simple mental functions

elements

its

Unless we

3.

are obliged to

becomes one which enables us

perfect definition

the object from

we

and the forms of

this

;

to

fall

back upon

their synthesis, a

build

up the idea of

alone can be called a genetic definition.

a complete and accepted analysis of our

may assume

ideas into elements which are perfectly definite in their determination,

and denoted by all in the same way, there can be no concepts in the logical sense, and this would make it generally impossible to solve any problem of definition as impossible as from an equation of which every term

an unknown quantity to determine any one of them.

is

Every

defini

tion presupposes a scientific terminology.

When

such a terminology

only in so far as

finition

it

is

not forthcoming

may be

we can form

a

good de

possible to find expressions in ordinary

language which are unambiguous, and which may serve, at any rate in practice, for the unerring subsumption of actual objects. Such, for instance, is

the case with jurisprudence in

may happen that to us, we have not

It

4.

its

application to the relations of daily

life.

although the elements of certain concepts are

ourselves as yet formed all the concepts which might be formed from them, nor completely learned the meaning of their denotations. Then the definition, when heard, serves both as a guide familiar

to the formation of our concepts

and

as

an interpretation of a word we

do not understand. Moreover, since

that

all

is

included in the logical ideal

is

that all the

elements and forms of combination should be conceptually established, the formation of composite concepts may be continually progressive. is the more true because of the impracticability of attempting all the combinations of concepts possible in the sphere of reality, until we can dis

This

cern the grounds of the real compatibility or incompatibility of particular characteristics,

some

new

definite

and of

their combinations, or until the occasion for

combination presents

concepts, and of coining

Hence

itself.

new words

forming

the necessity of forming

for them, to

which we must give

conceptually determined meanings.

The

definitions

the import of a

The

first

word

mentioned

set forth

analytical

equations, in which

expressed by means of an equivalent formula. equations, by means of which we first get definite expressions for new is

concepts, are determinative equations; they give import to a symbol by When we equating it with an expression consisting of familiar elements. first

form the mathematical concept of a function, we give a meaning to

THE CONCEPT word by means

the

nominal

of a formula,

but which

definition,

which stand

which has an external resemblance

is

We

new concept,

way

which language

merely serve to establish the In their original purpose these

actually used.

is

are merely attempts to justify this actual use of language,

reason for

it

by

definite concept,

named by

;

1

synthetical.

further distinguish between these two kinds of definitions

and those explanations of words which in

to a

of words

concepts already formed have been called analytical

for

must

Definitions

really different.

those which introduce the term for a 5.

291

showing that

which

word and

it

is

in

grounded

contained in the thought of

is

and

to give a

each instance upon a all

the objects

others, and they thus indicate the point of view from which language ranges many objects under the same name ( 40, 5, note).

the

When

in

no

they narrate the meaning,

these attempts are successful,

which, as a matter of

fact,

always belongs to a certain word.

It is

only to

explanations of this sort that the warning against making a definition too narrow or too wide originally applied, i.e., its characteristics must exclude

no objects which language continues to name by the word, and include none which language names by another word. But it is evident, first, that a definition is only possible when we presuppose characteristics which are conceptually determined, definition in this sense.

any have become between to

and then This

is

that

many words do

sometimes because

it necessary to distinguish meanings, sometimes because they are used only

extended, thus making

arbitrarily

their different

denote certain individual phenomena, and

even when they agree

not admit of

their denotations

in

possessing the

authorized by the use of language.

The

their

common

extension to others, characteristics,

is

greatest acuteness can find

not

no

simple definition of the word people, when we try to are meaning of the word. Words such as church, theocracy, feudalism,

give the usual

they merely denote certain historical phenomena The by their prominent features, and are thus names of single things. for ever. continue dispute as to the concept belonging to them may not symbols of concepts

Here

also,

when

;

the problem from which

we

start is that of

discovering

a concept from the objects to which ordinary language has given the same characteristics name, there is a meaning in the rule that the essential 1 definition the definiendum Drobisch, 117 sqq., rightly notices that in a synthetical this predicate being nothing more than the really occupies the place of the predicate, word as a name. In the case of the definitions at the beginning of Spinoza s Ethics the shows them to be definitions etc. id substantiam

formula employed of the second kind

Per

;

that

is,

quod, intelligo verbal denominations for definite ideas. they introduce simple

LOGIC

292 should be united in the concept

we have

to

do

is

For here, no doubt, what way that it may con

42, 8).

(cf.

to determine the concept in such a

ground upon which the name was given, and that only those may be included by which we were guided in giving the and name, upon which it depends whether or not new things will be called by the same name. Starting from the empirical extension of the tain the

characteristics

name

man,"

in the

"

without a

known men.

to all

for this is a character

tail,"

When, however, we have determined we should not be

similarity in all other respects,

assuming complete

that,

obliged by the laws of abstraction to include

concept the characteristic

common

istic

we should be

"

deterred by the external appearance of the rudiments of a

present in

human

beings, from continuing to

a man, then the characteristic

"

without a

tail,

which are

call the bearers of this "

tail

is

no longer a

limb

part of the

man ; it must not be included in the definition, because it is concept not taken into account in subsuming the particular under this concept. "

"

it depends entirely upon the point of view taken in classifying objects of language what is in this sense essential, and what is imma means by A characteristic may be immaterial in one aspect, while in another terial.

But

it is

essential.

From

problem of determining the actual meaning of a word from which it is used as a matter of fact, we must distinguish that way of stating the meaning in which certain words ought to be used in defi the

this

in

nite scientific statements or laws, as

opposed

to the uncertainty of their

the general concept under which they

fall to be Assuming this for determination serve and known, any purpose which may given marks the limits within which the word is to be applied with certainty,

ordinary use.

and without ambiguity, even though the distinguishing marks employed may be only derivative and accidental. As an extreme instance, we may take section

i

of the

German Penal Code, which

crimes, misdemeanours, and

transgressions, according to the

Taken

punishment attached to the actions. sense, this

would be a

logical monstrosity

within which certain terms are that the general

law

is

known,

that the 1

p.

Cf.

22

meant

to

;

measure of

as a definition in the ordinary as

merely marking the limits

be employed, when

it is

assumed

meaning of these terms as a punishable violation of the

it is

1

justifiable.

warm zone

is

We

find a similar instance in the statement

that which lies

what G. Riimelin has

sq.

distinguishes between

to say

on

between the

tropics.

this point in his Jurisiiscfo Begriffsbildung, 1878,

THE CONCEPT

may be that our only aim is to denote certain objects in such a we may be able to distinguish them confidently from all other Then it is not necessary to state the whole contents of objects.

6.

It

way

that

similar

293

the concept; a formula which states

its

distinguishing attributes,

and which

may be called a diagnostic definition, is sufficient. Chemical reactions which are peculiar to certain substances are instances of such characteris tics

;

they

make

concept when

and

to distinguish

blue

is

is

it

superfluous

the only object

them from

characteristic of iodine

sufficient to

is

to state the to

others. ;

complete contents of the

subsume given phenomena

The

hence the manifestation of

prove the presence of iodine, and

distinguish iodine from

all

is

other similar elements.

nection can this characteristic be substituted for significance lies in the fact that

its

correctly,

property of colouring starch

a

this

property

means by which

to

But only in this con the whole concept its ;

presence proves the presence of the

remaining characteristics which constitute the concept of iodine. We find similar distinguishing attributes of a derivative kind in the spectral lines of the particular substances.

point of view it is impossible, as Kant has shown, to give We must be content to definitions of natural products. exhaustive any include in our formulae a selection of characteristics which may state the

From one

most

as to enable us to distinguish the easily recognisable attributes so far

objects with confidence.

For

this reason, all definitions of

are diagnostic, inasmuch as they cannot enumerate

which belong to the object, nor even

knowledge of 1

it.

1

In such definitions

Nevertheless, there

we

tion to concrete existence.

all still

all

such objects

the characteristics

which are contained

in

our

remains a difference between

see a particular aspect of the nature of concepts in their rela So far we have not expressly considered a difficulty which has

been lately revived by Volkelt (Erfahrung und Denken, p. 342 sq.) with penetration and acuteness, the question, that is, as to whether the general idea as such is in any we not rather way conceivable; can we form any actual idea which is general, or must and that generality is to be agree with Berkeley that we have only particular intuitions, found in the word alone ? Referring to Lotze (Logik, edn. 2, p. 40 sq. ), Volkelt says that generality cannot be obtained by simply omitting the distinguishing characteristics. Must we not say that the thought of a triangle which is neither equilateral nor "

"

nor obtuse-angled, is no thought at all ? irregular, neither acute-angled, right-angled, with reference to the indeterminate totality Generality, therefore, can be conceived only the thought that the general idea is a con is in the of the

implied concept particular ; in the ceivable something only when accompanied by distinguishing characteristics, only it follows that the ideal expressed by the concept Hence or as the particular. particular be realized in a consciousness which should combine with the general idea its could

only and should do so, moreover, as infinite, appropriate intuition in one indivisible act, These propositions are no doubt true in so far as an allabsolute timeless thought.

LOGIC

294

those formulae which are only intended to afford the greatest possible for diagnosis,

facilities

contents of a concept.

and those which are

The

mental determinations, and

proximum

;

to

former, casual

them and

latter will give

will

also

meant

some

to represent the

at least of the

For the

applies the rule definitio ne fiat per acridens. superficial

funda

achieve this by a statement of the genus

distinguishing marks will suffice

;

they are

not intended to be characteristics of concepts, but only of the objects

which are to be subsumed under given concepts. embracing consciousness of this kind is the ideal of our thought ; a consciousness which should include the whole system of concepts with all its specifications, as well as its realization in concrete phenomena. At the same time, that view of concepts which solves the difficulty, and from which, moreover, general concepts as such derive their importance for actual thought, has been cepts are such,

for

lost sight of, the view, that

is,

that logical con

meant primarily to serve as predicates, and not to represent the existent as this must naturally always be particular, concrete, and determinate. The

thought of triangle" which is neither equilateral nor irregular, neither right-angled nor oblique-angled, is indeed nonsense ; if I am to think of triangle as a particular thing "a

But then, given in intuition, I must carry out the determinations, and not negate them. am I not to be able to affirm merely that a figure is a triangle, without concerning my magnitude or more exact shape ? All judgment, as well as all our con depends upon our power of analysis, and of thus making promi nent one aspect of a thing. If I have a clear idea of what an angle is, and of what the number three is, then "triangle" is assuredly a predicate which is completely deter mined and comprehensible by itself. Again, have I really no subjective correlative to self

about

its

struction of concepts,

this general word angle ? Certainly not, if I begin to think of complete intuitions, but I may find such a correlative in the process by which I intuit an angle, in the sudden change of direction which whether great or small is a matter of immediate feeling as "

"

I move Could I have no idea of the number three unless I also thought of eyes. definite objects? Is it not sufficient to be conscious of the process of counting three, a

my

process which I can apply to whatever I may choose ? It is not the part of conceptual formulae to take the place of intuitions of the particular they merely enable us to make a logical analysis of such intuitions. They are based on the fact that every particular ;

thing can be expressed by general predicates.

CHAPTER

II.

THE TRUTH OF IMMEDIATE JUDGMENTS. IMMEDIATE JUDGMENTS are those which we can state with a consciousness of their objective validity, without anything being presupposed beyond the ideas of subject and predicate which are connected in them (

The most obvious

18, i).

of these are (i) the merely explicative judgments, which

only state in the predicate what

thought in the idea denoted by the

is

subject word, and (2) judgments concerning the particular which rest

immediate

and which

upon

what predicate belongs to a given particular idea. Amongst the latter we may distinguish between (a) statements concerning ourselves, and (b) judgments of perception con intuition,

state

cerning the external world.

45-

For the truth of judgments which merely relations of our established concepts

Agreement, and patibility

of

we

find a

in so far as the relations of

certain

characteristics

state

something about the

ground

in the Principle of

concepts include the incom

and concepts,

in

the

Principle

of

Contradiction. 1.

truth

We or

have seen that we cannot speak

in

an unambiguous sense of the

falsehood of judgment unless the ideas presupposed in

completely determined.

it

are

16) deal only with ideas

Explicative judgments ( which are assumed to be already possessed by every one.

When

those

ideas are concepts in the logical sense, such judgments merely state the

between concepts which are already fully determined they are a repetition of the process of unification and differentiation which took place when the concept was formed. relations

2.

its

;

Positive judgments containing definitions, judgments which predicate

characteristics of a concept,

concept of a lower one,

all

and judgments which predicate

a higher

derive their necessary truth from the given

LOGIC

296 contents of subject and predicate. 3)

is

The

fact

which they presuppose

(

39,

that the concepts standing as subject or predicate should be actually

in thought, and, moreover, that they should

always and by necessary

ment

when

14).

(

be thought in the same way

But the law according to which the judgment is presupposed is none other than the law of agree

every one. this is

Now,

for the first time,

when

the invariability of our ideas

assured not merely for the moment of judging ( 14, 4, p. 82), but for the whole duration of consciousness, can this principle be applied not only

is

normal law of thought and because the con all, it becomes also a guarantee for the universal

as a natural law but as a

cepts are the

same

for

;

validity of the judgments.

Thus

does not depend upon anything in the nature of the Principle it is to be regarded as a natural or a normal law, but upon the data to which it is applied. In the first case, it is applied to in the that which happens to be present to consciousness at the moment it

of Agreement whether

;

second, to an ideal state in which

all

the ordered contents of the ideas are

present without change for one consciousness, an ideal which can never be

completely attained empirically. This ideal constancy alone can appear as the principle of identity in a normative sense, which demands that A

should = A, i.e., that in every act of thought the conceptual elements should be always the same, and should be known as the same (in praxi

we should always connect exactly the same meaning with a word). To satisfy this demand is possible only for a consciousness which is

that

of an invariability in its ideas independent of all temporal change ; a consciousness, therefore, which can think as if the whole world of concepts stood in unchanging clearness before a timeless

absolutely certain

But the principle of identity

intuition.

in this sense

of our judgment; for this unifies not that which

which

ment

not the principle

is

the same, but that

differs.

It

3.

is

might be asked upon what the validity of the Principle of Agree and in answer, we can only fall back upon our depends

itself

;

consciousness that the unification of elements which agree

When we

absolutely self-evident. are conscious of

it

reflect

is something judgment, we possible for us to be

upon our action

as always the same, just as

assured of the identity of our ego through

it

is

in

temporally different acts, past as well as future, and to represent in one act of thought the unvarying

repetition of the

and

just as

it is

same

"

I

am

"

all

through an unlimited series of moments

possible for us to retain the

same ideas

in

;

the mind, and

THE TRUTH OF IMMEDIATE JUDGMENTS to

be conscious that they are the same, so also

assured that in our judgment

we

certainly as

we

shall always

are ourselves the same.

297

possible for us to be

it is

same way as

in the

proceed

All consciousness of necessity

depends finally upon our immediate certainty that our action is invariable. For this reason it may be urged that, after all, it is only an inner experi ence which yields us

this certainty,

and

to this there

is

no answer.

But

then we must distinguish between the experience of the particular acts of our varying ideation and the experience which in each particular act is

accompanied by the certainty that it of the tary and changing conditions

is

not dependent upon the

particular act,

momen

but will continue the

It is this immediate certainty changing moments. which gives us the immediate and unanalysable intuition of necessity, and though this is indeed the object of experience, i.e., of an immediate

same throughout

all

consciousness taking place at a given point of time, yet

number

result of a

The

4.

and as

the necessity of

directly, to

negative judgments which distin

all

different concepts as wholes, and, according to the Principle

Contradiction

(

23,

p.

139),

of negative

judgments which deny

To

irreconcilable characteristics or concepts of a concept.

another way,

thing in

not merely the

establishment of definite relations amongst concepts leads also,

guish between of

it is

of experiences. 1

it

put the same

involves the necessary falsity of judgments which

it (contra attempt to attribute a predicate to a concept contradicted by The establishment of conceptual relations involves the dictio in adjecto).

an invariable relation incompatibility of certain characteristics as involves the necessity of denying

it.

ascribe b to a concept containing is

not

a, is

b

when a

is

to say that the

;

that

Thus

affirmed.

same thing

is

is,

to

a and

a.

The

5.

normal law has just the same Principle of Contradiction as a when it appears as a natural law, merely determining the

as

meaning meaning of the negation

;

possibility of consciously

that

A

is

not

b,

as a

but while as a natural law affirming at any

normal law

it is

it

states only the

moment both

that

definitely applied to the

A

is

b

im

and

whole range

cannot altogether agree with the view taken by Baumann mathematical iiber die Welt, p. 296 sq.) concerning our ideas we always form them in the when that The repeating experience necessity. cannot same way cannot of itself yield necessity the fact that anything actually happens consciousness that the exclude the thought that it might possibly be otherwise, only the of its necessityi.e., the consciousness fact will always actually be as it now actually is 1

For

this

(Philosophic

reason

als

I

Orientierung

;

can do

this.

LOGIC

298

of invariable concepts covered by the comprehending unity of conscious ness.

It

in this

is

known

generally

application that

as the

prindpium

it

becomes the ground

contradictionis, a principle

what

for

is

which then

ceases to be co-ordinate with the principle of identity (in the sense of the

A

formula

A) and presupposes

is

contradictio

we

that, so surely as is

and always

To

6.

will

in

as already

satisfied

adjecto,

ourselves remain the same, our action in denial always

be the same. 1

the establishment of conceptual relations

of judgments

by the absolute

here again the absolute validity of the

and consequently of those propositions which rests upon the immediate consciousness

Principle of Contradiction,

deny a

it

And

invariability of our concepts.

is

also

due the

validity

which attribute to a concept as yet unde

of possibility,

termined the possibility of receiving compatible determinations p. 207), and of disjunctions which are based upon division.

A

may cover a number of species, or be applicable and may therefore be predicated of different

concept

particular things,

To

the extent to which this

follows immediately is

B

"

is

or

JB"

from the relations of concepts.

true of the concepts, then the

"all

As

are Z?

s,"

is

true also.

and

rightly regarded as analytical,

of agreement. is

"2?

incompatible with

"

if

It is the

anything

is

A

it is

not

5,

many

subjects.

as

statement

"

is

2?"

is

falls

under

it

If the statement "

if

anything

is

A

also "

A

it is

Such judgments have always been owing

their certainty to the principle

same with negative judgments

A

to

34,

the case the hypothetical necessity of at

is

predicate of the concept to that which

tributing the

(

;

if

the statement

true of the concepts, then the statement also true.

we assume our concepts to be established, we have only to read off what we have ourselves put into them we are dealing only with fixed ideas, and no one who has exactly the same ideas 7.

In

all

these judgments,

if

;

can possibly doubt the judgments. For this reason they are independent of time and unconditionally valid ; according to Leibnitz they are eternal and necessary truths. But just for this reason they never make the direct 1

Mill (Logic, Bk.ii. _/?.) treats the principle of contradiction as one of our and most familiar generalizations from experience, and takes it to mean that belief and unbelief are two different mental states which exclude each other ; a fact which we learn from the simplest observation of our own minds. To some extent I agree with him, but then the puzzle is how do we know that they are not merely different but mutually exclusive ? If the certainty that they are mutually exclusive is to follow from a slight observation, still the necessity of this mutual exclusion must be a matter of im J. S.

earliest

:

mediate consciousness.

THE TRUTH OF IMMEDIATE JUDGMENTS statement that anything things, nor to

Kantian sense

for in

Kant has

as

judgment

;

shown

irrefutably

We

to the concept.

sponds

do they

neither

;

An

analytical in the is

is

existing objects.

first

refer

to definite, particular

judgment can never be

existential

an

299

existential

judgment the question

whether anything

which corre

exists

think of the subject of the existential

as without existence, then

we go on

to say that

it

also exists just

Thus the ground for affirming that something exists thought. cannot lie in the process by which we think the contents of an idea, in as

it

is

If there

conceptual thought.

present to consciousness 8.

But while

it is

is

which

is

any such ground, it must be a something distinct from conceptual thought.

easy to discern the truth of conceptual judgments

we are far from having exhausted the proper function of concepts. Conceptual judgments are valuable as constantly reanimating our concepts and keeping them before

when we assume

a completed system of concepts,

our minds, and as developing the abbreviation of the word into

meaning. concepts

its

fuller

Nevertheless the whole value and significance of a system of lies in

for predication,

its

application,

and

in the assistance

towards a knowledge of that which

the system as such.

the organon of

It is

knowledge itself; the apparatus with which

it

gives,

when used

not yet contained in knowledge, but it is not

all

is

we work, but not

the product.

our thought were but a monotonous recurrence of what we already know, and all our judgments but repetitions of those by which we formed If all

our concepts

as

is

tacitly

implied in the school logic

mind would be condemned to everlasting sterility. Its in constantly combining new elements with established

new concepts formed from

Nor does

these.

any more than a lexicon

progress of thought and ideas,

and our chief task

the

is

is

to

become

concepts, or with of a

problem of know of

a

new

nation. intuitions

The and

aware of the laws according to

and progress has a claim to truth

in its constant

which our judgment

literature

gives rise to

investigation

human

the ideal perfection

the universally accepted system of concepts complete ledge,

then the

progress consists

universal validity. 9.

This progress

in

thought and knowledge has

its

origin in the par

ticular individuals who form judgments, and spread them abroad by Since the predicate must always be communicating them to others. assumed to have been previously given, the condition upon which these

judgments

When

will

be formed

these are only

is

that

new

ideas shall arise to serve as subjects.

new conceptual

creations

brought about by deter-

LOGIC

300 minative definitions

48, 2) the question of their validity

(

the laws given above. to introduce

more than the

a term

;

new

serve only to effect a

any judgment concerning them

is

covered by

abbreviation and is

again nothing

explication of a concept.

It is different

must assume

They

when

the

new

We

subjects are ideas of particular objects.

for the present that the distinction

between the idea of a

and the thought of the contents of a concept is accepted one ( 7, p. 40 sq.)j if we express it by the distinction between intuition and concept, we must still assume that it is immediately particular thing

and known

to every

The most we can do

comprehensible.

and external concept

is

characteristics, to say that

determine

to

is

what we think

it

by derivative form of a

in the

purely mental, can be repeated at pleasure and without altera

dependent upon nothing but our own mental activity while, on the other hand, that which is intuited is presented to us at a given tion,

and

is

;

moment, and our thinking of relation to us

which

is

depends upon conditions placing it in a independent of our own mental activity, and com it

which might be expressed

pels us to locate in a particular object contents

general form.

in a It

am

may happen

that

when a

nevertheless aware that

if it is

particular thing

it is

presented to others also

peculiar to

it is

of creative imagination which for the

describe

beyond

it

must, in so far as

I

Then,

me

in intuition I

an individual, and that

me alone, or the moment appears

ject independent of voluntary thought. I

given to as

so only by chance.

with a dream, or a vision appearing to

of Agreement,

is

me

Such

is

the case

mental production as a particular

consciously retain the idea of the object,

a manner corresponding to its contents i.e. in but we can have no motive in seeking a ground for such judg

correctly,

this

ob

according to the Principle

;

ments, inasmuch as they are absolutely individual and incommunicable,

and can be believed by any one

to

whom

the object

is

not presented upon

authority alone.

But the ideas may be such as can be produced in every one alike, and, indeed, under certain conditions, must be produced in all alike, so that and then we they are naturally capable of being shared in by every one ;

have a motive that they

for

making our judgments concerning them

may be recognised as universally valid.

case with geometrical figures, 1 inasmuch as 1

tion

in

such a way

This, for instance,

we suppose

is

the

the idea of space to

Geometrical constructions occupy a peculiar position, in so far as in them the distinc between the particular image and the concept disappears from one point of view. So

THE TRUTH OF IMMEDIATE JUDGMENTS be the same

for

and the elementary data of geometry

all,

But more especially

intuitions.

When we

existing.

the case with

is it

all

we

affirm that anything exists,

thought, and the same for

thinkers

;

if

think of

it

the ground for which is common

exists,

in

to every one,

On

with the individual.

existent can only be true

same

im

It is further

independent of individual not through, but before

is

one person, incomplete affirming is not to be found

differ

as

as a par

different relations to different conceivably stand to one person, and not to another ; be the idea of it may present

may be complete

it

it

in

may

it

thought,

But

all.

be given as

which we regard

ticular thing, or as the determination of a particular thing.

of being, that the existent plied in the concept

to

301

for all

who know

it.

it

may

lie in

in another.

Inasmuch

as

in the conceptual thought

data of consciousness which

the other hand, a judgment concerning the

when

agree to

all

It is this

ground upon which the necessity

it,

since the existent

which makes us want

rests of

is

the

to ascertain the

our judgments concerning the

existent.

affirmed or assumed that something exists, we may generally the idea of the particular thing as subject, and the between distinguish 1 whether the latter be only tacitly understood (as it is, that judgment

When

is

it is

stated in an existential judgment. generally the case), or expressly

46.

Those judgments

in

which we

that immediate con give utterance to is present in every moment of our

sciousness of our own action which

waking

life

take the

the existent.

first

immediate judgments concerning place amongst

Their certainty cannot be analysed any

They

further.

in-

alone, we regard them merely as mental images, due to our constructive activity at the moment, but which can be repea images which are indeed particular intuitions an identity of the ideal contentat will in such a manner that their identity is purely the part.c of the idea and of the concept the such constructions far as

possess

as such

is

;

generality

as While, on the other hand, inasmuch

general.

it

is

presuppos

same way, and that they elements of such constructions are presented to all in the are allied by the fact that forced upon every one by external perception, they in a certain sense, of thei the same for all to the intuitable existent, and we can speak, ca

invest avoid repetition, we will reserve a more careful for Part III. them out of judgments arising i as the true generic concept to the par Being in general cannot be regarded

objective being.

To

name.

