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Full text of "The principles of logic"

THE 
PRINCIPLES OF LOGIC 



Oxford University Press, Amen House, London E.G. 4 

GLASGOW NEW YORK TORONTO MELBOURNE WELLINGTON 
BOMBAY CALCUTTA MADRAS CAPE TOWN 

Geoffrey Cumberlege, Publisher to the University 



THE 

PRINCIPLES OF LOGIC 



BY 

F. H. B R A D L E Y 

O.M., LL.D., LATE FELLOW OF MERTON COLLEGE, OXFORD 



SECOND EDITION 

REVISED, WITH COMMENTARY AND 
TERMINAL ESSAYS 



VOL. I 



OXFORD UNIVERSITY PRESS 
LONDON: GEOFFREY CUMBERLEGE 



FIRST EDITION, 1883 

SECOND EDITION, IQ22 

CORRECTED IMPRESSION OF IQ28 
REPRINTED, 195 




SET IN THE UNITED STATES OF AMERICA 
REPRINTED FROM PLATES IN GREAT BRITAIN 

AT THE UNIVERSITY PRESS, OXFORD 
BY CHARLES BATEY, PRINTER TO THE UNIVERSITY 



TO MY FRIEND 

E- R- 

THESE VOLUMES ARE 
DEDICATED 



PREFACE 



IT is with mixed feelings that this reissue of an old work is 
offered to the public. I am happy to find that a book of mine 
is still alive, and that after some forty years it has seemed 
worthy to reappear. On the other hand I regret that, while 
Logic during this interval has lived and moved, I myself have 
failed, except partially, to follow its advance. My available 
energy has been expended mainly in fields which more or less 
fall outside Logic proper. And it is too late for me now to 
make good my shortcoming, and to endeavour to master those 
more recent works which have succeeded in throwing, at the 
lowest estimate, much light on their subject. 

Hence I could not rewrite my book so as to offer it as an 
adequate account of contemporary Logic. And on the other 
hand simply to reprint it, or again, so far as I am concerned, 
to let it die, seemed alike open to objection. I therefore de 
cided, while reissuing the old volume, to add to it some notes 
and an appendix with a view to correct and supplement some 
part of its defects. At the same time I saw clearly that any 
such addition would still leave the book largely incomplete. 

The course which I have followed may even perhaps result 
in some gain to the reader. He can, if he pleases, now verify 
any advance which in 1883 may have been made by my work. 
And its faults both of manner and matter faults which recall 
to me those days when I was young may possibly with some 
readers themselves be of service. They may be more than 
excused if anywhere they help in any way to excite a more 
living and personal interest in logical problems. 

It is not that in this book or elsewhere I lay a claim to 
original discovery. In these pages there is perhaps no result 
which I do not owe, and where, if my memory served me 
better, I could not acknowledge my debt. But when a man 
has studied, however little, the great philosophers, and felt 

vii 



Vlll PREFACE 

the distance between himself and them, I hardly understand 
how, except on compulsion, he can be ready to enter on claims 
and counterclaims between himself and his fellows. And all 
I care to say for myself is that, if I had succeeded in owing 
more, I might then perhaps have gained more of a claim to 
be original. 

The present volumes contain a reprint of the book published 
in 1883. The text has not been altered except occasionally in 
the punctuation, and by the removal of mere misprints and of 
one or two obvious grammatical errors. The Commentary, 
which is new, has been placed after each chapter in the form 
of Additional Notes, and the Terminal Essays have none of 
them been published before. The Index, which I hope will 
be of service, is also new. But for this, however great its 
merits, I cannot claim to be responsible. 

I regret that Dr. Bosanquet s Implication and Linear In 
ference came too late to be used. But I cannot end this 
Preface without some expression of my gratitude to Dr. 
Bosanquet for all that, since 1883, I have owed to him, and 
without some acknowledgment of how deeply this reissue is 
in debt to his invaluable works on Logic. 

1922. 



PREFACE TO FIRST EDITION 



THE following work makes no claim to supply any sys 
tematic treatment of Logic. I could not pretend to have 
acquired the necessary knowledge ; and in addition I confess 
that I am not sure where Logic begins or ends. I have 
adopted the title Principles of Logic, because I thought that 
my enquiries were mainly logical, and, for logic at least, must 
be fundamental. 

I feel that probability is against me. Experience has shown 
that most books on Logic add little to their subject. There is 
however one reflection which may weigh in my favour. Both 
in England and in Germany that subject is in motion. Logic 
is not where it was, and can not remain where it is. And 
when one works with the stream a slight effort may bring 
progress. 

I have in general not referred to those works to which I 
have been indebted. Amongst recent writers I owe most to 
Lotze, and after him to Sigwart. Wundt s book would have 
been more useful had it come to me earlier; and I may say 
the same of Bergmann s. I am under obligations to both 
Steinthal and Lazarus. And amongst English writers I have 
learned most from the late Professor Jevons. I may mention 
here that I should have owed certain observations to Mr. 
Balfour s able work, had I not seen it first when my book was 
completed. I should be glad to state my debts in detail, and 
in this way to express the gratitude I feel, but I doubt if it is 
now possible. I could not everywhere point out the original 
owners of my borrowed material, and I could not clearly state 
how much is not borrowed. I lay no claim to originality, 
except that, using the result of others labour, I in some respects 
have made a sensible advance. 

I wished at first to avoid polemics altogether. But, though 
I have not sought out occasions of difference, it is plain that 

ix 



X PREFACE TO FIRST EDITION 

too much of my book is polemical. My impression is that it 
will not suffice to teach what seems true. If the truth is not 
needed the reader will not work for it, nor painfully learn it. 
And he hardly will need it where he stands possessed of what 
seems an easy solution. Philosophy now, as always, is con 
fronted with a mass of inherited prejudice. And, if my 
polemics bring uneasiness to one self-satisfied reader, I may 
have done some service. 

I fear that, to avoid worse misunderstandings, I must say 
something as to what is called " Hegelianism." For Hegel 
himself, assuredly I think him a great philosopher ; but I never 
could have called myself an Hegelian, partly because I can 
not say that I have mastered his system, and partly because 
I could not accept what seems his main principle, or at least 
part of that principle. I have no wish to conceal how much 
I owe to his writings ; but I will leave it to those who can 
judge better than myself, to fix the limits within which I have 
followed him. As for the " Hegelian School " which exists in 
our reviews, I know no one who has met with it anywhere 
else. 

What interests me is something very different. We want 
no system-making or systems home-grown or imported. This 
life-breath of persons who write about philosophy is not the 
atmosphere where philosophy lives. What we want at present 
is to clear the ground, so that English Philosophy, if it rises, 
may not be choked by prejudice. The ground can not be 
cleared without a critical, or, if you prefer it, a sceptical study 
of first principles. And this study must come short, if we 
neglect those views which, being foreign, seem most unlike our 
own, and which are the views of men who, differing from one 
another, are alike in having given an attention to the subject 
which we have not given. This, I think, is a rational object 
and principle, and I am persuaded that a movement which 
keeps to this line will not be turned back. 

In conclusion I may be allowed to anticipate two criticisms 
which will be passed on my work. One reader will lament 
that he is overdone with metaphysics, while another will stand 
on his right to have far more. I would assure the first that 
I have stopped where I could, and as soon as I was able. And 
in answer to the second I can only plead that my metaphysics 



PREFACE TO FIRST EDITION XI 

are really very limited. This does not mean that, like more 
gifted writers, I verify in my own shortcomings the necessary 
defects of the human reason. It means that on all questions, 
if you push me far enough, at present I end in doubts and 
perplexities. And on this account at least no lover of meta 
physics will judge of me hardly. Still in the end perhaps both 
objectors are right. If I saw further I should be simpler. 
But I doubt if either would then be less dissatisfied. 



VOLUME I 



Jn this Table the numbeis in parentheses refer to the sections of each chapter in 
Bocks I-III, while in Essays I-XII the numbers refer to the pages. 



BOOK I 
JUDGMENT 
CHAPTER I 

THE GENERAL NATURE OF JUDGMENT 

What judgment is. It implies ideas, and these are signs (1-3). A sign, 
what (4-6). Two senses of "idea" (6-). In Judgment ideas are 
meanings (9). Judgment defined (10), and errors refuted (11-12). 

Mistaken views criticized. Judgment not "association" (13-14); nor 
practical influence (15) ; nor a mere junction, nor an equation of 
ideas (16). Truths contained in the above errors (17). 

Development of Judgment. It is a late product (18), because at first 
the mind has no ideas proper (19-20). Conditions required for 
origin of Judgment (21-22). If the Association-theory were true 
it could never have appeared (23) ; but from the first universals 
operate in the mind (24-26) Pages 1-38 

Additional Notes 38-40 

CHAPTER II 

THE CATEGORICAL AND HYPOTHETICAL FORMS OF JUDGMENT 

Judgment is about fact (i). Preliminary objections answered (2). 
But how if all judgment is hypothetical (3) ? And if judgment 
keeps to ideas it all is hypothetical (4-6). This true of universal 
and again of both classes of singular judgments (7-8). 

But judgment is not confined to ideas. It refers to present reality (9). 
On the other hand it does not refer to reality as present (10). This 
explained and defended (11-14). 

Search for Categorical Judgment. I. Analytic Judgments of sense, and 
their varieties (15-16). Superstition as to names of Individuals 
(17-18). II. Synthetic judgments of sense. How can these refer 
to present reality (19) ? But they can not refer to mere ideas (20- 
21 ). Their true subject is unique. Thisness and This. Idea of 
"this" how used (21-27). 

xiii 



XIV CONTENTS 

But how then can Synthetic Judgments be true of this given reality 
(28)? Because the reality is not the mere appearance (29-30). 
These judgments rest on continuity of content (31), and that upon 
ideal identity (32-33). Past and future are not phenomena (34). 

Recapitulation (35). Memory and prediction not mere imagination 
(36-37)- Idea of Individual, what (38-39). Non-phenomenal Sin 
gular Judgments (41). Existential Judgments (42). Transition to 
Abstract Universal Judgments (43). 

These are hypothetical (44). Collective Judgments really singular (45). 
Hypothetical can not be reduced to Categoricals (46-47). A sup 
position, what (48). Real assertion contained in Hypothetical Judg 
ments (49-52). They are all universal (53-55). Result (56). 

Pages 41-90 

CHAPTER II (Continued) 

With hypothetical we seem to have left the real world, but have 
reached the world of Science (57). Presumption against the sin 
gular judgment of sense (58). Its claim (59-60) is untenable be 
cause it mutilates the facts (61-67). It is conditioned (68-70), and 
conditional (71) ; and is even false (72-73). It is an impure and 
imperfect hypothetical (74-78). Result (79-80). Remaining class 
of Judgments (81) Pages 91-107 

Additional Notes 107-113 

CHAPTER III 

THE NEGATIVE JUDGMENT 

Negation depends on the real (i), but is more ideal than affirmation 
is (2-3). It is not the denial of an affirmation (4), nor is it a kind 
of affirmation (5), nor an affection of the copula (6). It has a 
positive ground which is not explicit (6-7). 

Opposition and Privation. These distinctions here not vital (8), but 
call for explanation (9-11). Varieties of negative judgment. Nega 
tive Existentials (12). 

Logical negation is subjective, and is no real determination (13-14). It 
does not assert the existence of the contradictory (15). Idea of the 
contradictory, what (16). The asserted contrary not explicit (17). 
Contrary opposition not dual (18). Ambiguity of denial. It rests 
on covert assertion (19-20) Pages 114-125 

Additional Notes 125-127 

CHAPTER IV 
THE DISJUNCTIVE JUDGMENT 

It is not a mere combination of hypotheticals (1-2). Its basis is always 
categorical (3-6). Alternatives are rigidly exclusive. Erroneous 
views on this point (7-12). What disjunction presupposes (13). 
Recapitulation (14) Pages 128-137 

Additional Notes 137-140 



CONTENTS XV 

CHAPTER V 

PRINCIPLES OF IDENTITY, CONTRADICTION, EXCLUDED MIDDLE, 
AND DOUBLE NEGATION 

Principle of Identity must- not be a tautology (1-3). What (if any 
thing) it should mean (4-9). Principle of Contradiction does not 
explain anything (10). What it means (11-14). Further criticism 
and explanation (15-16). Principle of Excluded Middle is one 
special case of disjunction (16-19). Goes beyond it, how (20-21). 
Is wrongly objected to (22). Criticism of mistaken views (23-27). 
Double Negation, wrong account of (28). True explanation (29- 
31). Erroneous use of (Note) Pages 141-164 

Additional Notes 164-167 



CHAPTER VI 

THE QUANTITY OF JUDGMENTS 

Extension and intension (1-2). Mistakes about "connotation" (3-5). 

Law of inverse proportion of intent to extent, shown to be 

erroneous (6-10). 
Every judgment has two aspects, and can be taken both extensionally 

and in intension (11-12). The first defended against erroneous 

views (13-21). The second explained, and mistakes removed 
(22-29). 
Universal, particular, and singular; what these mean, and how far they 

can be real (30-36). The corresponding judgments, what (37-43). 

Pages 168-193 
Additional Notes 193-196 

CHAPTER VII 

THE MODALITY OF JUDGMENTS 

Modality affects not the form but the content of Judgment (1-3). 
Logical modality, what (4-5). The Assertorical (6). The Neces 
sary is hypothetical (7-11). And so is the Possible (12). Varieties 
of the latter (13-15). 

Modality does not exist in fact (16). This shown of the necessary (17), 
and the possible (18-19). But there must be a real basis for neces 
sity (20), and for possibility (21-22). 

Further explanations. The Potential not real (23). Conditions, as 
such, not facts (24). Permanent Possibilities ambiguous (25). 
The Problematic and Particular Judgments identical (26). The 
Impossible, what (27). The possible not the same as the mere not- 
impossible (28-31). 

Probability. Its principles logical (32). Is neither objective nor sub 
jective (33). Rests on an exhaustive disjunction (34~36), each 
alternative of which is equally credible (37-38). Expression of the 



XVI CONTENTS 

chances by fractions (39-41). Inductive probability implies no fresh 
principle (42-43). 

Errors refuted. Probability objective as well as subjective (44-45). It 
does not in its essence imply a series (46-50) ; nor a knowledge of 
the future (51). Fiction of the "long run" (52-54), and the truth 
which underlies this (55-57). Superstitious beliefs (58-59). Transi 
tion to Inference (61-63) Pages 197-236 

Additional Notes 236-242 



BOOK IL PART I 
THE GENERAL NATURE OF INFERENCE 

CHAPTER I 

SOME CHARACTERISTICS OF REASONING 

We are really agreed on three features of inference. What these are 
(1-3). Examples (4) Pages 245-246 

CHAPTER II 
SOME ERRONEOUS VIEWS 

The major premise is a superstition (i). And the syllogism is not the 
one type of reasoning (2). The ordinary syllogism in extension 
criticized (3-5). Principle of nota notes (6). Possible reform of 
the syllogism (7-8). Principle of "Related to same are related to 
each other" criticized (9-10) Pages 247-254 

Additional Notes 254-255 

CHAPTER III 
A GENERAL IDEA OF INFERENCE 

Inference a perception ensuing on a synthesis (i). Demonstration is 
seeing in a logical preparation, and that is an ideal construction 
(2-4) Examples (5). Superstitions to be abandoned (6). 

Pages 256-260 

Additional Notes 260-261 

CHAPTER IV 

PRINCIPLES OF REASONING 

These are special principles of interrelation (1-2). Examples of syn 
theses (3). But in what sense are they principles (4)? Not as 
canons and tests of individual inferences (5-6). No art of Reason- 



CONTENTS XV11 

ing (7). Illustration from Casuistry (8-9). Inadequacy of the 

syllogism (10) Pages 262-271 

Additional Notes 271-273 



CHAPTER V 
NEGATIVE REASONING 

Its general nature (i) and special principles (2). Can you argue from 
two negative premises? Yes, but not from two bare denials (3-7) 
When one premise is negative can the conclusion be affirmative ? On 
one special condition, yes (8-9) Pages 274-283 

Additional Notes 283-284 



CHAPTER VI 
TWO CONDITIONS OF INFERENCE 

Result reached (i). An identical point required in all reasoning (2). 

Mere likeness not enough (3). Principle of Identity of Indiscerni- 

bles stated and defended (4-9). 

And one premise at least must be universal (10-13) . Pages 285-297 
Additional Notes 297-298 



BOOK II. PART II 
INFERENCE CONTINUED 

CHAPTER I 

THE THEORY OF ASSOCIATION OF IDEAS 

The fact of psychical association is certain, but the theory which ex 
plains reproduction by the "Laws of Association" is false (1-7). 
Main ground of objection (8). The true explanation of the fact 
(9-12). 

Errors refuted. No association by Contiguity (13-17), even if assisted 
by Similarity (18). Similarity alone is left (19), and this too is a 
fiction (20-22), which the facts do not require (23-25). The true 
explanation (26-27). Misunderstandings removed (28-31). Wolff 
and Maas adduced (32). An objection answered (33). Practical 
conclusion (34-36). 

Note. Indissoluble Association and the Chemistry of Ideas. 

Pages 299-345 

Additional Notes 346-347 

2321. i h 



XV111 CONTENTS 

CHAPTER II 
THE ARGUMENT FROM PARTICULARS TO PARTICULARS 

This discussion has been anticipated (1-2). Supposed evidence for the 
Argument (3) is an ignoratio elenchi (4-5). We never argue from 
particulars as such (6-9), but from an universal (10-11). And we 
can not do otherwise (12-13). Mr. Spencer s theory of inference 
to be passed over (14) Pages 348-354 

Additional Notes 054 

CHAPTER III 

THE INDUCTIVE METHODS OF PROOF 

The question limited (1-2). Complete Induction (3). Mill s Canons 
of Induction. Their claim to be demonstrative (4-5). But (I) they 
can not start from fact (7-9). And (II) their conclusion need not 
be more general than some of their premises (10). And (III) they 
all have a logical flaw unless you confine them to the case in hand 
(11-14). Result (15-16) Pages 355-368 

Additional Notes 368-369 

CHAPTER IV 

JEVONS EQUATIONAL LOGIC 

The Enquiry limited and subdivided (1-2). A. Propositions are not 
equations, and can not assert mere identity (3-7). B. Reasoning 
does not consist in Substitution of Similars. It rather connects dif 
ferences (8-13). C. The Indirect Method (14) can not be reduced 
to Substitution (15-18). The Logical Machine. Its merits and 
defects (19-22). Result (23) Pages 370-387 

Additional Notes t ..*,..... 387-388 



VOLUME II 

BOOK III. PART I 
INFERENCE CONTINUED 

CHAPTER I 

THE ENQUIRY REOPENED 

Our former account of inference was insufficient. There are infer 
ences which will not come under our formula (1-9) Pages 389-392 
Additional Notes 392-393 

CHAPTER II 

FRESH SPECIMENS OF INFERENCE 

Tests of the existence of inference (1-3). Claim of fresh specimens. 
A. Three-term Constructions (4-5). B. Arithmetic and Geometry 
(6-15). C. Comparison and Distinction (16-17). D. Recognition 
(18). E. Dialectic (19-22). F. Abstraction (23-24). G. Disjunc 
tive Inference (25-29). H. Immediate Inferences (30-37). 

Pages 394-423 

Additional Notes 423-430 

CHAPTER III 

GENERAL CHARACTERISTICS OF INFERENCE 

Further character of inference as an ideal experiment (1-4). This type 
verified throughout our fresh instances (5-10). 

Not every mental activity is reasoning (n). Judgment is not inference 
(12-18) ; nor is all Reproduction (19-22) ; nor is Imagination (23- 
24). Result obtained (25) Pages 431-446 

Additional Notes 446-449 

CHAPTER IV 

THE MAIN TYPES OF INFERENCE 

Analysis and Synthesis are two main types (i). This not apparent (2), 
but shown throughout the whole of our instances (3-7). Tabular 
statement (8) Pages 45O-455 

Additional Notes 456 



XX CONTENTS 



CHAPTER V 

ANOTHER FEATURE OF INFERENCE 

A central identity required for each process of experiment (i). Dif 
ficulties (2-3). The identity shown in Recognition and Dialectic 
(4); and in Comparison and Distinction (5-6). This further ex 
plained (7-9). The identity shown in spatial Construction and in 
Arithmetic (10-12); and in Abstraction (13); and in Disjunctive 
Inference (14). Result (15) Pages 457-467 

Additional Notes 467-469 

CHAPTER VI 

THE FINAL ESSENCE OF REASONING 

Principles of our processes (i). Analysis and Synthesis are two sides 
of one process (2). Their sameness shown (3), and their differences 
pointed out (4-7). Analytic and Synthetic Methods (8-10). 

Judgment and Inference, how related (n). Every judgment involves 
synthesis and analysis (12-14) ; but itself is not inference (15). If 
however we go back far enough, judgment and inference seem two 
sides of one process (16-22). Their connection shown in the work 
ing of Reproduction (23-24). 

Beside Analysis and Synthesis there is a third principle of reasoning 
(25). Defects of Analysis and Synthesis (25-28). These defects 
suggest a self -developing function (29-30), which appears in our 
third principle (31-32). Recapitulation (33). Self-developement 
shows itself through the whole process of reasoning (34-35). 

Pages 470-494 

Additional Notes 494-501 

CHAPTER VII 

THE BEGINNINGS OF INFERENCE 

Gulf between explicit inference and the beginnings of soul-life (1-2). 
Yet from the first an intellectual activity is present, which slowly 
developes (3-8). Prevalent errors as to early intelligence (o-n). 
Obstacles to the right study of it (12-15) . . Pages 502-514 

Additional Notes SiS-Si8 



CONTENTS XXI 

BOOK III. PART II 

INFERENCE CONTINUED 

CHAPTER I 

FORMAL AND MATERIAL REASONING 

No reasoning with a bare form (2) ; nor need we even have a relative 
form if that means a mere formula (3). No material reasoning if 
that means an argument from the particular (4). There is a form 
or principle in every inference, and there is an irrelevant detail 
(5-6). We can extract this form (7) ; but it is not a major premise 
(8-13). The form is the principle which neither proves, nor is 
proved by, the instances (14-16) ; and this can be stated in a syl 
logism (17). Other meanings of "formal" (18). Pages 519-532 

Additional Notes 533-534 

CHAPTER II 

THE CAUSE AND THE BECAUSE 

Is the middle the cause (i) ? Meaning of this term must be limited (2). 
The cause is known by reasoning, since it implies ideal reconstruc 
tion of the case (3-5). Futile to ask if cause comes from mere 
habit (6). Explanation not perception of intermediate detail (7-10). 

But the reason need not be the cause (n). Ambiguity of "because" 
(12). The psychical cause and the logical ground distinguished 
(13-14). The consequence not more complex than the cause or 
ground (15). Result (16) Pages 535-548 

Additional Notes 548-550 



CHAPTER III 

THE VALIDITY OF INFERENCE 

The question has two main senses, but can here receive no final answer 
(1-2). Is reasoning formally valid? Not if we have interfered to 
make the conclusion (3). Do we interfere in Synthetical Construc 
tion without elision (4-6), or with elision (7)? Is the process 
capricious in Comparison, etc. (8-10), and again in Abstraction (n- 
15) ? The Disjunctive Argument (16-20). Sceptical doubts (21-22). 
Result (23). 