For, only a common cannot be a common charac is "Being" in a determination should have to show that this predicate had its origin

things which are

it is

conceptually regarded for us a relational predicate, ;

it

c<

existing things.

in

LOGIC

302

the judgment

certainty of

not only the

elude

"I

In so

as

assigning to

as occurring in a

each particular

"

"

I feel

pain,"

I

see

light,"

"I

wish this or

we presuppose

seem

valid, that they

for a logical investigation as to their justification

its

that,"

to leave

and the ground

Nor, indeed, can any one doubt their immediate truth

of their necessity. if

as

and so obviously

are so absolutely certain,

no room

the

also

action.

series.

temporal

Judgments such

1.

particular actions

and universal laws

series,

position in this

and

they are subject to time, these judgments presuppose a

far as

universal necessity to think of our

temporal

but

am,"

certainty of the reality of the unity between substance

and distinctness and complete

clearness of consciousness,

development of the concepts which serve as predicates.

Assuming

that

a person speaks the truth, no one can take

upon himself the right of doubt and whether his or not he is to be believed statements, questioning ing

in

what he says about himself.

have only to determine what

It

would seem then that

the difference between

is

at present

we

these and con

ceptual judgments.

This difference is fundamental. Conceptual judgments have subjects 2. which are assumed to be thought by every one in the same way. The I see," has a subject which can be present to no one as it is judgment, "

to

The conceptual judgment

me.

unfolds the contents of

contents being always contained in

which us in

denoted by a manner which

"

is

it

is

no

is

thought, and the fact that

"

judgment, a

;

in the

all

If I think of

;

it is

given to

other objects of

A,

I

must think

judgment of self-conscious

is

tells us nothing as to the but the see/ always includes the objects, judgment, am." We can always ask whether that which is contained "I

concept exists

teristics

it is

J3"

"

says,

subject, these

simply thought whenever anything is thought is the absolute presupposition of all

subject

its

I

its

the contents of that

The conceptual judgment

other thought. existence of

;

absolutely incomparable with

The

if.

same way

can never be exhaustively stated

as having the determination

ness there

in

in the

The conceptual judgment

thought. of

"

I

it

;

I

can never ask whether

I

exist.

The

charac

of the concept are unvarying; the predicates of the ego, with the

exception

of

the ego

every judgment

as

it is

change from moment to moment, and yet formed possesses an immediate certainty of truth,

itself,

which can only be acknowledged, and never proved. The Principle of does indeed that the Agreement guarantee general concept of the predicate shall agree with the action immediately intuited, but it cannot guarantee

THE TRUTH OF IMMEDIATE JUDGMENTS either the statement that the subject

statement involved in If

3.

we

this,

is

303

just performing this action, or the

that the subject exists. 1

are thus obliged to acknowledge that the utterances of every

self-consciousness possess a certainty which cannot be referred to

upon which

thing else

it is

dependent, then

all

some

that remains for us to

how much is involved in this acknowledgment. first place, we find that with reference to this subject

do

is

to ascertain

In the

mere thought of

possible to separate the

ment,

"I

am,"

differs

from

all

it

from

its

being.

is

ascribed

is

im

is

the judg

other existential judgments, in that

not the mere idea of an ego to which being and predicate are inseparably connected.

ject

it

Thus

;

its

sub

subject

Further, the immediate certainty of self-consciousness involves, at any rate

tion

upon this point, the reality of the synthesis between substance and ac and so far as actions may be referred to attributes, the reality also of

;

the synthesis between substance and attribute. Finally,

we

most fundamental

find that the

certainty with respect to

being attaches to a judgment which cannot be repeated in the same way by any one else, and which depends upon a purely individual act. For the idea which some one

myself;

it

else

refers to the

affirmation of being in individual,

has of me

same its

different

is

most

the 4.

is

have of the

an act peculiar to the

is

to

the

individual.

necessarily mediated, whether

it

or belief in his utterances.

acknowledgment of his being This immediate certainty, however, belongs only

moment

;

to the judgment which

in

states

is

idea of time, for

we

recollection of the act

to

what

the self-con is

present at

true only for a given point of time.

Thus the judgment which we are conscious of our particular

moment.

The way

I

Thus

same way.

and dependent upon conditions peculiar

sciousness of the the

form

original

Any judgment concerning another ego is

from that which

subject, but not in the

states involves the

are never conscious of a particular act without a

which preceded

it

in time,

and our self-conscious

ness always includes the consciousness of a self which is identical in time. at Now, in so far as every moment brings with it the thought of our being imfind we continuous our existence, of a previous time, and thereby

1 Kant s doctrine, that statements of the inner sense refer only to phenomena, because it of the subjectivity of time, does not affect the logical character of such judgments; and the meaning of the statement about reality, affects the

merely

metaphysical import,

which they involve. Their immediate certainty Kantian hypothesis as under any other.

as

judgments

is

as unassailable

under the

LOGIC

.304

mediate certainty here also

which

as unquestionable as

is

no

extends

further.

It

is

"

am

I

The

involves

when we

true that, that

cannot be questioned, but the belief

certainty.

"

an

"

was

I

before,"

But, strictly speaking, the certainty

itself.

memory, the statement,

particulars of so,"

the

;

"I

itself

are dealing with the

believe I once did so and

cannot lay claim to the same

inference of the reality of an actual previous event, from

the reality of a present recollection, could only be justified

there were

if

an absolutely necessary law, according to which I must, under all circum stances, retain the conviction of having at one time acted as I now believe myself to have acted

;

if,

that

is,

no such thing as the discovery true that we regard some of

there were

Now

of an error in our recollection.

it is

our recollections as absolutely certain, particularly those of more recent But it is just as certain that, occasionally at least, our memory events. deceives

us,

and

that there

is

no sure

criterion

between perfect and imperfect recollections

;

by which

to distinguish

in the last instance our only

warrant for the truth and trustworthiness of our recollections to place sistent

them in

all

in a conscious connection,

aspects.

a given action, because

to

is

our

is

ability

continuous and con

Thus the judgment that I have actually performed I believe that I remember doing so, cannot be

regarded as immediately certain. it

which

It is

a mediated judgment in so far as

infers from a present idea the reality of a previous action corresponding it,

and

certain

for judgment such .as this there and absolutely reliable. 1

is

no

rule

which

is

immediately

1 Compare W. Windelband s excellent pamphlet, Ueber die Gewisshcit der Erkcnntniss, a work which agrees in so many points with the position here laid down, that, with the With refer exception of a few passages, I could subscribe to it almost word for word. ence to the above question as to the source of our certainty that an idea is a recollection, he says (p. 87 sq.) that in the last instance it is nothing more than a distinct feeling accompanying the idea, which tells us that it has been presented before this feeling, however, is again due to the fact that with the idea there is associated the subconscious idea of its connection with, and reference to, the ego, which is excited together with it, and manifests itself in consciousness as a feeling of recollection. In this way he explains how it is that we are able to have ideas for the second time, without knowing them to be recollections, for this happens when we have not been clearly conscious of their connection ;

with the thinking ego.

This explanation

is

correct to the extent that there

is

a peculiar

by which we generally distinguish the known from the unknown. But this feel ing can yield no certainty unless it enable us to recall some accompaniment of the particular idea, other than that in which it now appears, and thus to connect the past with the present. I may, on seeing some person, experience most strongly the feeling which generally distinguishes the known from the unknown, but I shall not have perfect feeling

certainty until I recollect the circumstances under which I previously saw him, fit him into the complex of ideas, which constitutes my self-consciousness, and

and thus is

always

THE TRUTH OF IMMEDIATE JUDGMENTS

305

Here, again, we are met by the psychological difficulty which we find in being certain that our concepts are invariable, and hence in being certain that the logical ideal is attained. For since our thought takes place in temporally differentiated acts, the uncertainty of memory affects also my I now think is what I For this thought before. reason the logical ideal can only be approximately reached, and needs not only unremitting practice, but also external aids. these

consciousness that what

Amongst

and so great

writing takes the highest place,

to say that without writing science

On

5.

the other hand,

present action, in so far as

is

importance that

it is

safe

impossible.

we must note it

is its

that every

judgment concerning a

places this action in a temporal series, also

determines a particular point of time for

its

own

validity

;

this

"now"

is

an essential part of the judgment, because, if referred to another point of time, the validity of this judgment would be annulled by others. If, then, a judgment which thus includes the time of it is

valid,

the particular

moments of consciousness

in a

temporal series. be a time which is the same

moving

its

not sufficient to assume that there

universal validity, there

It is

for

must

all.

to

validity is

to

be objectively

appear to every one alike as

not sufficient, that

When

is

a universal necessity for

is,

that there should

such a judgment lays claim to

also be universal laws

making

assign a definite time to the truth of every judgment.

it

necessary to

my judg be valid and universally acknowledged, I must be able to de termine the time for which it is valid in a universally valid way. Thus the Kantian teaching that time in general is a necessary idea is ment

is

We

point of time which

need also the determination shall

measure of time according its

The

then,

to

not sufficient.

has

If,

place assigned to

question as to

be the to

same

for

all

;

in

an objective time of a

and we need a common

which every particular

fact of consciousness

it.

how

these

laws

may be

discovered cannot

be

answered by reference to any immediate certainty, for it depends upon a comparison between that which is immediately certain to me and the temporal ideas of others. with in our third part.

Its investigation

forms a problem to be dealt

In this consists that reference to the ego, rightly emphasized by Windelband not a reference to the abstract unity of self-consciousness, but to the empirical ego, and knowledge in the sphere of recollection is nothing but the continual review and con sistent combination of a number of acts of my past life. present. It is

S. L.

.

LOGIC

3 o6

47-

Immediate judgments concerning external existence are

As

PERCEPTION.

The

subject exists.

46) in so far as

(

perception

in

is

the

place subjectively certain

first

implies the statement that

it

idea of a definite existing thing

becomes

of perception

JUDGMENTS OF

ordinarily used, they include the statement that their

;

upon which a judgment

be a necessity to some existing thing, according to which we

objectively valid

to refer this subjective fact

have at the moment the

I

the condition is

that there should

are compelled to interpret the contents of a perception as the real predi cate of an existing thing.

which

my

spatial intuitions

tions of objects, real attributes

my

and

Especially must there be laws according to

may be

translated into the spatial determina

reference of attributes or changes to a thing into the

activities of substances,

and

my

idea of

its

relations into

real relations.

To

i.

ordinary consciousness the judgments of perception, in which

we make statements concerning external, appear as

that

is

immediately present and

as the

statements of immediate

which

immediately certain

self-consciousness.

These judgments of perception include first of all the consciousness an idea of a particular thing is at the moment present to me, and has

that

the

peculiar

guished from

and indescribable character whereby perception is distin memory and from merely inward ideation. Our possession

of fixed concepts and a denotation for the contents of what

is

them next enables us

to express

thus presented in a universally valid form. l

done

This

whole under a generic concept (a partly by subsuming process corresponding to the denominative judgment), partly by analysing it into its particular elements, and stating the predicates which correspond is

to these.

When

immediate

;

it

as a

these predicates are simple the judgment continues to be one element of the perception is recognised as agreeing with a conceptually determined characteristic (what I see is red). 2 But the

process

may be one

of subsumption under composite concepts

instead of an immediate

naming which

unifies a

;

and

then,

whole with a whole, we

1

8, 6, note. Concerning the term subsumption, cf. the extent in which there is a difficulty in maintaining the conceptual limits of distinctions which melt into each other in the merely internal reproduction of concepts, 2

To

the objective validity of such a judgment

(measurement,

etc.).

may no doubt depend upon

other processes

THE TRUTH OF IMMEDIATE JUDGMENTS

307

have the necessity of a comparison between the particular characteristics of the perception

and the

characteristics of the concept.

then becomes mediate, in that

it

is

the result of a

The judgment

number

of particular

judgments (cf. 56 on the inference of subsumption). 2. If no more were meant by a judgment of perception than that present sensation

is

of redness or sweetness, the

would

suffice here again to guarantee that the judgment such that every one having the same idea must affirm it. But such a judgment does not compare mere ideas.

to a particular object

which

is

my

Principle of

thought of as existing, and

is

Agreement necessary, and

It refers it

an idea

states a predi

cate as objectively belonging to this definite If the judgment thing. true, it is not sufficient that there should be a ground for the

be

is

to

agreement

of the particular idea with the general.

The

confident assumption of

ordinary judgment that this particular idea refers to a definite existing object, and that this object possesses the predicates which I attribute to

must also be well grounded. This is possible only if there is some law according to which the subjective affections and ideas of the individual it,

are referred to objective things with unfailing and universally valid neces Now the of the conviction that real objects correspond sity. universality to our sensations does indeed that we are under a psychological prove to affirm the of what is felt. But it is also obligation the reality proved

by our senses often, as it is said, deceive us, and by the conflicting statements of different observers of the same object, that this universal fact that

no guarantee of complete unanimity in each particular case. we may find, and often do find, that we have to distin guish between that which actually occurs according to psychological laws, and that which is universally valid, and we cannot speak of a sufficient obligation

So

is

that here again

foundation for such judgments unless eliminated.

This,

however,

is

all

subjective differences can be

only possible

if

we can bring

to light

which we necessarily refer the subjective according sensation to an objective reality, and can test every case by them. Then I am sure that I saw and perceived only can we pass from the judgment, universal laws

to

"

this or 3.

that,"

Once

to the it is

its

judgment,

this or that is there, has happened."

recognised that in perception we have at

jective occurrences,

given,

"

reference

and to

that only the presence of the idea

we need a

only sub

immediately

an external thing being a subsequent,

generally unconscious, step, then for every

existence

first is

law, according to

though

judgment concerning external which the idea must always at least

LOGIC

3 o8

be necessarily referred to some external existing is any such necessity, or, at any rate,

under certain conditions

Scepticism denies that there

object.

that

it

can be known to

we

but only in the sense that real external object.

To

Subjective idealism affirms the necessity,

us.

it

necessarily think of what

is

perceived as a

this affirmation of an external existence

is

a

mere act of Thought, and though the necessity thus leads to a second stage in our ideas, it does not lead to an existence independent of our selves. The reality which we affirm is only a reality of appearances, not of independent things.

We

are not concerned here to

sufficient to

show

this

settle

disputed

It

question.

is

that the immediate certainty of our judgments of per

some general law

ception does not rest upon any absolute necessity, until

has been shown according to which the fact of perception necessitates the recognition of the existence of an external object.

From law

this

a logical point of view is

moreover, quite indifferent whether

is,

represented as assuring us of the actual existence of external

that

things

it

is,

in the realistic

sense

or in the idealistic sense as only

;

necessitating that the idea of real objects should follow

The

logical

character

universal validity,

would be

of the

would be the same

meaning of the predicate

in the

Only the sceptical view that it ments would exclude them from

Now,

is

either case

in

"to

be"

upon perception. and

their necessity

judgments,

resulting

;

the only difference

(in the empirical sense).

impossible to attain to necessary judg

logical treatment.

the universal law for which

we

are seeking cannot be to the effect

perceive anything there exists something, which corre sponds to the particular idea developed according to psychological laws

that

whenever

from

my

again,

I

perception.

and from wholly

On

the contrary,

it

has been shown over and over

different points of view, that

it is

possible even to

doubt the existence of the whole external world, and it has been main tained that no logical necessity invalidating that doubt corresponds to the 1 psychological necessity of assuming such a world.

If,

then, there are,

ways and means of attaining to a conviction of external in reality, they are not to be found in the simple facts of perception, but the particular nature of our perceptions.

nevertheless,

4.

But even

if

we allow

that there are principles which necessitate the

reference of our perceptions to something really existing, 1

Cf.

Baumann

s

treatment of these propositions in the

als Orientierung iiber die Welt.

first

we have

still

to

chapters of his Philosophic

THE TRUTH OF IMMEDIATE JUDGMENTS consider

The

conditions

the

question

which these principles are applicable.

what are the presuppositions necessary in order that the of perception may warrant an objectively valid judgment ?

is,

subjective fact

The

under

309

extent to which judgments of perception

may

vary with different indi

viduals sufficiently shows that such judgments cannot under

circum

all

stances be universally valid, since they lead to contradictions.

Generally speaking, there are two grounds, to either of which these divergencies amongst individual percipients

may

lie in

may be

due.

The

difference

the very beginning of the process, in the empirical data from

which the formation of the subject idea and the judgment about

it

starts;

our organs of sense, or, more exactly speaking, in the manner in which we become aware of such affections. Or it may lie in in the affections of

the subsequent processes which in ordinary thought take place sciously, but which nevertheless do take place, and

principally

may

by means of the so-called deceptions of the senses

uncon

shown

be

be ana

to

logous to inferences.

With reference

5.

we

to the

first

of these grounds, the certainty with which

ascribe to objects our sensations of colour, temperature,

attributes, depends upon the conviction that there

is

etc.,

as

their

an invariable con

nection between the assumed object and ourselves, a connection such that the same attribute in the object always and invariably corresponds to the

same sensation lars

in

are colder in

every subject.

summer than

in

Even Bacon, in his firm belief that cel winter, assumed that his sensation of

temperature was an unvarying and infallible test of the whatever feels cold, is cold, and just as cold as it feels.

state of the object

to which this assumption leads,

and deny the same

thing, brought such

times.

was, to

From some

because of

its

by forcing us

to affirm

The

:

contradiction

judgments of the senses into discredit in very early

the very beginning of Greek philosophy sense-perception extent at least, excluded from the sphere of true knowledge, subjective variability

different individuals.

themselves that after

and the extent

to

which

it

differed in

Only since the time of Bacon have men bethought

upon which the greater part of and that all we have to do is to learn the art of using But the Logic which followed Plato and Aris all

this is

the basis

our knowledge rests, the instrument correctly. totle has perpetuated to the present day the neglect of the conditions The concept was thought to be are valid. which these

upon a more than

Kant showed

judgments

sufficient

substitute for an untrustworthy perception, until

clearly that in

mere conceptual knowledge we merely

retrace

LOGIC

3 io

our steps, and never advance any nearer to the object. incomplete which

fails

But any logic

is

to inquire into the conditions of the validity of

these judgments, for it is these which both guide us in our formation of concepts and justify its importance. A judgment of perception, then, can lay claim to universal validity 6.

only when the sense-affection upon which it depends is the expression of an invariable relation between the assumed object and the subject, when the sensation is the infallible sign of an objective quality. And it can

claim this validity only to the extent in which we can assure ourselves that

hence that every one has an exactly similar organization can be accurately corrected. In our

it is

invariable,

and

sensibility, or else that variations

third part

ceed

we

shall

in finding

have to investigate the means by which we may suc

a basis for our judgments which shall satisfy

our affections as will

The

7.

at least

such an absolute similarity or reducibility in enable them to be substituted for each other.

this necessity for

practically

idea of the spatial nature of that which

is

we

;

indis-

is

perceived

solubly connected with the perceptions of sight and touch

think of

what we see and touch as spatially extended and as having a definite form

and

size,

what we is

and we assign to it a have is a subjective

first

determined

definite position in space. idea,

in the first instance

by reference

to

our

centres from which our local determinations proceed.

tioned

how many

Here, again,

and the position assigned

own It

may be

of our spatial ideas are given from the very

inseparably combined with the sensation ideas, such as the idea of the corporeal

itself

;

that

to things

bodies as the

first,

some of our

form of objects and

ques

and are spatial

their distance

from us and from each other, are not originally presented with the sensa tion, but are the result of combinations which for the most part take place unconsciously, can be indisputably proved.

In the

first

place,

it is

judgment, not about

clear that

if

there

is

to be

an objectively valid

something which exists in space and has a definite extension and form, there must be absolute certainty that the idea of space is the same for all, and that the spatial interpreta

my

idea, but about

which we give to our sensations are necessarily determined in a Only when this is the case can the judgment concerning ob jective extension and spatial relations which results from my sensation be tions

given way.

objectively necessary,

and the

spatial object

be the same

for

all.

One

condition, therefore, of objectively valid judgments of perception is that the idea of space shall be the same for every one, not arbitrary or other-

THE TRUTH OS IMMEDIATE JUDGMENTS

311

wise liable to variations, but completely determined, and that every one shall think of space in the same way ; and such judgments cannot attain tion of space.

It is

we

science that

we recognise

these laws which govern the representa not merely with the possibility of pure geometry as a are concerned here. In geometry every one has his own

to certainty unless

space, and different spaces are only congruent, or at least similar; it makes no difference whereabouts in such a space we draw our lines or construct

our

Geometrical figures have no position

figures.

when we

assert that

same

all.

something

When

in space.

It is different

exists in the objective space "

which

is

the

this is here," or that is there," I judge that state something which is to be valid for every one and which determines the position of an object in such a way that the place where it is to be

for

"

I

found may be generally known, and its spatial relations be the same for all. Constant practice generally enables us to determine such relations in our immediate surroundings without special discipline

make

it

;

but this does not

any the less necessary in strict theory to investigate the conditions

and normal laws

for

an objectively valid determination of the form and In astronomy we have a proof of how many

place of particular objects.

presuppositions

are

involved

in

judgments concerning the position of validity, and how such judg

heavenly bodies which lay claim to objective

ments are really valid only when the presuppositions are acknowledged to be absolutely certain and necessary. But these presuppositions include not merely the universal propositions of geometry, they include also pro positions concerning the reference of sensations to a definite place,

these in their turn

depend upon

optical laws,

e.g.

and

that the rays of light

move

in straight lines throughout the same medium, but are refracted upon entering into another. We are not concerned here with the way in which we arrive at our knowledge of these presuppositions only so much is clear, that they must ultimately depend upon something which is imme if diately certain, and which does not derive its necessity from elsewhere, ;

judgment is to be objectively valid. The immediate perception of motion the same with motion.

the particular 8.

It is

cannot lead to a valid judgment unless we presuppose a local determina But this is not tion which has taken place according to necessary laws. sufficient.

that

is,

All

movement, so

far

as

we can

perceive

it,

is

only relative

a mutual change of position amongst visible objects.

;

But our

judgments are meant to bear the objective significance that A moves to wards j5, and hence we have need of universal laws according to which

LOGIC

3 i2

we may interpret relative change of position into actual movement, into change of position in space, and by which we may judge what is to be re Here again the history of as garded as in motion and what as at rest. tronomy proves to us that we cannot arrive at objectively valid judgments concerning motion unless we presuppose universal principles according to which the subjective perception of motion

is

referred to actual motion,

and the subjective phenomenon interpreted into an objective event. The difficulty of clearly distinguishing between the concepts of relative and absolute motion

sufficient

is

proof of the labour involved in discovering

these ultimate principles. Still

9.

more important

It

things.

is

is

the reference of our sensations to definite

true that the form in

sensation to permanent things

thought

;

is

and we could not throw

we would.

But

just

which we

refer the material

given by

part of the unalterable nature of our off this psychological constraint

even

it

because the thought of a thing is not already included we can conceive of a difference in the process. This

in the affection itself, is

difference, indeed,

hardly apparent

when we have

do with motionless

to

and permanent phenomena anything which, for our apprehension, is un changing, which keeps the same position in space, and has fixed limits, is ;

upon as one and the same thing. In the same way it assumed that two things cannot occupy the same position

unhesitatingly looked is

so universally

in space that all our references are founded upon this presupposition even spatial movement, if it is observed as continuous, is by itself

cient to

make

not

;

suffi

us uncertain in our reference.

But wherever we

find change of form, magnitude, or sensuous qualities, becomes a problem as to how the successive stages in the change should be referred to the assumed substance. The necessity appears of generally

it

accepted principles according to which the individual must guide his judg ment, if he wishes not merely to state his views, but to make objectively

When

valid propositions.

a column of quicksilver expands or contracts,

we

describe the succession in our perceptions by the proposition this grows smaller," or "this grows larger." We use the same words to describe "

the growth of a crystal or the diminution of a piece of ice in the air propositions

seem

to imply that in both cases

moreover, the same thing, which changes

its

less,

room

;

in the

it

is

the

is

volume.

the two propositions have a different meaning. really consider that

it

;

such

a definite thing, and,

But

In the

for the physicist

first

case,

he does

same subject which occupies now more, now

second case, the increased crystal or the half-melted

ice

THE TRUTH OF IMMEDIATE JUDGMENTS

313

no longer the same thing as before ; something has been added to the For the child water original thing or a part has been taken away. is

vanishes

when

it

water evaporates

one or the

and wood when

evaporates,

same thing remains, "

other.

it

only in

is

it

burns

;

for the physicist the

The

another form.

proposition "this has a quite different meaning as apprehended by the Kant has included the principle of the permanence of

substance amongst the a priori principles of the understanding. This it is not, if we mean that in all our references of sensations to objects this

by a natural necessity of the understanding; if it were words so, signifying beginning and ceasing, growth and diminution, could It is only never have arisen and been applied to things in any language. principle guides us

as a condition of consistent experience that a principle

manner

regulates the

in

which we add substance

is

necessary which

to accident in

thought but the principle, as Kant understands it, is impossible until it has been established that weight is to be the measure of the quantity of substance,

and

this

is

one of the

teaching on

later results of science.

this point

is,

judgment concerning the sense alone

is

it

that

we can have no

originally necessary

science of experience.

Whether we

only truth in Kant

consistent

s

and necessary

such a principle; in this necessary if there is to be any

particular unless there it is

The

;

is

are to accept

it

as necessary because

independent of all experience and self-evident, or because our experience can only be made thoroughly con sistent by means of this principle, is another question.

a priori

10.

in the ordinary sense of being

The

difficulty of establishing the real identity of the

upon the ground of temporally disconnected perceptions

is

same thing

only a special

case of the difficulty of applying the concept of the thing as that which identical with itself in time to particular instances. definite rules

upon which

is

Here again we need

to base the assertion.

validity of

shown that the conditions upon which the any judgment concerning the particular depends are different

from, and

much more complicated

11.

Our

analysis has already

analytical judgments, based

upon

than, those of the validity of merely

a generally accepted system of concepts.

judgments puts an end to the natural immediateness of narrative judgments, and necessitates their mediation in order that they may be true, and that we may be certain It

has further shown that the

demand

for perfectly valid

of their truth.