Is a conclusive inference practicable? Question explained but not 
answered (24-25) Pages 55^-572 

Additional Notes . . 572-578 



XX11 CONTENTS 

CHAPTER IV 
THE VALIDITY OF INFERENCE (Continued) 

Is inference valid really as well as formally? Question stated (1-2). 
Inference seems not always true of things. Instance of Comparison. 
Three alternatives (3). Does reality change through our caprice, 
or in harmony, or does it merely somehow correspond? Unless we 
utterly revolutionize our beliefs, we must give up complete identity 
of logic and fact (4-7). 

Reasoning is never quite true of presented fact, since it must be dis 
cursive (7-11). Even Dialectic, because discursive, seems unreal 
(12). Nor, if logic answered to the known series of phenomena, 
need it even thus be true; for that series is not given but inferred. 
To be true of the presented logic must be true to sense, v/hich is 
impossible (13-15). 

Can we then, denying the truth of sense-presentation, take reality itself 
as logical truth? Another alternative opposes us, and our logic still 
may prove untrue (16). Yet why should truth and reality have 
exactly the same nature (17)? Anyhow logic can not copy phe 
nomena Pages S79-5QI 

Additional Notes 591-595 



TERMINAL ESSAYS 

ESSAY I 
ON INFERENCE (pp. 597~62l) 

Logic, order in (597). Conclusion to be reached as to Inference 

(597-8). 

I. Inference defined (598-600). What Logic must assume (600). Can 
the claim of Logic be in any case made good (601) ? 

II. Specimens of Inference examined (601-11). Dialectical Method 
(601-2). Disjunctive reasoning (602-3). Syllogism (603). Arith 
metic (603-5). Construction, spatial and temporal (605-7). Anal 
ysis and Abstraction (607-9). Comparison (609-11). 

III. Defects of the above as inferences (611). A further failure in 
all Logic is its abstraction from the psychical process. Different 
scopes of Logic and Psychology. Each of these sciences alike is 
independent but defective (611-13). 

IV. Is Inference arbitrary and unreal? Objections as to triviality and 
irrelevancy answered (614-16). But in what sense is Inference 
"real" (616-17)? 



CONTENTS XX111 

V. Fallibility of all inference. Intrusion of what is merely psycho 
logical (617). And the logical types themselves are imperfect (617- 
18). Nor is any complete code possible, nor any " formal" criterion. 
Individuality of inference (618-20). 

VI. The Criterion what. Use and object of Logic (619-21). 



ESSAY II 

ON JUDGMENT (pp. 622-641) 

Inference appears always as one kind of judgment, but not all judg 
ment seems essentially to be inference (622-3). But this is never 
theless to be maintained as true (623). 

All judgment implies and is inference, and a mere judgment is merely 
an abstraction (623-4). An objection answered (625-6). 

The meaning of "judgment" and "idea," like that of "inference," 
varies according to the level at which it is used. Hence "judg 
ment" has both a wider and a more restricted sense. But its 
essence remains always the same and is confined to logical truth 
(626). 

An object, so far as aesthetic, is not in this sense true (627-8). 

All judgment is selective, and yet the subject of every judgment is 
the real Universe. An error here noted (628). 

This duplicity of the subject in every judgment makes every judgment 
an inference already in principle (629-30). 

All judgment depends on abstraction from certain conditions of its 
own being. Even as having an object it already abstracts, and, again, 
its "real world" is a further abstraction (630-1). And judgment 
abstracts always from its own psychical existence (631-2). It thus 
depends throughout upon conditions upon a " because " which in 
form it ignores. And hence, except in form, every judgment is 
already an inference (632). 

Further all judgment is not only condition^ but is also conditiona/ 
(633). On Ground and Conditions. On the difference between 
"because" and "if." An objection answered (633-5). 

The meaning of "if" further explained. Meaning of "uncondition 
ally." How far does "conditionally" imply doubt (636-7)? On 
"supposal" and on "hypothetical" (637-8). 

Every judgment is conditional Ideal of knowledge, what No such 
fact as a mere judgment, though in practice, here as everywhere, 
the relative must more or less be taken as absolute (639-40). 

And, as no "mere judgment," so also no "mere idea." The reality is 
the concrete whole from which such things are abstractions. But 
in Logic the order of treatment is to some extent artificial and so 
optional (640-1). 



XXIV CONTENTS 



ESSAY III 

ON THE EXTENSIONAL READING OF JUDGMENTS 
(pp. 642-646) 

Every judgment can be read in intension, but no judgment can be 

read merely so. And the same thing holds (mutat. mutand.) as to 

extensional reading (642-3). 
Can, again, all judgment be taken as asserting or denying about some 

"individual" or "individuals"? Certainly not so, if "individual" 

is taken in its more ordinary sense (643). And the attempt to 

read thus all judgments involves torture (643-4). 
The possibility of taking any idea as one particular psychical event 

makes applicable a mode of torture which still remains in principle 

irrational (644-6). 



ESSAY IV 

UNIQUENESS (pp. 647-658) 

Uniqueness two aspects of, one (a) positive and the other (b) nega 
tive. But the second, even if perhaps always present, rests in any 
case on the first. An objection answered (647-8). 

Uniqueness is absolute or relative, and holds again either in principle 
or merely de facto (648-9). Positive uniqueness as absolute. 
Claims to its possession considered, (i) The Universe. (2) One 
single quality (650). (3) Qualities as many. A distinction is to 
be made here. The Many as mere particulars; but this is a false 
abstraction and not a given fact (650-2). Attempts to defend its 
claim (a) by external relations, and (b) by an appeal to Designation 
(652-3). (4) The "This." Certainly it offers itself as unique, but 
this claim holds only so long as we remain at the stage of Feel 
ing (653-4). And even there the character of the "This" is incon 
sistent and not self-contained, and hence the claim of the " This " 
fails (654-5). (5) Finite Individuals. Their claim to uniqueness 
must be allowed if you take them as members in and of a perfect 
System (655-6). On the other hand this claim cannot be verified 
completely in detail (656-7). Recapitulation (657-8). 



ESSAY V 
THE "THIS" (pp. 659-661) 

" This " is not specially a mark of external perception. Like " mine " 
and "now" it belongs to all Immediate Experience or Feeling 
generally (659). 

Can it as an idea be predicated beyond its actual self? Certainly it 



CONTENTS XXV 

can be so used, but it cannot be used beyond the Universe that is 
indivisibly one with itself (659-61). 



ESSAY VI 
THE NEGATIVE JUDGMENT (pp. 662-667) 

Every judgment is selective, and hence in consequence is in essence 
both negative and disjunctive (662). But explicitly it need not be 
so, since Judgment (like Inference) exists at diverse stages (662-3). 

All Judgment involves the principle of Alternative ; and the negation 
which it contains implies a positive ground on both sides, and a 
whole which is disjunctive and systematic (663-5). 

Negation is not "unreal" and "subjective." It is "real" always, 
though we may be unable to see how in detail it is so. And it 
never in truth can be merely "subjective" (665-6). The negative 
is more real than what is taken as barely positive, since mere posi 
tion and bare exclusion alike are unreal abstractions (666). 

All negation must qualify, though we may be unable to see in detail 
how precisely it does so. And no judgment anywhere, whether 
negative or positive, can really be bare and purposeless (666-7). 



ESSAY VII 

ON THE IMPOSSIBLE, THE UNREAL, THE SELF-CONTRADICTORY, 
AND THE UNMEANING (pp. 668-673) 

The Possible what. Its dangerous ambiguities. Its negative aspect. 
The Real in what sense "possible" (668-9). 

The Impossible what. Its difference from the Unreal. " Nothing " 
what (669-71). The Meaningless what (671). The Self -contra 
dictory what. How it is thinkable, and in what sense it can 
exist (671-2). 

How far can the above ideas be used in practice indiscriminately? 
Their ultimate reality what. They all consist in one-sided Ab 
straction, which for finite experience is necessary, but which in the 
ultimate concrete Reality is throughout made good (672-3). 



ESSAY VIII 

SOME REMARKS ON ABSOLUTE TRUTH AND ON PROBABILITY 
(pp. 674-690) 

No knowledge can rest on, or be affected by, the Unknown and by 
ignorance taken as mere Privation (674). Absolute and Relative 
Truth what. How a truth can be imperfect and yet absolute 
(674 T 5). 

Any objection to absolute truth on the ground of Probability is un- 



XXvi CONTENTS 

tenable (675-6). Proper and improper sense of Probability. The 
former assumes a world of such a kind that the possibility of an 
"otherwise" is in principle excluded (676-8). 

General objections to absolute truth. In these there is nothing positive 
which I on my side am unable to accept (678-9). This shown in 
the case (i) of Irrationalism (679-80), and (2) of Pluralism and 
Realism (680-4). So far as these differ from my view, is that 
difference really anything positive (680-1) ? A compromise through 
Relativism is not possible (681-2). But I can understand Realism 
and Pluralism as urging nothing positive which is not accepted and 
included in my view. And that view can explain the existence of 
these other views (682-4). Recapitulation (684). 

How can a lower and subordinate truth seem more probable than one 
admittedly higher? This difficulty calls for examination (684-5). 
An explanatory digression on higher and lower truths (685-6). 
The above difficulty comes mainly from a false assumption as to 
the superiority of the " real world " of events, and from the (per 
haps unconscious) misplacing of a higher truth on this misleading 
level (686-8). The above illustrated in two aspects (688-90). 



ESSAY IX 

A NOTE ON ANALYSIS (pp. 691-694) 

A fundamental issue avoided by the Realist (691). A mistaken 
dilemma. No relational view has ultimate truth (691). The "fact 
of relatedness" must be, and yet is not, dealt with (692). The 
empirical evidence against Analysis as yielding ultimate truth is 
ignored. Terms and relations are abstractions, and they never are 
given in immediate experience (693-4). 

The category of Whole and Parts is not everywhere applicable, nor is 
it ultimately valid (694). 



ESSAY X 

A NOTE ON IMPLICATION (pp. 695-698) 

There is no sense in Implication unless it is indirect and through a 
whole. And there is no Implication (proper) where or so far as 
the whole is merely immediate (695). 

The meaning of Implication rests on the fact of Immediate Experi 
ence. And all predication, being relational, is irrational except so 
far as conditional. Implication in the end is nonsense apart from 
that which is both below and above the discursive stage of mind 
and truth. No self-subsistent entity can imply another (695-7). 



CONTENTS XXVli 

Implication cannot be one-sided unless there is abstraction from or 
alteration of conditions (697). "A before B" is really reciprocal. 
Nor is there incompatibility between "before" and "after" except 
under some condition (698). 



ESSAY XI 
ON THE POSSIBLE AND THE ACTUAL (pp. 699-712) 

The enquiry limited. The Possible may be opposed in three senses to 

the Actual, according as that is (i) not grounded, or (n) grounded 

fully, or (in) both at once. The second sense is the main one (699). 

The above illustrated. There is only one genuine Individual (699- 

7oi). 
The Actual is not the same as what " exists," nor is it always based 

on Existence (701-2) ; nor is such a position saved by an appeal to 

the distinction between relative and absolute possibility (702-3). 

As against what is " imaginary," that which " exists " may be merely 

possible (703). 
And within the world of Truth the possible is still opposed to the 

actual (703-5)- Why Logic can not be consistent ultimately (705). 

Designation what (706). Recapitulation (706-7). Possible and 

Actual within a grounded whole (707). 
The above contrasted with an opposite view (707-10). The world as 

a mere "And" or "Together" of independent entities (708). But 

on any such view there is really no "world" at all, and possibility 

can have in the end no meaning (708-10). 
Reality and Truth their true relation stated (711-12). 



ESSAY XII 

ON THEORETICAL AND PRACTICAL ACTIVITY (pp. 713-728) 

There is no such thing as a mere theoretical or mere practical activity 
(713-14). All theoretical activity is also practical (714-15). And 
all practical activity has a theoretical side and contains an idea and 
a judgment (715)- 

This position explained and defended against some errors (716-17). 
(i) In Practice the judgment has different levels (717). (ii) But 
its essence is not to anticipate a future fact even if any reference 
at all to the future is essential (717-19). And any appeal here to a 
lower stage of experience is useless (719-20). Further, Judgment 
can not consist in a mere passage to the future (720-21). " Practice 
for practice sake" as a gospel. Recapitulation (721-2). 

How far and in what sense is the distinction of "theoretical" and 
"practical" legitimate and useful? The answer to this question 
explained and illustrated (722-4). Religion as the unity of one- 
sidednesses (724-5). 



XXV111 CONTENTS 

A summary statement of some views which I advocate on Truth, 
Activity, and Practice (725^8). Truth as Anticipation and Predic 
tion, and as Experiment and Verification (726-7). Philosophy, its 
limits and genuine task (727-8). 

INDEX . . . 729-739 



THE PRINCIPLES OF LOGIC 

BOOK I JUDGMENT 
CHAPTER I 

THE GENERAL NATURE OF JUDGMENT 

I. It is impossible, before we have studied Logic, to 
know at what point our study should begin. And, after we 
have studied it, our uncertainty may remain. In the absence of 
any accepted order I shall offer no apology for beginning with 
Judgment. If we incur the reproach of starting in the middle, 
we may at least hope to touch the centre of the subject. 1 

The present chapter will deal with the question of judgment 
in general. It will (i) give some account of the sense in which 
the term is to be used; it will (n) criticize, in the second place, 
a considerable number of erroneous views; and will end 
(in) with some remarks on the development of the function. 

I. In a book of this kind our arrangement must be arbi 
trary. The general doctrine we are at once to lay down, really 
rests on the evidence of the following chapters. If it holds 
throughout the main phenomena of the subject, while each 
other view is in conflict with some of them, it seems likely 
to be the true view. But it can not, for this reason, be put 
forward at first, except provisionally. 

Judgment presents problems of a serious nature to both 
psychology and metaphysics. Its relation to other psychical 
phenomena, their entangled development from the primary 
basis of soul-life, and the implication of the volitional with 
the intellectual side of our nature on the one hand, and on 
the other hand the difference of subject and object, and the 
question as to the existence of any mental activity, may be 
indicated as we pass. But it will be our object, so far as is 
possible, to avoid these problems. We do not mainly want 
to ask, How does judgment stand to other psychical states, 
and in ultimate reality what must be said of it. Our desire 

i 



2 THE PRINCIPLES OF LOGIC BOOK I 

is to take it, so far as we can, as a given mental function; 
to discover the general character which it bears, and further 
to fix the more special sense in which we are to use it. 

2. I shall pass to the latter task at once. Judgment, in 
the strict sense, does not exist where there exists no knowl 
edge of truth and falsehood; and, since truth and falsehood 
depend on the relation of our ideas to reality, you can not 
have judgment proper without ideas. And perhaps thus much 
is obvious. But the point I am going on to, is not so obvious. 
Not only are we unable to judge before we use ideas, but, 
strictly speaking, we can not judge till we use them as ideas 2 . 
We must have become aware that they are not realities, that 
they are mere ideas, signs of an existence other than them 
selves. Ideas are not ideas until they are symbols, and, 
before we use symbols, we can not judge. 

3. We are used to the saying, "This is nothing real, 
it is a mere idea." And we reply that an idea, within my 
head, and as a state of my mind, is as stubborn a fact as any 
outward object. The answer is well-nigh as familiar as the 
saying, and my complaint is that in the end it grows much too 
familiar. In England at all events we have lived too long 
in the psychological attitude 3 . We take it for granted and as 
a matter of course that, like sensations and emotions, ideas 
are phenomena. And, considering these phenomena as psy 
chical facts, we have tried (with what success I will not ask) 
to distinguish between ideas and sensations. But, intent on 
this, we have as good as forgotten the way in which logic 
uses ideas. We have not seen that in judgment no fact ever is 
just that which it means, or can mean what it is ; and we have 
not learnt that, wherever we have truth or falsehood, it is 
the signification we use, and not the existence. We never 
assert the fact in our heads, but something else which that fact 
stands for And if an idea were treated as a psychical reality, 
if it were taken by itself as an actual phenomenon, then it 
would not represent either truth or falsehood. When we use it 
in judgment, it must be referred away from itself. If it is not 
the idea of some existence, then, despite its own emphatic actu 
ality, its content remains but " a mere idea." It is a something 
which, in relation to the reality we mean, is nothing at all. 
4. For logical purposes ideas are symbols, and they are 



CHAP. I THE GENERAL NATURE OF JUDGMENT 3 

nothing but symbols. 4 And, at the risk of common-place, 
before I go on, I must try to say what a symbol is. 

In all that is we can distinguish two sides, (i) existence 
and (ii) content. In other words we perceive both that it is 
and what it is. But in anything that is a symbol we have 
also a third side, its signification, or that which it means 5 . We 
need not dwell on the two first aspects, for we are not con 
cerned with the metaphysical problems which they involve. 
For a fact to exist, we shall agree, it must be something. It 
is not real unless it has a character which is different or 
distinguishable from that of other facts. And this, which 
makes it what it is, we call its content. We may take as an 
instance any common perception. The complex of quali 
ties and relations it contains, makes up its content, or 
that which it is; and, while recognizing this, we recognize 
also, and in addition, that it is. Every kind of fact must 
possess these two sides of existence and content, and we 
propose to say no more about them here. 

But there is a class of facts which possess an other and 
additional third side. They have a meaning; and by a sign 
we understand any sort of fact which is used with a mean 
ing. The meaning may be part of the original content, 6 or 
it may have been discovered and even added by a further 
extension. Still this makes no difference. Take anything 
which can stand for anything else, and you have a sign. 
Besides its own private existence and content, it has this 
third aspect. Thus every flower exists and has its own 
qualities, but not all have a meaning. Some signify nothing, 
while others stand generally for the kind which they repre 
sent, while others again go on to remind us of hope or love. 
But the flower can never itself be what it means. 

A symbol is a fact which stands for something else, and 
by this, we may say, it both loses and gains, is degraded and 
exalted. In its use as a symbol it forgoes individuality, and 
self-existence. It is not the main point that this rose or 
forget-me-not, and none other, has been chosen. We give it, 
or we take it, for the sake of its meaning; and that may 
prove true or false long after the flower has perished. The 
word dies as it is spoken, but the particular sound of the 
mere pulsation was nothing to our minds. Its existence was 



4 THE PRINCIPLES OF LOGIC BOOK I 

lost in the speech and the significance. The paper and the 
ink are facts unique and with definite qualities. They are the 
same in all points with none other in the world. But, in 
reading, we apprehend not paper or ink, but what they 
represent; and, so long as only they stand for this, their 
private existence is a matter of indifference. A fact taken 
as a symbol ceases so far to be fact. It no longer can be 
said to exist for its own sake, its individuality is lost in its 
universal meaning. It is no more a substantive, but be 
comes the adjective that holds of another. But, on the 
other hand, the change is not all loss. By merging its own 
quality in a wider meaning, it can pass beyond itself and 
stand for others. It gains admission and influence in a world 
which it otherwise could not enter. The paper and ink cut the 
throats of men, and the sound of a breath may shake the world. 

We may state the sum briefly. A sign is any fact that 
has a meaning, and meaning consists of a part of the content 
(original or acquired), cut off, fixed by the mind, and con 
sidered apart from the existence of the sign.* 

5. I must be permitted at this point to make a digression, 
which the reader may omit, if he does not need it. Through 
out this volume I do not intend to use the word " symbol " 
as distinct from "sign," though there is a difference which 
elsewhere might become of importance. A symbol is certainly 
always a sign, but the term may be appropriated to signs of a 
very special character. In contrast with a symbol a sign may 
be arbitrary. It can not, of course, be devoid of meaning, for, 
in that case, it would be unable to stand for anything. But 
it may stand for that with which internally it is not con 
nected, and with which it has been joined by arbitrary chance. 
But even when signs have a natural meaning, when their 
content carries us direct to the object of which they are 
used, yet, if we take symbol in a narrow sense, a natural 
sign need not be a symbol. We may restrict the term to 

*It would not be correct to add, "and referred away to another 
real subject"; for where we think without judging, and where we 
deny, that description would not be applicable. Nor is it the same 
thing to have an idea, and to judge it possible. To think of a 
chimsera is to think of it as real, but not to judge it even possible. 
And it is not until we have found that all meaning must be adjectival, 
that with every idea we have even the suggestion of a real subject 
other than itself. 7 



CHAP. I THE GENERAL NATURE OF JUDGMENT 5 

secondary signs. For example a lion is the symbol of courage, 
and a fox of cunning, but it would be impossible to say that 
the idea of a fox stands for cunning directly. We mean by it 
first the animal called a fox, and we then use this meaning to 
stand as the sign for one quality of the fox. Just as the 
image or presentation of a fox is taken by us in one part of its 
content, and referred away to another subject, so this meaning 
itself suffers further mutilation : one part of its content is fixed 
by the mind and referred further on to a second subject, viz. the 
quality in general, wherever found. It makes no difference 
whether we begin with an image or a sensible perception, for 
the perception itself, before it can be used, must be taken 
ideally, recognized, that is, in one part of its content. And the 
distinction again between the symbolism that is unconscious, 
and that which is reflective, does not touch the main principle. 

In order to obviate possible objections, I have thought it 
best to make these remarks; but since I propose to use sign 
and symbol quite indifferently, the discussion has hardly any 
bearing on my argument. 

6. We might say that, in the end, there are no signs 
save ideas, but what I here wish to insist on, is that, for logic 
at least, all ideas are signs. Each we know exists as a 
psychical fact, and with particular qualities and relations. 
It has its speciality as an event in my mind. It is a hard 
individual, so unique that it not only differs from all others, 
but even from itself at subsequent moments. And this char 
acter it must bear when confined to the two aspects of ex 
istence and content. But just so long as, and because, it 
keeps to this character, it is for logic no idea at all. It be 
comes one first when it begins to exist for the sake of its 
meaning. And its meaning, we may repeat, is a part of the 
content, used without regard to the rest, or the existence. I 
have the " idea " of a horse, and that is a fact in my mind, 
existing in relation with the congeries of sensations and 
emotions and feelings, which make my momentary state. It 
has again particular traits of its own, which may be difficult 
to seize, but which, we are bound to suppose, are present. It 
is doubtless unique, the same with no other, nor yet with 
itself, but alone in the world of its fleeting moment. But, for 
logic, and in a matter of truth and falsehood, the case is 

2321. I B 



6 THE PRINCIPLES OF LOGIC BOOK I 

quite changed. The " idea " has here become an universal, 
since everything else is subordinate to the meaning. That con 
nection of attributes we recognize as horse, is one part of the 
content of the unique horse-image, and this fragmentary part 
of the psychical event is all that in logic we know of or care 
for. Using this we treat the rest as husk and dross, which mat 
ters nothing to us, and makes no difference to the rest. The 
" idea," if that is the psychical state, is in logic a symbol. But 
it is better to say, the idea is the meaning, for existence and un 
essential content are wholly discarded. The idea, in the sense 
of mental image, is a sign of the idea in the sense of meaning. 8 

7. These two senses of idea, as the symbol and the 
symbolized, the image and its meaning, are of course known 
to all of us. But the reason why I dwell on this obvious 
distinction, is that in much of our thinking it is systematically 
disregarded. " How can any one," we are asked, " be so 
foolish as to think that ideas are universal, when every single 
idea can be seen to be particular, or talk of an idea which 
remains the same, when the actual idea at each moment 
varies, and we have in fact not one identical but many 
similars ? " But how can any one, we feel tempted to reply, 
suppose that these obvious objections are unknown to us? 
When I talk of an idea which is the same amid change, I do 
not speak of that psychical event which is in ceaseless flux, 
but of one portion of the content which the mind has fixed, and 
which is not in any sense an event in time. I am talking of 
the meaning, not the series of symbols, the gold, so to speak, 
not the fleeting series of transitory notes. The belief in uni 
versal ideas does not involve the conviction that abstrac 
tions exist, even as facts in my head. The mental event is 
unique and particular, but the meaning in its use is cut off 
from the existence, and from the rest of the fluctuating 
content. It loses its relation to the particular symbol; it 
stands as an adjective, to be referred to some subject, but 
indifferent in itself to every special subject. 

The ambiguity of " idea " may be exhibited thus. Thesis, 
On the one hand no possible idea can be that which it means. 
Antithesis, On the other hand no idea is anything but just 
what it means. In the thesis the idea is the psychical image ; 
in the antithesis the idea is the logical signification. In the 



CHAP. I THE GENERAL NATURE OF JUDGMENT 7 

first it is the whole sign, but in the second it is nothing but 
the symbolized. In the sequel I intend to use idea mainly in 
the sense of meaning* 

8. For logical purposes the psychological distinction of 
idea and sensation may be said to be irrelevant, while the 
distinction of idea and fact is vital. The image, or psycho 
logical idea, is for logic nothing but a sensible reality. It 
is on a level with the mere sensations of the senses. For 
both are facts and neither is a meaning. Neither is cut 
from a mutilated presentation, and fixed as a connection. 
Neither is indifferent to its place in the stream of psychi 
cal events, its time and relations to the presented congeries. 
Neither is an adjective to be referred from its existence, to 
live on strange soils, under other skies and through chang 
ing seasons. The lives of both are so entangled with their 
environment, so one with their setting of sensuous particulars, 
that their character is destroyed if but one thread is broken. 
Fleeting and self -destructive as is their very endurance, 
wholly delusive their supposed individuality, misleading and 
deceptive their claim to reality, yet in some sense and some 
how they are. They have existence; they are not thought 
but given.f But an idea, if we use idea of the meaning, is 
neither given nor presented but is taken. It can not as 
such exist. It can not ever be an event, with a place in the 
series of time or space. It can be a fact no more inside our 
heads than it can outside them. And, if you take this mere 

* There are psychological difficulties as to universal ideas, and we 
feel them more, the more abstract the ideas become. The existence 
and the amount, of the particular imagery or sensuous environment, 
give rise to questions. But these questions need not be considered 
here, for they have no logical importance whatever. I assume, after 
Berkeley, that the mental fact contains always an irrelevant sensuous 
setting, however hard it may be to bring this always to consciousness. 
But I must repeat that this is not a vital question. It is a mistake in 
principle to try to defend the reality of universals by an attempt to 
show them as psychical events existing in one moment. For if the 
universal we use in logic had actual existence as a fact in my mind, 
at all events I could not use it as that fact. You must at any rate 
abstract from the existence and external relations, and how much 
further the abstraction is to go seems hardly an important or vital 
issue. 

fThis statement is subject to correction by Chapter II. 9 



8 THE PRINCIPLES OF LOGIC BOOK I 

idea by itself, it is an adjective divorced, a parasite cut loose, a 
spirit without a body seeking rest in another, an abstraction 
from the concrete, a mere possibility which by itself is nothing. 

9. These paradoxical shadows and ghosts of fact are 
the ideas we spoke of, when we said, Without ideas no judg 
ment; and, before we proceed, we may try to show briefly 
that in predication we do not use the mental fact, but only 
the meaning. The full evidence for this truth must however 
be sought in the whole of what follows. 

(i) In the first place it is clear that the idea, which we use 
as the predicate of a judgment, is not my mental state as 
such. " The whale is a mammal " does not qualify real whales 
by my mammal-image. For that belongs to me, and is an 
event in my history; and, unless I am Jonah, it can not enter 
into an actual whale. We need not dwell on this point, for 
the absurdity is patent. If I am asked, Have you got the 
idea of a sea-serpent? I answer, Yes. And again, if I am 
asked, But do you believe in it, Is there a sea-serpent? I 
understand the difference. The enquiry is not made about 
my psychical fact. No one wishes to know if that exists 
outside of my head; and still less to know if it really exists 
inside. For the latter is assumed, and we can not doubt it. 
In short the contention that in judgment the idea is my own 
state as such, would be simply preposterous. 

(ii) But is it possible, secondly, that the idea should be 
the image, not indeed as my private psychical event, but still 
as regards the whole content of that image? We have a 
mental fact, the idea of mammal. Admit first that, as it 
exists and inhabits my world, we do not predicate it. Is there 
another possibility? The idea perhaps might be used apart 
from its own existence, and in abstraction from its relations 
to my psychical phenomena, and yet it might keep, without any 
deduction, its own internal content. The " mammal " in my 
head is, we know, not bare mammal, but is clothed with par 
ticulars and qualified by characters other than mammality ; and 
these may vary with the various appearances of the image.* 
* I may point out that, even in this sense, the idea is a product of 
abstraction. Its individuality (if it has such) is conferred on it by 
an act of thought. It is given in a congeries of related phenomena, 
and, as an individual image, results from a mutilation of this fact 
(Vid. inf. Chap. II.). 



CHAP. I THE GENERAL NATURE OF JUDGMENT 9 

And we may ask, Is this whole, image used in judgment? 
Is this the meaning? But the answer must be negative. 

We have ideas of redness, of a foul smell, of a horse, and 
of death; and, as we call them up more or less distinctly, 
there is a kind of redness, a sort of ofTensiveness, some image 
of a horse, and some appearance of mortality, which rises 
before us. And should we be asked, Are roses red? Has 
coal gas a foul smell ? Is that white beast a horse ? Is it true 
that he is dead ? we should answer, Yes, our ideas are all true, 
and are attributed to the reality. But the idea of redness may 
have been that of a lobster, of a smell that of castor-oil, the 
imaged horse may have been a black horse, and death perhaps 
a withered flower. And these ideas are not true, nor did 
we apply them. What we really applied was that part of their 
content which our minds had fixed as the general meaning. 

It may be desirable (as in various senses various writers 
have told us) that the predicate should be determinate, but 
in practice this need can not always be satisfied. I may 
surely judge that a berry is poisonous, though in what way 
I know not, and though " poisonous " implies some traits 
which I do not attribute to this poison. I surely may believe 
that AB is bad, though I do not know his vices, and have 
images which are probably quite inapplicable. I may be sure 
that a book is bound in leather or in cloth, thought the sort 
of leather or cloth I must imagine I can not say exists. 
The details I have never known, or at any rate, have forgot 
ten them. But of the universal meaning I am absolutely 
sure, and it is this which I predicate. 

The extreme importance of these obvious distinctions 
must excuse the inordinate space I allot to them. Our whole 
theory of judgment will support and exemplify them; but I 
will add yet a few more trivial illustrations. In denying that 
iron is yellow, do I say that it is not yellow like gold, or 
topaze, or do I say that it is not any kind of yellow? When 
I assert, " It is a man or a woman or a child," am I reasonably 
answered by, " There are other possibilities. It may be an 
Indian or a girl " ? When I ask, Is he ill ? do I naturally look 
for " Oh no, he has cholera "? Is the effect of, " If he has 
left me then I am undone," removed by " Be happy, it was 
by the coach that he deserted you " ? 



IO THE PRINCIPLES OF LOGIC BOOK I 

The idea in judgment is the universal meaning; it is not 
ever the occasional imagery, and still less can it be the whole 
psychical event. 

10. We now know what to understand by a logical idea, 
and may briefly, and in anticipation of the sequel, dog 
matically state what judgment does with it. We must avoid, 
so far as may be, the psychological and metaphysical dif 
ficulties that rise on us. 

Judgment proper is the act which refers an ideal content 
(recognized as such) to a reality beyond the act. 10 This 
sounds perhaps much harder than it is. 

The ideal content is the logical idea, the meaning as just 
defined. It is recognized as such, when we know that, by 
itself, it is not a fact but a wandering adjective 11 . In the act 
of assertion we transfer this adjective to, and unite it with, a 
real substantive. And we perceive at the same time, that 
the relation thus set up is neither made by the act, nor merely 
holds within it or by right of it, but is real both independent 
of and beyond it.* 

If as an example we take once more the sea-serpent, we 
have an idea of this but so far no judgment. And let us 
begin by asking, Does it exist ? Let us enquire if " it exists " 
is really true, or only an idea. From this let us go on, and 
proceed to judge " The sea-serpent exists." In accomplish 
ing this what further have we done? And the answer is, 
we have qualified the real world by the adjective of the sea- 
serpent, and have recognized in the act that, apart from our 
act, it is so qualified. By the truth of a judgment we mean 
that its suggestion is more than an idea, that it is fact or 
in fact. We do not mean, of course, that as an adjective 
of the real the idea remains an indefinite universal. The sea- 
serpent, if it exists, is a determinate individual; and, if we 
knew the whole truth, we should be able to state exactly how 
it exists. Again when in the dusk I say, That is a quadruped, 
I qualify the reality, now appearing in perception, by this uni 
versal, while the actual quadruped is, of course, much besides 
four legs and a head. But, while asserting the universal, I do 

* I may remark that I am dealing at present only with affirmation ; 
the negative judgment presents such difficulties that it can hardly be 
treated by way of anticipation. 



CHAP. I THE GENERAL NATURE OF JUDGMENT II 

not mean to exclude its unknown speciality. Partial ignorance 
need not make my knowledge fallacious, unless by a mistake 
I assert that knowledge as unconditional and absolute 12 . 

" Are the angles of a triangle equal to two right angles? " 13 
" I doubt if this is so," " I affirm that this is so." In these 
examples we have got the same ideal content; the suggested 
idea is the relation of equality between the angles of a 
triangle and two right angles. And the affirmation, or judg 
ment, consists in saying, This idea is no mere idea, but is a 
quality of the real. The act attaches the floating adjective to 
the nature of the world, and, at the same time, tells me it was 
there already. The sequel, I hope, may elucidate the fore 
going, but there are metaphysical problems, to which it gives 
rise, that we must leave undiscussed. 

ii. In this description of judgment there are two points 
we may at once proceed to notice. The reader will have 
observed that we speak of a judgment asserting one idea, or 
ideal content, and that we make no mention of the subject 
and copula. The doctrine most prevalent, on the other hand, 
lays down that we have always two ideas, and that one is 
the subject. But on both these heads I am forced to dis 
sent. Our second chapter will deal further with the question, 
but there are some remarks which may find a place here. 

(i) It is not true that every judgment has two ideas. We 
may say on the contrary that all have but one. 14 We take an 
ideal content, a complex totality of qualities and relations, 
and we then introduce divisions and distinctions, and w r e call 
these products separate ideas with relations between them. 
And this is quite unobjectionable. But what is objectionable, 
is our then proceeding to deny that the whole before our 
mind is a single idea; and it involves a serious error in 
principle. The relations between the ideas are themselves ideal. 
They are not the psychical relations of mental facts. They do 
not exist between the symbols, but hold in the symbolized. 
They are part of the meaning and not of the existence. And 
the whole in which they subsist is ideal, and so one idea. 

Take a simple instance. We have the idea of a wolf and 
we call that one idea. We imagine the wolf eating a lamb, 
and we say, There are two ideas, or three, or perhaps even 
more. But is this because the scene is not given as a whole? 



I2 THE PRINCIPLES OF LOGIC BOOK I 

Most certainly not so. It is because in the whole there exist 
distinctions, and those groupings of attributes we are ac 
customed to make. But, if we once start on this line and 
deny the singleness of every idea which embraces others, we 
shall find the wolf himself is anything but one. He is the 
synthesis of a number of attributes, and, in the end, we shall 
find that no idea will be one which admits any sort of dis 
tinction in itself. Choose then which you will say, There are 
no single ideas, save the ideas of those qualities which are too 
simple to have any distinguishable aspects, and that means 
there are no ideas at all or, Any content whatever which 
the mind takes as a whole, however large or however small, 
however simple or however complex, is one idea, and its 
manifold relations are embraced in an unity.* 

We shall always go wrong unless we remember that the 
relations within the content of any meaning, however complex, 
are still not relations between mental existences. There is a 
wolf and a lamb. Does the wolf eat the lamb? The wolf eats 
the lamb. We have a relation here suggested or asserted 
between wolf and lamb, but that relation is (if I may use the 
word) not a factual connection between events in my head. 
What is meant is no psychical conjunction of images. Just 
as the idea of the wolf is not the whole wolf-image, nor the 
idea of the lamb the imagined lamb, so the idea of their syn 
thesis is not the relation as it exists in my imagination. In 
the particular scene, which symbolizes my meaning, there are 
details that disappear in the universal idea, and are neither 
thought of nor enquired after, much less asserted. 

To repeat the same thing the imagery is a sign, and the 
meaning is but one part of the whole, which is divorced from 
the rest and from its existence. In this ideal content there are 
groups and joinings of qualities and relations, such as answer 
to nouns and verbs and prepositions. But these various ele 
ments, though you are right to distinguish them, have no valid 
ity outside the whole content. That is one idea, which contains 

* The psychological controversy as to the number of ideas we can 
entertain at once, can hardly be settled till we know beforehand what 
is one idea. If this is to exclude all internal complexity, what residuum 
will be left? But, if it admits plurality, why is it one idea? If, 
however, what otherwise we should call plurality, we now call single 
just because we have attended to it as one, the question must clearly 
alter its form. 15 



CHAP. I THE GENERAL NATURE OF JUDGMENT 13 

all ideas which you are led to make in it; for, whatever is 
fixed by the mind as one, however simple or complex, is but 
one idea. But, if this is so, the old superstition that judg 
ment is the coupling a pair of ideas must be relinquished. 

12. I pass now (ii) to the other side of this error, the 
doctrine that in judgment one idea is the subject, and that 
the judgment refers another to this. In the next chapter this 
view will be finally disposed of, but, by way of anticipation, 
we may notice here two points, (a) In " wolf eating lamb " 
the relation is the same, whether I affirm, or deny, or doubt, 
or ask 16 . It is therefore not likely that the differentia of 
judgment will be found in what exists apart from all judg 
ment. The differentia will be found in what differences the 
content, as asserted, from the content as merely suggested. So 
that, if in all judgment it were true that one idea is the subject 
of the assertion, the doctrine would be wide of the essence 
of the matter, and perhaps quite irrelevant. But (b) the doc 
trine (as we shall see hereafter) is erroneous. " B follows 
A," " A and B coexist," " A and B are equal," " A is south 
of B " in these instances it is mere disregard of facts which 
can hold to the doctrine. It is unnatural to take A or B as 
the subject and the residue as predicate. And, where exist 
ence is directly asserted or denied, as in, " The soul exists," 
or, " There is a sea-serpent," or, " There is nothing here," 
the difficulties of the theory will be found to culminate. 

I will anticipate no further except to remark, that in every 
judgment there is a subject of which the ideal content is 
asserted. But this subject of course can not belong to the 
content or fall within it, 17 for, in that case, it would be the 
idea attributed to itself. We shall see that the subject is, 
in the end, no idea but always reality; and, with this antici 
pation, we must now go forward, since we have finished the 
first division of this chapter. We must pass from the general 
notion of judgment to the criticism of certain erroneous 
views, a criticism, however, which is far from exhaustive, 
and in some points must depend for its fuller evidence upon 
the discussions of the following chapters. 

II. 13. Wrong theories of judgment naturally fall into 
two classes, those vitiated by the superstition of subject, 



!4 THE PRINCIPLES OF LOGIC BOOK I 

predicate and copula, and those which labour under other 
defects. We will take the last first. 

(i) Judgment is neither the association of an idea with a 
sensation, nor the liveliness or strength of an idea or ideas. 
At the stage we have reached, we need subject these views to 
no detailed examination. The ideas which they speak of are 
psychical events, whereas judgment, we have seen, has to do 
with meaning, an ideal content which is universal, and which 
assuredly is not the mental fact. While all that we have is a 
relation of phenomena, a mental image, as such, in juxta 
position with or soldered to a sensation, we can not as yet 
have assertion or denial, a truth or a falsehood. We have 
mere reality, which is, but does not stand for anything, and 
which exists, but by no possibility could be true. 

We will not anticipate the general discussion of " Asso 
ciation " (vid. Book II. Part II. Chap. I.), and will pass by 
those extraordinary views the school holds as to universals. 
We will come at once to the result. There is an idea, in the 
sense of a particular image, in some way conjoined with or 
fastened to a sensation. I have, for instance, sensations of 
coloured points; and images of movement and hardness and 
weight are " called up " by these sensations, are attracted to, 
and cohere with them. And this sounds very well till we 
raise certain difficulties. An orange presents us with visual sen 
sations, and we are to add to these the images just mentioned. 
But each of these images is a hard particular, and qualified 
by relations which exclude it from all others. If you simply 
associate this bundle of facts, who would take them as one 
fact ? But if you blend their content, if, neglecting the exist 
ence, you take a part of the quality of each, and transfer that 
to the object, then you may call your process by what name you 
please, but it certainly is not association (Vid. infr. Book II.) . 

But let us suppose that the ideas are united somehow 
with the sensation, yet where is the judgment, where is truth 
or falsehood? The orange is now before my sense or imagi 
nation. For my mind it exists, and there is an end of it. 
Or say, " Caesar will be angry." Caesar here is the percep 
tion, which, when further qualified, becomes " Caesar angry." 
But this image again is simply what it is, it does not stand for 
anything, and it can mean nothing. 



CHAP. I THE GENERAL NATURE OF JUDGMENT 15 

Let us suppose in the first place that the " idea " main 
tains itself, then no doubt, as one fact, it stands in mental 
relation with the fact of the sensation. The two phenomena 
coexist as a headache may coexist with a syllogism; but such 
psychical coherence is far from assertion. There is no affirma 
tion; and what is there to affirm? Are we to assert the 
relation between the two facts? But that is given, and either 
to assert it or deny it would be senseless.* Is one fact to 
be made the predicate of another fact? That seems quite 
unintelligible. If in short both sensation and idea are facts, 
then not only do we fail to find any assertion, but we fail to 
see what there is left to assert. 

But in the second place (giving up association proper) 
let us suppose that the " idea," as such, disappears, and that its 
mutilated content is merged in the sensation. In this case the 
whole, produced by blending, comes to my mind as a single 
presentation. But where is the assertion, the truth or false 
hood ? We can hardly say that it lies in the bare presentation 
itself. We must find it, if anywhere, in the relation of this 
presentation to something else. And that relation would be 
the reference of judgment. But on the present view both the 
something else and the reference are absent. We have first 
an unmodified and then a modified sensation. 

The only way to advance would be to suppose, in the first 
place, that, while the " idea " maintains itself, it is dis 
tinguished from its content; and to suppose, in the second 
place, that both of these are distinguished from the sensation. 
We have then two facts, a sensation and an image, and beside 
these a content held apart from the image. We have now 
reached a condition which would make judgment possible, 
but the advance to this condition is not explicable by Associa 
tion. Nor could the further steps be accounted for. You have 
the transference of the content from the image to the sensa 
tion, and the qualification of the latter as a subject; but both 
would be inexplicable. We may add that it is impossible for 
a sensation or sensations to serve as the subject in every 
judgment (vid. Chap. II.). And finally the consciousness 
that, what my act joins, is joined apart from it, is a fact not 

*We might say that, on this view, the denial of a falsehood must 
ipso facto be false. 



j5 THE PRINCIPLES OF LOGIC BOOK I 

compatible with the psychology we are considering 1 . To sum 
up the whole to merge the content of an image in a modi 
fied presentation, is but one step towards judgment, and 
it is a very long step beyond association: while conjunction 
or coherence of psychical phenomena is not only not judg 
ment, but would not serve as its earliest basis and beginning.* 
14. But the definition, I shall be told, is a "lively idea 
associated with a present impression," and I shall be asked if 
lively makes no difference. And I answer, Not one particle ; 
it makes no difference even if you suppose it true, and in 
addition it is false. The liveliness removes none of the 
objections we have been developing. Let it be as lively as 
you please, it is a mere presentation, and there is no judg 
ment. The liveliness of the idea not only is not judgment, but 
it is not always even a condition. The doctrine that an idea 
judged true must be stronger than one not so judged, will not 
bear confrontation with the actual phenomena. You may go 
on to increase an idea in strength till it passes into a sensa 
tion, and there yet may be no judgment. I will not dwell 
on this point, since the unadulterated facts speak loudly for 
themselves, but will give one illustration. We most of us 
have at times the images of the dead, co-inhabitants of the 
rooms we once shared with the living. These images, mostly 
faint, at times become distressing, from their strength and 
particularity and actual localization in those parts of the 
room which we do not see. In an abnormal state such images, 
it is well known, may become hallucinations, and take their 
place in the room before our eyes as actual perceptions. But 
with an educated man they would be recognized as illusions, 
and would not be judged to be outwardly real, any more than 
the fainter and normal images are judged to be anywhere 
but in our own minds. Yet lively ideas associated with present 

* It has been often remarked that, on Hume s theory of belief, there 
can be no difference between imagination and reality, truth and false 
hood, and that why we make this difference is incomprehensible. J. S. 
Mill with great openness professed on this head the total bankruptcy 
of the traditional doctrine. He seems somehow to have thought that 
a complete break-down on a cardinal point was nothing against the 
main doctrine of his school, nor anything more than a somewhat 
strange fact. It was impossible that he should see the real cause of 
failure. We shall deal with Professor Bain s views lower down. 



CHAP. I THE GENERAL NATURE OF JUDGMENT 17 

impressions if we have not got them here, where are they? 

15. We turn with relief from the refutation of a doctrine, 
long dead and yet stubbornly cumbering the ground, to con 
sider a fresh error, the confusion of judgment with practical 
belief. I cannot enquire how far any psychical activity is 
consistent with the theory of Professor Bain, nor can I dis 
cuss the nature of a psychical activity which seems physiolog 
ically to consist in muscular innervation; though I am bound 
to add that (doubtless owing to my ignorance) Professor 
Bain s physiology strikes me here as being astonishingly misty. 
And I must pass by the doubt whether, if we accept his view, 
we shall find the confusion between image and meaning in 
any way lessened 19 . 

We must remember that the question, Is judgment always 
practical, does not mean, Is the will in any way concerned in 
it. In that case it might be argued that all generation of 
psychical phenomena comes under the head Will. The ques 
tion means, Does the essence of judgment lie, not in the 
production of truth and falsehood states which alter nothing 
in the things they represent but rather in the actual produc 
tion of a change in real existence. Or, more simply, when an 
idea is judged to be true, does this mean that it moves some 
other phenomenon, and that its assertion or denial is nothing 
but this motion? The doctrine admits that an idea or ideas, 
when held true, differ vitally from the same when suggested; 
and it proceeds to assert that the differentia is the effect of the 
idea on our conduct, and that there is no other differentia at all. 