Thus from

the point of view of the conditions of science, as distinguished

from that of the psychological genesis of judgments, Kant was

right, after

LOGIC

314 all,

in regarding

and

synthetical,

only conceptual judgments as analytical,

all

others as

in inquiring into the principles of their synthesis

a priori

as the conditions of their objective validity. 12. The necessity of guiding principles is still more evident in judg ments of causality than in the inference from phenomenon to substance. We are so accustomed in our ordinary judgment to apply the idea of efficiency, and we make use of it in simple, every-day matters so entirely

without reflection, that judgments which state that a blow has broken a window-pane and that drinking quenches the thirst are formed as if they

were immediate;

in

events

is

unhesitatingly expressed by verbs

we

of efficacy, and

thought

efficacy as directly as

we unconsciously appro The given relation between

transitive verbs

employing

priate the idea of efficacy which they contain.

and adjectives containing the that we apprehend this

therefore believe

we do change

or

But

movement.

let

us reduce the

We particular verbs which express an effectuation to definite concepts. shall find that they contain some elements which are of a nature to be perceived

intuitively

change of the other. is

not intuitable, that

a

movement

But is,

The

perceive

it

by the

objective validity of our apprehension of events which

we can

to

is

an element which

itself, which implies that the the other, that it does not proceed produced by

the causal-relation

subsequent change is really from the subject in which cause.

of the one thing and a subsequent

in addition to these, there is

it

takes place, but

forced

is

upon

be estimated according to principles already laid down.

For the statement that a part of them is caused by something else we need a further fundamental principle, according to which a perceptible event

may be known,

with an objectively valid and necessary knowledge, to be

an instance of causality.

Only

in this

way can a

cerning the particular attain to objective validity.

than with the concept of substance, result of

human

it is

need

For here, even more

obvious that while

it is

a necessary

nature and of the laws according to which our thought

develops, that events are causally connected by us, rid of the

causal judgment con

to regard the

and

that

we cannot

one as the consequence of the other

;

get yet

does not exclude widely different applications of the same general principle, and wide differences in our way of referring the particular to causal connections. It was the natural desire for causality which drove this

men

to seek the causes of events in the

power of

spirits or in the position

but no such proposition has objective validity unless there is ; a fixed and necessary rule, according to which we may refer events to of the stars

THE TRUTH OF IMMEDIATE JUDGMENTS

and discover what is the cause of a given event ; indeed, it is only condition that any causal connection amongst particular events can

causes,

on

this

be asserted with his

315

was such a rule as

It

validity.

He

a priori principle.

looked

this that

Kant sought

in

for a condition of scientific experience

and of objectively valid causal judgments which should necessitate a particular manner of connecting the subjectively given manifold, and a particular

interpretation of that which

Kant

transforming (to use

1 judgment of experience.

empirically co-presented, thus

is

distinction) a judgment of perception into a

s

Here again he

believes that in the synthetical

principle a priori that everything which happens presupposes something upon which it follows according to rule, he has set forth this ultimate con

and

dition of objective judgments,

the ground

given

of

its

by showing it to be a priori he has But here again it may be asked this form is really to be acknowledged

that

necessity.

whether the fundamental principle in as necessary and a priori, or whether because

it is

Moreover,

consistently. it

is

sufficient, or,

tivity

it

merely accepted as necessary

is

the only hypothesis which enables us to shape our experience it

may even be

indeed, at

all fitted, to

of our causal judgments.

questioned whether in

this

form

serve as a basis for the objec

So much, however,

is

certain, that only in

proportion as our reference of perceptions to causal relations takes place

accordance with fixed rules can we assert

in

a

phenomenon, B,

is

sider

how

;

difficult

this

it

follows that

is,

it

often

is

to decide

that it

any particular instance that

and from

ground in a reference to the must be inferred and synthetical. If we con

every particular causal judgment must have general principle

in

the effect of another, A, its

what

is

the cause of a given event,

be the more ready to agree with the statement that there is absolutely no causal judgment, the necessity of which is immediately

we

shall

certain.

43.

The

final

and

upon which

highest general rules

all

besides the Principle of Agreement

other propositions are grounded, are either axioms of

when the sun shines on the His well-known example (ProL, 20) is the judgment stone it becomes warm." This is a mere judgment of perception, and however often I it may have perceived it or others may have perceived it, it contains no necessity ; merely the But when I say in this way. happens that the perceptions are generally connected sun warms the stone," the concept of cause has been added from the understanding to "

1

"

the perception, and this establishes a necessary connection between the concept of sun shine and that of warmth ; the synthetical judgment becomes necessarily and universally valid,

hence

it is

objective,

and passes from perception

to experience.

LOGIC

3 r6

the formation of concepts, or postulates concerning

assumptions made upon

The

the existent.

the ground of these postulates are ultimately

regulated by the law of contradiction.

From what has been

1.

said

it

will at least

be evident that the purely

empirical view, which regards the particular facts of experience taken as objective statements as that which is immediately certain and upon which all other propositions are

founded, can never be the ground for a science

consisting of universally valid propositions.

belong to the individual, valid

for

him

each

man

s

Nor could we

alone.

Since the facts of perception

statements about them are originally get

further

than this subjective

validity unless there were rules according to which a universally valid

inferred from the subjective fact.

may be

proposition

Any

view which

maintains that the facts of perception, as ordinarily understood, are the

must

final certainty,

either lead to the scepticism of

Hume, which

will

not

allow us to pass from subjective impressions to any statement concerning "being";

or else is

something one is for him. valid for

we

are allowed to proceed so far as to state that

In either case there

no

is

It is true that particular

all.

do aim

if

what appears to any possibility of a truth which is

to the proposition of Protagoras, that

empirical theories, such as that of

upon this foundation. But such theories some assume always surreptitiously propositions having universal validity Mill,

at erecting a science

;

times assuming as a matter of course that judgments of perception are the

same

for every one,

and

state objective being as well as guarantee

real

knowledge; sometimes setting forth our inferences from these judgments of

perception

as

assumption there 2.

although without some universally valid no manner of justification for them. 1

self-evident,

is

hope that I have shown that perception necessary and universally-valid judgment concern

In opposition to this view,

cannot be a ground

for

I

ing the existent, unless the necessity of our particular judgments

is

based

upon universal principles. Ultimately these principles must somehow be immediately certain ; and they cannot derive their certainty from an ex perience which, in the form of true judgments, is impossible without them. the question arises whether there are any immediately certain pro

Thus

Such propositions would state the necessity of positions of this nature. the processes by which, from the fundamental subjective facts of immediate sensation, 1

We

we

obtain the idea of a world of particular things existing in

reserve a detailed examination of Mill

process of induction.

s

theory until

we come

to investigate the

THE TRUTH OF IMMEDIATE JUDGMENTS

317

space and time, and the reality of their attributes and actions as of their Their general formula would be given the condi manifold relations. :

tions of individual perception, to obtain

necessary statements concerning the existence of objects, and given statements concerning the existence of these objects to obtain from them. other necessary statements. If,

from the

fact that

I

have definite spatial

intuitions,

it

could be in

ferred in accordance with these principles that a space, such as I imagine exists

it,

objectively

if it

;

followed that, because

I

have a sensation of

this space, there exists a bright object at this light at a particular point of

point, according to the principle that

which

in

it is

inherent

;

if,

from the

be inferred that another thing

any

felt

quality requires a substance

fact that a thing

is

or changes,

tions being as obvious as the principle of contradiction

be no

it

could

or changes, the necessity of such proposi

is

then there would

ground even for judgments of perception. For have this or that idea must be recognised as im

difficulty in finding a

the subjective fact that

mediately certain,

and

I

would be the empirical datum from which our

this

judgments concerning the existent would necessarily follow in accordance with such laws.

These propositions would have to be certain a priori, in the sense that invariable and in they would be merely the conscious expression of an and accompanied by the conviction

that so

are obliged to judge in such a way.

They

evitable function of our thought,

surely as

we

we

are ourselves

would not proceed from the contents of the object of thought as expressed in the concept, but would ascribe to these contents a predicate, derived not from themselves, but from the particular manner in which they happen To this to be presented, from the specific character of the perception. extent synthetical judgments might be grounded upon them. Here we may see how from this point of view also the Kantian ques tion, "How

are synthetical judgments a priori

mental importance.

For

it

is

evident

that

possible?"

is

of funda

upon the answer

to

this

from individual thought as it question depends the possibility of passing the subjec valid to recurs propositions, and from universally constantly tive formation of ideas to judgments concerning the existent. 3.

That there are such propositions is recognised whenever it is taught AXIOMS upon which our knowledge of the existent depends.

that there are

In accordance with Aristotle

s

1

teaching,

axioms have been distinguished

for which no further ground can be Treating of those elements of our knowledge i. 2 and 10, between d#w/*a (dpx*) Anal. in the Aristotle post. distinguishes given, 1

,

LOGIC

3 i8

from definitions and the analytical judgments following from these, on the one hand, and from postulates on the other. When thus distinguished they are looked upon as propositions having a truth and certainty which is immediately

Hence

evident.

their

contradictory

cannot possibly be

mere explications of concepts they form the ultimate presuppositions upon which all knowledge must be grounded. Moreover, the name Axiom is not given to particular judgments of im thought, and

mediate

as they are not

certainty

for

instance,

of extensive application. first

solutely

utterances

the

to

of immediate

self-

but only to universal propositions which express a necessity

consciousness

for

Aristotle,

instance,

and most universal axiom

in

addition to the ab

the principle of contradiction

recognised special axioms for each department of knowledge, e.g. mathe matical axioms. Postulates, on the other hand, are propositions which

admit of further proof or derivation, nor can be accepted as immediately and necessarily certain their certainty however is assumed,

neither

;

not upon the ground of logical necessity, but upon psychological reasons of a more general kind.

An

inquiry as to whether

the propositions which have at various

all

times been employed as axioms have really merited this

title could only be carried out by an investigation into the special departments of know Nevertheless our ledge which is beyond the scope of general logic. are a which to base an sufficient ground upon previous investigations

important distinction with reference to the import of such propositions,

one which has not generally been recognised, though it was indicated by We mean the distinction between axioms referring to the forKant. 1 3 dmy/c?/ etVcu 6C

^eiv rbv OTLOVV /mad^ffo/mevov 5etcu,

dvdyKr) x" T states that something

"

fj.r)S

^Q"f]ffo^vov

TL).

avro Kal SoKelv avdyKT]), and Oecrts (TJV /J.T] He again divides the tfe crts into U7r60e

is or is not, and which gives the what only, not the which contradicts the presuppositions of the learner is cur^/iia. The last term has never attained to any fixed meaning. The modern use of the term postulate has been determined though again not absolutely by Kant, when in the Kritik d. r. V. he refers to the mathematical use of the term the practical proposition which contains nothing but the synthesis whereby an object is presented to us, and its concept created, is a postulate." Accordingly he calls the principles of modality postulates because they point out the manner in which the concept of things is connected

which "

that."

While a

"

"

6/>toyids,

vir60e<Tis

"

:

with our faculty of knowledge. But a theoretical proposition though it

der practischen Vernunft a postulate is not demonstrable as such inasmuch as it is in

in the Kritik is

We

find separably dependent upon an a priori practical law of unconditional validity. the same discrepancy in Kant s Logic. I have given a wider meaning to the second definition in the text. 1

In his distinction between the mathematical and dynamical use of the synthesis of

the pure concepts of the understanding.

THE TRUTH OF IMMEDIATE JUDGMENTS

319

mation of concepts, and axioms referring to the knowledge of a particular existing thing.

We

have laid

it

down

that the possibility of a logically perfect formation

of our concepts depends upon our being able to state

according to which

our ideas are formed.

all

perfect concepts are

conscious synthesis

;

necessary laws

certain that logically

It is

no natural product, but have to be obtained by a and it is as certain that this synthesis must be

governed by rules which are obviously necessary, but which constitute primarily a ground only for the form of our concepts and the mutual reference of their elements, not for the assertion that a particular thing

Thus

exists.

real

the proposition that

we cannot

without presupposing a thing to which

think of any attribute as it

attaches

is

a rule which

determines the construction of our ideas and the relation between their elements. All propositions, again, concerning the incompatibility of certain char acteristics are

axioms

for the construction of concepts.

nature of our thought

bined

in

one

itself

and

idea,

by the

It is fixed

that certain determinations cannot be

this impossibility

can be certain

for us

com

only in the

same way

as the principle of agreement is certain. (Essentially different from these are propositions concerning incompatibility which are only

empirically inferred

;

as, for instance, that

a gaseous state

is

incompatible

with great specific weight.)

Mathematical axioms are to be classed with these axioms struction

of

concepts (when, that

is,

they

not

are

for the

merely

con

analytical

propositions, such as the principle that two magnitudes which are both

equal to a third are equal to one another, which follows analytically from the concept of equality).

For inasmuch as

all

geometrical figures pre

are governed by the nature of our idea of space, such but the manner of synthesis which is necessitated

suppose space and axioms express nothing

by our idea of space. It is upon the inevitable rules of this idea axiom two straight lines cannot enclose a space is based.

that the

"

"

From one

point of view

all

these axioms

may be

treated as analytical

though not derived is, from the concepts of the grammatical subjects, they are involved in the

propositions

;

when, that

we look

to the

fact that

nature of the ideas presupposed in these subjects

(

18, 5, p.

1

10

sq.).

That

be synthetical is due only to their being relational judg they appear which must have been preceded by a synthesis in the ideas without ments, which there would have been no relation. They are based upon the to

LOGIC

320 fact that the different

elements of our ideas are not independent of one

another.

Such axioms there are also in reference to all we think of as existent ; they hold good, however, only when it is the concept of being which is in ques tion, and not with reference to any assertion that this or that particular Spinoza s axiom otnnia quce sunt, vel in se vel in alio sunt is thing is. one of these and it refers to the fact that nothing but substance with :

accident can be thought of as existing.

But these axioms are not meant to serve as grounds for the judgment The one last quoted, for instance, particular thing is.

that this or that

leaves

it

quite undetermined to what

we

are to apply the concept of being

something else (independent and dependent being). Other axioms, however, are needed for our judgments concerning the axioms upon which we may base the assertion that a particular existent in

itself,

and being

in

;

certain particular thing it

in a certain way, or

And

is

it

just

this

must be thought

which constitutes

The axiom

the former axioms.

to exist because

we form an

because another particular thing either

is

says

that

move

to

in

one moment, it body the next in the same direction and with the same if

a given

from

their characteristic difference

of causality, for instance, as formulated in

the law of inertia, says nothing about the necessary idea of motion is

idea of

or has been.

actually

moves

at

;

what

it

continue

will

velocity,

and

motion another body is there which has influenced it. changes if I perceive a Thus the general formula of such axioms is sometimes it exists"; sometimes some under conditions, particular thing given that

its

if it

"

"if

particular thing

is,

then some other

the process, by which

We

my

is

also."

In

this

need only attend to what always takes place

ideas to

way they

regulate

ideas of the particular are interpreted as reality.

become conscious of

in the formation of

our

The

the necessity of the former axioms.

necessity of the latter, just because they refer to the existent, cannot be

derived from the necessity of thought so simply, except in so far as we

assume

as our highest

The

axiom

that thought

and being correspond.

how vain is the belief that 4. we can ground the statement that a given thing is, and is this or that, upon simple and immediate axioms, or that the universe of the particular can be derived from them as necessary consequence. Neither the principle non datur vacuum" nor the axiom that a a can take effect where it history of science proves irresistibly

"

thing

is,"

that

neither the assertion that "

"

like

only

only effects like/ nor the statement

the effect does not continue without the

cause,"

have been of any

THE TRUTH OF IMMEDIATE JUDGMENTS and the

avail,

criterion of inability to think otherwise has

321

been constantly

misconstrued as the psychological impossibility due to habit, instead of 1

logical necessity.

Even Kant

s splendid attempt to exhibit the synthetical judgments a which are the ground of all experience, has really only resulted in shewing that such synthetical judgments a priori must hold if

priori,

good

experi

be possible as science. He starts by assuming that there is a science of experience, and working back from this he seeks the conditions ence

of in

is

to

it, guided by the principle that all cognitions must admit of being united one consciousness. But neither his derivation of the from

categories

the forms of

in the traditional

Logic and supplemented by himself, nor yet the synthetical principles obtained from this basis and their proofs, have succeeded in convincing his readers that they have here

judgment given

propositions which are absolutely necessary and self-evident, whose contra dictory cannot possibly be thought,

and which are contained a priori in our understanding. On the other hand, again, the proof that our sensa tions as they occur must necessarily submit themselves to the categories

and a priori

principles leaves

Schopenhauer abandoned

much room

for question.

the extensive fortress of the twelve categories

he might maintain more strongly the citadel of causality ; is very instructive, it cannot take

in order that

but although his simplification of Kant

the place of the Kantian pure forms of the understanding and synthetical principles a priori.

Even

if

he aimed

at

nothing more than psychological

explanation of the process by which every one

and think of them

spatial intuitions

We

insufficient.

may,

indeed, infer

other than myself as the cause of scious of having produced this

cause

them

necessarily in space,

is

is

forced to objectify his

as external, the principle of causality

from

my

is

must assume something sense affections, since I am not con

myself.

nor that

that I

it

But it

tion itself considered as an existing thing.

it

does not follow either that

consists in the object of intui

No

doubt

scientific reflection

upon our sense perceptions, which begins by assuming that they are occasioned by external objects, finds itself confirmed in this assumption by the fact that

it

is

thus enabled to explain our sensations, and

reason that Schopenhauer it is

after all

s

it is

But

it

was intended to explain.

evident that the general principle of causality contains no 1

S. L.

for this

convincing only after we have already tacitly presupposed the

existence of objects, the assumption of which

When once

it is

theory has been approved by Helmholtz.

Cf. Mill s Logic, bk. 2, ch. 7,

and bk.

5,

ch. 3.

Y

LOGIC

322

information as to the nature of the cause of a given

from

possibility of inferring

There are

still

more

it

and

Even

we

if

caused

my

affections," is

I

be valid

allow that

as a

holds good as a uni

it

it

axiom

application involves the

which

see the im

cannot be the ground of our inference of I am not aware of having myself Thus a proof that I am really not their cause.

self-evident axiom,

external objects unless the proposition

its

we

when regarded

serious defects in this principle

principle of objective truth. versal

effect,

the existence of any definite cause.

"

that I

am

not the cause of anything

do not produce consciously an axiom which no one will assert a priori. Nor could it be a principle of objective truth unless ;

to it

were to guarantee that everything thus objectified by the individual were but the conditions It may be a natural law of our thought eo facto valid. ;

under which

Thus the

it

may become

a normal law are

principle of causality also

fails

still

to enable us to assert that this

or that particular thing necessarily corresponds to

my

like

idea of

for

it;

by

itself it

tells

be discovered. 1

to

my

perception, and

is

us nothing of the nature of the

cause. It

cannot be allowed, then, that the general propositions which guarantee

the objective validity of our judgments of perception, are obvious as simple, self-evident truths

;

nor that we find them in a form which, by

itself,

makes

the reference of our perceptions to an existing thing, and of certain per

ceptions to a certain thing, a priori certain.

But

still

it

remains open to

us to acknowledge the existence of an external world which all,

not

as a postulate of our search for science

avoid

believing, although

we

is

the same for

and knowledge which we can

recognise that

it

is

not

self-evident. 2

1 I agree with Windelband (p. 76 loc. cit.} that it is a first principle of knowledge more accurately of our attainment of knowledge which makes us seek a cause for every phenomenon but then this law is not sufficient to show the sufficient ground for Such a law, however, would be necessary as a ground for our judg every phenomenon. ments of perception. Cf. the criticism of this theory of causality in the work of Spir, Denken und Wirklichkeit, p. 121 sq. ;

2

Baumann s proof of to much the same

comes

Zeller s investigation

welt

"

(Vortragc

realism (Philosophic als Orient ierung iiber die Welt, p. 248 sq.) as this, so far as I can see.

"

iiber die

Griinde unseres Glaubens an die Realitat der Aussendritte Sammlung, p. 225 sq.), which is a model of

und Abhandlungen,

and caution, leads to practically the same result, although he attempts to dispose of the argument that I myself am the only real being which exists by a refutation to which he attributes the importance of a proof. The proof, however, is only derived by him from clearness

the fact that such an assumption would render the contents of consciousness inexplicable, and thus it presupposes the necessity not only of explanation but of causal explanation. But this necessity is in the first instance subjective, a necessity imposed by our desire to

know.

That the conviction of the

reality of

an external world

is

justified

by the necessity

THE TRUTH OF IMMEDIATE JUDGMENTS

323

This postulate being granted, the question arises What are the universal conditions required by the nature of our perceptions, if they are to be :

and

referred to an external existence,

are to be is,

made thoroughly

then, the aim,

consistent

and not the

our guiding clue in

the judgments resulting from

if

To

?

starting point of science.

we must

them

discover these presuppositions

Nevertheless for

back upon a principle whose likeness to the principle of contradiction may impose upon us, but which is really only a particular application of that i.e. it is principle impossible this

discovery

fall

;

same thing should both be and not be, and not be A. The principle of contradiction

that the

thought states that

it is

and deny the same nitely

If

system which

fixed conceptual

ideal consciousness,

and the same

it

as a

should both be

A

natural law of our

we should consciously both affirm we assume that there is a defi

impossible that

proposition.

that

present without variation to an

is

for all thinking beings,

then

all

concep

judgments are established by the principle of agreement. Hence it follows also from the principle of contradiction that all judgments contra dicting these are false, whether they are direct negations, or judgments tual

When

predicating incompatible characteristics. "

the

same cannot be both

B and not

concept, the definite contents of

my

B"

this is the

we mean by

sense in which

the same, the same

idea.

But when we are forming judgments about the existent, this principle prohibits us in the first place from thinking that the same thing both

and is not. If then we can infer from the assumptions we have made about the existent one conclusion, that a particular object of thought is, and another conclusion that the same particular object of thought is not is

the two propositions cannot both be true, and there must be something false in

Since

And

our assumptions.

same

that the

it is

particular

A

both

same way it is not B.

in the is

is

impossible to think

B and

part of the concept of being, that

think, so that true judgments about the

it

is

the

same

same thing must

for all

who

agree, whoever

We cannot accept it as an of explanation and understanding is true only as a postulate. axiom that nothing incomprehensible can exist indeed a complete understanding of all that is presented to us can never be more than a problem set before us which we shall the theory solve. never Though, therefore, I completely agree with him that ;

completely

which regards our ideas as only the products of the conscious subject is untenable, still of the reality of an I regard the final presupposition upon which is based our conviction This however is quite sufficient to en external world as nothing more than a postulate. the causes of able me to accept the statement of the problem as formulated on p. 263 of consciousness which we call perceptions must be determined in a those :

phenomena

way which

will

correspond to the

facts.

LOGIC

324 forms them,

it

and the same

when inferred by cannot be true of one

follows that contradictory judgments, even

different people

on the ground of

existing

thing.

their perceptions,

It is

true that this

argument

is

ultimately

based upon our concept of being, and that we cannot go beyond But there is no other scientific knowledge than the knowledge which us that

if

we would think

of anything as existing,

we must

this.

tells

necessarily think

we could suppose it possible for contradiction to be repugnant to our thought only, and to be admissible in the existent, all our efforts to know the existent would be rendered fruitless. In the third part, I hope to show how the nature of the problems to be solved, and the conditions under which we attain our knowledge, have

of

it

in a given way.

If

necessarily given rise to that process in our experiential is

knowledge which

exhibited by the history of the actual development of science.

show, that

is,

that the

whole task has consisted

I shall

affirming an existent

in

accordance with the postulate that something is, and upon the ground of our perception, and in making our hypotheses about it in such a way that in

our statements concerning it may be free from contradiction. The history of science shows us a continual process of re-construction and correction in

our ideas of the existent, a process which enters upon a

new

stage

whenever our hypotheses lead to contradictions. There is no other confir mation of our belief that any given thing is, than the complete con sistency of

our judgments with reference to the existent; the return of

all

the circle into

we accept with that the be such immediately certain, finally of perception, which was the starting point of the whole All the general propositions which

itself.

must

respect to the existent

the subjective fact process,

may

in its turn

be a necessary consequence of them.

the immediate assumption from which qualities are

accepting

it

immediate attributes of the

we were

we always

In

set out, that

existent, has

led to contradictory conclusions.

been

this

way

sensible

rectified

;

by-

In this way the

axioms of physics, the principle of the permanence of substance, etc., have been discovered. Kant, in his Antinomies, chose this same way to show that space

and time are only subjective forms of intuition, and that every is only phenomenal to assume that they are real in the

thing therein

;

ordinary sense leads in his opinion to contradiction. The principle of causality, at any rate in the form in which alone applied, enters into this process of building It enters, that is, as i.e.

it

can be

up knowledge from experience.

the postulate that the existent

is

knowable

determined according to universally valid laws.

as necessary,

For not even the

THE TRUTH OF IMMEDIATE JUDGMENTS firmest conviction that everything has

confidently

the

existence

of a

its

325

cause could enable us to assert

particular

thing,

if

causes

worked

by

chance. 1 1

In order to avoid repetition

causality to Part III.

I

postpone a complete exposition of the principle of

CHAPTER

III.

THE RULES OF INFERENCE AS THE GROUND FOR MEDIATED JUDGMENTS. IT has been shown in the previous section that judgments which

we were

immediate from the point of view of natural thought, must nevertheless admit of being presented as necessary consequences of obliged to regard as

when we have

a general law

to ask for the ground of their certainty. to follow from the principle of agree must be shown Analytical judgments ment judgments of perception from the laws, according to which we de ;

from our subjective affections the conviction that there are material And since these general laws can be known only in the form of things.

rive

judgments, the contents of the previous chapter are to a large extent dealt with under this one only the highest and ultimate laws, together with the ;

immediate utterances of self-consciousness, are excluded, as incapable of 1 being reduced to more remote principles. 49-

The most

general formula according to which we derive one judgment

from another

is

the

HYPOTHETICAL SYLLOGISM.

This

may be

either the sim

ple application of the proposition that the affirmation of the ground involves that of the consequence, the denial of the (in

which case

it is

called the

called Pure Hypothetical Syllogism)

the consequence of the consequence,

The

i.

consequence that of the ground

Mixed Hypothetical Syllogism) it

;

or (as the so-

may be based upon the principle that

is

the consequence of the ground.

process of drawing a conclusion or inference takes place psycho

whenever we are led

to believe in the truth of a judgment by our one or more other judgments, and not immediately by the ideas of the subject and predicate connected in it. There are many logically

belief in the truth of

ways

in

114

p. 1

which

sq.)