There is a logical mistake we may point out before pro 
ceeding, for it is the error which has led Professor Bain astray. 
Assume that an asserted idea causes action, and that an idea, 
not believed in, does not influence conduct. From these 
premises can we conclude, Therefore judgment is influence? 
If, in other words, when A changes to B, we have an unfailing 
difference q, and q is not found except after A, does this war 
rant the assertion, that the alteration consists in q ? Is it not 
quite possible that q follows from p, and that p is what really 
turns A into B ? We shall do well to keep our eye on this logi 
cal fallacy. The assertion we are to examine is not that prac 
tical influence induces us to judge, or results from a judgment : 
What is asserted is that judgment is nothing else whatever. 



l8 THE PRINCIPLES OF LOGIC BOOK I 

Against this false differentia I shall briefly maintain, (o) 
that the differentia may be absent from the fact, (b) that it 
may be present with other facts, (c) that the fact contains 
other characteristics, which are the true differentia, and are 
absent from the false one, (d) that the latter has a positive 
quality which. excludes the fact. 

(a) If we test the theory by abstract instances such as, 
The angles of a triangle are equal to two right angles, it 
collapses at once. It is impossible to find always a practical 
influence exerted by the ideas. We may be answered " But 
they might exert it, you surely would act on them." And 
such an answer may pass in the school of " Experience " ; but 
a poor " transcendentalist " will perhaps be blamed if he 
usurps such a privilege. He at least is not allowed to take 
tendency and possibility and mere idea for fact. And he can 
hardly be prevented from pressing the question, Is the influence 
there or not? If it is not there, then either Professor Bain s 
theory disappears, or he should alter his definition, and say that 
an idea passes into a judgment when enriched by potentialities 
and eventual tendencies 20 . If these are not ideas we should be 
told what they are ; but if they are only ideas that go with the 
first ideas, then our answer is plain. In the first place it is not 
true that they are always there; in the second place it is not 
true that, when added, they must exert a practical influence. 

(b) In the second place ideas may influence me, though I 
never do hold them for true. The feelings and emotions 
associated with an idea can often prevent or produce volitions, 
although the idea is not affirmed as true, and even while it is 
recognized as false. . Though I do not believe that a slow- 
worm can bite, or a drone can sting, I may shrink from 
touching them. I may avoid a churchyard though I believe 
in no ghosts. An illusion no doubt, if recognized as such, 
does not influence volition either so much, or always in the 
same way; but still it may operate in spite of disbelief.* 
And it can hardly be a true view which forces us to say, If 
you judged it an illusion you would wholly disregard it, for 
such disregard is judgment. 

* It may be said that when it operates the denial is suspended. But 
I confess I can find no ground for such a statement. At any rate it 
is certain that the idea can operate though a positive judgment is not 
there. 



CHAP. I THE GENERAL NATURE OF JUDGMENT 1 9 

I will not dwell on a point it would be easy to illustrate. 
In passing, however, I may remind the reader of that class of 
ideas which influences our actions without seeming to be true. 
I refer to practical ideas, the representation of a satisfied 
desire which is now felt to be unsatisfied. It is certain that 
these move us to active pursuit, and it is equally certain they 
are not judged to be real 21 ; for, if they were, then for that 
reason they would fail to move us.* 

(c) But suppose that all judgment did really move to 
action. Would this show that judgment was nothing but 
such motion? Most certainly not so. We can observe what 
takes place in us, when a suggested idea is judged to be 
true; and clearly an activity (however hard to describe) does 
show itself there, and yet is not directed (except per accidens) 
towards making a change in the world and in ourselves. 
And if this true differentia can be verified, that should settle the 
question 22 . And again, apart from direct observation, we can 
argue indirectly. Assertion and denial, together with the dif 
ference of truth and falsehood, are real phenomena, and there 
is something in them which falls outside the influence of ideas 
on the will. It is comic if the judgment, It will rain to-morrow, 
is the same as buying an umbrella to-day ; or, Put on your thick 
boots, is a truer form of, It rained hard yesterday. And when 
a child sees a berry and, as we say, judges, It made me sick 
before, it seems strange that the act of affirmation should con 
sist in practical abstention to-day and should be nothing else. 

(d) And not only are the genuine characteristics absent 
from a mere practical attitude, but we find present there a qual 
ity which is absent from real judgment. The truth of a sug 
gestion is not a matter of degree, and the act which attributes 
an idea to reality either refers it, or does not refer it. It can 
hardly do either a little more or less and to a certain degree 
(cf. Chap. VII.). In strictness of speech all half-truths are no 
truths, and, " It is more or less true," really means, " It is true 
with a qualification," or " More or less of it is true, though as a 
whole it is not true." But the practical influence of ideas must 
have degree, and so possess a quality which judgment has not. 

For these reasons, each of which can stand almost alone, 
it seems clear that the doctrine before us has failed. And 
* I may refer on this point to my Ethical Studies, Essay VII. 



20 THE PRINCIPLES OF LOGIC BOOK I 

one cause of the error seems to lie in the neglect of some 
important distinctions we may proceed to notice. Judgment 
is primarily logical, and as such has no degrees; the relation 
of the ideal content to reality must be there or not there. 
Belief, on the other hand, is primarily psychological, and, 
whether theoretic or practical, exists in a degree, (a) Intel 
lectual belief or conviction is the general state which corre 
sponds to the particular acts of judgment. To believe that A 
is B may mean that, whenever the idea A B is suggested, I 
go on to affirm it ; or, further, that the idea fills much space in 
my mind, is a persistent habit and ruling principle, which 
dominates my thoughts and fills my imagination, so that the 
assertion A B is frequently made and has wide intellectual 
ramifications and connections. I should believe A B less, if 
it more seldom arose, by itself or by implication, and had in 
ferior influence. I should believe less still if, when A B was 
suggested, I sometimes doubted it; and even less, if I affirmed 
it more seldom, and then with hesitation, against doubts, and 
with inability to maintain the attitude. On the other hand I 
should not believe at all, if I only were more or less convinced, 
perceiving more or less reason on both sides, inclined in one 
direction, but unable to cross the line and to affirm, (b) But 
in practical belief, beside these degrees of intellectual convic 
tion, there is another element of more and less. Not only is 
the truth of the intellectual content more or less present, but 
in addition it can influence my will more or less. A desire 
stronger or more persistent, or more dominant generally, may 
answer to it on the one side, or on the other a weaker and 
more fleeting impulse. Beside existing more or less, it can 
move more or less. It is, I think, not easy to keep clear of con 
fusion unless these ambiguities are noticed and avoided. But 
the main logical mistake which Professor Bain has committed 
is to argue from the (false) premise, " Belief must induce ac 
tion," to the inconsequent result " Belief is that inducement." * 

* In the third edition of his Emotions (1875) Prof. Bain apparently 
reconsiders the question, but I can neither tell if he abandons his 
theory, nor what it is that, if so, he puts in its place. As I am entirely 
unable to understand this last theory, my remarks must be taken to 
apply to the earlier one. Since this volume was written I have made 
acquaintance with Mr. Sully s criticism on Prof. Bain s doctrine (Sensa- 



CHAP. I THE GENERAL NATURE OF JUDGMENT 21 

1 6. (ii) Leaving now the first group of erroneous views 
we may proceed to consider another collection. These may 
be classed as labouring under a common defect, the false 
notion that in judgment we have a pair of ideas. We were 
engaged with this fallacy in n, and it will meet us again in 
the following chapter, so that here some brief remarks may 
suffice. In their ordinary acceptation the traditional subject, 
predicate, and copula are mere superstitions 24 . The ideal 
matter which is affirmed in the judgment, no doubt possesses 
internal relations, and in most cases (not all) the matter may 
be arranged as subject and attribute 25 . But this content, we 
have seen, is the same both in the assertion and out of it 26 . If 
you ask instead of judging, what is asked is precisely the 
same as what is judged. So that it is impossible that this 
internal relation can itself be the judgment ; it can at best be 
no more than a condition of judging. We may say then, if 
the copula is a connection which couples a pair of ideas, it 
falls outside judgment; and, if on the other hand it is the sign 
of judgment, it does not couple. Or, if it both joined and 
judged, then judgment at any rate would not be mere joining. 
I will dwell here no more on the general error. We shall see 
its effects in some mistaken views we may proceed to notice. 

(a) Judgment is not inclusion in, or exclusion from, a 
class. The doctrine that in saying, " A is equal to B," or " B 
is to the right of C," or " To-day precedes Monday," I have in 
my mind a class, either a collection or a description, of " things 
equal to B," or " to the right of C," or " preceding Monday," 
is quite opposed to fact. It is as absurd as the assertion that, 
in " It is our son John," or " It is my best coat," or " 9 = 7 + 
2," I think of a class of " our sons John," or " my best coats," 
or " that which is equal to 7 + 2." If the view stood apart 
from implied preconceptions, and by itself as an interpreta 
tion of fact, it would scarcely, I think, be so much as discussed. 
And, as we shall be forced to recur to it hereafter (Chap. VI.), 
we may so leave it here. 

lion and Intuition, 2nd ed. 1880). But he, I find, treats Prof. 
Bain s third edition (1875), in which an earlier edition of his own 
criticism is treated with the greatest respect, as if it either had no 
existence, or at all events was somehow irrelevant to the issue. For 
myself I must say that for the reason given above I confine myself 
to the earlier theory. 23 

2321. i c 



22 THE PRINCIPLES OF LOGIC BOOK I 

(b) Judgment is not inclusion in, or exclusion from, the 
subject. By the subject I mean here not the ultimate subject, 
to which the whole ideal content is referred, but the subject 
which lies within that content, in other words the grammatical 
subject. In " A is simultaneous with B," " C is to east of 
D," "E is equal to F," it is unnatural to consider A, C, 
and E as sole subjects, and the rest as attributive. It is 
equally natural to reverse the position, and perhaps more 
natural still to do neither, but to say instead, " A and B are 
synchronous," " C and D lie east and west," " E and F are 
equal." The ideal complex, asserted or denied, no doubt in 
most cases will fall into the arrangement of a subject with 
adjectival qualities, but in certain instances, and those not a 
few, the content takes the form of two or more subjects 
with adjectival relations existing between them. I admit you 
may torture the matter from the second form into the first, but, 
if torture is admitted, the enquiry will become a mere struggle 
between torturers. It requires no great skill to exhibit every 
subject together with its attributes as the relation between 
independent qualities (subjects), or again even to make that 
relation the subject, and to predicate all the remainder as an 
attribute. Thus, in " A is simultaneous with B," it is as easy 
to call " exists in the case of AB " an attribute of simultaneity, 
as it is to call " simultaneous with B " an attribute of A. We 
may finally observe that existential judgments do not lend 
themselves easily to the mistake we are considering. And 
such negative judgments as " Nothing is here," will be found 
hard to persuade. But on both these points I must refer to 
the sequel (Chaps. II. and III.J. 

(c) Judgment is not the assertion that subject and predi 
cate are identical or equal. This erroneous doctrine is the 
natural result of former errors. You first assume that in 
judgment we have a relation between two ideas, and then go 
on to assume that these ideas must be taken in extension. 
But both assumptions are vicious; and, if we consider the 
result, asking not if it is useful but whether it is true, we can 
hardly, I think, remain long m hesitation. That in " You are 
standing before me," or " A is north of C," or " B follows D," 
what we really mean is a relation either of equality or 
identity is simply incredible; and torture of the witness goes 



CHAP. I THE GENERAL NATURE OF JUDGMENT 23 

to such lengths that the general public is not trusted to 
behold it.* 

However useful within limits the equation of the terms 
may be found, if you treat it as a working hypothesis (vid. 
Book II. Part II. Chap. IV.), yet as a truth it will not bear 
any serious examination. Let us look at it more closely. 

(i) If what is asserted be equality, then that of course is 
identity in quantity, and is nothing else whatever 27 . And I 
must venture to complain of the reckless employment of this 
term. To use the sign for qualitative sameness, or for 
individual identity (I do not ask here if these are different), is 
surely barbarous. No harm perhaps may come, but there 
should be some limit to the abuse and confusion we allow 
ourselves in practice. Let us then first take equality in its 
proper sense, to stand for an identity in respect of quantity. 
But, if so, if the subject and predicate are equated, if " Negroes 
are men," when written " All negroes = some men," is on a 
level with 2= 12 10 if what is said and signified is that 
between the terms, if you compare them numerically, there is 
no difference whatever, we can at once pass on. It is certain 
that some judgments, at least, can not express this relation of 
quantity, and it is certain again that, of those which can, it is 
only a very small class which do. Illustration is hardly 
wanted. " Hope is dead " would mean that, " In hope and a 
fraction of dead things there is exactly the same sum of 
units." And, in asserting that " Judgment is not an equation," 
I should express my belief that to divide both by 2 would not 
give the same quantity. 

But the sign = does not seem to mean equality. It does 
not mean that the units of the subject and predicate are iden 
tical in quantity. It would appear to mean that they are the 
same altogether. The identity it asserts is not quantitative, but 
seems absolute. In " All Negroes = some men," the " = " rep 
resents exclusion of difference both quantitative and qualitative. 

(ii) The identity is (a) not likeness ; it is not a relation con 
sisting in a partial qualitative identity, definite or indefinite. 
" Iron some metal " can hardly mean " Some metal is similar 
to iron." Not only do the facts exclude this interpretation, but 
the theory would not work with it. If " similars " and " like- 
* Vid. Jevons, Principles of Science, Chap. i. 12. 



24 THE PRINCIPLES OF LOGIC BOOK I 

ness " are phrases that occur, this is a proof that here, as in 
the case of =, the theory does not mean what it says, or quite 
know what it is doing. That when A is like B you may write 
one for the other, is of course quite untrue (cf. Book II.). 

(b) The identity again is not definitely partial, consisting 
in sameness in some particular point or points of quality. 
For, on this interpretation, you could make no advance, until 
the point of sameness had been specified. And even then 
the equational theory would not work. 

(c) Unless we suppose that both sides differ only in 
name, and that this difference of names is the import of the 
judgment a view we shall glance at in a future chapter 
(Chap. VI.) we must take the sign = to mean total sameness 
to the exclusion of all difference. But, if so, the theory 
must reform itself at once, if it desires to be consistent. It 
will not be true that " Negroes = some men," for certainly 
" some men " are not " = negroes." Nor again will it be true 
that negroes are equal to a certain stated fraction of mankind. 
That stated fraction is an universal adjective which might 
be applicable to other men as well as to negroes. If "is " or 
" = " stands for " is the same as," then it is as false to say 
" A is H B," as it was before to say " A is some B." " Some 
B" covers not only the B which is A; it may hold just as 
much of the other B, which we take as not-A. And it is so 
with " ^ B " ; that applies just as much to the % which are 
not-A, as it does to the third which is identical with A. The 
quantification of the predicate is a half-hearted doctrine, 
which runs against facts, if " = " does mean equal, is ridicu 
lous if " = " comes to no more than plain " is" and is down 
right false if " = " stands for " is the same as." 

To be consistent we must not merely quantify the predi 
cate, we must actually specify it. The men that are negroes 
are not any and every set of men, who have a certain number. 
They are those men who are negroes, and this is the predicate. 
Negroes = negro-men, and iron = iron-metal. The predicate 
now really and indeed seems the subject, and can be substi 
tuted for it. The idea is a bold one, and its results have 
been considerable; but if we look not at working power but 
at truth, the idea is not bold enough, and wants courage 
to remove the last contradiction. 



CHAP. I THE GENERAL NATURE OF JUDGMENT 25 

That A should be truly the same as AB, and AB entirely 
identical with A, is surely a somewhat startling result. If 
A = A, can it also be true that to add B on one side leaves the 
equation where it was? If B does not mean o, one would be 
inclined to think it must make some difference. But, if it 
does make a difference, we can no longer believe that A = AB, 
and AB = A. If "iron-metal" is the same as "iron," how 
misleading it is to set down the two sides as different terms. 
If there really is a difference between the two, then your 
statement is false when by your " = " you deny it. But if 
there is no difference, you are wrong in affirming it, and in 
opposing " iron " to " iron-metal." 

There is only one issue. If A is AB, then the A that is 
AB is not A but AB. Both sides of the assertion are just 
the same, and must be so stated. Negro-men are negro-men, 
and iron-metal is iron-metal.* For consider the dilemma. 
B either is or is not an addition to A. If it is not an addition, 
its insertion is gratuitous; it means nothing on either side, 
may fall upon whichever side we choose, is absurd on both 
alike, and should be got rid of then A = A. But if B is an 
addition, then A = AB cannot be true. We must add B on 
both sides, and AB = AB. In short B must disappear or 
have a place on each side. 

We have now reached consistency, and the reader may 
ask, Is the result still false? I do not like to seem obstinate, 
and I prefer to reply, Do you think it is true? 1 will accept 
your answer. If you say that identical propositions are all 
false, I shall not contradict you (cf. Chap. V. i), for I also 
believe that a judgment which asserts no difference is nothing. 
But if you pronounce on the side of truth, I should like to 
ask a question. For an assertion to be true must it not 
assert something, and what is it that you take to be asserted 
above? That where there is no difference, there is no differ 
ence, that AB will be AB as long as it is AB? You can 
hardly mean that. Is the existence of AB what is secretly 
asserted ? But, if so, we should say openly " AB exists," and 
our reduplication of AB is surely senseless. We know that 
it exists, not because we double it, but, I suppose, because we 
know of its existence. 

* Cf. Lotze, Logik, 80-2. 



2,6 THE PRINCIPLES OF LOGIC BOOK I 

But what then do we assert by AB = AB ? It seems 
we must own that we do not assert anything. The judg 
ment has been gutted and finally vanishes. We have followed 
our premises steadily to the end, and in the end they have 
left us with simply nothing. In removing the difference of 
subject and predicate we have removed the whole judgment.* 

17. We have seen the main mistakes of the foregoing 
doctrines. It is a more pleasing task to consider the main 
truth which each one of them has seized, (i) The views we 
began to criticize in 13, have avoided the error of subject 
predicate and copula. They have seen that in judgment the 
number of ideas is not the main question, and that the 
essence of the matter does not lie in the ideas, but in some 
thing beyond them. Nor, to be more particular, is the impli 
cation of will in all judgment a complete mistake. It is 
true that, in an early stage of development, the intelligence is 
so practical that it hardly can be said to operate independ 
ently. It is true again that, in the evolution of self-con 
sciousness, the opposition of idea and reality depends, to a 
degree I will not here discuss, upon volitional experience. 
And in these points there is truth in the theory, which, how 
ever much he may abandon it, we shall place to the credit 
of Professor Bain. And the view that in judgment we have 
an association of idea with sensation, and a coalescence of 
both elements, is far from being wholly destitute of truth. 
For (as we shall see in the following Chapter) the subject 
in all judgment is ultimately the real which appears in per 
ception; and again it holds good that the lowest stage, in 
the development of judgment and inference alike, is the red 
integration of ideal elements with sensuous presentation, in 

* It is not worth while to criticize in detail a doctrine we can show 
is fallacious in principle. Cf. Chap. V. But among minor objections 
to the quantification of the predicate is its claim to silence you, and 
prevent you from saying what indubitably you know. It tells you 
you must not say "A is B," unless you also certify how much of B is 
A. But, even supposing that " so much of B " is the truth that you 
would affirm if you could, in numerous cases you can not affirm it. 
You know that A possesses a quality B, and, as to how the B, that is A, 
stands in extent to the B which is not A, you have no information. 
You must either then decline to quantify, or must abstain from speak 
ing the truth you know. But it is not worth while to criticize in detail. 



CHAP. I THE GENERAL NATURE OF JUDGMENT 27 

such a manner that the two are not distinguished, but run 
into one whole. 

(ii) And from the second class of errors we may also 
collect important results. In the first place it is true that the 
content asserted is always complex. It can never be quite 
simple, but must always involve relations of elements or 
distinguishable aspects. And hence, after all, in judgment 
there must be a plurality of ideas. And, in particular, (a) 
though it is false that the predicate is a class in which the 
subject is inserted, and a fundamental error to take the 
universal in the form of a collection, yet it is entirely true 
that the predicate must be always an universal. For every 
idea, without exception, is universal. And again (&) though 
assertion is not attribution to a subject in the judgment, 
though it is false that the grammatical subject is the reality of 
which the predicate is held true, yet in every judgment there 
must be a subject. The ideal content, the adjective divorced, 
is made real once again by union with a substantive. And 
(c) the doctrine of equation, or identity of the terms, has itself 
grasped a truth, a truth turned upside down and not brought 
to the light, but for all that a deep fundamental principle. 

Turned upside down, and made false, it runs thus. The 
object of judgment is, despite their difference in meaning, to 
assert the identity of subject and predicate when taken in 
extension. But turned the right way up it runs thus. The 
object of judgment is, under and within the identity of a 
subject, to assert the synthesis of different attributes. When 
ever we write " = " there must be a difference, or we should 
be unable to distinguish the terms we deal with (cf. Chap. V.). 
And when a judgment is turned into an equation, it is just 
this difference that we mean to state. In " S = P " we do 
not mean to say that S and P are identical. We mean to say 
that they are different, that the diverse attributes S and P are 
united in one subject; that S P is a fact, or that the 
subject S is not bare S, but also S P. And the reason why 
the theory of equation works, and is not mere nonsense, is 
that in fact it is an indirect way of stating difference. " The 
subject is the same " implies, and may be meant to convey, 
the truth that the attributes differ. We must refer to the 
sequel for further explanation, but at present our concern is 



28 THE PRINCIPLES OF LOGIC BOOK I 

briefly to point out that an identity must underlie every judg 
ment. 

But how is this possible ? A is " prior to B," or " to the 
left of C," or "equal to D." The judgment asserts the 
equality, or sequence, or position of two subjects, and it surely 
does not say that both are the same. We must try to 
explain. We saw that all judgment is the attribution of an 
ideal content to reality, and so this reality is the subject of 
which the content is predicated. Thus in " A precedes B," 
this whole relation A B is the predicate, and, in saying this 
is true, we treat it as an adjective of the real world. It is 
a quality of something beyond mere A B. But, if this is so, 
the reality to which the adjective A B is referred is the 
subject of A B, and is the identity which underlies this 
synthesis of differences. 

It is identical, not because it is simply the same, but because 
it is the same amid diversity. In the judgment, beside the 
mere distinction of the terms, we have an opposition in time 
of A to B. And the subject of which A B is asserted, 
being subject to these differences, is thus different in itself, 
while remaining the same. In this sense every judgment 
affirms either the identity which persists under difference, or 
the diversity which is true of one single subject. It would 
be the business of metaphysics to pursue this discussion into 
further subtleties. We should there have to ask if, in the 
end, every possible relation does not involve a something in 
which it exists, as well as somethings between which it exists, 
and it might be difficult to reconcile the claims of these prepo 
sitions. But we have already reached the limit of our 
enquiries. The real subject which is implied in judgment, 28 
will meet us again in the following Chapter ; and that, we hope, 
may make clearer some points which at present remain obscure. 