;

this belief

and

it

often

may be brought about psychologically ( 19, 3-4, happens that we are not even clearly conscious of

For some appropriate remarks on the Schuppe s Erk. Logik, p. 12454.

relation

between judgment and inference,

cf.

THE RULES OF INFERENCE. the process of mediation by which

we

327

derive the certainty of one judgment

from that of another.

This mediation depends frequently upon habits of association and combination which are governed, as a matter of fact, by fixed rules of which we are not expressly conscious. Every expectation of a future event

is

based upon an inference which extends beyond what is given ; is to be found in previous experi

but the ground of our expectation, which ences,

is

not expressly present in consciousness in the form of a universal

we expect

proposition every time

that an unsupported

body

will fall to the

ground, that eating will satisfy hunger, or that

stood of those

who

what we say will be under without conscious mediation from the pass

We

hear.

certainty of the given event to the certainty that a future one

will also

take

place.

But

logical theory

which inference

is

has to enquire as to what are the conditions under

That

valid.

is

to say, since every inference involves the

one judgment (the conclusion or inferred proposition) is true, because one or more other judgments (the premises) are true, we have to belief that

investigate the logical necessity of this belief that the premises are sufficient

ground

a

for the conclusion.

The

2.

another,

question as to how one judgment may be grounded upon may be regarded from two points of view. We may either start

from a given judgment which is accepted as valid, and ask what further judgment can be grounded upon this or we may start from a question, from the tentative suggestion of a mediated judgment, and ask how can this ;

"

judgment be grounded, and under what conditions? in order that

it

may be

valid

What must

be certain

"

?

It is evident that, given a valid judgment A, another and a different 3. cannot be safely grounded upon it unless there is an uncon judgment ditional and universally valid proposition A is true, is true." All

X

"If

that

is

expressed by this hypothetical judgment

is,

that

X X

is

the necessary

consequence of A, and that any one who accepts A must also accept X. Without such a rule there would be no logical justification for an inference

;

if

A

might be true without

X being true,

the certainty of the former would

be no ground for the certainty of the latter. Thus the objective validity of an inference from A to must always be dependent upon the validity of

X

this hypothetical rule.

Hence

the most general, logical scheme for

mixed hypothetical syllogism 1

Cf.

Kanl

s

Logik (Hartenst.,

all

inference

is

the so-called

1 :

i,

p.

453

57)

:

"The

general principle upon which

LOGIC

328

A If

A

is

Therefore

The order

X

then

X

A

If

is true.

true,

is

true

is

A

is

then true

Therefore

true.

is

true,

;

of the premises depends

X

is

true.

;

X

is

true.

upon what the movement of thought

judgment A represents the matter-ofhappens to be. element in the ground, the datum from which the inference is made, while the hypothetical judgment is the law which contains the necessity, the If the validity of the

fact

rule according to

other

may come

which the inference

is

made, then either the one or the But in logical ter

in the actual course of thought.

first

minology the rule according to which we infer is always called the major premise (G. Obersatz), the datum from which we infer the minor premise (G. Untersatz) or assumption. If

4.

which

A

tells

the rule which rule

"

:

A

Is

itself

presents

us that is

true,

if

A

is

applied

if

A

if

X

is

is

is

also true ?

X because of A

true,

i.e.,

"

But

"

present, the question

first

and

In the latter case the rule

be applied

X

is there a judgment on the contrary, it is if, whether we can apply the

the question arises

first,

true

is

"

?

It may capable of a two-fold application. as certain but it may also be recognised

is is

;

not true, according to the law that the denial of the con

sequence involves the denial of the ground. In this way there arises the inference If

A

is

true,

Xis not Therefore

A

Xis

:

true,

true; is

not true.

All the ways in which we can make an inference of a simple 5. statement must admit of being reduced to one of these two forms, which

are generally

known

as the

hypothetical syllogism,

1

modus ponens and modus

tollens of the

since by inference in this sense

mixed

we cannot under

stand anything else but that one judgment necessarily follows from the other.

We

may, then,

lay

following formula in

down

as certain that the validity of a

judgment can

made by reason may be definitely expressed in the under the condition of a rule falls under the rule This proposition contains just that view of the nature of inference which is given

depends the validity of itself."

it

all

inference

that

which

modus

tollens

:

falls

what follows. 1

The

so-called

always infer from the judgment is not true, A is not true."

may "if

itself

A

is

be reduced to the modus ponens,

true, then

X

is

true,"

for

we can

the other judgment

"

if

X

THE RULES OF INFERENCE

329

never be inferred from one single judgment, but that two premises at least are always essential.

One judgment of the premises

is

can be inferred from others only upon condition that one an unconditionally valid judgment, the expression of a

necessary connection.

premise which really carries us from one certainty to the other, for our progress is the law that the affirmation of the (hypo

It is this

and the ground

thetical) ground involves that of the consequence, the denial of the conse quence that of the ground. 1

The

6.

hypothetical judgment which mediates a conclusion, indeed the proposition that is a

be mediated and inferred

consequence of

A

is

consequence of A.

The

principle

known

If

then

If

A

If

Mis

If

A

is

is

M

upon which

is

true

is

true

X

is

itself

necessary

a consequence of a

;

;

then

follows that

it

is true.

this syllogism

may be

it

if

may

true that

it is

true, X true, X

;

be necessary

to

is true,

concept of consequence

consequence

X

:

grounded follows from the

is

formulated

the consequence of the

"

the consequence of the

2 ground."

1 Another proof that this form of hypothetical inference is the natural and general for mula for all inference is its universal appearance in the phrases which we generally em since because hence ploy to state our conclusions. Such conjunctive forms as etc. are nothing more than verbal abbreviations of the schema, for these particles have a "

for,"

,

double import

; they express the validity of both propositions, antecedent as well as con sequent, and they also express the necessity of the connection between them, thus pointing to a hypothetical judgment.

2

The

principle that denial of the consequence involves denial of the ground

applied in two ways

may be

:

I.

If

A

is

true,

B

is

true.

C is true, B is not true. If A is true, C is not true. If C is true, A is not true.

If

therefore

/.
if

and two premises have contradictory consequences, each involves the denial of the

other.

A A

is

true,

If

is

not true,

C

therefore If

C

is

B

B

is

not true, not true,

II.

and

If

If

B

is

true. is true. is

true.

C is

true.

the consequence of an affirmation and the consequence of its denial are mutually ex Both these formulae, however, may be reduced to the two given above. Instead of the minor premise in I. we may substitute

i.e.

clusive.

:

If

B

is

true,

C

is

not true

;

LOGIC

330 This

is

the so-called pure hypothetical syllogism

members holds good of an unlimited number: the involves that of every consequence of

its

here again

;

may be arranged I.

In the

two ways

affirmation of the

A

is

true,

B

If

B

is

true,

C is true.

If

C is

true,

If

A

is

is

D true, D

ground

the hypothetical sorites,

and

first

its

ground

premises

:

If

first

further

still

in

is

see the

consequence, and thus we are en

abled to obtain a complete series of inferences connecting the with the last consequence. This

we

But what we have said of two

necessity of having at least two premises.

true.

is

II.

A If A

is true.

D

true,

C is

true.

is

true,

B

true.

is

true, D

Cis

B

If

true.

true,

is

If

If

is

is

true.

is true.

case the premises proceed from one consequence to another

removed from the

original

ground

(epi-syllogistically)

;

in the

second case they proceed backwards to anterior grounds (prosyllogistically).

5In the mixed hypothetical syllogism the hypothetical rule only enables us to derive

one given judgment from one other given judgment.

But

if

the consequence follows merely from the attribution of a given predicate to

any subject, then the hypothetical rule may be applied to an indefinite number of judgments. In this case the minor premise serves for the intro duction (Trpoo-A^i/as) of a definite subject, and so leads to the conclusion.

The

logical theory of inference would be now complete if our only were to express in a general formula the essential conditions to be object i.

fulfilled

all

by

inference in deriving the validity of one judgment from the

validity of another.

But

this

formula of the hypothetical syllogism

is

deficient in a

way

which seriously impairs its value. If we could make no inferences except in accordance with it, we should need a special rule every time we deand then we

get, If

A

is

true,

If

B

is

true,

A

that

may

B

is

C is C is

true.

not true.

If is true, not true. a simple progress from consequence to consequence. substitute for our major premise is

:

If

B is not true, A

is

not true.

A is not true, C is true. If B is not true, C is true. If

In the same way in

II.

we

THE RULES OF INFERENCE. rived one simple rules as

we had

judgment from another

;

so that

331

we should have

as

many

instances of their application, while for the derivation of

a

hypothetical .judgment two others would be necessary. Moreover, before any inference could be made, everything which enables us to pro ceed from one judgment to another must have been already fully thought out ; so that any real progress, any truly synthetical would be

thought

of any value

is

judgment, which alone in the process of

new judgments

Progress to

impossible.

always presupposed as having already taken

is

place by the hypothetical syllogism in

For the knowledge we seek

is

just

simplest form as given above.

its

this

necessary dependence of one

judgment upon another. 2. Any further development of the theory of inference must then start from the question upon what is this necessity of connexion between A and based ? and from the further question as to whether there is no "

X

"

other means of attaining to a hypothetical judgment than by way of the

pure hypothetical syllogism, which always presupposes other hypothetical whether, that is, we may regard all particular connexions of

judgments

;

and unanalysable, or whether

this sort as ultimate

the necessity from a smaller

In

many

number

no doubt, a connexion of

cases,

it

is

possible to derive

of laws. this kind,

which obtains be

tween a definite antecedent and a definite consequent, and a hypothetical

judgment Whenever

immediately.

is

ultimate resolve

I

some

owes

its

or contract depends

ought to be,

A

is,

will

;

and the

upon the

therefore

expressed by given

a promise under certain conditions,

judgment which

fulfilment of the intention, promise, "

if

simple, hypothetical syllogism

B ought

is

definite course of action in the

contract, I give rise to a hypothetical

my

validity to

is

and the necessary sequence

upon a

make

event of certain circumstances, or or enter into

;

A

is,

B

The connexion is established my actual volition. The necessity

to be.

by my will, and owes its validity to grounded thereon admits of no further analysis the dependence of the one judgment upon the other is determined directly (cf. Appendix B,p. 383). But the law according to which follows from A is not necessarily 3. ;

X

the

"

judgment

ference (Eth., lutely infinite

Being

C is

i.e.

if i,

A

is true,

n):

Being

God

exists.

that

is

true."

anything

now

;

D (God exists),

when we know

if

X

exists,

I certainly exist,

Expressed

follows from the

if

A

is

Spinoza makes the following in then there also exists an abso

B,

C is

Z>,

in

a

therefore an absolutely infinite

general form

judgment but also

A

is

B

:

the

(I exist)

when we know

judgment not only

that

if

any-

LOGIC

33 2 B,

is

thing

judgment

when

ject;

C is

D.

That

the inference holds good if the inferred whenever the predicate belongs to any sub

is,

necessarily follows

the consequence not merely of predication concerning a

it is

but of predication concerning any subject whatever with

given subject, this predicate.

Such a law by virtue of its generality covers an unlimited number and it owes its generality to the fact that the conse

4.

of particular cases,

quence depends only upon the predicate, not upon the particular subject to which this predicate may be ascribed.

Thus besides the inference expressed by the hypothetical syllogism we introduced in place of the indefinite substra

find here a definite subject

tum

of the predicate, the process called by the Aristotelians TrpoVA^t/as. 1

Because the same predicate particular subjects, the

ment seen

in

necessity 5.

which

this

31, 8, p. 187,

(

is

The

may be

33,

197), this

2, p.

is

of

for every particular

And

assignment actually takes place.

and

number

assigned to an indefinite

consequence holds good

judg as we have

the only form in which the

recognisable as such.

may be one which makes one

hypothetical judgment

predicate

depend upon another predicate of the same subject if anything is A, the same thing is also B. Then it would not only be applicable to a plurality :

of data having the same consequence, but would also include a

number of

consequences the introduction of the definite subject would take place both in the antecedent and in the consequent. ;

If anything

is

A,

it is

B

CisA C

Therefore

Here we have no longer a

is

B

simple, hypothetical syllogism.

ated by the fact that in the minor premise a definite subject

It is

is

medi

named

to

which the predication applies, while at first only the general possibility of a subject was assumed. The hypothetical judgment includes in its for

mula the several judgments B) 1

etc.,

C is

if

:

A, then

thus necessitating an indefinite

In the inference

is

;

if

D

is

A, then

D

the

ov rb

Trp6
B

/card TOIJTOV rb

B

Kara TOV

A

Kara TOV

A

F F

Cf. Prantl,

I,

376

is

of particular consequences.

:

/co,0

the minor premise

C is B

number

sq.,

and

my Programm,

p. 8.

THE RULES OF INFERENCE There

is

added

to the necessity expressed

property of being universally applicable

The same

6.

is

by the major proposition the

become

the rule has

:

333

true of hypothetical judgments

a law.

which attach conse

quences not to simple predications, but to connections between relations, and thus become more complicated in their expression. The proposition

two magnitudes are equal to a third they are equal to one another, connexion between relations which holds good for any objects When I infer therefrom that whatever which come under these relations.

that

if

states a

because

A=B

and

CB^

therefore

A = C,

have again introduced into

I

the general formula the definite magnitudes A, B, C, to which the rela

The minor premise does

tional-predicate of equality applies.

not say that

any two magnitudes are equal to a third, but that these definite magni In this case the introduction tudes A and C are equal to the third B.

must take place by means of a number of particular judgments, which must be taken together to allow of the application of the antecedent. The proposition that one of the premises must state a necessary 7. connexion seems to be contradicted by many instances from ordinary, and even from scientific, practice. 1 I infer, A is the father of B, B the father of C, therefore

A

C

B to

;

A

is

the grandfather of

therefore Breslau

in Prussia,

that

A>B,

B>C,

in

is

therefore

the right of C, therefore

A

C

;

that Breslau

Prussia; that

is

A

>

C

;

that

is

in Silesia, Silesia

A = B, B=C, therefore A is to the right of B,

to the right of C,

and so on.

But

a sufficient ground for though these premises seem by themselves to be the conclusion, and there appears to be no universal major premise, it is

not really

No

so.

doubt we make our inferences

in

such cases with the

conscious of a universal major premise, greatest confidence, without being or without expressly formulating it; in the last example it would be the "

proposition,

A

when A

is

to the right of Jj,

and

B to

the right of C, then

But would the syllogism be valid unless either this proposition were true, or the still more general one that whatever lies to the right of a second thing which is to the right of a is

necessarily to the right of

C"

third, lies also to the right of this third?

It

is

true that because the rela

tions of space or of magnitudes are so immediately intuitable, and because we are saved the necessity of they are so incessantly present to thought, Never which in words the laws by they are governed.

always formulating

theless nothing but the validity of the necessary connexion between the a work which 1 Cf. F. H. Bradley, in his Principles of Logic, London, 1883, p. 227 in its frequently excellent criticisms. eminently original and very instructive ;

is

LOGIC

334

various relations can support the conclusion ; in mathematics, indeed, the fundamental principle that two magnitudes which are equal to a third are Logical in equal to each other, is expressly put before everything else.

not concerned with that which

is

vestigation

in the actual process

consciously emphasized that

which must be true

if

a syllogism

is

to

is

be

valid,

be a necessary consequence of the premises.

to

do not

B=C,

expressly thought

of inference

The

really constitute the only premises

if

and

but only with the conclusion is ;

propositions

A = B,

of the syllogism; they

merely contain the assumtio, which here consists of two propositions. We cannot pass from them to the conclusion A = C unless we can see that if

A = B,

and

B = C,

it is

necessary also that

A = C.

But these examples show the importance of that class of connexions which we have just noticed (6), and the frequency of inferences from major premises which state that the two relations in which one object stands to two others necessitate a third between these two others.

Many

of the propositions upon which all inference is ultimately based will for this reason take the form of hypothetical judgments with antecedents

which have two members because they contain a twofold

Identity itself

infer identity.

The premises

of thought.

A

yield the conclusion

follows from the two therefore,

relation.

is

first

A

is

is

To

which we

belongs also the principle according to

this class of inference

nothing but a relation between objects is identical with C, identical with B,

B

identical with

C

only because the third identity

by virtue of the concept of identity because, that two objects of thought which are ;

the law holds good

identical with a third are identical with

each other.

In the same way when we substitute an equivalent expression for the whether it be a different manner subject or predicate in any judgment of denoting one and the same individual, or a different expression for a

we are only justified in so doing by our knowledge same predicate must be affirmed or denied of the same subjects. 1 concept

8.

The

that the

psychical operation actually taking place in such a process of

inference presents different aspects, which have led to different views of

the syllogism.

On

the one hand,

it

is

pointed out that what really takes

place in inference is a synthesis of different elements, 1

In such examples as

we have

directly

some

indirect

is

level of

and

that the con-

was the philosopher of Stagira. Aristotle was the tutor of Alexander, therefore, etc., but the substitution of one expression for another only when there implication can such inferences as this be significant and rise above the

mere verbal

:

Aristotle

;

trivialities.

THE RULES OF INFERENCE. elusion

an immediate judgment,

is

When

synthesis. left

I infer that

A

of C, therefore

is

premises suffices to give position,

Thus

and from

this

to

me

inasmuch

because

A

the

of

left

is

as

it

this

only analyses

to the left of

B, and

B to the

the combination of the two

C,

the three points A, B,

immediately evident that

it is

335

the essential part of the syllogistic process

is

(7,

A

is

in this particular

to the left of C.

the combination of

one whole, a construction which yields complete all In the same way suppose we have an of tangible and visible attributes, individual S, possessing a complex and in this complex a perceptible attribute S and and form, as it different elements in

that

is

1 expressed in the conclusion.

M

P

to it

M

;

P

Our knowledge that P appertains and on the same ground, as that belongs to

the image of a single thing.

were,

S is

certain, as evidently,

P belongs

or that

to

M.

The

M

premises effect a combination, and the

intuition of this gives us

an immediate knowledge of the

elements connected

conclusion belong together. 2

opposite view,

in the

inference

consists

in

fact that the

According to the comparing the two premises and

recognising the necessity of attributing a predicate

P

to the subject

S

;

only a discernment of this necessity can be the ground for actually think ing the unity SP.

According to

this view, the

person making the inference

stands in the same position as some one hearing the judgment SP spoken he first receives the ideas apart from one another in the two premises, and

;

is

In other words, according to the

then called upon to unify them.

view, the real inference takes place

first

before the formulation of the conclu

an analytical expression of knowledge already acquired while, according to the second view, the inference first creates must be attributed to the subject S, the conviction that the predicate sion,

this

being

only

;

P

This latter thus giving rise synthetically to the thought of the unity SP. view is more emphasized in ordinary accounts of the syllogism, in propor tion as they

aim

at

making inference mechanical by the

of the syllogism, and at turning

it

rules

and

into a species of calculation.

figures

In an

work only with symbols; not until I have finished do I interpret the equation I have obtained, and then I realize again what I get my result not before the conclusion, but I have denoted by symbols algebraical calculation I

;

But even when the process of inference is by means of the conclusion. not one which is at first carried on merely in words or symbols, the result afterwards realized, it still depends upon the nature of premises and being

1

Cf.

2

Schuppe, Erk. Logik,

Bradley, Principles of Logic, p. 235. p. 260.

LOGIC

33 6

conclusion whether or not the former will at once blend into one whole,

which can then only be expressed analytically. When we have to do with a negative premise, such a synthesis is prohibited by the nature of the

But even with positive premises Bradley s theory breaks down to deal with relations which are less immediately and

negation. as soon as

we come

obviously intuitable than the simple spatial relations from which he

starts,

do not belong to those contents of the concept denoted by the middle term which are invariably present to thought. But in any case this distinction in the syllogistic operation applies or with predicates which

the question as to whether or not the

only to the psychological process

conclusion follows necessarily from the premises

For when the synthesis actually takes place only analytical expression in the conclusion,

ambiguous unless there any

prohibits

the

of B,

left

the

left

The

spatial relations.

the premises,

The

other.

B to

is

and

it

some law which synthesis

A-B-C,

it

not affected

by

prescribes this synthesis results

of C, only because

it is

truth of the conclusion

makes no

is

it.

such a way that it finds is not necessary and un

in

from the premises

and

A

to

prescribed by the law of

depends upon the truth of dependence whether in

difference to this

any particular instance there is unconscious obedience to the law in the synthesis, or whether it forms a conscious ground by which the synthesis is guided. 51-

The is

general hypothetical rule according to

of a synthetical nature

which

is

when

it

taken as a ground, or in

Such

sources.

rules

is

made

not already included in the judgment

its

elements, but

may be either axioms,

relations, or general propositions,

laws which state

which an inference

is

is

added

to

it

from other

which serve to connect

gained by induction from experience, or

some connection

established by the will. Other hypothetical rules are given with the judgment itself from which the inference is made, and may be analytically developed from it. They

may be

derived from the form of the judgment, in so far as the act of

judgment

is

governed by universal logical laws, or from the contents of

the concepts of which

it is

composed

in so far as these

concepts contain

universal judgments. i.

Hypothetical propositions which

explained in sources.

the preceding paragraph

state

a universal connection as

may be derived from very

different

THE RULES OF INFERENCE In the

337

place, there are the universal propositions which are the expression of an immediately obvious necessity to be found in the relations of certain objects of thought (synthetical judgments a priori in Kant s The most important of these are the mathematical axioms which sense). first

<

how the relations of number, space and time are connected. constant experience without any exception may be the ground of our belief in other universal connections. We shall have to enquire in Part III.

state

A

how it is possible to pass from particular perceptions to judgments having a universal and unconditional validity ; here we may be content with the universal conviction that many necessary connections be inferred from

may

That a body expands when

experience.

it

is

heated, that white light

is

broken up when passed through a refracting medium, are instances of such laws.

If the condition

that the result

mentioned

ultimately based

at

is

law

in the

upon simple

any time present, we confidently infer will also appear, and our confidence is of perception which have

facts

shown us

the one event connected with the other.

We

wide

find a

field,

our inferences in the application of

for

again,

general laws which have their origin in our

In laying

that will.

down

will

and are meant

to regulate

a general rule of conduct, our will determines

that there shall be a universally valid connection between certain conditions

and

certain

modes

necessary that if

our will

is

of

action.

we should

to

will

If

we

will

the general law,

it

is

logically

the particular actions prescribed by the law,

be constant and consistent, and valid

agrees in willing the general law.

for every

one who

All penal codes in imposing a penalty

of imprisonment for theft, of capital punishment for murder, lay down a series of hypothetical judgments which establish a universal connection

between committing the crime and incurring the penalty. These judg may also be regarded as theoretical propositions in so far

ments, moreover,

as they express the general obligation

of the judge to give sentence in

accordance with the law. In analytical geometry an equation such as^ a px determines the con struction of a curve by means of it to every value of the abscissa is ;

assigned the appropriate value of the ordinate.

x andjv has will

to

This relation between

and may be selected at any spatial image, and to this

the force of a hypothetical judgment,

enable us

to

extent such a formula

construct is

freely

comparable with the positive establishment of a

law.

In cases like these s. L.

we add

to the

judgment A, which

is

the ground of z

J

LOGIC

33 8

our inference, a general law which analytically contained in

The

2.

not thought with the judgment, nor

is

it.

case would be different with connections involved in the fact

judgment was uttered or thought rules, that is, which could itself, and which would tell us upon the ground of universally valid laws, that if this judgment be true, some other must also be true rules which could be adduced without applying to any that a certain

;

be derived from the judgment

;

external source.

B

is true yield any further How can the fact that the judgment A is knowledge ? It may do so in two ways. It may be that the particular form of synthesis between the two elements in the judgment A is B,

renders it possible and necessary to apply other forms of connection (in that is, there are ; judgments) quite apart from the meaning of A and laws by which all judgment is governed, and according to which any judg

B

ment whatever But

it

will

may also be

yield other

judgments containing the same elements.

B of the

that the predication of

subject

A

involves other

B in

judgments by reason of the particular meaning attaching to A and In the former case the rules will be formal, in the judgment.

this

latter,

material.

52-

The of the

so-called

IMMEDIATE INFERENCES, which

same judgment, are based upon is the same, however the matter

ment, which

generally find enumerated

the inferences of OPPOSITION, of

CONVERSION, and of CONTRAPOSITION. 1. The most obvious inferences of entirely

all,

from the meaning of judgment

The judgment "

it is

"

A

is

B"

Amongst these we CHANGE OF RELA

varies.

TION, Of .EQUIPOLLENCE, of SUBALTERNATION, of

and

are only formal variations

the universal nature of the judg

A

is

B

of

and those which can be derived

itself,

are generally quite omitted.

involves the judgments

necessary to state that

MODAL CONSEQUENCE,

"

;

"

is

it

also that

"

true that

A

and

A

is

B are

B"

com

patible."

2.

This leads to the INFERENCE OF OPPOSITION,

inference, that

is,

from

one judgment to the falsity of its contradictory opposite, and, from the falsity of one judgment to the truth of its contradictory

the truth of vice versd,

This kind of inference is based upon the principle of contradic and of twofold negation, which simply tells us that the two judgments is not and is false that A is B? and the two judgments "A is

opposite. tion "

A

"

"it

THE RULES OF INFERENCE and

"

"it

is

false that

A

is

not

have just the same meaning.

B,"

the same with respect to hypothetical judgments.

ment

"

if it is

true,

is

B

true,

is

is

"

should be true

"

;

A

is

judgment

is

"even

the latter

if

It is

denial of the judg if

true.

When we change

3.

the unconditionally universal

into the hypothetical

s

B

The

equivalent to the judgment

is

true,"

not necessary that

the former

false,

j?

A

339

"

judgment

if

anything

is

all A s are B? we take for

judgment

A,

it is

"

our predicate that necessity which, in the unconditionally universal judg ment formed the ground of its universality and the unconditionally uni versal judgment, when substituted for the hypothetical, expresses univers ;

ality as the

consequence of necessity. In the same way, when a disjunctive broken up into hypothetical judgments, or when several hypo-

is

judgment

theticals (if

A

disjunctive

(A

is

C

not B,

it is

either

B or

is

if

;

A

not C,

is

C), the

it is

B)

are

combined

meaning of the verbal forms

in

one

finds a

different expression.

Other forms generally given are

4.

:

INFERENCES OF ^EQUIPOLLENCE.

(a)

A

infer that

makes

is

From

the judgment

A

is

B

we may

not non-2?, an inference which the indefiniteness of non-2?

(The inference that snow

worthless.

is

white and therefore not red

cannot be regarded as purely formal it presupposes a judgment concerning the matter of the predicate, the judgment that anything white is not red.) ;

INFERENCE BY SUBALTERNATION.

(b)

ment

all

As

falsity of the all

As

"

all,"

are

are

B

judgment some

B (not

and hence

2?).

A

s

are

this inference

number

contained in the greater.

here

is

(not

B)

;

in the universal

judgment

judgment

is

the contents of the

The same

rule enables us to conclude etc

;

so that the inference

merely a conclusion drawn from the meaning of the pre should have as much justification for saying that the inference

it is

We

that the part

must be where the whole

In inference by what

(c)

and from the

not a formal transposition authorised by the nature of the act of

judgment dicate.

(or not 2?),

the falsity of the

only a particular instance of the rule that the smaller

where there are three there must be two, is

inferred from the judg

it is

dependent upon

is

and

that

B

But the true predicate

predicate,

is

Here

A s are B

(or not B} that some

is

called

is, is

immediate.

MODAL CONSEQUENCE we

are said to

derive actuality and possibility from necessity, and possibility from actu ality

;

further the negation of actuality

and necessity follows from the nega So far

tion of possibility, the negation of necessity from that of actuality.

as concerns the act of

judgment

itself,

there

is

no distinction between

LOGIC

340 necessity, possibility,

and

actuality

on the other hand, these terms are

if,

;

reality, then the inference depends here. has no and place upon the time of Aristotle the CONVERSION of judgments has played 5. Since the most important part in the doctrine of immediate inferences. By

used as predicates, having reference to their contents,

means of

this

process

obtain another having

it is

B

taught that by conversion

The are

A

B

from the judgment A is we may A for and its We are predicate. subject

that

said

for its :

universal affirmative judgment,

all

A

are B, will give us

s

some

j5 s

(conversio per accident, the quantity being changed).

The

universal negative,

no

A

B, gives us no

is

B A is

(conversio simplex

the quantity being unchanged).

The

particular affirmative

some

A

s

B

are

gives us

some

.Z?

s

are

A

(conv. simplex).

While the particular negative some

As

are not

B

we may

point out that,

admits of no conver

sion.

predicate

the affirmative judgments,

first

Taking conversion

is

if

their

have any meaning, they must be judgments in which the the generic idea to the subject, both belonging to the same

is

to

category, so that the predicate

may become

subject in the

same sense

as

They must be, moreover, judgments concerning in so that it is no strain to their meaning to interpret them

the original subject. dividual subjects,

by saying that the subjects named may be included amongst the objects denoted by the predicate-term. They must, that is, be such judgments as etc. ; where the correctness of no larches are all firs are trees," "

"

firs,"

the conversion

Where

may be proved by enumeration.

these conditions are not complied with, the conversion has a

forced sound, and the "

all

planets

change

it

into

move

meaning of the judgment

in ellipses

"some

things

"

is

moving

taking the predicate for subject

is

altered.

The judgment

based upon the category of action in ellipses are

planets,"

we have introduced

a

;

and instead of

new

subject;

we

have connected the concept of thing with the predicate, and, since it is absurd to determine a concept of substance by a temporal process our Instead of a judgment of action we concept is an unnatural creation. In passing, therefore, from have obtained a judgment of subsumption. one judgment to another, we are not really independent of the meaning of the terms employed.

The

true significance of such conversion

is first

to tell us that the predi-

THE RULES OF INFERENCE cate

341

compatible with the subject, and next to supplement the universal that though it may be necessary to think of A as

is

B

judgment by showing

B

does not follow that

It is this warning belongs exclusively to A. which is the most important part of the meaning of the conversion, and it coincides with the rule that we may not infer the ground from the con

it

Applied to the hypothetical judgment, it prohibits us from is true, and inferring simply transposing the judgment if A is true, then that if is true, then A is true. All that we can infer is that if is true,

sequence.

B

B

A may

B

be

which corresponds to the

true,

converted

particularity of the

categorical judgment.

The

case

different with the conversion of the universal negative

is

This expresses the

ment.

always mutual; that

if

that exclusion

fact

a subject

A

judg between two concepts is

excludes a predicate B,

B

cannot be true that anything possessing

can be A.

it

certainly

Or we may avoid

the awkwardness of changing adjectival and verbal predicates into sub

by making use of the hypothetical formula, and then, from the

stantives

judgment If

anything

is

If anything

is

A

it is it is

B,

not B,

it

follows that

not A.

Where the consequence, the negation of B, is denied of any object, there we can no longer use the subject-concept as a name for it. 6. Besides conversion we have also CONTRAPOSITION. Here a new judg ment

is

formed from

A

is

B by taking the so-called contradictory

of the predicate as subject, altering the quality of the

negation and vice versa.

from

all

from no

from some from some

We may

is

A A

opposite

original subject as predicate,

and

changing affirmation into

that is, judgment this means we may obtain ;

By

As are

A

and the

no non-Z?

B,

is

some non-^

B, is

B,

nothing,

is

not B,

some non-^

A, is

A,

is

A.

leave the reader either to prove these inferences himself or to

We

find the proofs elsewhere.

need not point out

that this

form

is

nothing

sense really contained perversion, which conceals the good in these propositions by introducing the unmanageable non-Z?, and by the predicate-concepts to take the form of substan

but an

artificial

arbitrarily constraining tives.

The

results

of this process are propositions such as

having equal diagonals

is

a

rectangle."

"

nothing not

LOGIC

342

The whole meaning

of contraposition

is

clear at

once when we use the Instead of

as predicate. hypothetical form and retain the predicate

A s are B

all

we then have

If anything

is

A,

If anything

is

not

B, and from not A.

it is

B

this

it

follows that

it is

Contraposition in this form is parallel with the conversion of negative judgments, which from the judgment If anything If anything

is is

A,

it is

not B, infers that

B,

it is

not A.

Both these instances of what

called simple conversion

is

and contraposition

have a meaning and are useful they express the complete meaning of the statement that a predicate must either belong, or not belong, to a subject. ;

The remaining obtain any

cases yield only particular judgments; that

we cannot

is,

definite conclusion, but only the denial that certain

concepts

are incompatible or necessarily connected.

No A If

is

B,

anything

i.e.,

is

A

it is

not B,

but this does not necessitate the inference that because something

A, although

it is

The

7.

it

doctrine of immediate inferences

to apply to the disjunctive judgment.

If

may be

A

is

it is

not

B

further extended

still

either

B

or

C,

both

it is

is

clusion follows entirely from the

meaning of

is

false

it is

false

it

If B and C, and false that neither B nor C. that A either B or C, then A may be both B and C, or A neither B nor C, or A may be either B or C or D. Here again

that

is

may be A.

may be the con

and quite inde

disjunction,

pendently of the particular elements of the judgment. Finally, by extending the concept of immediate inference beyond customary sphere, we may also include all those operations by means of which we combine a plurality of particular judgments, and thus form and A is C it follows From A is conjunctive or copulative judgments. 8.

its

B

that

A

A

neither

is

is

both

B and

B nor

C.

C

;

The

pression of the fact which

of both judgments; serves to

make

it

from

is

tells

A

is

not

B and A

is

conjunctive judgment

not

is

C

it

follows

that

only the verbal ex

involved in our consciousness of the validity us nothing

new

as to the matter,

and merely

us expressly aware of a connection which was already there.

These operations are of great importance

to thought, in

its

arrangement

THE RULES OF INFERENCE and combination of

and

particular items of knowledge,

343

for this

reason they

are worthy of being mentioned here.

The

9.

value of this doctrine of the so-called immediate inferences

consists, as Mill rightly said, in enabling us to recognise

ment

in different

the

The judgments

forms and expressions.

same judg

thus inferred

from each other may be simple transpositions of a given statement, which enable it to be reduced to a form more convenient for the context to which

refers

it

;

or they

make prominent

serve to

may

special aspects

the statement which are not emphasized by the verbal expression finally,

may

they

;

of or,

serve as precautionary rules, teaching us not to confuse

one judgment with another

like

or to find

it,

more

in

it

than

it

really

contains.

53-

Given a simple judgment, we may derive from

ground

by rules which may

it

others having their

In so doing we must be guided be obtained either from an analysis of the predicate-

contents of

in the

its

elements.

concept, or by reference to the extension of the subject-concept. is B, then it is evident that in affirming If it is true that i.

A

B

of

A

A

B. In the everything which we think of as connoted by same way by affirming B of A we exclude from A everything excluded by the connotation of B.

we

affirm of

Suppose

that

B contains

the conceptual characteristics c, d, e, or the that it excludes the characteristics /i, and

derivative determinations f, g, i,

n, o }

we must

and the concepts P, Q, also affirm

c,

These conceptual

In this

d,

e,

,

f, g, h,

A

nota

est

and deny m,

n, o,

affirm

If

anything

is

B,

it is c, d, e,

If

anything

is

B,

it is

not

B of A,

P, Q, R.

relations find their simple expression in the

judgments

:

etc.

;//,

not

,

not

P

t

etc.

and by enumerating the way, by analysing the concept B,

characteristics incompatible with

from

Then, because we

etc.

we obtain

it,

the rule by which to pass

Nota another judgment in accordance with the principle the we Thus following rei. get nota rei, repugnant nota repugnat

is

B to

forms of inference

:

i.

If

anything

is

B, then

A\s Therefore

A

it is c,

B is c, d, e

d, e

LOGIC

344 If anything

2.

B, then

is

A Therefore It is clear

not P, Q,

it is

A

not P, Q, J?

is

that these inferences are valid, whatever

and whatever the sense

ticular thing or a

R

is

in

A

which

may be

B

is

a par

attributed

concept is predi Everything contained in the thought of the concept cated by it ; everything excluded by it is denied when it is predicated

B

to A.

new judgments

the

are necessary consequences of predicating

A

It is clear also that if

way

is

B

a definite particular subject, there

of passing beyond the judgment

A

is

B

;

of A.

no other

is

without having recourse to

other propositions.

one, that

name the

in

is,

judgment

is

B may

is

be explicative or unconditionally univer is not used as the

which the denotation of the subject

of a certain particular thing, but as the symbol of a concept, so that

A

is

In this case there

A

A

The judgment

2.

sal

B to a

B has is

itself

the significance

another way in which we

one

different

predicated, or which

we may

;

attribute

"if

anything

is

A,

it is

J3"

may pass from the judgment to everything of which A

B

contained in the sphere of A. Our judgment then reverts to the particular kinds of A, or to the individuals compre is

hended

in

A, and

A

is

is

B

serves as major premise. is A K Z are

If anything

_

X,

it is

B

A__

Therefore X, Y, Zare

B

In the former kind of inference the content of the original predicate was unfolded, and we proceeded from it to particular determinations or deriva In the latter kind the extension of the original subject

tive predicates.

is

specified, and the predicate is attributed to the subjects comprehended by the and in so doing we are guided by the rule known as the original concept ;

Dictum de omni, Quidquid

valet de

omnibus valet etiam de ,

rule has reference to the fact that the formula

"

singulis.

If anything

generally appears as the so-called universal proposition,

"

All

is

A,

As

This

it is

are

B

"

1 ."

1

In his essay, von der falschen Spitefindigkeit der vier syllog. Figuren, Kant has shown briefly and clearly that what is called the Dictum de omni follows from the prin That is, the particular thing falls under a concept only ciple "nota notes est nota ret." because this concept is to be found in it as its characteristic. This does not make the

two formulae equivalent,

as

B.

Erdmann maintains

(Philos. Aufsatze zu

Jubildum, p. 202) ; the first as being original and primary second, which is derivative and secondary.

is

E. Zeller s

distinguished from the

THE RULES OF INFERENCE Here again the treatment

A

of the negation runs parallel with that of the

If in place of the affirmative

affirmation.

N

meaning anything which is negation applies to everything which is A. is

not

345

That which

N

N

A is not Z are A

is

X, Y, X, Y,

judgment we have the negation A is not then the same

Z are

N

not

(Dictum de nul/o.)

A

3.

and the

comparison between these two cases, the analysis of the predicate shows that notwithstanding the differ

specialization of the subject,

ence between them, they both lead to the same formula. If anything

is

A,

Sis

The

difference

especially of the

under

its

(S

B

(it is

not

W)

not

W}

only in the significance of the predication, and more

is

When

minor premise.

this serves

to

genus, the predicate being thus fitted to take

concept without changing is

is

it is

A

Sis

to specialise the

In the

place as subject-

meaning, then the function of the inference

its

extension,

unfold the contents.

subsume a subject its

other case the inference serves to

in the

first

case

is

it

natural to express the major

premise (the rule) as a general proposition, but not in the second while latter

it

the major premise which stands

is

it is

I

mortal,

:

All

pass from

subject-concept.

men

are mortal

;

Caius

In the inference

the

pass from

my "

"

ill

"

it.

particular individuals.

But

"having

We may

ordinary form for our major premise

is

"

fever"

:

ill,

a person having fever,

Therefore he

to the further determi is

not a generic idea

take a universal proposition of the

All people having fever are

Caius

a man, therefore Caius

is ill,

having fever

original predicate

connoted by

is

;

having fever Therefore Caius is ill,

to

and

:

Any one

nation

;

in

original proposition to the extension of the

my

Caius has fever

I

former,

the minor premise.

In the inference is

in the

first

is ill,

LOGIC

346

and

this inference

seems

have the same contents as the one preceding.

to

But the way in which the major premise is expressed is forced, and the minor premise seems to be intended to state a subsumption under a generic concept, while 4.

It is

it

really

denotes a temporal condition.

evident that the more complicated relational-judgments

treated in just the

same way by

this explication

may be

of intension and specializa

when they contain analogous predicates or subjects, and even though the respective terms may not appear verbally as

tion of extension, this is true

the grammatical subject or predicate.

The

inference

"

and a feather

may be

(in a

On

resolved into two inferences.

ment of the predicate of the term

"

into

its

same

the

Gravitation imparts

therefore a piece of lead

bodies, rate,"

consequences; on the other, a specialization

denotes that concerning which the statement

by making

a forced transposition.

all

which, though not the grammatical subject, really

all bodies,"

fluous to begin

velocity to

vacuum) fall at the same the one hand, it is a develop

this

We

made.

is

It

would be super

term the grammatical subject by means of

much

are as

justified in substituting species

and there is there genus as if the major premise were All A s are fore no need for a special principle of substitution in addition to the "

for

J3"

dictum de omni by which to justify such inferences.

They

differ

from

others only in the grammatical form of their propositions. 5.

When we

predicate

is

from a negative judgment it does not hold good that necessarily contained in the thought of the negated

start

everything which

is

When

also negated.

not deny that

it is

attributes are present.

Hence no

ing the negated predicate. If

We

inference

cannot say

anything

A

may be is

black.

it

is

is

Therefore

Nor does

this figure is a square, I

deny that

I

rectangular or quadrangular

B

I

only deny that

all

do the

possible by merely analys

:

d

it is
B

not

it is

is

;

not

c,

d

hold good that anything excluded from the negated predicate it does not follow that because ; something is not red it

affirmed

Hence

it is

no valid inference If anything

A

is

is

B,

not

Therefore

to say

it is

B

it is

C

not

:

C

THE RULES OF INFERENCE

347

The

invalidity of this inference follows obviously from the rule that the negation of the ground does not necessitate the negation of the conse

quence. It is

the

same when we turn

A

follow that because

Here again

to the extension.

not B, therefore that which

is

is

not

it

does not

AisB;

we

are

unable for the same reason to infer If

anything

C is

is

A,

not

Therefore

it is

not

B

A

B

it is

But when the judgments are such as express conditions having the negated predicate for consequence, or judgments which specialise the ex

we

tension of the predicate, then

A

B

not

is

If anything

is

C,

Therefore

A

is

These may be shown

get the following inferences

to

A it is

not

B

C,

C

A

B B

is

not C, D,

is

E

be applications of the rule that the denial of the

That which

A

is

C is

not

B

C is

not

A

is

:

B

is

C in

is

N N

not

C is

These are the only ways possible

judgment

E

D,

Therefore

consequence involves that of the ground

6.

not

is

:

not

A

which we can pass from a simple

"\

judgment by means of the conceptual rela The one is of them we are led by two principles.

to another definite

tions present.

In

all

contained in the connotation of a concept must be affirmed of everything of which the concept is affirmed, hence of all the

that all which

is

species of the concept other, that whatever

is

and of

all

the individuals which

excluded from a concept

thing in the thought of which this concept

whole extension.

modus

We

is

is

fall

under

it.

The

excluded from every

contained; hence from

its

have moreover shown how the modus ponens and reappears in these forms. start differently from the other point

tollens of the hypothetical inference

7.

We

49,

2),

obtain the same result if we and ask whether or not there are any grounds for some synthesis A is B. This question may be solved at once if we can recognise B as But if not, contained in A, the judgment thus proving to be analytical. we are to unless and A is us that B, some mediation is needed to assure (

/

LOGIC

34 8

adduce propositions from elsewhere, this mediation can consist only in A a predicate from which If the necessarily follows.

X

discovering in

two propositions, valid, then we can

infer that

X

A

X,

is

anything

"If

process whether

B

B,

is

it is

and

B"

makes no

It

"A

is

X"

are both

essential difference to

B

the generic idea to A, and

belongs to it, or another predicative determination of which forms part of the connotation ; all that is affected is the meaning of the minor premise is X.

this

whether

is

B

it is

A

In the same way, is

true that

if

if

we can is

anything

The

the negative.

discover in

a determination F, of which

not B, the question can be decided

it is

F,

A

inference then

is

:

If anything

is

F,

A

is

Y

Therefore

it

in

A

is

it is

not

not

B

B

These two forms represent the shortest and simplest way of arriving at as to a suggested synthesis, and they represent the only way

some decision if

we assume beforehand

must be derived

that all necessary connections

from the relations which already exist between concepts, hence that they must be ultimately reduced to analytical judgments. It is this which

makes the middle concept important in inference as being both predi A and subject of a universal affirmative or negative judgment having

cate of

the predicate to the subject

The

B

it

;

mediates the attribution or negation of the predicate

negation of the hypothesis

less direct

mented by a second, anything which

is

B

Then

"that

is

Z,

That which

is

A

is

Therefore first

formula;

A

is

manner when the judgment,

immediately obtainable.

The

A

is

B is Y

B may also if

anything

the judgment

which

and

A

not

is

is

B

"

A

Y

is

Y

Therefore

not

2?, is

is

B Z

A

is

is

Z

not

B

Cf. Kant,

not

really reducible to the preceding negative

from the major premise

it

follows that that which

is

not B. 1

in a

may be supple we may know that

not

That which is

it is

Y"

F; or else Then we get

A

is

be brought about is

not

is

not Z.

not B.

of these formulae

for

B

A. 1

von der falschen Spitzfindigke.it der vier

syllogist.

Figuren,

I.

Fis

THE RULES OF INFERENCE This kind of mediation cate

is

subjects

cannot be compatible.

when

A

is

tion arises

It is

naturally substituted for the preceding

a substantival concept,

such as are

Fand Z being

ill adapted to become subjects. whether this stone is a diamond,

possess double refraction, and I argue

That which

is

a

This

is

more

method

predicate determinations

Suppose,

know

I

e.g.,

that

that the ques

diamonds do not

:

diamond does not possess double

This stone possesses double refraction Therefore it is not a diamond.

ns

349

based upon the principle that when a predi affirmed of one subject and denied of another, these two is

refraction.

;

natural than to say, Everything possessing double refraction

not a diamond.

Thus our investigation of the different kinds of mediation by means of which any given question may be decided leads to exactly the same result in all cases. If our inference is to be based upon simple analytical rela tions and opposition of concepts, then the modus pomns and modus tollens in their different

applications, prove to be the only forms of inference

which we can make

The

of

use.

ordinary doctrine of the CATEGORICAL SYLLOGISM, which has grown

out of the Aristotelian theory,

is

based upon the presupposition of the pre

that our inferences are

grounded upon established rela between concepts. The distinction of figures and moods was justified from the point of view of the Aristotelian doctrine but, from the point of ceding section

;

i.e.,

tions

;

view of the traditional doctrine, they are superfluous specializations, which may be resolved into the more general formulae of the preceding paragraph.

Both the Aristotelian doctrine of the syllogism and the ordinary teaching which has grown out of it presuppose established relations i.

Aristotle himself assumes an objective system of amongst concepts. which realizes itself in the material world in such a way that the concepts

concept manifests itself everywhere as constituting the essence of things and as the cause of their particular determination. Thus all judgments containing true knowledge are for him the expression of necessary relations, and the function of the syllogism is to reveal the whole force and bearing of each particular concept in our

knowledge

by combining particular

^

LOGIC

35 o

judgments and making them mutually dependent through their concep The verbal expression of these conceptual relations is due tual unity. the fact that they always appear as the essence of particular things,

to

which

are, therefore,

judgment

when conceptually determined,

way the

in this

;

relations

the real subject of

between concepts manifest themselves

or negative, judgments. Ordinary based upon a subjective system of concepts, the process of knowledge, but is assumed as a

universal or particular, affirmative

in

logic,

on the contrary,

which

is

is

not sought for in

preliminary datum. 2.

Now

it

;

the fundamental relation

The

cepts.

thus

if

A, B,

F

other,

their relation

B

Kara

A

Kara

is

Trai/ros

that the terminology

F

F

;

rov T.

A

A

;

Kara Travrbs

and from these we obtain, by means of the from

It is

this

relation of subordination

derived, according to which

is

opos (terminus medius),

(terminus major),

expressed in the two propositions

ros rov

Trai

is the concept next above which are subordinated to each

three concepts,

are

rov B,

syllogism,

that of the subordination of con

is

natural predicate lo every concept

and

aKpaA

two

F, the

B

is

called the

being the

the eA-arrov aKpov (terminus minor).

For

//,etoi/

this

reason

which predicates the highest concept (the predi cate of the conclusion) of the middle concept, has been called the major proposition ; the second, which predicates the middle concept of the lowest also the first proposition,

(the subject of the conclusion), the

syllogism

is

minor proposition

;

the result of the

the conclusion.

M

P

for the highest concept, for the middle Taking the usual symbols, and 6* for the lowest, then the form in which the nature of the syllogism is most directly and immediately obvious is the familiar

concept,

M

Omne Omne 5

Ergo omne 3.

est

est

6"

P

M

est P.

Aristotle next proceeds to introduce the distinction

and affirmative judgments, and he shows that negative,

it is still

if

between negative

the major proposition

is

possible to have an inference with a negative conclusion.

No Mis All

Sis

P

M

Therefore no 6

1

is

P.

THE RULES OF INFERENCE

351

If, on the other hand, the major proposition were affirmative, and the minor negative, no inference could be drawn, for nothing would follow as When P is true of all M, necessary from the validity of the premises." "

while

M

(living

is

not true of any S, then

being

man

thing be inferred

When

living

P may

be true of

being

man

when both premises

all S,

stone).

or it may not Nor can any

are negative.

the distinction between universal and particular judgments

introduced,

be

horse-;

it

particular,

is

follows for similar reasons that the major premise cannot though the minor premise may be a particular affirmative

judgment.

We may

then infer

Some 5

is

M

Therefore some

These are the four

6"

rpoiroi or

is

modi

M

Some S is Some S is

P

not

P

of the syllogism, which result from

two premises, in the first of which the middle concept is subject, while in the second it is predicate. They are the four perfect syllogisms and in them the four kinds of judgment are deduced (cruAAoyi(rju.ot rcA.ei.ot), from premises which contain the middle concept in the way we have stated. 4.

But

it

may

premises, or subject in both premises.

second

concept is predicate in both In the former case we have the

that the middle

also be

figure, in the latter the third (Sev repov

and

rptVov o-x^/xa).

figures the syllogisms possible are

In the second figure

:

Mood

Mood

i.

No P is All 5 is

M M

No S

No 5

is

P

No S

Mood

3.

No

P

is

Some 6

Some S

is

All

2.

M

P^

M

is

P

is

Mood

M M

Some 5

is

P

Some S

not

is

not

All

P is

4.

M

not is

M

P

In these

LOGIC

352 In the third figure

Mood

M

All

M

All

:

Mood

i.

P

No

M

is

P

Some Mis

is

5

All ^/

is

5

All J/is

P

Some

All^ is P

Some

is

Mood Some J/ 6"

3.

is

Some S

Some

Mood

2.

Mood

4.

is

is

M

Some 5

/*

Some S

No

6"

P

not

is

M Some M

P

not

is

P

is

Mood

5.

is

M

All

6"

P

not

is

.S"

Some

-S is

P

5

6. is

P

is

not

S

P

syllogisms of these two figures are not recognised by Aristotle as

The perfect,

and he reduces them

to the

figure either

first

by conversion of the

He

then proceeds to investigate in a various inferences from similar manner the premises which are judgments

judgments or by indirect proof.

and

of necessity 5.

possibility.

attacks, this Aristotelian doctrine has always

many

Notwithstanding

reasserted itself as the essential part of

all

scholastic logic, although

its

original meaning and the significance which Aristotle attached to it has in most cases been lost sight of. This misunderstanding is obvious from

the introduction of the so-called fourth figure

1 i

and more

particularly from

the fact that instead of recognising the necessity of conceptual relations to

be

at

the root of

premises as 1

It

all

was discovered, that

is,

middle concept, that in which minor.

By

it

inference,

mere statements

introducing this

it

as to

is

:

2.

P s are M All Ms are S are

All

P

M

No S 4-

No P is

M

not

is is

Some

Af

S

All

P

.

P

M

Some S

is

is is

M S

P

5

No

P is M

Some Mis S

AllJlfisS is

3

P s are

No

Some S

upon the

predicate of the major premise and subject of the was found that five additional moods were possible it

All

s

to look

are related in their exten-

had overlooked one way of arranging the

that Aristotle

I.