III. 1 8. We have given some preliminary account of 
judgment, and have tried to dispose of some erroneous views. 
We pass now to our third task, and must make some remarks 
on the development of the function. As we have defined it 
above, judgment does not show itself at all the stages of 
psychical evolution. It is a comparatively late acquisition of 
the mind, and marks a period in its upward growth. We 



CHAP. I THE GENERAL NATURE OF JUDGMENT 2Q 

should probably be wrong if we took it as a boundary which 
divides the human from the animal intelligence; and in any 
case we should be ill-advised to descend here into the arena 
of theological and anti-theological prejudice (vid. Book III. 
Part I. Chap. VII.). It is better to treat the mind as a single 
phenomenon, progressing through stages, and to avoid all 
discussion as to whether the lines, by which we mark out this 
progress, fall across or between the divisions of actual classes 
of animals. Thus with judgment we are sure that, at a cer 
tain stage, it does not exist, and that at a later stage it is 
found in operation; and, without asking where the transition 
takes place, we may content ourselves with pointing out the 
contrast of these stages. The digression, if it be such, will 
throw out into relief the account we have already given of 
judgment. For judgment is impossible where truth and false 
hood, with their difference, are not known ; and this difference 
cannot be known where ideas are not recognized and where 
nothing exists for the mind but fact. 29 

19. I do not mean that the lower forms, or that any 
form, of soul-life is confined to the apprehension of simple 
sensations. If the soul is ever the passive recipient of a given 
product, to which it does not contribute and which it does not 
idealize, yet in all actual mind a further step is made, and 
we always possess more than what is given through sense. 30 
The impression, so to speak, is supplemented and modified 
by an ideal construction, which represents the results of past 
experience. And thus, in a sense, the lowest animals both 
judge and reason, and, unless they did so, they must cease 
to adjust their actions to the environment. But, in the strict 
sense, they can neither reason nor judge; for they do not 
distinguish between ideas and perceived reality. 

That the thing as it is, and as it appears in perception, are 
not the same thing, is, we all are aware, a very late after 
thought. But it is equally an afterthought, though not equally 
late, that there is any kind of difference between ideas and 
impressions. For a more primitive mind a thing is or it 
is not, is a fact or is nothing. That a fact should be, and 
should yet be an appearance, should be true of, and belong 
to, something not itself; or again should be illusion, should 
exist and yet be false, because its content is an adjective 



3O THE PRINCIPLES OF LOGIC BOOK I 

neither of itself nor of any other substantive these distinc 
tions are impossible for an early intelligence. A nonentity is 
not anything it can apprehend, and to it an error is never an 
illusion. And hence for this mind ideas never could be sym 
bols. They are facts because they are. 

20. The presentations of the moment, the given sensa 
tions, are received into a world of past experience, and this 
past experience now appears in the form of ideal suggestion. 
In the lowest stages of mind there is as clear a difference 
between the datum that is given and the construction that is 
made, as there can be in the highest. But it is one thing to 
have a difference in the mind and another to perceive it; and 
for an early intelligence this contrast between sensation and 
idea, is quite non-existent. A presentation AB, by a feeling d, 
produces an action de, or, by an ideal transition b-d, is trans 
formed into ABD ; or may become AC, by the action of a-g, 
if g banishes B, and c is supplied. But, in all these cases, and 
in any other possible case, the process remains entirely latent. 
The product is received as a mere given fact, on a level with 
any other fact of sense. 

If the object, as first perceived, could be compared with 
the object as finally constructed, there might be room for a 
doubt if the fact has become, or has been made by the mind. 
And still more if the ideas which perception excludes were 
ever attended to; if rejected suggestion, conflicting supple 
ment, wrong interpretation, and disappointed action, were held 
before the mind, then a reflection might take place, which 
would antedate the slow result of development ; and the sense 
of illusion would awaken the contrast of idea and reality, truth 
and falsehood. But all this is impossible. For the leading 
feature of the early mind is its entire and absolute practicality. 31 
The fact occupies the soul no longer and no further 
than it tends to produce immediate action. The past and the 
future are not known except as modifications of the present. 
There is no practical interest in anything but the given, and 
what does not interest is not anything at all. Hence nothing is 
retained in its original character. The object, in its relation to 
present desire, changes ceaselessly in conformity with past 
adventures of failure or success. It contracts or extends itself, 
as the case may be, but it still remains the mere given object. 



CHAP. I THE GENERAL NATURE OF JUDGMENT 31 

And while the ideas it assimilates become part of presentation, 
the ideas it excludes are simply nothing at all. 

At a late stage of mind, among intelligent savages, the 
doctrine of a dream-world brings home to us the fact, that a 
mere idea, which exists and is unreal, is a thought not easy to 
lay hold of thoroughly. And, if we descend in the scale no 
further than to dogs, we are struck by the absence of theo 
retical curiosity. Let them see an appearance to be not what 
is seemed, and it instantly becomes a mere nonentity. An 
idea, we may say, is the shadow of an object; and that to a 
savage is another kind of object, but to a dog it is the thing 
or just nothing at all. The dog has not entered on that 
process of reflection which perhaps has not led to any very 
sure result. When his heart, like ours, is baffled and 
oppressed, and gives matter to his brain it has no strength to 
cope with, he can neither send his hopes into another world 
than this, nor repeat like a charm, and dream that he believes, 
that appearances may be nothing to a soul which feels them. 
I do not know the formula which would prove to his mind a 
satisfactory solution of his practical troubles; but his system 
of logic, if he had one, would be simple; for it would begin, 
I am sure, and would end with this axiom, " What is smells, 
and what does not smell is nothing." 

21. It would be difficult to detail the steps of the process 
by which ideas, as such, become objects of knowledge, and 
with truth and falsehood judgment comes in. And, apart from 
this difficulty, there is a question of fact which would con 
stantly arise. Given a certain stage of development, does 
judgment already exist there or not? It might perhaps be 
right to connect the distinctions of truth and falsehood in 
general with the acquisition of language, but it is hard to say 
where language begins. And, in the stage before language, 
there are mental phenomena which certainly suggest the 
effective distinction of sensation and idea. 

The provision made beforehand for changes to come can 
not always be taken as valid evidence. It seems clear that, 
in many cases, we should be wrong in supposing any know 
ledge of the future, as opposed to the present. It is certain 
at least that a presentation, accompanied by or transformed 
by feelings, is as effective practically as the clearest idea. But 



32 THE PRINCIPLES OF LOGIC BOOK I 

in certain animals there are much stronger indications. When 
artful contrivances, suitable to unseen events, are used in the 
pursuit of prey, 32 we are led to conclude that the difference of 
the situation, as it actually is and as it is anticipated, must 
come before the mind. And, where desire is unsatisfied, it is 
not always mere feeling, as against the object, which pervades 
the soul. The image of the desired, as against present per 
ception, floats or is held before the attention, and the feeling 
of pain, we may suppose, must sharpen the contrast until at 
length the difference is seen. And we can mention here what 
perhaps may be an outward symptom of the change. No 
one can have been much with domestic animals, and failed 
to observe their constant and increasing use of the imperative. 
They seem at least to know what they desire, to expect assist 
ance, and to be surprised at non-compliance. And though 
mere urgency of feeling, in the absence of ideas, might account 
for their tone, this interpretation would at times somewhat 
strain the phenomena. 

But, if this is so, then judgment must come before lan 
guage, and certainly cannot be distinctively human. And, just 
as after language has been developed, we do often dispense 
with it; just as the lowest, and perhaps the highest of our 
thinking, goes on without any words in the mind, so, we may 
suppose, before speech was developed, the differentia of judg 
ment already existed. 

We are not concerned in the controversy to which this 
might give rise. If we only know what we mean by judg 
ment, it is little to our purpose where first it appears, and 
what animal first reaches it. The question is not at all easy 
to settle, and in passing I will merely suggest a reflection. It 
is not enough to show that in the mind of an animal an image 
exists together with a presentation of sense, and that this 
image, partly the same as the presented, is in collision with it, 
and again leads to action in relation to the presented. All 
this may exist, and yet the differentia still be absent; the 
image may not be seen to be mere appearance, to be either 
not real at all, or less real than the sensation. For, if the 
image is taken in relation to the perception, they may both be 
apprehended as one continuous changing fact ; the prey may 
be seen as pursued and captured, and the actual object may 



CHAP. I THE GENERAL NATURE OF JUDGMENT 33 

appear to pass into the desired. And, where failure makes 
this impossible, what may after all be wanting is the intel 
lectual identification of the image with the object. Apart 
from this logical process, we have a mere collision in the mind 
of two realities, whose struggle is felt. We have contest, and 
perhaps a following ejection; but we have no subjection, no 
degradation of one fact to the level of an appearance, that 
exists but in our heads. And in this case judgment would 
not have taken place. 

22. It might be interesting elsewhere to discuss at length 
these puzzles in psychology, but it will repay us better to pass 
to what is more certain. It is, in the first place, the retention 
of the false idea which tends to provoke comparison with 
reality, and which leads the way to the knowledge of appear 
ance and truth and falsehood. And, in the second place, it is 
language which, if it does not originate, at least ensures and 
sharpens the contrast. When gregarious animals utter their 
ideas, the word is in a manner more permanent than the 
thought, and maintains itself against the fact it tries to ex 
press. And the spoken thoughts of the different individuals 
are sometimes in collision. They are not the same with one 
another, and therefore not the same with the single fact. And 
speech in its perversion to lies and deceit makes the dullest 
comprehend that words and ideas can be and be real, and can 
yet be illusion and wholly unreal in relation to facts. At this 
point it is seen that the word and the thought are not like 
other things. They not only exist but also mean something, 
and it is their meaning alone which is false or true. They are 
seen to be symbols, and this insight it is which in the strict 
sense constitutes judgment. 

For in the early stage, to repeat it once more, the image 
is not a symbol or idea. It is itself a fact, or else the facts 
eject it. The real, as it appears to us in perception, connects 
the ideal suggestion with itself, or simply expels it from the 
world of reality. But judgment is the act which, while it 
recognizes the idea as appearance, nevertheless goes on to 
predicate it. It either attributes the idea to reality, and so 
affirms that it is true, or pronounces it to be merely a bare 
idea, and that the facts exclude the meaning it suggests. The 
ideal content which is also fact, and the ideal content which is 



34 THE PRINCIPLES OF LOGIC BOOK I 

nothing beyond itself, are truth and falsehood as they appear 
in judgment. 

23. Our object in the foregoing has been, not to 
chronicle a psychological transition, but to mark out distinc 
tive stages and functions. We must endeavour, in conclusion, 
to obviate a very fatal mistake. The gulf between the stage 
of mind that judges and the mind that has not become aware 
of truth, may seem hard to bridge, and the account we have 
given may seem to rend facts apart. We may be thought in 
our extremity, when with natural conditions no progress is 
possible, to have forced upon the stage a heaven-sent faculty. 
On one side of your line, we may be told, you possess explicit 
symbols all of which are universal, and on the other side you 
have a mind which consists of mere individual impressions 
and images, grouped by the laws of a mechanical attraction. 
The distinction you have made amounts to a divorce. The 
higher stage can not exist as you describe it, or can not at 
least be developed from the lower. 

In the sequel I shall criticize the whole doctrine of the 
" Association of ideas," but at present I will say thus much by 
anticipation. 33 I agree that, if the lower stages of the mind 
were really what they are in most English psychologies, it 
never would in any way be possible to pass to the stage where 
ideas are used in judgment. And this consequence I desire 
to accentuate and to emphasize. But the fashionable doctrine 
of "association," in which particular images are recalled by 
and unite with particular images, is, I think, not true of any 
stage of mind (vid. Book II. Part II. Chap. I). It does not 
exist outside our psychology. From the very first beginnings 
of soul-life universals are used. It is because the results of 
experience are fixed in an ideal and universal form, that 
animals are able, I do not say to progress, but to maintain 
themselves in bare existence. 

24. In England, I am afraid, the faithful tradition of 
accumulated prejudice, in which are set the truths of the 
" Philosophy of Experience," well-nigh makes idle an appeal 
to the fact. But I will try to state the fact, however idly. It 
is not true that particular images are ever associated. It is 
not true that among lower animals universal ideas are never 
used. What is never used is a particular idea, and, as for 



CHAP. I THE GENERAL NATURE OF JUDGMENT 35 

association, nothing ever is associated without in the process 
being shorn of particularity. I shall hereafter have to enlarge 
on the latter statement, and at present will deal with the false 
assertion, that merely individual ideas are the early furniture 
of the primitive mind. 

In the first place it seems patent that the lower animals 
have not any idea about the individual. To know a thing as 
the one thing in the world, and as different from all others, is 
not a simple achievement. If we reflect on the distinctions 
it implies, we must see that it comes late to the mind. And, 
on turning to facts, we find that animals of superior intelli 
gence are clearly without it, or give us at least no reason 
at all to think that they possess it. The indefinite universal, 
the vague felt type, which results from past perceptions and 
modifies present ones, is palpably the process of their intel 
lectual experience. And when young children call all men 
father, it is the merest distortion of fact to suppose that they 
perceive their father as individual, and then, perceiving other 
individuals, confuse a distinction they previously have made. 

But this is hardly the real point at issue. To know the 
individual as such will be admitted to be a late achievement. 
It can hardly be maintained that a rude intelligence, when it 
holds a type and rejects what disagrees with it, can be aware 
of that type as an unique individual. The question is really as 
to the use made of images in early knowledge. Are they used 
as universals, or used as particulars? 

25. It is agreed on both sides that, as psychical exist 
ences, ideas are particular like all other phenomena. The 
controversy is confined to the use we make of them. I should 
maintain that, so far as they remain particular, they are simple 
facts, and not ideas at all ; and that, where they are employed 
to extend or to modify experience, they are never used in 
their particular form. When A-B is presented in perception, 
we are told that the result of a past perception B-C appears 
as particular images b-c, and that these images, called up, 
unite with the presentation. But nothing could be more false. 
It is not true that all the marks, and relations, and differences, 
which constitute the particularity of b and c, appear in the 
resultant A-B-C, or were in any way used in order to produce 
it. The image c, besides its content as c, had the indefinite 



36 THE PRINCIPLES OF LOGIC BOOK I 

detail of all psychical phenomena; but it was not this but 
the universal c which was used in A-B-C, and it is the per 
ception A-B that re-particularizes c in accordance with itself. 
And, if this is so, we must say that what really operates is a 
connection between universal ideas. We have already, in an 
unconscious form, what, when made explicit, is the meaning 
of symbols. 

I must trust to the sequel for elucidation (vid. Book II. II. 
Chap. I.), but the subject is so important that I will venture to 
insert some illustrations. When to-day I reach the place where 
yesterday my dog has either chased a cat or fought with an 
antagonist, the perception as we say " calls up " the ideas, and 
he runs eagerly forward. His experience, we will suppose, 
was of a white cat or a black retriever with a large brass 
collar. To-day images are " called up," not so definite perhaps, 
but still certainly with some detail, and we will suppose that 
the detail reproduces the experience. To-day it is a black 
cat that is found in the place, but with an ordinary dog that 
will make no difference. The whiteness of the image is quite 
irrelevant. 3 * Or again, if to-day another dog be perceived, if 
only that dog be not glaringly different, an ordinary dog will 
certainly attack him, and the less intelligent he is the more 
catholic is his action. For it is not the whole image but a 
portion of the content which operates in his mind. He may 
turn from a small dog or a white dog or a smooth-coated dog, 
but size, blackness, and roughness, are the typical ideas which 
will certainly operate. It may be said, no doubt, that the 
ideas are particular, that they differ from the perception, and 
that it is the fault of the animal which fails to distinguish 
them. But why, I reply, does it fail to distinguish? Is a 
creature, intelligent as is a terrier, unable to see the difference 
between a white and black cat, or a Newfoundland and a 
sheep dog? "Yes," I shall be told, "he can if he attends to 
them, but here, although they both are present,* he does not 

* This is a false assumption as will be shown hereafter. In the first 
place it is not true that, when the mind goes from A B to C, it has to 
pass through a particular image b. In the next place, if the particu 
lar b be present, we have no reason to suppose that it will have the 
qualities of the original perception B. If a white cat has been seen 
to-day, we saw that next day, if its image is white, the whiteness 
of that image need not be used; and again if its whiteness was not an 



CHAP. I THE GENERAL NATURE OF JUDGMENT 37 

attend to them." But if so, I must rejoin, if the differences 
are not used, but remain inoperative, is not this a clear proof 
that what operates, and what is used, is a portion of the con 
tent, which is permanent amid differences, and which later 
becomes the universal meaning? 

Again, if an animal has been burnt one day at the kitchen 
fire, the next day it may shrink from a lighted match. But 
how different are the two. How much more unlike than like. 
Will you say then that the match can not operate unless it 
first summons up, and then is confused with the image of a 
kitchen fire; or will you not rather say that a connection 
between elements, which are none of them particular, is pro 
duced in the mind by the first experience? But, if so, from 
the outset universals are used, and the difference between the 
fact and the idea, the existence and the meaning, is uncon 
sciously active in the undeveloped intelligence. 

26. We must anticipate no further. In another place 
we shall show the fictitious nature of the " Laws of Asso 
ciation," as they have been handed down by our prevalent 
tradition. Our object here has been, in passing, to show that 
the symbolic use of ideas in judgment, although no early 
process of the mind, is a natural result of mental develop 
ment. From the very first beginnings of intelligence it is 
the type that operates and not the image. The instance as 
such is never, and can never be, retained in the soul. The 
connection of certain elements in its content is all it leaves 
behind. You may call it, if you please, mere impotence of our 
imagination, or you may call it that idealizing function of the 
mind which is the essence of intelligence, still the fact remains 
that never at any stage can any fact be retained without some 
mutilation, some removal of that detail which makes it par 
ticular. The lower we descend in the growth of our own 
functions, or in the scale of animate nature, the more typical, 
the less individual, the less distinct, the more vaguely uni 
versal and widely symbolic is the deposit of experience. It 
is not symbolic in the sense that the meaning is at first per 
ceived to be other than the fact. It is not universal in the 

object of interest, there is no reason whatever why the image should 
be white, and not of some other hue. The generalized result left by 
past experience is always mutilated. 
2321.1 D 



38 THE PRINCIPLES OF LOGIC BOOK I 

sense that analysis has distinguished the relevant from the 
irrelevant detail, and found elements more simple, and syn 
theses wider than are suggested by mere sense. But in the 
sense of not using the particular as particular, and of taking 
the meaning while leaving the existence, in the sense of in 
variably transcending the given, and of holding true always 
and valid everywhere what has ever and anywhere once been 
experienced, the earliest and the latest intelligence are the 
same from one end to the other of the scale of life. 



ADDITIONAL NOTES 

1 On the question of Order in Logic cf . T. E. I. 

2 "We can not judge till we use them as ideas." This requires 
correction. See Appearance, Index, and Essays, pp. 32-3 and Index. 
And cf. the Index of this book s. v. Idea. 

3 " In England." This was published in 1883. 

**" Symbols." This is wrong or at least inaccurate. A " sign " or 
"symbol" implies the recognition of its individual existence, and this 
recognition is not implied in an "idea." See Essays, p. 29, and the 
Index, s. v. Idea. 

s "That," "what," "means" and "stands for" (cf. Chap. VI. 2). 
All of these distinctions imply judgment, though that may not be 
explicit. And wherever you have any such distinction you have 
transcendence and an idea though not always an explicit idea (see 
Note 2). Each of these distinctions, again, if you could perfect it, 
would imply and pass into all the rest. 

6 " Original content." This distinction (cf . the words " content 
(original or acquired)" at the end of 4) refers to the difference 
pointed out in 5. The point is, however, irrelevant, and 5 should 
have been omitted. 

7 This footnote is wrong throughout, for there are no ideas not so 
" referred." See Essays, Chap. Ill and Index. The words in the text, 
"cut off, etc." are also incorrect. There are no ideas before or apart 
from their use, and that at first is unconscious. See Note 2. 

8 Here again we must remember that we are not to say (i) that an 
idea is there apart from its being used, or (ii) that, in using it, we 
must be aware of it as a mental thing. Further (iii) I was wrong to 
speak, here and elsewhere, as if with every idea you have what may 
be called an " image." How far and in what sense the psychical exist 
ence is always capable of being verified in observation is a difficult 
point to which I have perhaps not sufficiently attended. Still every 
idea, I must assume, has an aspect of psychical event, and so is 
qualified as a particular existence. In the footnote to p. 7 " sensuous " 
should have been "psychical." The amount of imagery required is 



CHAP. I THE GENERAL NATURE OF JUDGMENT 39 

much exaggerated in p. 9. Cf. on the other side Chap. II, 36, 
37. 

9 What I meant here was probably to remind the reader that the 
" categorical " may turn out to be really " conditional." 

10 " Judgment (proper) is etc." (i) In this definition the word 
" act " raises a question, important in psychology and in metaphysics 
(see Appearance and Essays, the Indexes), but (so far as I see) not 
necessary in logic, (ii) "Recognized as such" is wrong (see Note 2). 
What I should recognize on reflection I may in fact ignore. Cf. 10 
and 13. (iii) "Beyond the act," and (below) "independent of it," are 
right for logic. For metaphysics, on the other hand, the problem raised 
here can not be ignored (see Essays, Index, s. v. Act}. But as to 
recognition of the act (to return to that) the text is wrong. A per 
ceived object changed by an idea, and the change ignored except as 
the development of the object though not of the mere perceived 
object here is the beginning of judgment in the proper sense. But, 
again, to take judgment as present wherever we have an object at all 
before the mind is a view which is tenable. 

11 " Wandering adjective" should be "loosened adjective." And 
(three lines lower down) "relation" should be "union." 

12 " Partial ignorance absolute." The meaning and the great im 
portance of these words have, I hope, been to some extent brought 
out in this book and in my later writings. 

13 (i) "Are the angles &c.?". The false doctrine of "floating 
ideas " is involved here. See Essays, Index, (ii) " The same ideal 
content." Not so. See ibid. And cf. Bosanquet, K 6- R, pp. 114-15, 
119, and Logic, I. 33. 

14 This statement (cf. pp. 49, 56) requires correction. It is true 
that the ideal meaning is one; but it is also true that the subject 
is a special subject, and that it, in its special sense, must be there 
within the meaning (cf. Bosanquet, loc. cit.). The twofold nature 
of Reality as the subject of judgment was not sufficiently recognized 
by me. See below on p. 13. And cf. pp. 114, 477, and Index. 

15 Cf. Mind, N. S. No. 41, pp. 20 foil. 

16 " The relation is the same." But see Note 13. 

17 "The subject can not belong to the content." This statement 
again requires correction. We have not a case here of mere Yes or 
mere No. See T. E. II. and Index. And cf. Essays, and again Appear 
ance, the Indexes. 

18 " And finally, &c." See Note 10. 

19 On Bain s theory of Will cf. Mind O. S. No. 49, PP- 27 foil. 
The unjust neglect of Bain by Pragmatists, or their inability to learn 
from his adventurous errors, has, I think, cost them dear. See Essays, 
pp. 70-1. The reader will notice that, already in 1883, I was dealing with 
the question, What is practical? See for this the Note on p. 506, and 
T. E. No. XII. 

20 Cf. here Essays (ibid.). 

21 "Not judged to be real." We should here add "in our existing 



4Q THE PRINCIPLES OF LOGIC BOOK I 

world," as otherwise the statement is not true. See Essays, Chap. Ill, 
and specially p. 35, and cf. T. E. XII of this work. 