Some 5

became customary

how concepts

P

Some S

is

not

P

evident that any one forcing the concepts into this unnatural position must have for gotten all the fundamental presuppositions of the Aristotelian theory ; the need of sup plementing the Aristotelian doctrine could only have been felt in a treatment which It is

dealt with the external form alone.

THE RULES OF INFERENCE was

sions.

It

was

the

in

353

reason that the cogency of the premises as proof instance based upon the relations between numerical

for this

first

expressions, as

the object of inference were to find one or

if

more par

number, and its problem to think of the objects a under all at once, and then to find out what is included falling concept and them what is not. The same misunderstanding has led to amongst ticular things in a given

method

the favourite

means of a purely concepts

as

;

of proving the particular figures of the syllogism by comparison of the spheres of the particular

intuitive

the function of

if

all

judgments were to place the subject and to exhibit it as a part of a

within the sphere of the predicate concept, greater

what

number of

it

is

objects bearing the

and what

the irrational

manner

same name, and not rather

This mistake

does.

it

in a large

is

which the particular judgment

in

to state

measure due

to

usually treated.

is

Thus

the doctrine of the syllogism degenerated into a sort of calculating machine, by means of which any one who would take the trouble to re

member the 19 moods by aid of the versus memoriales, and to practise them upon meaningless examples, could learn everything from the external forms of judgment, from the position of subject and predicate, without

need of further

reflection.

Leaving the presuppositions of the doctrine for the present untouched, what strikes us first is that in the fig. i the distinction between 6.

the third and

important.

first,

No

and between the fourth and second, moods,

change whatever

the minor proposition the

"some

mean

is

in the course of

quite un

is

thought because

and fourth moods.

particular in the third

Since

and of the conclusion must always predicate is attributed to them because of

5,

and since the

a conceptual determination which inference

made

of the minor proposition

S"

same

the

is

is

exactly the

same

as

is

common

when

to both, the

the subject

is

meaning of the

universal.

It

is

the

value of the result with respect to the determination of the concept

which

differs,

this difference

not the operation of inference of value that Aristotle,

view as the principal object, the

form of deduction we have,

inference

L.

and

it

was

who always kept

his

distinction.

strictly

speaking,

J/ sare

P

(All,

some, one)

,5

are

M

(All,

some, one)

S

are

P

(All, (All,

S

in reference to

the conclusion in

So

far

as concerns

only two

kinds

:

All

s.

made

;

No Mis

P

some, one)

S

some, one)

are

S are

Af

not A A

P

of

J

LOGIC

354 In the

first

case the middle concept adds a predicate to

the second case [n the

it

its

subject

;

in

excludes one.

same way the moods of the fig. 2 may be reduced to two kinds when a predicate M, which is excluded from another concept

of inference

;

P

is itself excluded from the contained in any subject S, then subject and when a concept M, which comprehends another concept P, is

P,

;

is

Thus we have

(All,

Now, its

S

P

is

M

some, one)

6"

All

S are

some, one)

M P

are not

(All,

some, one)

the indispensable rule according to which

most appropriate expression, runs If anything

is JB, it is

A

is

not

it is

C are

Certain subjects it

follows

;

it

we

M

is

S are 6"

not

makes

are not

infer,

M P

when reduced

for the first figure as follows

If anything

B,

P

some, one)

(All,

(moods

i

and

X (moods

In both cases the assumption takes the form

and

the subject

expressed as universal or as particular.

is

:

No (All,

to

Pis excluded from

excluded from a subject, then

no difference whether the

2

:

3).

and

4).

:

B,

:

Therefore they are A, therefore they are not X.

But the second

figure must also be based upon these same rules, for no other method of inference from simple conceptual relations. In the second figure, however, we infer from the fact that the consequence

there

is

is

wanting

;

that

is,

we

infer

from the invalidity of the consequence to the

invalidity of the ground. If anything

Now C

is

C,

(all

Therefore If

anything

Therefore

C,

it is

A

some C)

it is

is

Now C (all

B B

not it is

not

is

not A,

B (moods not

some C}

it is

;

2

and

4).

X;

is

X,

C (moods

i

and

3).

Thus both the connexion between the first and second figures, and their difference become evident when we see that in the first figure we from the validity of the ground to the validity of an affirmative or negative consequence, while in the second we infer from the invalidity of

infer

THE RULES OF INFERENCE

355

1 the affirmative or negative consequence to the invalidity of the ground. first two of the Aristotelian coincide with the figures, therefore, exactly results of 53.

The

All the

moods of

the

first

single formula in such a

and how they

as to

can thus be exhibited

figures

in

a

show both the grounds of inference

differ.

Major premise If

and second

way

:

anything

is

B,

A

it is

not X.

it is

Minor premise and conclusion of fig. i C (all, some, one C) is B, Therefore C (all, some, one C) Minor premise and conclusion of fig. 2. :

C

(all,

some, one C)

C

Therefore

The

7.

(all,

is

A

not

is

some, one C)

particular judgments of

fig.

is

A

is

not X.

X, is

not B.

differ essentially in

3.

meaning

from the particular judgments of figs. i. and 2. In the latter the term which is particular stands from the first as subject, and the fact that

is

it

particular

verbal expression are the same.

unimportant,

may indeed be due merely

But in the third

figure the particular

conclusion, and possesses therefore

in the

It is

particular.

third figure there

is

that

is

term

is

subject only

the indefiniteness of the

all

equivalent to a mere judgment of possibility, and in the

can be no such thing as a necessary consequence in the first, third and fourth moods alike, the essential

two predicates belong

identical

with

some M.

the two predicates are compatible,

same

to the

and fourth the burden of inference which

the

to

In the

ordinary sense. point

;

is

the subjects of the minor premise and of the conclusion

But i.e.,

subject, for in the

third

only upon that part of

rests all

that follows from this

do not exclude each

all is

M

that

In

other.

same way the common characteristic of the second, fifth and sixth moods is, that one predicate P is absent from a subject to which the the

other

predicate

belongs,

and from

this

it

that

follows

they are

This gives us also a solution for such difficulties as that two negative premises not that which is not yield a conclusion notwithstanding Aristotle s rule ; is not M, whence it follows that S is not P. 1

Mis

e.g.>

The

conclusion

is

doubtless true, but

premises in the Aristotelian sense.

The

it

is

false that

proposition

it

"that

P

not

may /-",

S

follows from two negative is not P," is is not

which

M;

M

and the connexion s are negative merely in form ; really it is equivalent to all between the negatives is based upon the positive relation between the predicates. Ob jections such as these arise only where the method of treatment is quite superficial.

LOGIC

356

to Strictly speaking, then, the rule according necessarily connected. which the inference takes place, and upon which the deduction of the conclusion from the premises is based, finds no expression in the premises.

The major premise suppressed predicates belong to the

same

minor

this

for

moods

the affirmative

"

is

:

two

If

do not

subject, they are compatible, they

necessarily exclude each other

the

in

the two premises taken together form

"

;

In

suppressed major premise.

negative conclusions, again, the major premise

"

is

the

moods

with

one of two predi

If

:

cates belongs to a subject, but not the other, then they are not necessarily

connected

here again the two premises together represent the minor

"

;

to the above-stated rule.

That which

is

then, in this figure

inferred,

the definite denial of a

is

necessity, either of a necessary

exclusion or of a necessary connexion.

The weakness

of the third figure

is

only deny

and

conclusion

From may not

is

P

expression in the fact that the

its

Lotze shows

this point of view, as

(p.

113),

two negative premises If J/is

is

not S,

it

that

which

denied

is

is

is

P

not

is

does not neces

S

"

judgment

M

negation of the disjunction of these inferences

may be

be expressed by any

ot the

not

P."

S

But

and

this

P

t

That

either

is

"

:

"M is

M

P or

S."

neither

is

either

P or

would be expressed by The two premises may

P

nor

S,"

which

Aristotle

S."

is

the

exclusion

s

explained by the fact that their results cannot kinds of judgment which he had in view

follow the ordinary formula, the conclusion

concepts

the affirmation

not necessarily S, and vice versa.

therefore the connexion which

be combined in the judgment

we

P

follows that the negation of

involve the affirmation of S, nor the negation of

the disjunctive

S is

cannot prove necessity, but can

it

particular.

P and M

which

if

that

weakness finds

this

yield a similar conclusion as to the negation of a necessity.

sarily

of

it,

tells

us nothing

must run

"

;

for

some not

about the relation between the

neither whether they exclude each other wholly or

partially, nor whether they wholly or partially coincide. ex mere negativis nihil sequitur in its original signification

although the proposition that everything must be either refuted by an instance in which

Z is

neither

X nor K

1 On Schuppe s attempt further to extend the number of drawn from the combinations of premises rejected by Aristotle,

Thus is

X or

the rule

not affected,

Y may

be

1

inferences which can be see

Appendix C.

THE RULES OF INFERENCE

357

55-

Where

the categorical

concerning concepts as

an analytical judgment

syllogism presupposes its

major premise,

it

>/

cannot serve as a basis for

thought in

its perpetual Its sole function is progress to fresh knowledge. before us the established relations between our keep concepts in every The categorical syllogisms gain a higher application of them. significance n vhen we make them subservient to the formation of our concepts, as_was done by Aristotle ; or when their major premises are not merely

to

^J

judgments concerning concepts, but synthetical propositions

Kan

in the

tian sense.

The whole

i.

of regarding

it

becomes of doubtful value

syllogistic process

means

as a

to the construction of

instead

if,

\

J

concepts by a Socratic

eVaywyy, we look upon it in the light of the scholastic logic. If, that is, we accept it as based upon a finished system of concepts incapable of further growth, and upon the analytical judgments yielded by such a

ftj

system,

That S,

M,

is to say, if the normal syllogism consist of three concepts, P, in simple subordination to each other, then the presupposed

P

of these concepts involve the conclusion 5 is as directly as they involve the minor premise 5 is M, or the major premise Mis ; forms a part of the intension of the concept S other just as much as relations

P P

any

of

its

characteristics or combinations of characteristics.

a particular thing,

we cannot be

have enumerated

all

can say that figure," "the

it

is

P

M.

the predicate

square

is

a

characteristics

its

those which constitute

certain of

indeed,

its

is

certainly not

parallelogram,"

"

i,

to

infer

that

parallelogram and therefore a quadrangular figure

The

"

this figure

5

that

the square

more remote than

and

a parallelogram

S

represent

M

until

we

p. 306), thus including

we must know

In the proposition

if

subordination to

47,

(

But

is

is

P before

we

a quadrangular

in the proposition "the

is

square

a

"

is

quite superfluous.

"

"

this presupposes that a particular figure cannot be recognised as a figure is quadrangular it is a parallelogram until it is known to be quadrangular hence to infer

proposition

is

"

;

"

;

parallelogram and therefore quadrangular

"

is not merely superfluous but Again, what do we gain by this process of continuous ascent to higher concepts ? If our object is to extend our knowledge by means

perverse.

of judgments,

we

are

become poorer and

moving

in

the

less significant,

we

wrong direction

;

our

predicates

learn less about our subjects,

and

>/

LOGIC

358 lose instead of gaining

parallelogram, I

inferences which is

it

a being of attain

finally

by our

If I know that a square is a can learn by erecting a ladder of

progress.

know much more than

I

end by teaching me that it is spatial or divisible, or that some kind. To this last predicate all inferences must

which mount the conceptual pyramid by successive steps

(from species to genus).

The

2.

logic,

nature of the syllogistic process, as represented in the scholastic

appears most clearly from the success achieved by the theory that

syllogistic inference

is

really only

Beneke

term for another.

*

tells

concerned with the substitution of one us that in syllogistic inference

we

replace

one of the elements of a given judgment by another, being led to do so by a second judgment, which tells us of a relation between the first term

The

and the new one.

substitution

take place whenever the

may

new

no way surpasses the old (keeps within the limits of the old). Either the substituted element may be the same expressed differently,

element

or

it

in

may be

ference

"

a

part of that

some quadrangular

are parallelograms, therefore

for

which

figures

it

is

some quadrangular

;

all

figures are not

have substituted rhombs for parallelograms, the part

I

In the in

substituted.

are not parallelograms

for

rhombs

rhombs,"

the

whole.

some parallelograms are oblique-angled all parallelo grams are quadrangles, therefore some quadrangles are oblique-angled," I have substituted another expression (some quadrangles), for the same In the inference

"

;

(some parallelograms). In the first instance the new element in the (rhombs) is a part of the extension of the old (parallelogram) second instance the substituted element (quadrangle) is a part of the

subject

;

intension of the old (parallelogram),

and enables us

to think of the

same

thing under another expression.

From

this

theory Beneke derived

all

possible kinds of inference, and the

conclusion he then came to was that such inferences in no way extend or enrich our thought. The part must always be contained in the whole,

and

in substituting the

former for the

latter I lose rather

than gain in the

ideas which form the material for thought. It is only in inferences with

made 1

;

for

when we

System der Logik, from that which

differs

a negative conclusion that any progress

think of a concept,

i,

p.

217.

Cf.

we do not

Ueberweg, Logik,

we have mentioned above

is

think of evejything 120.

This substitution

50) as Introduction of the Minor There the process is one which supplies a definite subject where one was (7rp<So-\77^is). wanting, here we substitute one definite concept for another in which it is contained. (

THE RULES OF INFERENCE which

it is

not,

and the syllogism thus serves

359

new

to introduce

differentia

But every concept as such belongs to us only in so far as it is member of a system and disjunct from its co-ordinate members. Hence

tions.

and most important negations are certainly included in the of the thought concept itself, and nothing is to be gained by adducing others which are remoter and less relevant. If I know that man is an the proximate

animal, that

is

sufficient to distinguish

are most nearly allied

metal nor a geometrical

him from other

need no syllogism

I

;

existing things

to assure

me

that he

is

which not a

figure.

From this point of view, then, the syllogism can at most serve to warn us, when we connect no definite concepts with our words, of all that is involved in a statement by reminding us of what

By

predicate.

recalling all that

lead us to analyse failed to

understand

stand.

It

is

really said

involved in our statements,

is

it

by our would

them

it would thus ; interpret a proposition when we but would not help us forward when we did under

it,

would be an aid

in teaching, or a

To demand,

organon of knowledge.

polemical weapon, but not an

therefore, that the syllogism should

proceed entirely according to the so-called principle of identity, as, for instance, Leibnitz emphatically did, is to render the syllogism worthless.

The importance of the syllogism, or more exactly of the form in 3. which the syllogism is ordinarily presented, was attacked from another 1 In the inferencepoint of view by J. S. Mill.

men

All

Socrates

are mortal is

Therefore Socrates the conclusion seems to be

;

a man, is

mortal,

drawn from the major premise.

the major premise presupposes the conclusion, for before all

men

are mortal I must

as there

men

is

are mortal

"

is

Logic,

already that Socrates

book

ii.,

ch. 3,

it

this

is

But

in reality

can know that

mortal

;

as

proposition, the proposition

long "

all

Every such inference, therefore, con It is no presupposes what it is meant to prove.

not yet certain.

tains a petitio principii, 1

know

any uncertainty about

I

8

2.

2

In the same way the minor premise also presupposes the conclusion, as Lotze (Logik, 2. ed., p. 122) has shown most completely with reference to conceptual judgments of Where would be the truth of the minor premise, Socrates is a man," if subsumption. "

were doubtful whether or not the attribute mortality belonged to him as well as the other attributes of men, for the major premise adduces mortality as a general characteristic common to all men. it

LOGIC

360

solution of the difficulty to say that the conclusion

and ever to

directly in the

we

We

premises.

not stated explicitly

is

are not, of course, called upon,

when

state a universal proposition, to think of all the particular instances

which

it

applies for all

proposition

;

nevertheless our statement involves the validity of the

and

particular instances,

we

it is

are already certain of

a statement for which

we

particular instances.

have no ground unless Must we then say that the syllogism is absolutely useless and without Mill endeavours to avoid this conclusion by means of a significance ? all

The real ground for my statement that any man now living men are mortal"; this be the general proposition cannot is mortal if valid, that I have some means of knowing that those who presupposes, But we may find the ground in our previous are now living are mortal. distinction.

"all

experience of a

number

really infer

who

now

are

living will also

from particular cases to other particular

that the general proposition

is

quite superfluous,

our way in passing through it. Nevertheless it has a meaning. instances

Because a number of men

of particular cases.

have died we infer that those

known

to us

It

It

would seem

(

and

that

evident that

is

Thus we

die.

cases.

we go out the

of

particular

cannot enable us to infer a new instance with confi

dence, unless they provided a sufficient

This general proposition

tion also.

is

ground for the general proposi an abbreviated formula for all that

we hold

ourselves justified in inferring upon the testimony of experience contained the only real inference, and what follows is merely a deciphering our notes which we have made to remind us that experience We may have forgotten these justifies us in passing to further instances. in

it

;

is

"

"

particular instances,

and remember only

grounded upon them. interpret

it

;

we do not

We infer

experience, but according to

it.

or of a general rule accepted on interpret that

which the

this

from

was

that the general proposition

then turn to

the

and

general proposition

abbreviation of the results of our

In the same way the application of a law some authority is an interpretation we ;

legislator or authority

meant

to say.

Thus, though we do not naturally pass through the general proposition we add greatly to the security of our process by so doing.

in inference,

For the experience which such as

is

sufficient

justifies

ness of the general proposition

is

hasty and ill-grounded inference. fully the

the inference to

to support the general

proposition

most valuable It

adequacy of our experience

obliges ;

and

if

one case must be ;

and a conscious

in enabling us

us to consider there

happen

to

to

avoid

more care have been

THE RULES OF INFERENCE

361

any contradictory experiences, our attempt to frame a universal judgment recalls them to mind.

These

criticisms of Mill s are

weak point tion of in

lies "

true

its

is

while disclosing a

(

an involuntary confirma-

\

instructive, for

and fundamental importance.

the meaning ordinarily

which

most

in the syllogism, they, nevertheless, are

The weak

point disclosed

attached to the proposition

"

All

A

s

are

taken to be a mere summation of particular judgments in an

abbreviated expression, an enumeration of particular instances. If this were so, then, of course, the certainty -of the judgment with regard to the sum-total would depend upon its certainty in regard to the particular items.

\

But the universal major premise should not be understood as the statement of this numerical generality ; it is the statement of the necessity of connect This necessity cannot be attained,

ing the predicate with the subject.

even by a complete enumeration ; indeed it can never be known at all in a directly empirical manner. To investigate the conditions under which

we may they

infer

that such

from particular experiences to a necessary law upon which

and we hope to show an inference can never be possible unless we assume that some the main object of a theory of induction

rest, is

unconditionally valid principles are to be found. to the extent

particular data,

Mill

which are the

real

proof for

s

position

is

justified

drawn ultimately from those judgments which have

the universal major premise

that

;

is

major premise might be Only by proving necessity can the particular His argument rests upon a confusion data be proof of any particular case. between the two processes of describing the psychological process of

reference to the empirical

but

;

jt is

false that the

dispensed with in inference.

inference

and laying down

logical laws for

it.

There

is

iS\ *\^

no doubt that we

from one particular case to another, but the question is whether we are justified in so doing. This question is decided by the

frequently infer

validity of the general proposition,

sents

which does not merely as Mill repre is the one thing which makes the

yield a collateral security, but

inference legitimate.

cases to a

new

be inferred

;

Mill himself allows that the inference from particular

instance

and

is

not justified unless the general proposition

in reality the truth of the universal

condition of the truth of the conclusion.

Thus

major premise

is

may the

the conclusion does, after

depend upon the major premise, and cannot be proved without it. But all that is maintained by the Aristotelian doctrine of the syllogism

all,

nothing more than is

this

:

that a satisfactory

possible only in the syllogistic forms,

and

is

scientifically valid inference

and on condition of a universal

(

LOGIC

362

major premise.

we

Aristotle himself teaches that

premises by means of induction.

But then

arrive at universal

his induction

is

major

certainly not

based upon the purely empirical ground of a collection of instances, which, it can yield no necessity, would make logic impossible ; but upon the

as

phenomena are governed by conceptual which must therefore be knovvable from particular instances.

presupposition that particular necessity,

Thus rales

the attack

fails

to

touch the absolute validity of the syllogistic is to be made from one judgment to

wherever a reliable inference

another.

It

is

only

upon the

entirely

when the attempt

so-called

is

of

principle

made

to base the syllogism

when

identity that

premises are purely analytical propositions

therefore

the

the syllogistic process

seems to be without value. 4.

So

from being Aristotle

far is this

view that he regards the syllo

s

gism as the preliminary means of attaining that which is presupposed in His premises are mainly empirical judg definition. the scholastic logic ments concerning that which is given in intuition, and the syllogism is the

means by which he arranges these items of knowledge exhibit their mutual dependence.

In

in such a way as to way the material dependence

this

of the conceptual determinations realized in being, the true causal relation is

exhibited

and thus an exhaustive definition

;

is

framed, which expresses

dependence of the special determinations upon the general correspond It is for this reason that the middle ing to these conceptual relations. a

concept selected

amongst

is

said

to

correspond to the cause, and that the premises are in such a way as to represent the real dependence

and arranged things.

Although the syllogism as thus applied

is

most closely connected with

the Aristotelian metaphysics, yet the logical laws are not limited to this special application in

;

the end in view merely determines the particular

which they are formulated.

The

but has retained the formulation to which

it

the exclusively categorical treatment, and

more

led,

and which

formulae

of logic

is

apparent in

especially in the coordina

tion of the particular with the universal judgment.

the

way

traditional logic has forgotten the end,

It is

no wonder

that

no longer correspond to the altered problems of

science. 5.

Mathematics, which throughout makes use of the syllogism and owes

its scientific

certainty to this form,

upon the theory of the ing that

all

syllogism.

is

often cited as an answer to

This

is

all

attacks

quite justifiable so far as

show

mathematical propositions, with the exception of axioms and

THE RULES OF INFERENCE

363

which the

proved by syllogisms, or at any rate on the principles by But to overlook the wide syllogistic forms are determined.

difference

between mathematical propositions and the examples of the

definitions, are

scholastic logic, with their analytical judgments, find such inferences as

the circle

"

quadrangular it is

a conic

trifling

figure,"

in

section,"

subsumptions

square

"the

?

is

Do we

a great mistake.

a parallelogram, therefore

is

it

is

a

a curve of the second degree, therefore

is

geometry ? does it ever concern itself with such This is all included in the definition of the par

ticular object,

and the syllogism

this definition

;

not there for the purpose of repeating

is

the real task of geometry

is

to

develop the laws of the

which certain conditions bring about between particular objects, such as lines and angles, the relations, that is, of equality, inequality, etc. relations

From are

the point of view of the concept these relations are predicates which

added

to

it

from without

cannot be learned from

;

they are not contained in the definition, and

indeed they do not exist until the particular In the concept of the triangle that objects enter into spatial relations. in

is,

its

definition,

we

it

;

find absolutely nothing about the fact that

are equal to two right angles, the idea of two right angles

its

angles

not contained

is

The judgment is based firstly upon the addi and secondly upon their comparison with two adjacent It is based upon relations which have to be created.

in the idea of the triangle.

tion of the angles, angles, that

is,

it

forms no part of the concept of the right-angled triangle that the square of the hypotenuse is equal to the sum of the squares of the two remaining sides ; for in the concept of the triangle I think of nothing more nor less than a plane surface, bounded by three intersecting straight this there is

nothing to oblige

then compare them. construction that

I

me

to construct squares

upon

lines,

and

the sides

in

and

have done so by means of inventive can investigate the relations in which these squares It is

not until

I

stand to each other.

Geometry, then, always goes beyond mere conceptual judgments in seeking its propositions, and by combining necessary relations taken from

some other source with

that

which

is

given in the definition,

dicates which are not contained in the definition.

But just

it

obtains pre

for this

reason

we cannot, as a rule, regard its major premises as judgments of subsumption, and though its syllogisms may appear to be framed in the scholastic form Barbara, they are not so 1

System der Logik, edn.

Logik,

I, p.

297.

Cf.

my

3, p.

304

in ;

reality.

edn.

5, p.

"

Logische

Fragen,"

360.

Ueberweg,

1

for

instance, gives

We find a similar example in

Vierttljahrschr, f. iviss. Pliil.,

Wundt,

iv. p.

478.

LOGIC

364 as an

example of

this figure

All triangles with proportional sides are

:

angles with respectively equal angles

therefore all triangles with proportional sides

angles are similar figures are similar figures All negroes are

;

and

men,

inference

this

all

tri

triangles with respectively equal

all

men

to

is

appearance the same as

all

are mortal, therefore

In reality, however, the difference

is

all

There

very wide.

:

negroes are mortal.

no

is

cept formed from the concept of triangle by means of the

specific

differentia

con

"

pro nor any general concept similar figure to which the specific concept might be subordinated by means of the middle concept triangle with respectively equal angles." The inference does not proceed "

"

portional

sides,"

"

by means of such subordination at all, but solely by means of relations which form no part of the concept triangle. Where two or more triangles are given having proportional sides,

equality of angles

will also

volves the similarity of the triangles is

a

follows that the other relation

it

be present; and because equality of angles it

in

follows that the relation of similarity

given together with the relation of proportionality of sides. It is only by crude inaccuracy of expression that these propositions can take the form

of a proposition concerning if

"

"

all

triangles

of a particular construction, as

the predicate might be true of each particular triangle in

inference, correctly expressed, If

would run

itself.

The

:

two or more triangles have proportional

sides, they

have equal angles.

two or more triangles have equal angles, they are similar. Therefore, two or more triangles have proportional sides, they are similar. If

if

It is

evident that from the nature of the case the propositions must be

expressed hypothetically,

if

what they mean

that one relation

is

between

different things necessitates another. It is significant that

the guiding principle of mathematical inferences

is

the proposition that two magnitudes which are equal to a third are equal to

each other

between

;

that

relations.

is,

it is

a proposition concerning necessary connection

Equally significant

is

it

that mathematical reasoning

frequently proceeds by substituting one magnitude for another to which it is equal. Processes such as these find no place in the ordinary forms of the syllogism, though by means of these general laws they can always be

exhibited as strictly syllogistic. 6.