22 On the nature of the feeling of Consent see Essays, p. 377, note, 
and Mind, N. S. No. 46, PP- 13 foil. 

23 Whether (see Prof. Sully, p. 79, note) Bain really modified his 
view, it is needless here to enquire. My own difficulty with Bain 
was to get any rational idea as to what he meant by " intellect " and 
" knowledge " which apparently can remain itself in the absence of 
belief. He (like J. S. Mill) is faced here by a problem, which, on 
their inherited premises, is quite insoluble, because radically perverted. 
See Essays f pp. 376-7. Bain s view of intellect is again noticed in 
pp. 324, 491 of the present work. 

24 "Copula." Dr. Bosanquet (K & R, pp. 167 foil.) rightly remarks 
here that the copula is essential, so far as it points to the analysis and 
synthesis, and the conditioned assertion of reality, which are present 
in all judgment. 

25 "(Not all)" should be "(though not in all cases except in the 
end)" Cf. below, 16, 17. And see Note 28. 

26 " The same both in the assertion and out of it." But see Note 13. 
2 ? " Equality." The reader may consult here Dr. Bosanquet s re 
marks (K & R, pp. 104 foil.) though I do not wholly assent to them. 

28 All judgment falls fn the end under the head of subject and 
attribute, in the sense that every judgment in the end asserts of a 
subject both diversity in unity and identity in difference this subject 
being at once the ultimate and also a special reality. For this funda 
mental and all-important doctrine see the Index of this work. 

29 The reader must not forget here that our definition of judgment 
was more or less arbitrary. See Note 10. 

30 The reader will notice that, in 19 and 20, much too little is 
made of movement and action following direct on sensation. But for 
the purpose here in hand this point is perhaps not material. 

si " Absolute practicality." But see Bk. III. Pt. I. Chap. VII. For 
the character of "the early mind" cf. Essays, pp. 356-7, 376. The 
further statement about "the dog" is of course exaggerated. 

32 " In the pursuit of prey," and of course also otherwise. With 
regard to the Imperative, though I still think that this remark was 
certainly worth making, I would emphasize the need of caution here 
as to correct interpretation of the facts. 

33 On "Association &c." See later, Bk. II. Pt. II. Chap. I. The 
remark on " most English psychologies " belongs, of course, to the date 

1883. 

34 There is some exaggeration here as to the amount of particular 
detail, but what is said holds good, I think, in principle. 



CHAPTER II 

THE CATEGORICAL AND HYPOTHETICAL FORMS OF 
JUDGMENT 

I. In the foregoing chapter we have attempted roughly to 
settle the main characteristics of judgment. The present chap 
ter will both support and deepen our conclusion. It will deal 
with problems, in part familiar to those who have encountered 
the well-known discussion aroused by Herbart. The length 
and the difficulty of this second chapter may perhaps be little 
warranted by success, but I must be allowed to state before 
hand that both are well warranted by the importance of the 
subject in modern logic. 

A judgment, we assume naturally, says something about 
some fact or reality. If we asserted or denied about anything 
else, our judgment would seem to be a frivolous pretence. 
We not only must say something, but it must also be about 
something actual that we say it. For consider; a judgment 
must be true or false, and its truth or falsehood can not lie in 
itself. They involve a reference to a something beyond. And 
this, about which or of which we judge, if it is not fact, what 
else can it be? 

The consciousness of objectivity or necessary connection, 
in which the essence of judgment is sometimes taken to lie, 
will be found in the end to derive its meaning from a reference 
to the real. A truth is not necessary unless in some way it 
is compelled to be true (vid. Chap. VII.). And compulsion is 
not possible without something that compels. It will hence 
be the real, which exerts this force, of which the judgment is 
asserted. We may indeed not affirm that the suggestion S P 
itself is categorically true of the fact, and that is not our 
judgment. 1 The actual judgment asserts that S P is forced 
on our minds by a reality x. And this reality, whatever it 
may be, is the subject of the judgment. It is the same with 
objectivity. 2 If the connection S P holds outside my judg 
ment, it can hardly hold nowhere or in nothingness. It must 



42 THE PRINCIPLES OF LOGIC BOOK I 

surely be valid in relation to something, and that something 
must be real. No doubt, as before, S P may not be true 
directly of this fact; but then that again was not what we 
asserted. The actual judgment affirms that S P is in connec 
tion with x. And this once again is an assertion about fact. 

There is a natural presumption that truth, to be true, must 
be true of reality. And this result, that comes as soon as we 
reflect, will be the goal we shall attain in this chapter. But 
we shall reach it with a struggle, distressed by subtleties, and 
perhaps in some points disillusioned and shaken. 

2. Less serious difficulties we may deal with at once. " A 
four-cornered circle is an impossibility," we are told, does not 
assert the actual existence of a four-cornered circle (Herbart, 
I. 93). But the objection is irrelevant, unless it is maintained 
that in every case we affirm the reality of the grammatical 
subject.* And this clearly is not always what we mean to 
assert. And such further examples as " There are no ghosts," 
or " This thought is an illusion," may be likewise disposed of. 
It is not the first form and haphazard conjunction of every 
proposition which represents reality. But, in every proposi 
tion, an analysis of the meaning will find a reality of which 
something else is affirmed or denied. " The nature of space 
excludes the connection of square and round," " The world 
is no place where ghosts exist," " I have an idea, but the 
reality it refers to is other than its meaning," we may offer 
these translations as preliminary answers to a first form of 
attack. And when Herbart assails us with " The wrath of 
the Homeric gods is fearful " (I. 99), we need give no ground 
before such a weapon. In Homer it is so ; and surely a poem, 
surely any imagination, surely dreams and delusions, and 
surely much more our words and our names are all of them 
facts of a certain kind. Such plain distinctions as those be 
tween existences of different orders 3 should never have been 
confused, and the paradox lies on the side of those who urge 
such an objection, f 

*Ueberweg seems to make this mistake, Loglk, 68. 

fl admit that there are difficulties which for the moment we 
ignore. When no one reads Homer, of what subject can we predicate 
the wrath of his deities? Though the meaning of a term is a fact, 
most certain and quite undeniable, yet where is that fixed connection 



CHAP. II FORMS OF JUDGMENT 43 

And if, further, the discussion take the misleading form of 
an enquiry into the copula, we find merely the same misunder 
standings unknowingly reproduced. Wherever we predicate, 
we predicate about something which exists beyond the judg 
ment, and which (of whatever kind it may be) is real, either 
inside our heads or outside them. And in this way we must 
say that " is " never can stand for anything but " exists." * 

3. But Herbart, we shall find, is not so easily disposed of. 
He was not the man first uncritically to swallow the common- 
sense doctrine that judgment is of things, and then to stagger 
at the discovery that things are not words, or fall prostrate 
before a supposed linguistic revelation of the nature of the 
copula. In denying that judgment asserts a fact, he knew 
well what he stood on. It was no puzzle about the gram 
matical subject, but a difficulty as to the whole nature of truth 
and of ideas. We reflect about judgment, and, at first of 
course, we think we understand it. Our conviction is that it 
is concerned with fact; but we also see that it is concerned 
with ideas. And the matter seems at this stage quite simple. 
We have a junction or synthesis of ideas in the mind, and this 
junction expresses a similar junction of facts outside. Truth 
and fact are thus given to us together, the same thing, so to 
speak, in different hemispheres or diverse elements. 

But a further reflection tends to dissipate our confidence. 
Judgments, we find, are the union of ideas, and truth is not 
found except in judgments. How then are ideas related to 
realities? They seemed the same, but they clearly are not 
so, and their difference threatens to become a discrepancy. 
A fact is individual, an idea is universal ; a fact is substantial, 

to be found? Does it lie in the dictionaries when no one opens them, 
or in the usage when no one is employing the word? But these 
questions bear as hardly on fact as on legend, and on things as on 
names. Mathematical truths at the least hold good inside mathematics. 
But where are mathematics? And we all believe that arsenic 
poisons, but if at the moment no dose is operating, nor any one in 
the world is thinking of arsenic, it poisons nothing. We shall here 
after return to the discussion of this problem. 

* The reader may consult Jordan. Die Zwcideutigkeit des Copula 
bei Stuart Mill, Gymn. Prog. Stuttgart, 1870; Brentano, Psychologic, 
Buch ii. Cap. 7. On the other side see Drobisch. Logik, 55-6, 
Sigwart, Logik, I. 94. 



44 THE PRINCIPLES OF LOGIC BOOK I 

an idea is adjectival; a fact is self -existent, an idea is sym 
bolical. Is it not then manifest that ideas are not joined in 
the way in which facts are? Nay the essence of an idea, the 
more it is considered, is seen more and more to diverge from 
reality. And we are confronted by the conclusion that, so far 
as anything is true, it is not fact, and, so far as it is fact, it can 
never be true. Or the same result may have a different form. 
A categorical judgment makes a real assertion in which some 
fact is afBrmed or denied. But, since no judgment can do 
this, they all in the end are hypothetical. They are true only 
of and upon a supposition. In asserting S P I do not mean 
that S, or P, or their synthesis, is real. I say nothing about 
any union in fact. The truth of S P means that, if I sup 
pose S, I am bound in that case to assert S P. In this way 
all judgments are hypothetical.* 

The conclusion, thus urged upon us by Herbart, follows, I 
think, irresistibly from the premises. But the premises are 
not valid. Judgment, we saw in the foregoing chapter, can 
not consist in the synthesis of ideas. And yet it will repay 
us to pause awhile, and to enlarge on the consequences of this 
erroneous doctrine. To see clearly that, if judgment is the 
union of ideas, there then can be no categorical judgment, is 
a very great step in the understanding of Logic. And, through 
the next few sections, we shall endeavour to make this con 
clusion plain. 

4. The contrast and comparison of reality and truth no 
doubt involve very ultimate principles. To enquire what is 
fact, is to enter at once on a journey into metaphysics, the 
end of which might not soon be attained. For our present 
purpose we must answer the question from a level not much 
above that of common sense. 4 And the account which repre 
sents the ordinary view, and in which perhaps we may most 
of us agree, is something of this sort. 

The real is that which is known in presentation or intuitive 
knowledge. It is what we encounter in feeling or perception. 
Again it is that which appears in the series of events that 
occur in space and time. It is that once more which resists 
our wills; a thing is real if it exercises any kind of force or 

* Herbart, Werke, I. 92. He refers here to Wolff, by whom, in this 
point, he had been partially anticipated. Cf. Fichte, Werke, I. 69, 93. 



CHAP. II FORMS OF JUDGMENT 45 

compulsion, or exhibits necessity. It is briefly what acts and 
maintains itself in existence. And this last feature seems 
connected with former ones. We know of no action, unless it 
shows itself by altering the series of either space or time, or 
both together ; 5 and again perhaps there is nothing which 
appears unless it acts. But the simplest account, in which the 
others possibly are all summed up, is given in the words, The 
real is self-existent. And we may put this otherwise by saying, 
The real is what is individual. 

It is the business of metaphysics to subject these ideas to 
a systematic examination. We must content ourselves here 
with taking them on trust, and will pause merely to point out 
a common misunderstanding. It is a mistake to suppose 
that " The real is individual " means either that the real is 
abstractly simple, or is merely particular. Internal diversity 
does not exclude individuality, and still less is a thing made 
self-existent by standing in a relation of exclusion to others. 
Metaphysics can prove that, in this sense, the particular is 
furthest removed from self -existence. The individual is so far 
from being merely particular that, in contrast with its own 
internal diversity, it is a true universal (cf. Chap. VI.). Nor 
is this a paradox. We are accustomed to speak of, and believe 
in, realities which exist in more than one moment of time or 
portion of space. Any such reality would be an identity 
which appears and remains the same under differences; and 
it therefore would be a real universal.* 

5. Such, we may say, are some of the points which con 
stitute reality. And truth has not one of them. It exists, 
as such, in the world of ideas. And ideas, we have seen, are 
merely symbols. They are general and adjectival, not sub 
stantive and individual. Their essence lies within their mean 
ing and beyond their existence. The idea is the fact with its 
existence disregarded, and its content mutilated. It is but a 
portion of the actual content cut off from its reality, and 

*The following reflection may interest the reader. If space and 
time are continuous, and if all appearance must occupy some time or 
space and it is not hard to support both these theses we can at once 
proceed to the conclusion, no mere particular exists. Every phenom 
enon will exist in more times or spaces than one ; and against that 
diversity will be itself an universal. 



46 THE PRINCIPLES OF LOGIC BOOK I 

used with a reference to something else. No idea can be 
real. 

If judgment is the synthesis of two ideas, then truth con 
sists in the junction of unreals. When I say, Gold is yellow, 
then certainly some fact is present to my mind. But universal 
gold and universal yellowness are not realities, and, on the 
other hand, what images 6 of yellow and gold I actually pos 
sess, though as psychical facts they have real existence, are 
unfortunately not the facts about which I desired to say any 
thing. We have seen (Chap. I.) that I do not mean, This 
image of gold is in my mind joined psychically with this other 
image of yellow. I mean that, quite apart from my mental 
facts, gold in general has a certain kind of colour. I strip 
away certain parts from the mental facts, and, combining these 
adjectival remnants, I call the synthesis truth. 

But reality is not a connection of adjectives, nor can it so 
be represented. Its essence is to be substantial and individual. 
But can we reach self -existence and individual character by 
manipulating adjectives and putting universals together? If 
not, the fact is not given directly in any truth whatsoever. 
It can never be stated categorically. And yet, because adjec 
tives depend upon substantives, the substantive is implied. 
Truth will then refer to fact indirectly. The adjectives of 
truth presuppose a reality, and in this sense all judgment will 
rest on a supposal. It is all hypothetical; itself will confess 
that what directly it deals with, is unreal. 

6. More ordinary considerations might perhaps have led 
us to anticipate this result. The common-sense view of facts 
outside us passing over into the form of truth within us, or 
copying themselves in a faithful mirror, is shaken and per 
plexed by the simplest enquiries. What fact is asserted in 
negative judgments? Has every negation I choose to invent 
a real counterpart in the world of things? Does any logical 
negation, as such, correspond to fact? Consider again hypo 
thetical judgments. // something is, then something else fol 
lows, but should neither exist, would the statement be false? 
It seems just as true without facts as with them, and, if so, 
what fact can it possibly assert? The disjunctive judgment 
will again perplex us. " A is b or c " must be true or false, 
but how in the world can a fact exist as that strange ambiguity 



CHAP. II FORMS OF JUDGMENT 47 

" b or c?" We shall hardly find the flesh and blood alterna 
tive which answers to our " or." 

If we think these puzzles too technical or sought out, let 
us take more obvious ones. Have the past and the future we 
talk of so freely any real existence? Or let us try a mere 
ordinary categorical affirmative judgment, " Animals are 
mortal." This seems at first to keep close to reality; the 
junction of facts seems quite the same as the junction of ideas. 
But the experience we have gained may warn us that, if ideas 
are adjectives, this can not be the case. If we are uncon 
vinced, let us go on to examine. " Animals " seems perhaps 
to answer to a fact, since all the animals who exist are real. 
But, in " Animals are mortal," is it only the animals now 
existing that we speak of? Do we not mean to say that the 
animal born hereafter will certainly die? The complete col 
lection of real things is of course the same fact as the real 
things themselves, but a difficulty arises as to future individ 
uals. And, apart from that, we scarcely in general have in 
our minds a complete collection. We mean, " Whatever is an 
animal will die," but that is the same as // anything is an 
animal then it is mortal. The assertion really is about mere 
hypothesis; it is not about fact. 

In universal judgments we may sometimes understand that 
the synthesis of adjectives, which the judgment expresses, 
is really found in actual existence. But the judgment does 
not say this. It is merely a private supposition of our own. 
It arises partly from the nature of the case, and partly again 
from our bad logical tradition. The fact that most adjectives 
we conjoin in judgment can be taken as the adjectives of 
existing things, leads us naturally to expect that this will 
always be the case. And, in the second place, a constant 
ambiguity arises from the use of " all " in the subject. We 
write the universal in the form " All animals," and then take 
it to mean each actual animal, or the real sum of existing 
animals. But this would be no more an universal judgment 
than " A B and C are severally mortal." And we mean noth 
ing like this. In saying " All animals," if we think of a collec 
tion, we never for a moment imagine it complete; we mean 
also " Whatever besides may be animal must be mortal too." 
In universal judgments we never mean " all." What we mean 



48 THE PRINCIPLES OF LOGIC BOOK I 

is "any," and "whatever," and "whenever." But these 
involve " if." 

We may see this most easily by a simple observation. If 
actual existence were really asserted, the judgment would be 
false if the existence failed. And this is not the case. It 
would be a hazardous assertion that, supposing all animal life 
had ceased, mortality would at once be predicated falsely, 
and, with the re-appearance of animal existence, would again 
become true. But cases exist where no doubt is possible. 
" All persons found trespassing on this ground will be prose 
cuted," is too often a prophecy, as well as a promise. But it 
is not meant to foretell, and, though no one trespasses, the 
statement may be true. " All triangles have their angles equal 
to two right angles " would hardly be false if there were no 
triangles. And, if this seems strange, take the case of a 
chiliagon. Would statements about chiliagons cease to be 
true, if no one at the moment were thinking of a chiliagon? 
We can hardly say that, and yet where would any chiliagons 
exist? There surely must be scientific propositions, which 
unite ideas not demonstrable at the moment in actual existence. 
But can we maintain that, if the sciences which produce these 
became non-existent, these judgments would have ipso facto 
become false, as well as unreal? 

The universal judgment is thus always hypothetical. It 
says " Given one thing you will then have another," and it 
says no more. No truth can state fact. 

7. This result is however not easy to put up with. For, 
if the truth is such, then all truths, it would seem, are no 
better than false. We can not so give up the categorical 
judgment, for, if that is lost, then everything fails. Let us 
make a search and keep to this question, Is there nowhere to 
be found a categorical judgment? And it seems we can find 
one. Universal judgments were merely hypothetical, because 
they stated, not individual substantives, but connections of 
adjectives. But in singular judgments the case is otherwise. 
Where the subject, of which you affirm categorically, is one 
individual, or a set of individuals, your truth expresses fact. 
There is here no mere adjective and no hypothesis. 

These judgments are divisible into three great classes. 7 
And the distinction will hereafter be of great importance, (i) 



CHAP. II FORMS OF JUDGMENT 49 

We have first those judgments which make an assertion about 
that which I now perceive, or feel, or about some portion of 
it. " I have a toothache," " There is a wolf," " That bough is 
broken." In these we simply analyze the given, and may there 
fore call them by the name of Analytic judgments of sense * 
Then (ii) we have Synthetic judgments of sense, which state 
either some fact of time or space, or again some quality of the 
matter given, which I do not here and now directly perceive. 
" This road leads to London," " Yesterday it rained," " To 
morrow there will be full moon." They are synthetic because 
they extend the given through an ideal construction, and they 
all, as we shall see, involve an inference. The third class (Hi), 
on the other hand, have to do with a reality which is never a 
sensible event in time. " God is a spirit," " The soul is a sub 
stance." We may think what we like of the validity of these 
judgments, and may or may not decline to recognize them in 
metaphysics. But in logic they certainly must have a place. 

8. But, if judgment is the union of two ideas, we have 
not so escaped. And this is a point we should clearly recog 
nize. Ideas are universal, and, no matter what it is that 
we try to say and dimly mean, what we really express and 
succeed in asserting, is nothing individual. For take the 
analytic judgment of sense. The fact given us is singular, it 
is quite unique; but our terms are all general, and state a 
truth which may apply as well to many other cases. In " I 
have a toothache" both the I and the toothache are mere 
generalities. The actual toothache is not any other toothache, 
and the actual I is myself as having this very toothache. But 
the truth I assert has been and will be true of all other tooth 
aches of my altering self. Nay " I have a toothache," is as 
true of another s toothache as of my own, and may be met by 
the assertion, " Not so, but / have one." It is in vain that we 
add to the original assertion " this," " here," and " now," for 
they are all universals. They are symbols whose meaning 
extends to and covers innumerable instances. 

Thus the judgment will be true of any case whatsoever 

* These analytic and synthetic judgments must not for one moment 
be confounded with Kant s. Every possible judgment, we shall see 
hereafter, is both analytic and synthetic. Most, if not all, judgments 
of sense are synthetic in the sense of transcending the given. 



5O THE PRINCIPLES OF LOGIC BOOK I 

of a certain sort; but, if so, it can not be true of the reality; 
for that is unique, and is a fact, not a sort. " That bough is 
broken," but so are many others, and we do not say which. 
" This road leads to London " may be said just as well of a 
hundred other roads. " To-morrow it will be full moon," does 
not tell us what to-morrow. Hereafter it will constantly be 
true that, on the day after this day, there will be a full moon. 
And so, failing in all cases to state the actual fact, we state 
something else instead. What is true of all does not express 
this one. The assertion sticks for ever in the adjectives; it 
does not reach the substantive. And adjectives unsupported 
float in the air ; their junction with reality is supposed and 
not asserted. So long as judgments are confined to ideas, 
their reference to fact is a mere implication. It is presupposed 
outside the assertion, which is not strictly true until we qualify 
it by a suppressed condition. As it stands, it both fails as a 
singular proposition, and is false if you take it as a strict 
universal (cf. 62 foil.). 8 

9. But judgment, as we saw in the foregoing Chapter, is 
not confined to ideas, and can not by any means consist in 
their synthesis. The necessity for two ideas is a mere delusion, 
and, if before we judged we had had to wait for them, we 
certainly should never have judged at all. And the necessity 
for the copula is a sheer superstition. Judgments can exist 
without any copula and with but one idea. 

In the simplest judgment an idea is referred to what is 
given in perception, and it is identified therewith as one of its 
adjectives. There is no need for an idea to appear as the 
subject, and, even when it so appears, we must distinguish the 
fact from grammatical show. 9 It is present reality which is 
the actual subject, and the genuine substantive of the ideal 
content. We shall see hereafter that, when " this " " here " 
and " now " seem to stand as subjects, the actual fact which 
appears in perception is the real subject, to which these 
phrases serve to direct our attention. But of this in the 
sequel; we have seen already, and have further to see, that 
all judgments predicate their ideal content as an attribute of 
the real which appears in presentation. 

It is from this point of view that we must resume the 
discussion. Standing on this basis, we must examine afresh 



CHAP. II FORMS OF JUDGMENT 5! 

the various judgments which have passed before us, and must 
ask for their meaning and further validity. Some difficulties 
in our search for categorical judgments may have already 
disappeared; but others as formidable must perhaps be 
awaited. And, if we come to the result that all truth in the 
end is true of reality, we must not expect to maintain that 
doctrine in its crude acceptation. 

10. Our first movement however must be towards a 
definition. A phrase we have used was designedly am 
biguous. Are we to hold that the real, which is the ultimate 
subject, and which, as we said, appears in perception, is 
identical with the merely momentary appearance? We shall 
see that this can not be, and that such a view could not 
possibly account for the facts. At present we may offer 
a preliminary argument against this mistake. 

The subject which appears in the series of time, and to 
which we attribute our ideas as predicates, must itself be real. 
And, if real, it must not be purely adjectival. On the 
contrary it must be self-existent and individual. But the 
particular phenomenon, the momentary appearance, is not 
individual, and is so not the subject which we use in judgment. 