What we have said of geometry applies also What we have to establish by inferences

science.

contained in the concept, not given analytically hand, relations,

;

to other branches of

are elements not yet

and these

are,

on the one

on the other everything which depends upon varying and

THE RULES OF INFERENCE

365

changeable events, more especially therefore all causal relations. The inference of the judge does not proceed by subordinating particular oftences.

When

once the case before him

murder he does not

an infringement of the

commanded by punished by

"

infer analytically law,"

is

subsumed and recognised as it is a crime, and therefore

therefore

but he proceeds at once to the conclusion therefore it is to be

the synthetical rule of the law

Capital punishment

death."

the concept of murder,

it is

is

"

not analytically contained in

synthetically connected by the

lator with that particular crime.

The

physician

ness as typhus does not go on to infer that

it

ill

therefore an infectious

is

he infers that therefore the treatment must be

disease, but

will of the legis

who has diagnosed an this or that

;

the

counteract typhus are not analytically contained in its When but are synthetically demanded by the rules of experience. concept,

remedies which

the physicist

knows

him nothing

to analyse the concept of the

that a

body has

particular value into the formula

the

fall is

fallen for four fall

S\gf

l

;

seconds

but

if

would

it

avail

he introduces the

he knows that the distance of

15 x 16 feet.

Here again Kant

s

His question unconditionally and universally

teaching becomes important.

are synthetical judgments a priori,

i.e.

"

How valid

also the vital question, synthetical judgments, possible ? is for the syllogism without which it is but a barren process. From what has been said we may understand how important for 7. all those general principles which have reference to necessary connections between relations, and by means of which we obtain relational Such are the principles that two concepts or objects which judgments. are identical with a third are identical with each other that two magni

inference are

;

tudes which are equal to a third are equal to one another are

added

to equals the results will

be equal

;

;

that

if

equals

as well as those principles

which govern spatial relations. It is, after all, a question of secondary im looked upon as analytical portance whether these principles are themselves or whether of because derived from the concepts identity, equality, etc. ;

The important point a they are accepted as synthetical judgments priori. to pass beyond the us enable relations to refer is that because they they which alone are treated of by the ordinary merely analytical judgments logic. 8.

For

this

narrow, and

reason the scholastic categorical syllogisms are much too to serve as general formulae of easy application.

ill-adapted

For judgments of subsumption, and judgments which state simple predi-

LOGIC

3 66

we have

cates of a subject, they are the natural expression; so soon as

do

to

with more complicated relations, such as the dependence of a predicate

upon

several conditions, they

form with

its

consequent

comprehending

all

become

inapplicable.

universal categorical judgments,

naturally presents itself for use,

Here the hypothetical

becomes the natural expression

Trpoo-A^i/rts

more

it is

especially because in

not generality appears as the true basis of inference.

We

as

;

the formula which it

necessity

and

need but glance

at

any mathematical or physical textbook to assure ourselves that by far the greater number of propositions which are used as major premises do not take the form of universal categorical judgments, but are hypothetical

Propositions such as

rate in nature.

expression or at any which intersect have no

common

upon which the predicate

in the

same way the

first

is

in

circles

are hypothetical in nature

centre,"

relative proposition states the condition

And

two

"

;

the

denied.

axioms are of the nature of hypothetical

The proposition two straight lines cannot enclose a space judgments. means no matter where or how I draw two straight lines, the two together "

"

"

not include a space

will

sense of stating an "

"

it

;

attribute

says nothing about two straight lines in the

which

is

common

everything which happens has a cause

the

to both.

The

proposition,

"

presupposes by the predicate of clause that something actually happens it does not develop the

first

;

concept of happening, but states the connection of every particular event It is the same with the formulae ot with something else which exists. analytical

mechanics

;

these and others of the

judgments, and inferences

thetical

are

made

same description

are

hypo

accordance with them by

in

1 substituting definite values for the general symbols. 1

Some

Wundt.

include amongst the forms of inference I, p. 291) and even of equation but I consider this superfluous. We might as well give a special place and name to the inference therefore a^c. The peculiarity of these forms does not lie in the manner of inference itself, but in the particular principle upon which they are based, though this, no doubt, is frequently not A the same as B, B the same as C, expressly formulated because it is taken for granted. therefore A the same as C, is nothing more than an application of a principle referring a special

writers

"

e.g inference of

(Logik,

"

"

identity,"

;

a)l>,

>r,

to the particular predicate of identity. The only possible reason for laying special em is phasis upon this inference is that in inaccurate language the judgment frequently

A

means

On

identity without expressly saying so. the whole it seems to me that there is

B

be gained by specializing the doctrine

little to

of inference any further. On the contrary, I prefer to emphasize the common element in all kinds of inference instead of multiplying distinctions of form which in fact consist merely in the different contents of the premises which determine the conclusion ; to ex

haust these would be impossible.

mula

for all inference.

which are

common

"

It is true that

Wundt

When different judgments

attempts to give a general for are related to each other by concepts

to both, then the other concepts in the

judgments which are not com-

THE RULES OF INFERENCE

367

56.

The

which has a CONJUNCTIVE

syllogism

JUDGMENT

for

its

major

premise serves to subsume the particular under established concepts by

means of

their definitions.

The

i.

syllogism finds a special function in subsuming the particular

under established concepts, and

in so doing

it

falls

B

concept

than by showing that

these are to be found in

B.

contains

it

all

Here, then, the middle concept

is

A

falls

under a

the characteristics of

without exception, then

it

certain forms

into

adapted to this purpose. There is no other way of finding out whether any thing

it falls

B

\

if

under the concept

not a single predicate, but a series

of predicates which are combined in a conjunctive judgment, but which

assume the function of a

One

under a concept tion

is

single concept just because they belong together.

characteristic alone

B

if it

is

show

sufficient to

belong to

A

and

that a thing

excluded from

is

A ;

does not

fall

the subsump-

then rejected by a syllogism of the second figure ; i.e., modo the forms having for major premise a definition

Thus we get ,

B

:

tollente.

P

is a, b,

or the reverse

That which

S is

a, b,

and

this

01 exclusion

is

P;

c,

Therefore

The form

is a, b, c is

6"

is

P.

:

P

is a, b, c

S

is

not a

S

is

not P.

;

coincides with the syllogisms of the second figure modo

tollente.

to both are also related, and this relation finds its expression in a new judgment. But even if we disregard the vagueness of this formula, the proposition is false, because and is P ? Lotze too wide how are the concepts S and P related when S is not as would not merely again, remarks that the most important inferences would be such but would show how the parpredicate a general P of S through the mediation of M, which belonged to the S necessitated a particular form of ticular modifications of the

mon

M

;

M

M

P.

no special mode of inference ; it quite true so far as it goes, but it involves involves principles different from those which are ordinarily noticed in the

This

merely

is

to which every modi principles which state the law according categorical syllogism from which our conclusions must fication of brings with it a modification of P, but Let S be a inference. always be drawn according to the simple rules of hypothetical Then V (P-P a states the law according and eccentric. an

M

figure,

M

ellipse,

P

E=

:

which every modification of the relation of the axes involves a modification of the from which we may eccentricity ; but the equation is by nature a hypothetical judgment, to

draw conclusions by

substituting definite values.

LOGIC

3 68

57-

Inference from a DIVISIVE JUDGMENT, which

some

logicians have called

inductive inference, cannot lead to an unconditionally universal judgment

when

the division

is

If it is logical, the inference is super introduced incidentally, say, as a link in a chain

only empirical.

fluous, unless, indeed,

it is

of inferences.

An

1.

attempt has been

made

to

add

to the syllogistic forms the so-

called inductive syllogism, which resembles the inference from definition, in that the

middle concept

is

not simple in form.

A

complete division of a concept

enumeration of the individuals which belonging to

A

is

partly

J/and But

in this

M,

partly IV,

N and O A

Therefore 2.

fall

under

the species or individuals, then

all

When,

that

is,

we have

a

M, N, O, or a complete and a common predicate

into the species

are

all

and

it,

we

partly

get the syllogism

O

:

\

P,

P.

is

formula there lurks an ambiguity, which

may be

cleared

between empirical and logical extension. Let us begin by considering an example, that, for instance, given by

away by our

Apelt

distinction

! :

Major premise

The

:

solar system consists of the sun,

Mercury, Venus, Earth, Mars,

and the planets

etc.

Minor premises Mercury moves round the sun from west moves round the sun from west to east, etc. :

Conclusion

All planets

:

move round

Here the major premise conclusion affirms of

is

Venus

the sun from west to east.

states the extension of the

concept planet

;

the

planets a predicate which, according to the minor

all

premises, belongs to each one by

But what

to east,

itself.

Not an unconditionally

this ?

gained by

universal judgment,

attributing to the concept planet the necessity of moving from west to east

;

but merely an empirically universal judgment which combines the particular subjects of the minor premises under one name, after lished by the

major premise that those mentioned are

course, only so far as as the definite

we know

at present.

symbol of a

definite concept,

number of

particular things.

iudgment

is

grounded upon 1

The word

has been estab the planets

of

planet does not serve

but only as the

Hence

it

all

common name

of a

the inference in which one

others, refers only to our right to substitute a

Theorie der Induction, p. 17.

THE RULES OF INFERENCE common sum of

369

denotation for the proper names, and the expression the particular planets. 1

everything which

"

for the

"

all

however, in no way proved that a planet must necessarily move from west to east. The

is

It

is,

judgment which merely contains an empirical enumeration of the planets cannot tell us whether they owe their proper movement to the attributes on account of which they

fall

under the concept of planet, or

cause, which, so far as concerns the concept in question, it

could, then

it

must also follow that because

all

been called Frederick and William, therefore necessity be so called.

older metals were known,

The

metals

"

is

because of their

common and

all

kings of Prussia must of

silver, iron, etc.,

heavier than water

metals are heavier than water.

all

meant those which were known and were so

common

But

properties.

it

such an inference inductive

is

a fundamental error, since the

essence of inductive inference consists in passing

from empirical data to

For such an inference

an unconditionally universal judgment.

show that those attributes upon which the

grounded necessitate also the new predicate. If again the judgment should rest upon a 4. 1

called

does not follow that these

properties necessitate a specific weight greater than that of water,

call

sary to

:

conclusion has been refuted by the discovery of kalium.

this

To

If

the kings of Prussia have

was a valid inference to say

silver, iron, etc., are

Therefore all

it

metals are gold,

Gold,

"

some other

known

the empirically

By

to

accidental.

same when, instead of naming the individuals, we name species of a genus. At one time, when none but the

It is just the

3.

is

common

it is

neces

denotation

is

such as

logical division

in full the premises would be sun from west to east. Mercury, Venus, Earth, etc., move round the Mercury, Venus, Earth, etc., are planets. Therefore so many planets move round the sun from west to east.

Given

:

of these planets is equal to the number of all the planets. the planets move from west to east round the sun. nature of the inference is just the same as when I infer from the premises

The number Therefore

The

all

MI Mi that therefore three

Afs have

M M have MM 2

2

3

3

attribute

are three

:

P

Ms,

attribute P.

Thus the inference by which we obtain a judgment of empirical universality is based a definite numerical concept ; upon counting, upon the expression of a given plurality by the identity of the num s for three 2 3 is based upon ray right to substitute "

ber.

Cf.

5. L.

above

52, 4.

M

"

MMM

LOGIC

370

would guarantee the absolute completeness of all members of the division, For if one predicate the inference would be a superfluous circumlocution. necessarily belongs to

all

from which

may be

it

the species of a genus, this predicate must have

common

a ground in something

inferred

to

them

all

;

i.e.,

in their generic concept,

:

Parallelograms are squares, oblongs, rhombs or rhomboids.

rhombs and rhomboids have diagonals which

Squares, oblongs,

bisect

each other. Therefore

all

parallelograms have diagonals which bisect each other.

is an instance of unnecessary circumlocution, have been derived directly from the determinations might

Such an inference for the predicate

as this

which constitute the concept of the parallelogram. There are cases, however, in which we naturally pass through a complete enumeration of particular cases on our way to the universal proposition.

The

proof that the angle at the centre of the circle

at the circumference

on the same

of the angle at the circumference the angle at the centre, or

double the angle

is

arc,

begins by showing that the apex

falls

either

upon one

side

produced of

upon a chord falling within or without the

In any one of these three cases it may be shown that is double the angle at the circumference ; therefore

angle at the centre.

the angle at the centre it

is

universally true that

when an angle

angle at the circumference stand

Here

the latter.

common to

upon

again the proof

each case

;

is

at the centre of

the

a circle and an

same arc the former

is

double

drawn from conditions which are

but in each case the conditions are subsumed under

major premises, and we arrive at the truth of the minor premises It is, however, clear that this can happen only when different ways.

different in

when they are immediately certain. such a division seems to give rise to an in In the second figure 5. If it is true a different that somewhat ference in way. the minor premises are inferred, never

A

is

S is then

it

follows that

C or

Z>,

B nor C nor

falls

itself.

that the generic attributes are not to species.

Z>,

not A.

under none of the species of a genus cannot fall under But here again we may say that if the division is em the inference is invalid, for the empirical extension is no guarantee

That which the genus pirical,

S is

B,

neither

If,

on the other hand, the

be found outside of the known

division

is

logical,

then the charac-

THE RULES OF INFERENCE which excludes

teristic

genus, and

it is

S

from

all

371

must be incompatible with the

species

unnecessary to go through the division.

58.

The so-called DISJUNCTIVE SYLLOGISM has no special principle of its own ; it ought not therefore to be given as a particular kind of syllogism. In addition to the hypothetical and categorical syllogisms ordinary These have a disjunctive judgment logic gives also disjunctive syllogisms. for their major premise, and it is upon the relation of terms expressed in i.

the disjunction that the inference depends. tion

of two terms, and

is

predicate

we exclude

A

either

is

B

for instance, the

If,

disjunc

or C, then by attributing one

the other, while the denial of one predicate necessi

tates the affirmation of the other. I.

Modus ponendo

tollens

A

is

:

B or C B (or C\

either

A

But

is

A

Therefore II.

Modus

tollendo ponens

A

is

is

when

B).

\

A

C

is

C\

(or B}.

more terms the

the disjunction contains

conjunctive

only

B or C B (not

not

Therefore

Where

C (not

:

either

A

But

not

is

;

first

the second gives a

negative judgment;

modus

leads to a

simple affirmative all

is a conjunctive judgment denying not the case the conclusion only limits the

the minor proposition

the terms but one

;

where

this is

disjunction to fewer terms. I.

A

is

either

A

is

B,

Therefore II.

(a)

A A

B

or

neither

it is

either

neither

Therefore A A is either B A is not By Therefore

The major premise

D

D.

;

D.

or

it is

;

C nor

B or C or D B nor C,

is

is

is

(b)

C or

C or

either

D

;

C or

D.

does not yield the as here formulated, however,

most

LOGIC

372

general formula of the disjunctive syllogism,

of the major premise

B

Either the judgment

B B There

2.

ciple of

its

place, that

is is

not true, therefore

no ground here

own. its

true, or the

is

C is

true, therefore

is

it is

only a special instance

:

judgment

C

;

not,

C

etc.

is,

for a special syllogistic form, with a prin

All that the disjunctive judgment

us

tells

is,

in the first

terms are mutually exclusive, hence that the affirmation of

one involves the exclusion of the other

;

that

modus ponendo

the

is,

an inference from the hypothetical judgment contained in the in the second if A is B, it is not C (neither C nor D] ; disjunction tollens

is

"

"

place, that the negation of all the terms but tion of this

one

;

that

A

is

neither

B

the hypothetical judgment

more terms

has

A

if

inference differs in no

modus

the

is,

is

"

if

way from

judgment owes

one necessitates the affirma

tollendo ponens

not

C

JB, it is

nor

D)"

an inference from

is

(when the disjunction

Thus

the principle of the

that of the hypothetical syllogism.

The

importance to the fact that it expresses this twofold necessity, but the distinction between the disjunctive and hypo thetical syllogisms is based upon the grammatical form alone. disjunctive

3.

In the actual use of disjunctive inference the major premises are

frequently

in

irpocrX. rjif/t.s

dis at least hypothetical judgments having a and from these the inference is drawn by means of

meaning,

junctive consequent

a

its

;

:

If anything

S is

is

A,

either

it is

B or C

;

A, and also B,

Therefore

it is

not C.

S is

A, but not JB, Therefore it is C.

Such inferences serve

more and more 4.

for the progressive

subsumption of an object under

definite concepts.

Further, the inference which, from the denial ot

all

the terms of

a disjunction, infers the denial of the antecedent presupposition to all

is

akin to the form of inference given in If

A

is

But neither Therefore

Or by making use

of a

A

B nor C is

is

57, 4.

B or C

true, then either

true,

not true.

is

true

;

common

THE RULES OF INFERENCE If

S

is

neither

A

is is

P,

it is

M nor

S is

Therefore In the categorical form

S

is

anything

either

M or

^

IV;

lV

t

not P.

:

either

neither

Therefore

B or C; B nor C,

S is

not A.

Here we have the inference

is

so-called dilemma, Here again the trilemma, etc. based upon the general principle that the denial of the con

sequence involves the denial of the ground; the only difference here the consequence exclusive possibilities.

is

is

that

not simple, but consists of a number of mutually

59-

The

rules of the syllogism apply in just

the same way even when the premises are not stated as valid judgments, but only as assumed hypo theses. They then give rise to a hypothetical judgment, which exhibits the conclusion as the necessary consequence of the premises. In this way the principles that the ground involves the consequence, and the denial of the consequence the denial of the ground, are applied to the relation between the truth of the conclusion and the truth of the

premises, as well as the propositions that the negation of the ground does not necessitate that of the consequence, nor the affirmation of the conse quence that of the ground.

There would be no object

i.

in a detailed investigation of the different

combinations which may be added

to the list of inferences by means of verbal abbreviations, or the introduction of copulative, conjunctive and The inference is always brought about by the disjunctive propositions.

same means ; its fundamental condition is a major premise which in some form or another includes a necessary consequence, and constrains us to affirm a proposition in case another proposition

is

true.

To

this is

added

the minor premise which indicates an instance to which the major premise is

applicable.

thetical in

it

This

may be done

either directly, as in

the

mixed hypo

syllogism, or by applying a general rule to a special case included

by means of a judgment which shows

major premise

is

that the general rule of the

applicable to a certain subject.

For

this

reason

we

shall

not here investigate the sorites, which are nothing more than repeated appli cations of the rules of the syllogism, expressed in an abbreviated form.

LOGIC

374 In every syllogism

2.

follows from the

of the premises

validity

syllogism are observed this

to

major premise.

its

form

if

A

is

and

true

rules of the

the premises are only hypo-

hypothetical syllogism then reduces

itself

Others, which contain more than the simple assump

tion of the hypothesis, "

and where the

;

when

true even

is

The simple

assumed.

thetically

asserted that the validity of the conclusion

it is

may be

B

is

exhibited in hypothetical judgments of the

true,

then

C is

true

"

(if

all

men

are mortal,

judgments which emphasize

and Caius

is a man, then Caius is mortal) ; only the relation of consequence, apart from the validity of the premises.

Most hypothetical judgments are such as these ; when one premise stated, they then

based upon syllogistic relations taken for granted and not expressly

really is

appear as hypothetical judgments with a simple ante

cedent. 1

From

3.

this

it

follows that

the

principles concerning the relation

between ground and consequence may be applied to the relation between conclusion and premises when these are regarded as nothing more than hypotheses.

Not is

only, then,

may we

say that

necessarily true, but also that

from which

it

if

necessarily follows

if

the premises are true the conclusion

the conclusion

must be

is

false.

false

then the ground

But since this ground

two premises, we can infer from the falsity of the conclusion either of major or minor only the falsity of one at least of the premises

consists of

premise.

But also

be

must

it

does not follow that

false

;

nor does

also be true.

it

if

the premises are

follow that

Indeed

it

if

false,

the conclusion

may happen

the conclusion must is

true the premises

that a true conclusion follows

with syllogistic necessity from false premises.

More

especially, therefore,

it

does not follow that

if

one premise and the

conclusion are true, the other premise must also be Hence, the fact that a proposition known to be true can be represented as the syllogistic consequence of two premises, one of which is also known to be true, does true.

not enable us to infer that the other premise

is

also true.

and the examples there given. The necessity expressed Caius is a man, he is mortal" is grounded upon the if the earth moves round suppressed proposition that all men are mortal. The judgment the sun, the fixed stars have an annual parallax presupposes a whole series of inferences in which the premises are geometrical propositions of absolute certainty, and in no way partaking of the hypothetical nature. But besides these hypothetical judgments there are others of which the necessity is immediately known. 1

Cf.

my Programm,

in the hypothetical

p. 40,

judgment

"if

"

"

APPENDICES

tx t/

r

APPENDIX THIS view of the negation, and of

P

a predicate

wayswith

mind

P of 5

between

is

with which

as invalid.

P

affirmation

at

is

variance

though

in different

the view of Lotze, Brentano, Bergmann, Windelband (in the

co-ordinating affirmation predicates

relation to the positive statement that

belongs to a subject S,

Strassburger Abhandlungen, 1884,

of

its

A.

p.

at first

These writers all agree in teach that the thought which they

167

and negation

;

sq.).

undecided, and that according to the attitude

we approach

this

thought we state

it

either as valid or

But Lotze (edn. 2, p. 61) regards the thought of the relation and as the essential part of the judgment, and represents the 6"

and negation of

which predicate

this

thought as two opposed minor judgments it ; while the other logicians take

validity or invalidity of

the opposite course, and consider the essence of the judgment to

lie in this

decision as to validity or invalidity; the subject of the decision, they say, is not a judgment, but a combination of ideas, or like Bergmann simply

an

idea.

They have been tion or negation,

led to this sharp distinction between the act of affirma

and the subject which

that in the former

a psychical

essentially

from the mere formation of

a function

more nearly akin

Brentano (Psychologic,

ment i,

to this distinction,

p. 46),

who

calls

is

affirmed or denied, by the fact

becomes

function

ideas, or of

which

active

differs

combinations of ideas,

to practical action than to ideation.

i, p.

266

sq.)

was the

first

to give a

decided state

and he was followed by Bergmann (Reine Logik,

judgment a

critical attitude

with respect to an idea,

a reflection upon its validity. He adds decision as to the validity of an idea that which judgment adds to mere ideation is something more "

:

than a merely theoretical relation

gence its

as

opposed

to the will,

it is

not only a function of the

a manifestation of the

practical nature, the faculty of willing,

Windelband takes the same is

;

it is

view,

spirit, in

intelli

which

participates."

and since

his treatment of the subject

the most thorough and the most carefully reasoned,

it

will suffice to ex-

APPENDICES

378

amine

As regards Bergmann and Brentano,

his arguments.

the Vierteljahrschr. f. wiss. Phil.,

v.

97

and

sq.,

my

I

may

refer to

Impersonalien,

p. 58.

Windelband distinguishes (Prdludien, p. 28 sq.) between judgments simply The former express (Urtheile] and (Beurtheilungeri) critical judgments. that

two ideal contents belong together, the latter the attitude of the In a judgment we consciousness towards the object thought of.

critical

always state that a certain idea (the subject of the judgment) is added in thought to another idea (the predicate of the judgment), the relation be In tween them differing according to the different forms of the judgment. a criticism, on the other hand, the critical predicate

is

attributed to

some

be completely known, or of which we have a This predicate in of idea the critical proposition). complete (the subject no way extends our knowledge of its subject, but expresses the feeling thing which

is

assumed

to

of approbation or disapprobation with

which the

regards the object in thought (a thing

white

pleasant, an idea

is

is

an action

true or false,

critical

a thing

good or bad, a landscape

is

Moreover, none of these

beautiful or unpleasing, etc.).

consciousness pleasant or un

is

critical

is

predica

have any meaning except in so far as the object thought of corre sponds or not to an ideal with reference to which it is estimated by the

tions

Critical predicates contain a reference to a

consciousness.

critical

con

sciousness which sets before itself certain ideals.

A

particular application of this theory

In so

desire for knowledge.

to

is

be found

our

in reference to

as our thought aims at

far

knowledge

i.e.

our judgments are subject to criticism, which expresses either the validity or the invalidity of the combination of ideas which has taken at truth

all

The purely theoretical judgment is to be found place in the judgment. only in the so-called problematical judgment, which combines certain ideas but says nothing as to the truth of the combination. Whenever a judgment

is

affirmed or denied, there

that of a criticism as to

are combinations

its

truth

is

...

of ideas whose

added

to the theoretical function

All the propositions of

knowledge

value for truth has been decided by

affirmation or negation.

Every willing

critical

and

judgment (he continues,

p.

the point of view from which the criticism contradictories pleasant beautiful

others

all

34)

the

is

feeling individual against a certain ideal content.

and

ugly.

and unpleasant,

The

first

is

is

true

made,

and

pair peculiar contain a claim to universal validity.

to

is

reaction of a .

.

.

But

expressed by the

false,

good and bad,

the individual, the

The same view

is

to

be

APPENDICES found in the Abhn.,

p.

"Bcitrage

where

170),

3?9

zur Lehre vom negativen it

is

Urtheil"

said that the negation

(Strassburger a practical judg

is

ment, a criticism, that it expresses not merely a relation between ideas but a disapproving attitude of consciousness towards the attempt to relate

them

in this that

the rejection consists. ; For this reason Windelband not follow Brentano in placing judgment, as a special class of psychical activity, between the theoretical formation of ideas and the practical activities of love and hatred. He to rank the it is

will

prefers logical estimation of ideas on the practical side of psychical life, and holds that value from the point of view of truth must be co-ordinated with other values.

cannot completely agree with these views, much as there is of truth in them. I have myself (Introdn., 1-4) laid stress upon the fact that logic as such as a critical and normative science starts from an ideal, the ideal I

of truth actual

;

that

it

presupposes the desire to think

judgment by

this final ideal

;

and

that

it

truly, and estimates every seeks to distinguish between

the mental operations which are conducive to this aim and those which

thwart

The

it.

logical treatment of these operations, as distinguished from

the psychological,

is based entirely upon the consciousness of the ideal, agree also with the further argument of the Prdludien (p. 43) that logic starts from the ideal of a normal consciousness (cf. 32, 7 and vol.

and

I

6 1, 62).

ii.

But not even the logician can infer from of affirming or denying he assumes a

ticular instances

this

that in par

practical attitude

towards the judgment because he estimates the particular combination of ideac by the universal ideal of truth

and not

feeling or will,

theoretical at

;

or that his activity

all.

When

make

I

is

a reaction of

my

it

aim

to

keep

good health, no doubt I do so by means of my will and by reason of some feeling and if on this account I give up some bad habit or myself

in

;

refuse the temptation to excess, there

giving

up the habit

haviour with a view to

But

after all this will

the habit

is

feeling have

my health

is

my

aim, and

is

"

my No

is

that it

;

my

will is active in

determines

a practical

"I

my

be

will not.

based upon the purely theoretical knowledge that My will and

no

direct share in this

knowledge as

to

what

is

conducive to

or the reverse, for this depends upon our experience of the nature

know

an act of

and

no doubt

injurious, the temptation fraught with danger.

of things, not upon willing or feeling. desire to

is

or rejecting the temptation

the truth, therefore

will.

criticism

"

The

distinction

my

Nor does critical

it

follow that because

I

judgment of a proposition

between a purely objective judgment,

with reference to some aim

is

important enough so

far as

APPENDICES

380 regards their contents

ments, which

but after

;

may be

all

such criticisms are

and

true or false,

differ

all

of them judg

only in that they are

judgments about the relation of the object to me and to my aim, not judgments about the object by itself. This relation, moreover, simply exists and is recognised ; it is not approved or disapproved. Sunshine "

is

pleasant"

criticism

a criticism of sunshine in relation to

is

which the proposition expresses,

itself,

is

feeling; but the

my

neither feeling nor will

but the simple recognition of the fact that sunshine excites a certain is his enjoyment ofwarmth ; feeling in me. The^reactipn^of majijis feeling the proposition jnjvvhich he gives expression to this ^n joy men t_J_s_a function He has formed the general ideas of pleasant and un _of Jhis thought. ing,

>

_

pleasant from his experience of contrary feelings, and by means of these which are not themselves feelings he expresses the relation which

ideas

between himself and certain

actually exists

good and bad,

beautiful

and

It is

things.

The judgments

ugly.

the

same with

which these are

in

predicated differ from others only in the nature of the predicates, not in the function of judgment itself; and these predicates express a relation be tween an object and myself, my will and feeling, which reappears in particular instances.

But the predicates true and to will

and

feeling, as

is

false

True and

ordinates with them.

contain not even such direct reference

contained in the pairs which Windelband co false

as general ideas

relation to the practical side of our life

ing nor is

upon our will what is true or beautiful and what is good. For

any objects of which

it

;

false, as

true

it

and

feel

depends upon them what

false

form an idea or about which

I

do not denote a

depends neither upon our

are not predicates of I

think

;

nor are they

Windelband somewhat inaccurately says predicates of concepts. are As he says more accu They predicates of judgments formed by us. as

rately elsewhere,

thej^ejiejo_c^m^ations of

ideas, not, that

is,

to ideas

to _ggmpleteo^ combinations, as if it sjiould be said that ^rggjy_c^)mbined, tree green OLJjggJLJL01 56 were true orj^lseTTFls^the act itself of combin "

r ing the ideas^the^act throughjvhich the consciousnessjj[mni^ anse si lo_ Thus it is not ideas ojLani...sort_of_pbiects_

wluch_&e_^ititheMS^^i^_

wjiich^we_cnticise by the.predicates_true ;

and

false,

but the judging activity

jtselfc_

Now

it

is

perfectly true that

where the question

where we actually find these predicates,

arises as to the truth or falsehood of a

tentative or completed, there

is

in the

judgment either background an ideal which, if not

APPENDICES is

distinctly conceived,

381

at least vaguely striven after

;

this is

the ideal of

no significance when we are speaking of knowledge, and merely trifling with thoughts. It is this ideal which arbitrary fiction, affords us a standard by which to estimate the statements which suggest for the antithesis has

themselves to us or the assertions of other people

forming to the ideal, others as contradictory to

we regard some

;

it.

con

as

In one sense we

may

indeed say that this involves an approval and disapproval for in propor tion as the ideal is clearly conceived and earnestly striven after, the agree ment of a given judgment with it is certain to arouse a feeling of pleasure, ;

disagreement a feeling of pain (though in the narrower and stricter sense approval and disapproval could extend only to actions regarded as as the conse voluntary ; we disapprove of error when it is a fault, such

its

quence of inattention). Nevertheless, it is presupposed by this approval and disapproval that the relation of a tentative or completed judgment to the ideal of truth should have been recognised as completely objective. We disapprove of the false because it is false, but it is not false because

we disapprove of

it.

Our

must be grounded upon the theoretical true or false, just as we must know that the

feeling

knowledge that a judgment is means will lead to our end before we choose them. But from the logical point of view, where we estimate every judgment by the standard of

to truth or falsehood extends to truth, the question as also that they are of

We say negations negations as well as affirmations. for denying that the true and false, and this alone is sufficient reason antithesis of approval

coinciding with that find in

it

any ground

and disapproval is to be unhesitatingly set down as nor can we of affirmative and negative judgments; and affirmation negation. for the co-ordination of

are estimated of fact both positive and negative judgments be therefore distinguish must and we according to a logical standard, its ideal, the to tween this logical treatment, which criticises, according treat movements of thought as they actually occur, and the psychological actual our in thought, takes what place The latter inquires as to ment. uni is possible that the how the negation arises in its course, and how it of approval or disapproval, versal ideal of truth, which is the ground view of the quesi state

As a matter

should arise at

which

in all

all.

Here

I

may

briefly

my

Windelband essential points agrees with

s.

I

from

start

in

from intuition acts of judgment which arise simplest immediate the consciousness and ideas the between we have the connection ;

validity, given together

can without any reflection, nor

it

be said

t

tl

.

tl

j

APPENDICES

382

These are acts of judgment which and with all the confidence of a take place quite unintentionally process such as the and which is natural necessary, recognition of objects around are in any

us, the

of an ideal.

way conscious

judgments that

this

is

here and that

there

is

such judgments are

;

accompanied by the immediate certainty that they are evident.

If

we

were psychologically unable to combine ideas in any other ways than this, we should never think of inquiring as to truth and falsehood. But our thought does extend beyond that which tions

and

is

regarded as expressions of that

expect to find a familiar object in

must have a

when

judgments which actually

associations,

its

Mediated by recollec

given.

arise which,

is

first

when,

;

familiar place, or

formed, are also for instance,

assume

we

that a flower

But some of these conjectures prove to be at variance when we fail to find what we expected, we ;

scent.

with the immediately certain

become conscious of the thing

;

that of

anticipated in our

judgment. its

conjecture by denying

mind

distinction

between the mere idea and the actual

which we are immediately certain

in that the subjective

ness of certainty

;

it

Here

differs

from what we had

the negation appears,

validity.

and annuls the

This introduces a new attitude of

combination

is

separated from the conscious

compared with a certainty and recognised as dif

is

In this way there arises the conception of invalidity. But this attitude of mind presupposes not only the subjective combination, but also ferent.

its validity. The negation as Fichte says is conditioned in matter, and unconditioned in form only, just as the con

a tendency to maintain

ception of difference (the importance of which for the negation

is

rightly

emphasized by Schuppe) presupposes the idea of distinguishable objects, but

not given with

is

it,

the general idea arising only after reflection

Thus

particular acts of distinction.

the negation

upon

is

doubly dependent object a thought which

upon the positive judgment. It presupposes as its was expected to be valid, and it rejects an attempted statement. The ground of its rejection, again, is ultimately something positive, an object given to intuition and recognised as different from my idea verum sui index

et falsi.

truth

becomes conscious

true has

It is

only through experience like this that the ideal of

we cannot

;

drawn our attention

feel the

value of truth until the un

We

must have experienced both the immediate and evident certainty of immediate judgments, and the differ ence between subjective combinations and immediate certainty, before we can form the idea of

The

to

it.

truth.

negation, then,

is

not co-ordinate with the positive judgment, but

APPENDICES presupposes

the certainty of this synthesis, and in language.

3 g3

both in the synthesis between subject and predicate and in

it

this relation finds a clear expression

If the

view that affirmation and negation are two co-ordinate modes of regarding a problematical synthesis Severe correct, it would be strange that while the negation finds special expression in language the affirmation, as a rule, has none (Bergmann and recognise

this).

find the ^

/x,i)i/,

indeed, verily,

Windelband

A

invalid.

that

A

is

not

confirms

it

proposition

etc.

is

we might go on

B\\.

is

true that

A

is

not

true proposition, etc.

position, etc.

B

;

A

B\\.

a false proposition

is

But

this

is

no

false

170) that

p.

if

we

carried

indefinitely with the predicates valid

B\\.

is

is

is

it is

true that

A

is

false that

A

true that

difficulty for our

by showing that the judgment is

threatened with denial do we

is

rightly points out (Strassb. Abh.,

our reflexion further

and

Windelband expressly

Only when a statement

"

view

;

not is

A

B

is

B

is

B\\.

false

a true pro

on the contrary,

the proposition

a

is

is

is

it

true, the

"

differs in

but

its predicate from nothing any other judgment. The same never-ending reflection takes place with respect to our self-consciousness qui sat, eo ...
tum

21) though indeed it is an abstract possibility only. In reality we always come to some point where there is a certainty which reflection fails to separate from that to which it refers, and which is not (Spinoza, Eth.,

ii.

therefore specially emphasized.

Thus

the objection proves what

it was no judgment which is not ulti mately based upon that immediate judgment in which we can no longer

meant

to refute

;

it

proves that there

separate the connection of ideas from

is

"

"

approbation

APPENDIX

or

"

confirmation."

B.

THIS view that the hypothetical judgment states the consequent as neces sary consequence of the antecedent seems contrary to the way in which logic

and grammar generally speak of the antecedent as presupposition or of the consequent. For if we understand condition in its

condition

ordinary sense as meaning the conditio sine qua non, as that which must

be realized before something

else

happens or

is

valid,

then

it

seems

to

imply that the negation of the antecedent involves that of the consequent,

and true.

that the consequent ceases to be valid

But

this

is

just

when

the antecedent

not

is

what necessary consequence does not involve

;

the

APPENDICES

384

consequence may be there even when the ground indeed,

it

the sole ground, and

is

all

is

wanting, unless,

agree that the invalidity of the

The proposition antecedent does not involve that of the consequent. not state that the does that if a triangle is equilateral it is acute angled is

attribute equilateral

a condition of the attribute

sense that no triangle which

is

acute angled in the

On

not equilateral could be acute-angled.

the other hand, that which merely a condition of an event does not for even if we take condition of itself suffice to bring about that event is

;

mean an

to

the

in

whole cause,

integral part of the

it

is

hypothetical judgment the antecedent

is

conditions of the consequent,

The

sequent necessary.

contradiction disappears

The

its

we

distinguish between state

subjective condition of the affirmation of the consequent

and the judgment

certainty,

states that in

the certainty of the consequent

Only

if

the con

and the matter of the

the subjective conditions of the statement

ment.

make

in itself sufficient to

is

it

only a part, while not merely one of the still

in so far as the

is

my

is

present stage of thought

dependent upon that of the antecedent.

antecedent

valid

is

am

I able or willing to affirm

anything about the subject of the consequent; unless the antecedent is valid I will affirm nothing unless the condition is fulfilled I will not answer ;

for the result

mean

that

you run hard, you

if

e.g.

will catch

quence of the

is

fulfilled

Bergmann (Reine

when

unless the former

the condition contained is

Logik,

19,

i,

judgment

it

the necessary conse

p.

202 sq.) considers the essential it makes a decision about

to be that

depend upon a decision about the hypothesis.

tinguishes between two meanings of the hypothetical as

does not

latter.

feature of the hypothetical thesis

this

running is the conditio sine qua non of stand still, etc. On the other hand, I cannot

the antecedent

the

But

objectively quick

catching him, for he may guarantee that the consequent will be true in

him.

He

dis

judgment according

indicates only a relative decision, a decision with a reservation (as

Wolff teaches), or

is

intended to emphasize the connection between the

validity of the hypothesis

and

:

completely general theory of equations from the results of past attempts.

There

is

no doubt

that

As examples

that of the thesis.

meaning, he gives the propositions if it is fine, Rome was governed first by kings, if Livy

in

will

I will visit is

of the

first

you to-morrow

a reliable authority

never be found

if

a

we may judge

such judgments we wish to lay special is not unconditionally asserted, but

emphasis on the point that the thesis

APPENDICES

385

only with the reservation that the hypothesis must be true.

But does

this invalidate the

proposition that every hypothetical judgment affirms the connection between the validity of hypothesis and the validity necessary of thesis, that by this alone does that

then

have never said

(I

"?

it

connection which

this

is

it

framing the judgment

we

as

is

name

deserve the

of judgment, and

expressed by the verbal form

Bergmann

pp. 204, 208

asserts,

if-

"

that in

are concerned only with the connexion between

hypothesis and thesis, nor that the proposition

A

"

if

is

B

true,

true

is

"

is

an inadequate expression for is the necessary consequence of A"). In the last two examples the statement of the connexion is at once "B

obvious

If

:

a reliable authority, that which he

is

Livy

us that

tells

Rome

was

first

us

tells

ruled by kings, therefore

true

is

Rome

was

he

;

really

the truth of the thesis follows with logical necessity first ruled by kings In the last example, again If we are from the truth of the hypothesis. :

justified in inferring

from past

must be

results to future, then future failure

inferred from actual past failure

;

here again there

logical necessity of

is

the consequent.

The visit

example contains an apparent exception to morrow I shall This seems to be really no more than a conditional

first

:

if it is fine.

you

statement in which necessary connexion

have the

visit

for

presses

is

is

fine

weather

But upon more

necessary consequent

?

careful

can

What

this

This resolution,

given.

am now bound by my at this

moment

in itself

promise, for

upon the appearance of a given I will

How

absent.

example proves to be no exception. an intention, a resolution which is formed as well

examination even

which

its

is

is

it is

fact

and

as such,

is

ex

it

as a promise

not conditional

;

I

of an action just this dependence

which

is

contained in

that the consequence

my

will

;

what

shall actually take place

and then by my will I establish a connexion, will resoluiion the that affirm I by virtue of this willed connexion statement This is be carried out so soon as the condition present.

together with the condition

finds

its

ground

same with

all

in

my

will,

;

which cannot be

promises, threats,

certain events; by

my

will I

self-contradictory.

determine that a future action

condition. unfailing consequence of the realized is

work by Enrieccerus

1888,

p.

1

6,

175

sq.),

:

Rtehtsgeschaft,

s.i,

the

is

(cf.

what

is

be the I

state

said in

Bedingung und Anfangstermin,

but this connexion, in that

a real connexion which exists

shall

Here again what

the connexion between condition and consequence

the

It

and contracts which are conditional upon

it

independently of

is

my

willed, differs will

from

and which

cc

is

APPENDICES

386

As such a statement

expressed by a purely theoretical statement. proposition

"if

it is

fine, I will visit

to-morrow" is false, for

you

objectively necessary connexion as in the proposition

buds will open to-morrow"; it assumed that my will is able to will

remain

We

still

then

"

"

if it

is fine,

objectively valid only because

is

realize the

hence that

constant,,

there

shall

I

the

is

no

these it

is

connexion willed, and that it not be untrue to my promise.

hold therefore that statements containing a conditional are judgments only in so far as they state a necessary connexion.

"if

APPENDIX THE number

C.

of conclusions which can be drawn from those combinations

of premises which are rejected

Aristotle

by

128

Schuppe (Erkenntnissth. Logik, p. Even when the two premises a

extended much further by

is

sq.).

not

is

b,

and b

is

not <-,

express mere

us, he says, that a and c coincide in the one they yet of not and under certain circumstances this may be a most point being b,

difference

tell

Still important discovery forming the only connexion between a and c. this discovery may be expressed by merely repeating the two premises so that Schuppe together in the proposition "neither a nor c are />";

acknowledges that

in this case again

it is

true that ex mere negativis nihil

sequitur.

But he holds that is

false.

obviously

plained on sition

"

judgments of necessary connexion this principle proof of this he selects the instance ex

his first

456 of an inference having which is not Mis not

p.

that

From

"no

for its

major premise the propo

P."

Mis

no ground

find

in

For

in

P"

M

and

for

"

S is

not

M"

denying P of

S,

we

infer that

"a

result

we can

which

certainly

may sometimes

be very important when we are contending with vague ideas which deny of 5 because of its similarity with M, though without any definite state ment, a result therefore which may lead us to recognise that 5 is

P

P."

Schuppe omits to illustrate his principles with examples we shall find it easier to test them if we take one which corresponds to the above words. ;

"

No

say

fish

has

we can

to fish to

warm blood

the whale

is

not a

fish."

From

this

he would

we must not be led by the similarity of the whale it has warm blood. But do we really draw this con

infer that

deny

thai

clusion from both premises?

If

we

are in danger of concluding that

APPENDICES because the whale

mise alone which

is

like a fish

check

will

33 7

has cold blood, it will be the minor pre not both together. That when

it

us,

we,

is,

have the premises

That which

The whale

is

is

not warm-blooded

fish is

not a

;

fish,

the minor premise alone which prevents the possibility of subsumpthe possibility of ; any conclusion whatever is prohibited by the rule that we cannot infer from the failure of the hypothesis to the failure of the it

is

tion

So that here again Schuppe merely tells us in other words this kind no conclusion can be drawn. For these

thesis.

that

from premises of

mises give us absolutely no information as to whether

P

belongs to

pre

S

or

not.

M

"From no P is and Schuppe has misplaced here)

to

be denied of

5 because

this respect at least

S

make

the possibility of

change the

(I

M

M

that

SP

5

is

M;

must be

which

letters

P

the similar inference that

feared

is

is

not

therefore, that in

Here

maintained."

prevented by the minor would of course yield the conclusion

S not alone. 5 is M S is not P- but from S not we PHOT that 6 is not P. Mis not P,

premise

n

of a vague idea that

the false conclusion which

again

M

not

is

"we

is

S

get nothing definite, neither that

1

is

SandP

may both be

but

Mis

not

S

either,

absent from the same subject (Lotze

proves that inference

s

which we mentioned above).

He

questions in the same way the rule ex mere particularibus ni/iil Some only, but at least some, s are P, and some only, but

M

"

sequitur. at least

what

which

some,

6"s

S

6"s

are is

are

M,

P."

M, where we do

not yet

know what

M

s

are

P

and

assures us of the possibility of at least one case

But an assured

possibility (in distinction

in

from one which

and grounded only upon complete ignorance) would seem found only where it is known that S and do not exclude each other; can we then infer from "some men are blind and some seeing is

quite vague

P

to be

creatures are

men,"

seeing creature "

the assured possibility that in

may be

blind

?

"

Such

often lead to the valuable knowledge

:

some

premises,"

(i) that

particular case a

he goes on to

P belongs

to or

is

say,

depen

dent upon the specific or individual differences of M, though it is not necessitated nor excluded by the conceptual content of M. (2) That

M

belongs to the specific or individual differences of S, necessitated nor excluded by the conceptual content

though S.

it

is

(3) that

neither

whether

APPENDICES

3 38

S appears

with or without

or absence of

P this

i

no way connected with the presence

in

is

Propositions

M."

and

2,

however, are not inferred from

both premises together they merely present an interpretation of one of No doubt this one, as formulated above, Some only, but at least them. ;

"

M

some,

are

s

"

as

consists

P"

M

Some

s

Schuppe himself shows later on in two s are not some and it is only from

M

are P,

judgments, these two propositions taken together that we can infer that Pis neither necessitated nor excluded by the concept M." These two judgments form P,"

"

the application of the major premise

M

predicate

excluded by

M

all

s

are

one time but not

at

"

it

according to

;

P nor

no

that

Mis

"

which

that

another

at

connected with the

is

neither necessitated nor

is

this familiar rule

we can

neither say that

P.

But the third of these propositions, the only one which can be inferred from both premises, are

M,

let

Instead of some

is false.

us take, for example,

some quadrangles

are regular

"

some

are

s

P

t

and some

cannot say that whether the

do with the

quadrangle appears as rectangular or not this has nothing to

absence or presence of the attribute regular

;

the regular quadrangle

is

necessity rectangular. crystals"

mineral having double refraction this has nothing to do with the fact of being or not being a crystal ?

On are

}

some

133 he continues

p.

P

some

M

s

M

s

of

some

Again, crystals have double refraction, some must we infer from this that when we find a "

minerals are

.S s

regular figures are rectangular,

We

figures."

M

are S,

:

"It

is

certain that the propositions,

P

do not connect the predicates

because of the attribute

M

M;

if

some

S

and

its

M

s

with the

they did, then the predicates must

s; they connect them with specific or individual differ belong to all ences which fall under the concept and thus we are assured of the } conclusion that in any particular the attributes and S are neither

M

M

P

necessitated nor excluded by the characteristic if it is

that

also true that

what we do

some

is first

Pis

(MiP, MoP)

that

second (MiS,

MoS)

and then

to

sum up

M

s

to infer

are not P,

and some

above

from the

as

But

M."

M

s

first

this is

S

is

So

pair of premises

M, from

the

neither necessitated nor excluded by

M,

neither necessitated nor excluded by

that

only true

are not S.

the two judgments in one

"P

necessitated nor excluded by the characteristic

and

S

are neither

M" But this process is not one in which we gain a definite relation between and Pby eliminat ing M; no such relation can be determined in any way, not even nega tively, from these premises. 6"

APPENDICES it

are P, no 5 is M, it follows that if 5, or one S is not so by virtue of It is is enough to know that in order to know that 5 can have no other predicate virtue

certainly

M

not of

P

M

is

<>

by

M.

"The

statement that in the form

be affirmative

is

fundamentally

safely infer partial identity

may be such spoken on

p.

which

is

premises must not

"

Here, he holds, we

137).

(p.

also inferred

in

The

affinity.

this partial identity as

85 of this term

long run that

PM and SMboth

false

sometimes even

make

as to

partial difference

in the

389

J/ s

all

"From

may

nature of

M

valuable a result as the

the second figure.

We

have

" "

partial identity

;

if

we

we

let it pass,

find

all

things are partially identical, and the conclusion is therefore without value. If, again, it depends upon the nature of whether or not it has any value, we must regard the judgment, Both and S are Af, as a simple summation in which the middle is not

M P

concept

eliminated.

That

it

may be

useful to

know

this as

a preliminary step

towards the operations of classification, I do not of course but dispute we must not call it an inference unless we are to call every combination of two judgments into a conjunctive or copulative proposition an in ;

ference.

We may

make the same answer to Wundt when he brings forward an of comparison (Logik, i. p. 324) which is, he says, sometimes an inference of agreement, sometimes of difference. In the first case we "

"inference

have

"

A

has the characteristic

B agree in teristic M, B has A

and

one

M,

B

has the characteristic J/, therefore

characteristic"; in

not the characteristic

the second

M,

"A

therefore

A

has the charac

and

B

have a

But what ground is there for the there distinguishing fore of the first inference? Evidently it must be the major premise that if two objects or concepts have the same characteristic they agree in one characteristic a mere tautology from which we can learn nothing "

characteristic."

"

whatever as to any other relations between the objects or concepts com pared, nothing as to whether they are identical or opposed, or anything else.

In the second inference, again, the

cording to

Wundt s

"therefore"

presupposes, ac

rendering, nothing more than the major premise,

"if

one of two objects has a characteristic which the other has not, then they have a distinguishing characteristic." Here indeed very little would be would contain no more than the two

told us by the inference

itself, for it

premises themselves

us in another form.

tell

objects have a distinguishing characteristic

But from the

we may

fact that

two

further infer that they

APPENDICES

390 differ as

wholes, that they cannot be identical, and,

when we

are dealing

with concepts, that they cannot be predicated of each other in any sense.

We and

have therefore

at

a negative determination of their relation,

least

and opposition

as the recognition of difference

mental operations of our thought not merely a question of like that of

"

partial "

"

partial identity

;

is

one of the funda It

this result is certainly important. difference,"

from

partial

as

Schuppe represents

identity nothing

can be

is

it,

in

it follows (p. 138) that S and / are not identical as wholes, that they cannot be predicated of the same thing nor of each other. It is of course presupposed that one of the premises

from

ferred, but

"partial

contains a necessity, and that It certainly

was

is

we do not compare merely casual states. in my room yesterday

does not follow that because the stove

hot, while the stove in

stove

"

difference

my room

not the same as the

the major premise

tells

first

;

to-day

is

cold, therefore the

second

a conclusion can be drawn only

when

us that a predicate must be necessarily affirmed or

denied of a subject, so that the absence or presence of this predicate in volves that of the subject itself. From what we have said it would appear therefore that Aristotle was perfectly right in recognising only a negative result

I

in the

second

figure,

saying of two positive premises

cannot therefore allow that

ou/c

co-rat

this criticism of the traditional doctrine is

Nevertheless Schuppe

is right in emphasizing an inference from two drawing premises we frequently clusion, not from the premises by themselves, but from which alone enables us to get any result from combining

justified.

:

the view that in

obtain our con a major premise

the contents of

one premise with the contents of the other. Here we must distinguish between two cases either one of the premises is itself a hypothetical :

judgment,

in

which case we merely need the general principle that the

affirmation of the ground involves that of the consequence, the denial of

the consequence that of the ground

;

or else the two premises need a

more

special principle of which they are the application, and by means of which they yield the conclusion according to the general principle of inference. Inferences of the first and second figure which presuppose a universal

major premise belong

to the

first

class

;

inferences of the third figure to

the second. B. Erdrnann (Philos. Aufsdtze zuin Doctorjubiliium E. Zellers, p. 201) maintains that by introducing definitions we may get universal affirmative conclusions in the second and third figures ; e.g., all mammals have lacteal

APPENDICES glands,

all

391

whales have lacteal glands, therefore

But he overlooks the

all

whales are mammals.

fact that the

major premise does not tell us that it is a definition, and the conclusion does not follow from what it does tell us, For the inference to be valid it must stand only mammals have lacteal "

glands";

i.e.,

our inference

that which has lacteal glands is

in the

END OF VOL

Butler

&

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a

mammal;

then, however,

first figure.

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