11. We naturally think that the real, at least as we 
know it, must be present. Unless I come into contact with it 
directly, I can never be sure of it. Nothing in the end but 
what I feel can be real, and I can not feel anything unless it 
touches me. But nothing again can immediately encounter 
me save that which is present. 10 If I have it not here and now, 
I do not have it at all. 

" The present is real " ; this seems indubitable. And are 
we to say that the momentary appearance is therefore real? 
This indeed would be mistaken. If we take the real as that 
which is confined to a single " here " or a single " now " (in 
this sense making it particular), we shall have questions on 
our hands we shall fail to dispose of. For, beside the diffi 
culties as to the truth of all universal judgments, we are 
threatened with the loss of every proposition which extends 
beyond the single instant. Synthetic judgments must at once 
be banished if the real is only the phenomenon of a moment. 
Nothing either past or future in time, nor any space I do not 



52 THE PRINCIPLES OF LOGIC BOOK I 

directly perceive, can be predicated as adjectives of our one 
" now " and " here." All such judgments would be false, 
for they would attribute to the existent qualities which con 
fessedly are non-existent, or would place the real as one 
member in a series of utter unrealities. 

But perhaps we feel we may escape this consequence ; or at 
all events feel so sure of our premise that we can not give it 
up. " The real is confined to one here or one now." But 
supposing this true, are we sure we know what it is we under 
stand by our " now " and " here " ? For time and extension 
seem continuous elements; the here is one space with the 
other heres round it; and the now flows ceaselessly and 
passes for ever from the present to the past. 

We may avoid this difficulty, we may isolate the time we 
call the present, and fix our now as the moment which is, and 
has neither past, nor future, nor transition in itself. But here 
we fall into a hopeless dilemma. This moment which we 
take either has no duration, and in that case it turns out no 
time at all; or, if it has duration, it is a part of time, and is 
found to have transition in itself. 

If the now in which the real appears is purely discrete, 
then first we may say that, as characterized by exclusion, the 
phenomenon, if apparent, is not self-subsistent, and so not real. 
But apart from that objection, and to return to our dilemma, 
the now and the here must have some extension. For no 
part of space or time is a final element. We find that every 
here is made up of heres, and every now is resolvable into 
nows. And thus the appearance of an atomic now could not 
show itself as any one part of time. But, if so, it could never 
show itself at all. Or, on the other hand, if we say the 
appearance has duration, then, like all real time, it has suc 
cession in itself, and it would not be the appearance of our 
single now.* From all which it is clear that a momentary ap 
pearance will not give us the subject of which we are in search. 

* It is the business of metaphysics to prove these points at length. 
If time consists of discrete parts, it is hard to see how the fact of 
succession can possibly be explained, unless time be taken between 
these parts of time. And that would lead to untenable conclusions. 
But it is the fact of change which shows that time is continuous. 
The rate of change, the number of events in every part of time, may, 



CHAP. II FORMS OF JUDGMENT 53 

12. It is a mistake to suppose that the present is a part 
of time, indivisible and stationary, and that here and now can 
be solid and atomic. In one sense of the word the present is 
no time. Itself no part of the process, it is a point we take 
within the flow of change. It is the line that we draw across 
the stream, to fix in our minds the relations of one successive 
event to another event. " Now," in this sense, stands for 
" simultaneous with " ; it signifies not existence but bare po 
sition in the series of time. The reality is not present in the 
sense of given in one atomic moment. 

What we mean, when we identify presence with reality, is 
something different. The real is that with which I come into 
immediate contact, and the content of any part of time, any 
section of the continuous flow of change, is present to me if I 
directly encounter it. What is given in a perception, though 
it change in my hands, is now and here if only I perceive it. 
And within that perception any aspect or part, which I spe 
cially attend to, is specially present, is now and here in 
another sense than the rest of that content. The present is 
the filling of that duration in which the reality appears to me 
directly ; and there can be no part of the succession of events 
so small or so great, that conceivably it might not appear as 
present. 

In passing we may repeat and may trace the connection 
of those shades of meaning we have found in " presence." (i) 
Two events in time are now to one another, if both are given 
simultaneously in my series, (ii) Since the real appears in the 
series of time, the effort to find it both present and existmg 
within that series, creates the fiction of the atomic now. (iii) 
If the real can never exist in time, but only appear there, then 
that part of the series in which it touches me is my present, 
(iv) And this suggests the reflection that presence is really 
the negation of time, and never can properly be given in the 

so far as we know, be increased indefinitely; and this means that in 
every part. of time more than one event may take place. If the parts 
be discrete, then not only will motion imply that a thing is in several 
places in one time (and this is a fact), but also (which is absurd) 
that throughout all these places no time elapses, that they are strictly 
contemporaneous. I should be glad to enter into the discussion at 
length, but the subject cannot properly be treated by logic. 

2321. I E 



54 THE PRINCIPLES OF LOGIC BOOK I 

series. It is not the time that can ever be present, but only 
the content. 

13. But we must leave these intricacies. We must be 
satisfied with knowing that the real, which (we say) appears 
in perception, does not appear in one single moment. And 
if we will pause and reflect for a little, we shall see how 
hardened we are in superstitions. When we ask for reality, 
we at once encounter it in space and time. We find opposed 
to us a continuous element of perpetual change. We begin to 
observe and to make distinctions, and this element becomes 
a series of events. And here we are tempted to deceive our 
selves grossly. We allow ourselves to talk as if there existed 
an actual chain of real events, and as if this chain were some 
how moved past us, or we moved along it, and as if, whenever 
we came to a link, the machinery stopped and we welcomed 
each new link with our " here " and our " now." Still we do 
not believe that the rest of the links, which are not here and 
now, do all equally exist, and, if so, we can hardly be quite 
sure of our chain. And the link, if we must call it so, which 
is now and here, is no solid substance. If we would but 
observe it, we should see it itself to be a fluid sequence whose 
parts offer no resistance to division, and which is both now, 
and itself without end made up of nows. 

Or we seem to think that we sit in a boat, and are carried 
down the stream of time, and that on the banks there is a 
row of houses with numbers on the doors. And we get out 
of the boat, and knock at the door of number 19, and, re- 
entering the boat, then suddenly find ourselves opposite 20, 
and, having there done the same, we go on to 21. And, all 
this while, the firm fixed row of the past and future stretches 
in a block behind us and before us. 

If it really is necessary to have some image, perhaps the 
following may save us from worse. Let us fancy ourselves in 
total darkness hung over a stream and looking down on it. 
The stream has no banks, and its current is covered and filled 
continuously with floating things. Right under our faces is a 
bright illuminated spot on the water, which ceaselessly widens 
and narrows its area, and shows us what passes away on the 
current. And this spot that is light is our now, our present. 

We may go still further and anticipate a little. We have 



CHAP. II FORMS OF JUDGMENT 55 

not only an illuminated place, and the rest of the stream in 
total darkness. There is a paler light which, both up and 
down stream, is shed on what comes before and after our 
now. And this paler light is the offspring of the present. 
Behind our heads there is something perhaps which reflects the 
rays from the lit-up now, and throws them more dimly upon 
past and future. Outside this reflection is utter darkness; 
within it is gradual increase of brightness, until we reach 
the illumination immediately below us. 

In this image we shall mark two things, if we are wise. It 
is possible, in the first place, that the light of the present may 
come from behind us, and what reflects the light may also 
bestow it. We can not tell that, but what we know is, that 
our now is the source of the light that falls on the past and 
future. Through it alone do we know there exists a stream 
of floating things, and without its reflection past and future 
would vanish. And there is another point we must not lose 
sight of. There is a difference between the brightness of 
the now, and the paler revelation of past and future. But, 
despite this difference, we see the stream and what floats in it 
as one. We overcome the difference. And we do so by see 
ing the continuity of the element in past, present and future. 
It is because, through the different illuminations, there are 
points of connection offered by what floats, in other words, a 
sameness of content, that the stream and its freightage be 
come all one thing to us, and we even forget that most of 
what we see is not self-subsistent but borrowed and adjecti 
val. We shall perceive hereafter that time and space beyond 
here and now are not strictly existent in the sense in which 
the present is. They are not given directly but are inferred 
from the present. And they are so inferred because the 
now and here, on which the light falls, are the appearance 
of a reality which for ever transcends them, and upon which 
resting we go beyond them. 

14. But this is to anticipate. The result, which at pres 
ent we have wished to make clear, is that the now and here, 
in which the real appears, are not confined within simply 
discrete and resting moments. They are any portion of that 
continuous content with which we come into direct relation. 
Examination shows that not only at their edges they dissolve 



56 THE PRINCIPLES OF LOGIC BOOK I 

themselves over into there and then, but that, even within 
their limits as first given, they know no repose. Within the 
here is both here and there; and in the ceaseless process of 
change in time you may narrow your scrutiny to the smallest 
focus, but you will find no rest. The appearance is always a 
process of disappearing, and the duration of the process which 
we call our present has no fixed length. 

It will be seen hereafter that in the above reflections we have 
not been wandering. Nor will it be long before we return to 
them, but we must now rediscuss from a better point of view 
those forms of judgment we before laid down (7). 

15. Judgment is not the synthesis of ideas, but the refer 
ence of ideal content to reality. From this basis we must 
now endeavour to interpret the various kinds of judgment we 
have met with. And, beginning with the singular judgments 
of 7, let us take the first division of these, which were called 
Analytic judgments of sense. 

I. The essence of these is to hold only of the now, and not 
to transcend the given presentation. They may have neither 
grammatical subject nor copula, or again, on the other hand, 
may possess one or both. 

A. In the judgments that have neither copula nor subject, 
an idea is referred (a) to the whole sensible reality, or (/?) to 
some part of it. 11 

(a) When we hear the cry of "Wolf," or "Fire," or 
" Rain," it is impossible to say that we hear no assertion. He 
who raises the cry is always taken to affirm, to have uttered a 
sign and to have used it of the real. The practical man would 
laugh at your distinction that, in exclaiming " Wolf," I can 
not be a liar, because I use no subject or copula, but that, if 
I go so far as " This is a wolf," I am thereby committed. 
Such a plea, we must allow, would be instantly dismissed. In 
the " Wolf " or " Rain " the subject is the unspecified present 
environment, and that is qualified by the attribution of the 
ideal content " Wolf " or " Rain." It is the external present 
that is here the subject. But in some moment of both outward 
squalor and inward wretchedness, where we turn to one an 
other with the one word " miserable," the subject is here the 
whole given reality. 



CHAP. II FORMS OF JUDGMENT 57 

Such single words, it may perhaps be said, are really 
interjections and never predicates. If they were really inter 
jections, we must stubbornly maintain, they could not be the 
vehicle of truth and falsehood. And a real interjection that 
is nothing besides, is not so common as some persons suppose. 
An habitual interjection soon gets a meaning, and becomes 
the sign of a received idea, which, in reference to the content, 
may be an assertion of truth or falsehood. 

But the fact is really beyond all question. You may utter 
a word which conveys to you, and which you know conveys 
to others also, a statement about fact. Unless then you are 
deceiving, you must be judging. And you certainly are judg 
ing without any other subject than the whole sensible present. 

(/?) But this is an extreme case; in nearly all instances 
but one piece of the present is the real subject. We qualify 
by our idea some one given aspect. But no subject or copula 
appears even here. A common understanding, or the pointing 
of a finger, is all that serves to limit the reference. Of a 
visible wolf I may predicate the words " asleep " or " running," 
or in watching a sunset, it is enough for me to say the word 
" down " or " gone," and every one knows I am judging and 
affirming. It might be said, no doubt, that the subject is 
elided, but this would be a mere linguistic prejudice. The 
genuine subject is not an idea, elided or expressed, but it is 
the immediate sensible presentation.* 

And again it might be said that what we call the predicate 
is really the subject of an unexpressed existential judgment. 
But this cardinal mistake will be soon disposed of, when here 
after we deal with that class of judgments (42). 

15. B. We pass next to those analytic judgments where 
a subject is expressed. The ideal content of the predicate is 
here referred to another idea, which stands as a subject. But 
in this case, as above, the ultimate subject is no idea, but is 
the real in presentation. It is this to which the content of 
both ideas, with their relation, is attributed. The synthesis of 
the ideal elements is predicated either (a) of the whole, or (yj) 
of a part, of that which appears. 

(a) In such judgments as " Now is the time," " It s all so 
dreary," or " The present is dark," an idea takes the place of 
*For a further explanation, vid. Chap. III. 2. 



58 THE PRINCIPLES OF LOGIC BOOK I 

the unspoken reference of the preceding section. But the 
subject remains in both cases the same. An idea, it is true, 
intervenes between the reality and the predicate, and holds the 
place of immediate subject. But a moment s consideration 
will assure us that the subject of our assertion is still the 
presented. The immediate subject is the sign of a reference, 
either simple or embodying implications, to the whole given 
reality. 

(/?) We have a further advance when the presented fact 
is not the whole sensible environment, but only a part of it. 
In " There is a wolf," " This is a bird," or " Here is a fire," 
" there " " this " and " here " are certainly ideas, and stand no 
doubt for the subject of the judgment : * but, the moment we 
examine them, we find once more a reference to the reality, 
not now indefinite and embracing the whole, but still no more 
than a sign of distinction and indication. If these ideas are 
the true subject of a judgment, then so is a silent pointing 
with the finger. 

1 6. There is really no change when we go a step further, 
and take such judgments as " This bird is yellow," " That stone 
is falling," " This leaf is dead." The idea, which stands as the 
grammatical subject, is certainly more than an indefinite refer 
ence, more even than a sign of indication. It not only distin 
guishes a part from the environment, but it also characterizes 
and qualifies it. But if, before, the subject we meant was not 
an idea, but was presented fact, so also now does this remain 
the truth. It is not the bare idea, symbolized by " this bird," 
of which we go on to affirm the predicate. It is the fact dis 
tinguished and qualified by " this bird," to which the adjective 
" yellow " is really attributed. The genuine subject is the 
thing as perceived, the content of which our analysis has 
divided into " this bird " and " yellow," and of which we predi 
cate indirectly those ideal elements in their union. 

The same account holds throughout all the variety of these 
analytic judgments. Let us complicate our assertion. " The 
cow, which is now being milked by the milk-maid, is standing 

*It sounds, perhaps, rather shocking to call "there" or "here" 
subjects, but, if the text is understood, I need make no defence. On 
the nature of the ideas of "this," "now," and "here," we shall find 
later on a good deal to say. 



CHAP. II FORMS OF JUDGMENT 59 

to the right of the hawthorn tree yonder." In this judgment 
we have not one thing but several, and more than one state 
ment about their relations. But it is still a part of the pre 
sented environment which is actually the subject and the real 
substantive of which this whole complex is indirectly asserted. 
If you deny this, then show me where you draw your line, 
and what point it is in the scale of judgments at which the 
idea takes the place of the sensible fact, and becomes the true 
subject. And confine the assertion to mere ideas. Take the 
ideal elements of a cow and a hawthorn tree and a milk-maid, 
and combine them ideally in any way you please. Then after 
they are combined, stand in presence of the fact, and ask 
yourself if that does not enter into your judgment. If, with 
the fact before you, you begin to reflect, you will find that, 
if you keep to mere ideas, you remove from the assertion just 
the thing you mean. In 20 we shall return to this point, 
but at present we may deal with a popular error. 

17. There is a curious illusion, now widely spread, on 
the subject of proper names. 12 We find it laid down that a 
proper name has not got connotation, or, to use the more 
common technical term, it has no intension. In ordinary lan 
guage, it stands for something but does not mean anything. 

If this were true, it would be hard to understand what is 
signified by such judgments as "John is asleep." There are 
thinkers indeed, who fear no consequence, and who will tell us 
that here the name John is the subject of the proposition. And 
against these adversaries I confess I have no heart to enter 
the lists. They may say what they please without hindrance 
from me. But, if we are inclined to accept a less heroic 
solution, and to suppose the man John to be the subject of the 
judgment, then I do not quite see the purpose of the name, if 
we are not to mean by it anything at all. Why not simply 
omit it, and, pointing to the man, say the word " asleep " ? 

" But it stands for the man," I shall hear the reply, " and, 
even when he is present, it is a mark which serves to dis 
tinguish him much more clearly than pointing." But that is 
just what puzzles me. If there is an idea conveyed by the 
name, whenever it is used, then it surely means something, or, 
in the language which pleases you, it must be " connotative." 
But if, on the other hand, it conveys no idea, it would appear 



60 THE PRINCIPLES OF LOGIC BOOK I 

to be some kind of interjection. If you say that, like " this " 
and " here," it is merely the ideal equivalent of pointing, then 
at once it assuredly has a meaning, but unfortunately that 
meaning is a vague universal. For anything and everything is 
" this " and " here." But if you asseverate that it is the ideal 
counterpart of pointing in particular to John, then you must 
allow me to doubt if you comprehend what you are saying. 

The word " mark " has two senses which perhaps we may 
confuse. It is something which may be made a means of 
distinction, or something which has been made such a means. 
I suppose, for I can do no more than suppose, that mark is 
not taken in the former sense, and that our man was not seen 
to be distinct from other men, because he was found to have 
the marking John. But, if it is the latter of these senses we 
adopt, then a name is a mark because it is a sign, and mark 
and sign are here identical. 

Now a sign can not possibly be destitute of meaning. 
Originally imposed as an arbitrary mark, that very process, 
which makes it a sign and associates it firmly with the thing 
it signifies, must associate with it also some qualities and 
characters of that which it stands for. If it did not to some 
extent get to mean the thing, it never could get to stand for it 
at all. And can any one say that a proper name, if you are 
aware of its designation, brings no ideas with it, or that these 
ideas are mere chance conjunction? What connection, I would 
ask, would be left between the bare name and the thing it 
stands for, if every one of these ideas were removed? All 
would vanish together. 

The matter is so plain I do not know how to explain it. 
The meaning of a sign need of course not be fixed. But is 
the thing it stands for quite invariable? If the " connotation " 
is unsteady, does the " denotation " never change? But where 
the latter is fixed there the former on its side (within limits) 
is stationary. You may have no idea what " William " con 
notes, but if so you can hardly know what it stands for. The 
whole question arises from a simple mistake and misunder 
standing. 

18. " But after all the name is the sign of an individual, 
and meanings are generic and universal. Therefore the name 
can not have any content of which it is the sign." I have 



CHAP. II FORMS OF JUDGMENT 6l 

purposely put an objection in that form which suggests the 
conclusion I wish to arrive at. The name of a man is the 
name of an individual, which remains amid changing par 
ticulars, and therefore no judgment about such an individual 
is wholly analytic. It transcends the given, it becomes syn 
thetic, and with it we pass into the second great division of 
singular judgments. 

Proper names have a meaning which always goes beyond 
the presentation of the moment. It is not indeed true that 
such names must stand for objects, which endure through a 
train of altering perceptions. The unique thing they designate 
may appear but once, as an event shut up within one presen 
tation. But that object would not be unique, nor proper to its 
own especial self, if it did not involve a reference to a series 
from which it was excluded. And mere analysis of sense 
could never suggest that limiting relation which gives it 
uniqueness. 

And, when we take the proper names of objects which last 
and which reappear, then the given is transcended in a still 
higher sense. The meaning of such a name is universal, and 
its use implies a real universality, an identity which transcends 
particular moments. For, unless the person were recognized 
as distinct, he would hardly get a name of his own, and his 
recognition depends on his remaining the same throughout 
change of context. We could not recognize anything unless 
it possessed an attribute, or attributes, which from time to 
time we are able to identify. The individual remains the same 
amid that change of appearance which we predicate as its 
quality. And this implies that it has real identity. Its proper 
name is the sign of a universal, of an ideal content which 
actually is in the real world. 

This assumption, and the practice of giving proper names, 
may no doubt be indefensible. What concerns us here is 
that the practice transcends presented reality. In "John is 
asleep," the ultimate subject can not be the real as it is now 
given ; for " John " implies a continuous existence, not got by 
mere analysis. We have reached the class of synthetic judg 
ments. 

19. II. In this second class of singular judgments (7) 
we make generally some assertion about that which appears 



62 THE PRINCIPLES OF LOGIC BOOK I 

in a space or time that we do not perceive, and we predicate 
of a presentation something not got by analysis of its content. 
If I say " There is a garden on the other side of that wall," 
the judgment is synthetic, for it goes beyond perception. And 
in "Yesterday was Sunday," "William conquered England," 
" Next month is June," I certainly do not analyze what is 
merely given. In synthetic judgments there is always an 
inference, 13 for an ideal content is connected with the sensible 
qualities that are given us. In other words we have always 
a construction, which depends on ideas, and which only indi 
rectly is based on perception (vid. Book II.). 

And, this being so, it seems as if now we were unable to 
proceed. If the subject is the real that appears in perception, 
how can events in the past and future, or a world in space out 
side the presentation, and how even can qualities not given to 
sense be referred to the object and considered as its adjectives? 
We have already glanced at the solution of this problem, and 
what we now wish to show is the following. In synthetic 
judgments the ultimate subject is still the reality. That is not 
the same as the momentary appearance, and yet synthetic 
judgments are possible only by being connected with what is 
given at this very instant. The ideas of past and future events 
are projected from the base of present perception. It is only 
in that point that they encounter the reality of which they 
wish to be true. 

" But past and future," the reader may object, " are surely 
realities." Perhaps they are, but our question is, Given a 
synthesis of ideas within my mind, how and where am I able 
to get at a reality to which to attribute them ? 14 How am I to 
judge unless I go to presentation? Let the past and future 
be as real as you please, but by what device shall I come in 
contact with them, and refer to them my ideas, unless I 
advance directly to the given, and to them indirectly? It is 
possible, I am aware, to assert that past realities are directly 
presented, and possible also (for all I know) to say the same 
of the future, and of all the space I am not in contact with, 
and of all the qualities that I do not perceive. In this way, 
no doubt, we dispose of the difficulty, and indeed may make 
a very simple matter of any kind of problem, if indeed any 
problems any longer will exist. 



CHAP. II FORMS OF JUDGMENT 63 

20. But the persons I write for, and who are not so 
blessed with easy intuitions, will feel this difficulty, and there 
may come a temptation to fall back once more on the aban 
doned heresy and to say, In these synthetic judgments the 
subject can not possibly be the reality. It must be an idea, 
and in the junction of ideas must lie the truth. And I think, 
perhaps, at the cost of repetition, we had better see where 
this temptation leads us. 

When we say " It rained last Tuesday," we mean this last 
Tuesday, and not any other; but, if we keep to ideas, we do 
not utter our meaning. Nothing in the world that you can 
do to ideas, no possible torture will get out of them an asser 
tion that is not universal. We can not escape by employing 
ideas of events in time, particulars as we call them. The 
event you describe is a single occurrence, but what you say 
of it will do just as well for any number of events, imaginary 
or real. If you keep to ideas it is useless to make a reference 
to the present, and say, " The Tuesday that came before this 
day." For we have seen before (8), that in analytic judg 
ments we are equally helpless. The real is inaccessible by 
way of ideas. In attempting to become concrete and special, 
you only succeed in becoming more abstract and wholly in 
definite. " This " " now " and " mine " are all universals. 
And your helpless iteration, " not this but this," will not get 
your expression any nearer to your meaning. If judgment is 
only the union of ideas, no judgment is ever about the indi 
vidual. 

21. We must get rid of the erroneous notion (if we have 
it) that space and time are " principles of individuation," in 
the sense that a temporal or spatial exclusion will confer 
uniqueness upon any content. It is an illusion to suppose that, 
by speaking of " events," we get down to real and solid par 
ticulars, and leave the airy region of universal adjectives. For 
the question arises, What space and time do we really mean, 
and how can we express it so as not to express what is as 
much something else ? It is true that, in the idea of a series of 
time or complex of space, uniqueness is in one sense involved ; 
for the parts exclude one another reciprocally. But they do 
not exclude, unless the series is taken as one continuous whole, 
and the relations between its members are thus fixed by the 



64 THE PRINCIPLES OF LOGIC BOOK I 

unity of the series. Apart from this unity, a point on its recur 
rence could not be distinguished from the point as first given. 
And elsewhere we might ask, how far such an unity is itself 
the negation of mere exclusivity. 

But, to pass by this question, it is clear that exclusion 
within a given series does not carry with it an absolute unique 
ness. There is nothing whatever in the idea of a series to 
hint that there may not be any number of series, internally all 
indistinguishable from the first. How can you, so long as you 
are not willing to transcend ideas, determine or in any way 
characterize your series, so as to get its difference from every 
possible series within your description? It is idle to say 
" this," for " this " does not exclude except in this sphere, and 
it is idle to say " my," for it is only in my element that yours 
and mine collide. Outside it they are indifferent, and the ex 
pression " my " will not distinguish one world from the other. 
If we simply attend to the series itself, 15 and, declining to look 
outside, confine ourselves to the consideration of its character, 
then all that it contains might be the common property of innu 
merable subjects, existing and enjoyed in the world of each, a 
general possession appropriated by none. The mere quality 
of appearance in space or time can not give singularity. 

22. The seeking for judgment in the synthesis of ideas 
once more has led us where there is no exit. With however 
little hope we must return to the doctrine, that judgment is 
the reference of an ideal content to the real which appears in 
time and space, which is to be encountered directly in presen 
tation, but which can not be limited to a momentary instance. 
It is not by its quality as a temporal event or phenomenon of 
space, that the given is unique. It is unique, not because it 
has a certain character, but because it is given. It is by the 
reference of our series to the real, as it appears directly within 
this point of contact, or indirectly in the element continuous 
with this point, that these series become exclusive. We per 
haps may be allowed to express this otherwise by saying, it 
is only the " this " which is real, and ideas will suffice so far 
as " thisness," but can never give " this." It is perhaps a hard 
saying, and announces difficulties we shall need both courage 
and patience to contend with. 

23. Everything that is given us, all psychical events, be 



CHAP. II FORMS OF JUDGMENT 65 

they sensations, or images, or reflections, or feelings, or ideas, 
or emotions every possible phenomenon that can be present 
both is " this " and has " thisness." But its stamp of unique 
ness and singularity comes to it from the former and not from 
the latter. If we distinguish the aspects of existence and 
content 16 (Chap. I. 4), and put on the one side that anything 
is, and on the other side what it is, then the thisness falls 
within the content, but the this does not fall there. It is the 
mere sign of my immediate relation, my direct encounter in 
sensible presentation with the real world. I will not here ask 
how " this " is related to existence, how far it holds of the 
actual fact, and how far only of the mere appearance ; whether 
it is or is only for me. Apart from that, at least so much is 
certain, that we find uniqueness in our contact with the real, 
and that we do not find it anywhere else. The singularity 
which comes with presentation and is what we call " this," is 
not a quality of that which is given. 

But thisness on the other hand does belong to the content, 
and is the general character of every appearance in space or 
time. Thisness, if we like, we may call particularity. Every 
thing that is given us is given, in the first place, surrounded 
and immersed in a complex detail of innumerable relations to 
other phenomena in space or time. In its internal quality 
we find again a distinction of aspects, which we always can 
carry to a certain length, and can never be sure we have quite 
exhausted. And the internal relations of its component ele 
ments in space or time are again indefinite. We are never 
at the end of them. This detail appears to come to us on 
compulsion; we seem throughout to perceive it as it is, and 
in no sense to make or even to alter it. And this detail it is 
which constitutes thisness.* 

*The apprehension of this character, it may be objected, takes time, 
and, if any time for observation is given, the product, for all we know, 
has been altered. But this difficulty occurs in all observation. We 
everywhere assume, first, that things are not different unless we can 
discriminate them. And we assume, in the second place, our ability to 
distinguish a change in ourselves from a change in the object. We 
assume that more of the same object is observed, unless we have 
reason either to suppose that our fancy has wandered away from 
that object, or that the object itself has undergone a change. I do not 
here ask if these assumptions are valid. But I may remark in passing, 



66 THE PRINCIPLES OF LOGIC BOOK I 

But such particularity in space or time, such an exclusive 
nature, after all, is only a general character. It falls in the 
content and does not give the existence. It marks the sort 
but it misses the thing. In abstraction from the this it is 
merely ideal, and, apart from the this, ideas as we know can 
not reach to uniqueness. No amount of thisness which an 
event possesses will exclude the existence of self -same events 
in other like series. Such exclusiveness falls all within the 
description, and that which is only of this description is simply 
such and can not be this. 

In every judgment, where we analyze the given, and where 
as the subject we place the term " this," it is not an idea which 
is really the subject. In using " this " we do use an idea, and 
that idea is and must be universal; but what we mean, and 
fail to express, is our reference to the object which is given 
as unique. 

24. And here we encounter an awkward question. The 
reader possibly may be willing to accept our account of this 
ness. He may agree that, so far as in our use of the term we 
mean mere relativity in space or time, in other words particu 
larity, we do not at all go beyond the content. And he may 
allow the consequence that we have so an idea which is 
only universal. But in using "this," he may go on 
to object that we have in addition another idea. We have 
the idea of immediate contact with the presented reality; 
and it is that idea which is signified by "this," and which 
qualifies the idea which stands as the subject of our analytic 
judgment. 

We answer, Assuredly, if such were the case, the reference 
to fact would inevitably and always fall outside the judgment. 
Once again we should be floating in the air, and never be more 
than hypothetical. But the question raised need not so be 
dismissed, for it leads to an interesting if subtle reflection. 

that the doubt if in introspection we examine a present, or only a past 
state of mind, should change its form. It should not take the two as 
exclusive here, unless it faces the same problem elsewhere. For the 
observation of external phenomena labours under the identical diffi 
culty. If an internal fact can not possibly be both present and past, 
then an external fact must be likewise restricted. The two kinds of 
observation are not essentially different. External facts are not abso 
lutely fixed, nor are internal facts in absolute flux. 17 



CHAP. II FORMS OF JUDGMENT 67 

The idea of " this," unlike most ideas, can not be used as a 
symbol in judgment. 

It is certain, in the first place, that we have the idea. 18 
Indeed we could scarcely deny that we had it, unless in so 
doing we actually used it. Beside the idea of exclusion in a 
series, which is mere thisness, we have also the idea of my 
immediate sensible relation to reality, and, if so, we have 
" this." We are able to abstract an idea of presence from that 
direct presentation which is never absent; and presence, 
though it does not fall within the content, though we can 
hardly call it a quality of the appearance, yet is recognized as 
the same amid a change of content, is separable from it, and 
makes a difference to it. Thus ideally fixed " this " becomes 
an universal among other universals. 

25. But, despite the likeness, it is very different from an 
ordinary idea. Ideas, we shall remember, are used as symbols 
(Chap. I.). In my idea of a "horse " we have (i) the exist 
ence of an image in my head, (ii) its whole content, and (iii) 
its meaning. In other words we may always distinguish (i) 
that it is, and (ii) what it is, and (iii) what it signifies. The 
two first of these aspects belong to it as a fact. The third is 
the universal which does not belong to it, but is thought of 
without a relation to its existence, and in actual judgment is 
referred away to some other subject. 

The idea of " this " has a striking difference. Distin 
guished as an aspect of presented reality, when we call it up 
we take any perception or feeling that is given, and, attending 
to the aspect of presence within it, recognize that as 
the meaning of our term. We contemplate it ideally, with 
out any reference to the content of that which is actually 
before us. 

But how shall we fare when, attempting a judgment, we 
attribute the adjective we have so cut loose to another sub 
stantive? It is here we are stopped. For any judgment so 
made we discover must be false. The other fact can not be 
presented without ipso facto altering the given. It degrades 
our given to one element within a larger presentation, or else 
it wholly removes it from existence. The given disappears 
and with itself carries our idea away. We are now unable to 
predicate the idea, since we no longer possess it, or if we still 



68 THE PRINCIPLES OF LOGIC BOOK I 

have it, then what supports it excludes that other fact to which 
we wish to refer it. 

26. To repeat the above, the presented instance of reality 
is unique. By discrimination we are able to fix that uniqueness 
in the shape of an idea. We thereupon try to make it the 
idea of something else. But, for the idea to be true of some 
thing else, that something else must be present and unique. 
We have then either two unique presentations, or one must 
disappear. If the first one goes, the idea goes with it. If 
the last one goes, there is now no fact for the idea to be re 
ferred to. In either case there can be no judgment. The idea, 
we see, is not the true idea of anything other than its own 
reality. It is a sign which, if we judge, can signify nothing 
except itself. To be least alone then when most alone, and to 
enjoy the delights of solitude together, are phrases which have 
a very good sense ; but, taken in their bare and literal meaning, 
they would exemplify the contradiction we have here before us. 

Between the fact and the idea of the " this " in judgment, 
there can be no practical difference. The idea of this would 
be falsely used, unless what it marks were actually presented. 
But in that case we should be trying to use a sign, when we 
have before us the fact which is signified. We can use the 
idea so far as to recognize the fact before us as a fact which 
is " this ; " but such a use does not go beyond the given. It 
affirms of the subject a predicate without which the subject 
disappears. It implies discrimination within the fact in which, 
since the aspect discriminated is not separable from the given, 
that given with its aspect still remains as the subject. So that 
the addition of the idea adds nothing to the subject. And 
if again it were possible to import the idea from the content 
of another fact, the operation would be uncalled for and quite 
inoperative. 

And it is not possible. It would be, as we have seen, the 
attempt to have before us two unique facts at once. What 
we mean by " this " is the exclusive focus of presentation 
which lights up its content, and it is of that singular content 
that we use the idea. And to treat that idea as a meaning 
which could be true elsewhere, would be to bring into our focus 
another content. But since both must be unique, as well as 
the same, a dilemma arises which we need not draw out. 



CHAP. II FORMS OF JUDGMENT 69 

27. And if " this " be used in a different sense, if it does 
not mark the presence of the whole sensible detail that falls 
within the focus ; if it is used for that which I specially attend 
to, the result will be the same. If I make A my object to the 
exclusion of all others, then this special relation to myself 
must be false, if used of any other. If applied to A it can not 
possibly also be applied to B. 

" But," it may be said, " I exclusively attend to both. A 
and B are both elements within the given this, and hence I 
can predicate this of either. I can transfer the idea, which 
I find is true of one, and use it as a predicate which is true of 
the other. And so, after all, the idea of this will be used 
symbolically." I am afraid of losing the main question in 
subtleties, but I must reply by pointing out a confusion. Since 
A and B are both taken together, you can not exclusively 
deal with each separately. So much is now clear. But, on 
the other hand, if you take each by itself as a mere element in 
the " this," then you can not predicate " this " of either. Both 
will belong to the " this," but neither will be that to which 
they belong. They will be presented, but neither by itself will 
be the unique presentation. They will not have the " this " in 
common, but the " this " will have them. It will be their 
common substantive which will share its own exclusive nature 
with nothing. 

I hardly think that by further intricacies we shall make 
more clear what can not be made obvious. If anything in the 
above has been grasped by the reader, I trust to have shown 
that the use of " this," as a symbol in judgment, is not only 
impossible, but that, if it existed, it would be wholly nugatory.* 

28. We escape from ideas, and from mere universals, by 
a reference to the real which appears in perception. It is thus 

* " This " is not the only idea which can never be true as a symbol. 
I will not ask to what extent " this " means " for me," but what has 
been said of " this " will hold in the main of " I ", " me " and " mine." 
But there are difficulties here which we can not discuss. We may 
remark in passing that, for the purposes of metaphysics, it would be 
necessary to find all those ideas whose content appears not able to be 
used as the adjective of something else. This would bear on the 
so-called " ontological proof." For the ideas of uniqueness &c., vid. 
infr. 38, 39- 19 

2321. I F 



70 THE PRINCIPLES OF LOGIC BOOK I 

our assertion attains the uniqueness without which it would 
not correspond to the fact. And analytic judgments, it may 
seem, are thus secured to us. But now, when we return to 
the question we asked in 19, and when we pass to judgments 
that are synthetic, and extend to spaces and times not falling 
within the radius of direct presentation, we seem at first 
sight to be no better off. What we have gained, it may 
now appear, has been at the expense of everything beyond. 
The series of all our spaces and times will now have to be 
referred to the one unique point of contact with reality. 
It is only so that their content can, be stamped with 
the mark of fact. But it seems impossible to establish this 
relation. 

The content of these synthetic assertions we know is uni 
versal. It may be true of innumerable other series. This 
unsubstantial chain, if left to itself, does not touch the ground 
in any one point. On the other hand, the given source of 
reality refuses, it seems, to have anything to do with these 
floating threads. Their symbolic content can not be directly 
attributed to the presentation, because it is irreconcileable 
with the content of that. And, if we can not have another 
presentation, where is the fact in connection with which our 
universals can attain reality? 

29. We must turn in our difficulty to a result we got 
from a former discussion. 20 We saw that the real, which 
appears in perception, is not identical with the real just as it 
appears there. If the real must be " this," must encounter us 
directly, we cannot conclude that the " this " we take is all 
the real, or that nothing is real beyond the "this." It is 
impossible, perhaps, to get directly at reality, except in the 
content of one presentation : we may never see it, so to speak, 
but through a hole. But what we see of it may make us 
certain that, beyond this hole, it exists indefinitely. If by 
" this " we understand unique appearance, then, as " this " was 
not any part of the content, so neither is it any quality of the 
real, in such a sense as to shut up the real within that quality. 
It would belong to metaphysics to discuss this further, and we 
must here be content with a crude result. The real is what 
appears to me. The appearance is not generic but unique. 



CHAP. II FORMS OF JUDGMENT 71 

But the real itself is not unique, in the sense in which its 
appearance is so. 21 

The reality we divined to be self -existent, substantial, and 
individual ; but, as it appears within a presentation, it is none 
of these. The content throughout is infected with relativity, 
and, adjectival itself, the whole of its elements are also 
adjectival. Though given as fact every part is given as 
existing by reference to something else. The mere perpetual 
disappearance in time of the given appearance is itself the 
negation of its claim to self -existence. And again, if we take 
it while it appears, its limits, so to speak, are never secured 
from the inroads of unreality. In space or in time its outside 
is made fact solely by relation to what is beyond. Living by 
relation to what it excludes, it transcends its limits to join 
another element, and invites that element within its own 
boundaries. But with edges ragged and wavering, that flow 
outward and inward unstably, it already is lost. It is ad 
jectival on what is beyond itself. Nor within itself has it any 
stability. There is no solid point of either time or space. 
Each atom is merely a collection of atoms, and those atoms 
again are not things but relations of elements that vanish. 
And when asked what is ultimate, and can stand as an indi 
vidual, you can answer nothing. 

The real can not be identical with the content that appears 
in presentation. It for ever transcends it, and gives us a title 
to make search elsewhere. 

30. The endeavour to find the completeness of the real, 
which we feel can not exist except as an individual, will lead 
us first to Synthetic judgments of time and space. But, before 
we proceed, we may pause for a moment, to reflect on the 
general nature of the attempt. If the reality is self-existent, 
self-contained, and complete, it needs, one would think, no 
great effort of reason to perceive that this character is not to 
be found in a mere series of phenomena. It is one thing to 
seek the reality in that series ; it is quite another thing to try 
to find it as the series. A completed series in time or space 
can not possibly exist. 22 It is the well-known phantasm of the 
spurious infinite, a useful fiction, it may be, for certain purposes 
and at certain levels of thought, but none the less a phantasm 



72 THE PRINCIPLES OF LOGIC BOOK I 

which, until it is recognized, stops the way of all true philo 
sophic thought. It emerges often in the school of " experience," 
in its Logic and again in its Hedonistic Ethics, where it begets 
and will continue to beget chimeras. We shall meet it again 
in the present chapter, but must return to our search for reality 
within a series of phenomena, a search not yet degraded to a 
pursuit of phantasms, but carrying in itself the root of illusion. 

31. The real then itself transcends the presentation, and 
invites us to follow it beyond that which is given. On the 
other hand, we seem to find contact with reality and to touch 
ground nowhere, so to speak, outside the presented. How 
then is a content to be referred to the real, if it can not be 
referred to the real as perceived? We must answer that the 
content is referred indirectly. It is not attributed to the given 
as such; but, by establishing its connection with what is 
presented, it is attributed to the real which appears in that 
given. Though it is not and can not be found in presentation, 
it is true because it is predicated of the reality, and unique 
because it is fixed in relation with immediate perception. 
The ideal world of spaces beyond the sensible space, and of 
times not present but past and future, fastens itself on to the 
actual world by fastening itself to the quality of .the immediate 
this. In a single word continuity of content is taken to 
show identity of element. 

32. But such continuity, and the consequent extension 
of the " this " as given, depend, like every other ideal con 
struction, on identity. 23 An inference always, we shall see 
hereafter, stands on the identity of indiscernibles. Sameness 
of quality proves real sameness (vid. Book II. Part I. Chap. 
VI.). And the identity here has a double form, (i) In the 
first place the symbolical content must have " thisness." 
(ii) In the second place it must share some point with the 
" this." 

To explain, (i) the idea we are to connect with perception 
must be the idea of something in space or some event in time. 
It must have the character of particularity, the general idea of 
indefinite detail and endless relation. We know by this that 
it is of the same sort as the content of the given. The de 
scription of both is one and the same. They both have 
" thisness," and therefore their element may be identical. 



CHAP. II FORMS OF JUDGMENT 73 

(ii) But, so far as we have gone, we still are left in the 
world of universals, which may or might touch the ground in 
some place and meet the fact which appears in perception, 
but which do not certainly do thus. We wish, on the one side, 
to pass beyond presented content, and, on the other side, to 
connect with this content an ideal series; and we seek for a 
link by which to fasten them together. 

That link is found by establishing a point which is the 
same in both, and is the same because its quality is the same. 
The " this " contains a complex of detail, either times or 
spaces (or both) in series, which we may call c. d. e. f. The 
idea, on its side, contains a series of particulars a. b. c. d. 
The identity of c. d. in each extends the perception c. d. e. f. 
by the ideal spaces or times a. b., and the whole is given 
by synthetical construction as a single fact a. b. c. d. e. f. 
The whole series now is referred to the real, and by the con 
nection with unique presentation, has become a series of events 
or spaces, itself unique and the same as no other series in the 
world. It is thus by inference that we transcend the given 
through synthetic judgments, and our following Books must 
explain more clearly the nature of inference, and the enormous 
assumption on which it reposes. 

33. Mental pathology will afford an illustration. There 
are cases where the subject or, if we please, the Ego seems 
divided in two. When one self is present the other is absent, 
and the memories of either self are distinct. Their pasts and 
futures do not ever touch. The explanation that is offered, 
and which seems sufficient, will illustrate our theme. It is 
because the present selves are different, that the past and 
future selves are foreign. It is because one system of ideas 
has not got a point of connection with the other system, or 
has rather some point which excludes the connection, 24 that 
the one can never be used to extend ideally a present which 
belongs to the other. Some mode of morbid feeling or dis 
eased perception, given now in presentation, links on to itself 
the ideas that are grouped by the same characteristic. The 
whole ideal region where that colouring fails, may perhaps be 
suggested, but can never be fixed in continuous relation with 
the present perception.* 

*Cf. Lotze, Mikrokosmus, I. 371. 



74 THE PRINCIPLES OF LOGIC BOOK I 

34. If we mean by phenomena the things we perceive, 
or the facts or appearances that are given to us, then the 
whole of England below our horizon (to say nothing at all of 
America and Asia), and every event that is past or future are 
not phenomena. They are not perceived facts. They exist in 
our minds as mere ideas, as the meaning of symbols. A phe 
nomenon, I repeat, that is past or future is a sheer self-contra 
diction. It is time we thought of giving up our habit of talking 
about the " series of phenomena," or " thread of perceptions," 
or Heaven knows what else, as though we held these facts in 
our hands. One thing or the other. Either a phenomenon 
may be ideal, the content of a symbol and not even predicated 
directly of the present perception, or there is no phenomenon 
but what I here and now perceive. It is idle perhaps to ap 
peal to facts in protest against the philosophy of " analysis " 
and the school of " experience." It is impossible, I know, to 
persuade the man who is wedded to these names, that he has 
failed to earn a legitimate title to neglect the first and to be 
false to the second. Profuse protestations, and jealousy of 
the untitled, are services found not too exacting, and which 
satisfy those who have long ago and cheaply become 
cool. But, for the sake of others, I will repeat once 
more. If a fact or event is what is felt or perceived, then 
a fact that is past is simple nonsense (cf. Book II. Part II. 
Chap. I.). 

Of course, I know, it is easy to say that past events are all 
really there, and, being there, are remembered; as I presume 
the future, being all there, is anticipated. But suppose that 
there is a series of facts, both past and future, outside our 
minds, the question remains, How can they get in? You may 
say, if you like, They are fond of a change, and walk in and 
out bodily and meet and converse there. Or an omnipotent 
Creator has endowed the mind with an extraordinary organ, 
which perpetually can do what no one understands, and, defy 
ing the insidious arts of the analyst, proves by the way the 
immortality of the soul. Or perhaps you may find it a " final 
inexplicability." Ultimate facts always are inexplicable, and 
we must not be put out if they contradict those doctrines they 
must know to be true. For it is natural for the inexplicable 
to behave inexplicably. 



CHAP. II FORMS OF JUDGMENT 75 

But perhaps there are readers content to remain on a level 
with ourselves. If so they will continue to believe the conclu 
sion that facts have brought to us. And that conclusion is that 
events past and future, and all things not perceived, exist 
for us only as ideal constructions connected, by an inference 
through identity of quality, with the real that appears in 
present perception. In what character (if any) these things 
may really exist for themselves, is a question for meta 
physics. 25 

35. Synthetic judgments thus cease to be merely adjec 
tival, and they express a series of unique events by indirect 
reference to the real which appears in unique presentation. 
They are connected by an inference with the content of this 
appearance, and so far are directly related to perception. But 
their ideas are never referred as adjectives to the presentation 
itself. They are attributed to the reality, which both shows 
itself there, and extends itself beyond. The content of our 
perceptions, and the content of our ideal constructions, are 
both the adjectives of one reality. They are both appear 
ances, which come to us in different ways, but which both 
(unless our assumptions are false) are valid and true of the 
real world. 

36. Memory of the past, and prediction of the future, 
are separated clearly from mere imagination. 26 In the former 
we have the reference to that reality which appears in per 
ception. We have a judgment which is either true or false, 
because it implies a relation to fact. But imagination is with 
out this reference. The merely imagined, we have seen before 
(Chap. I. 14), may be stronger than that which we judge to 
be true. What we only fancy may have more thisness; it 
may have more compulsory and particular detail than that 
which we remember. But what it wants is a point of identity 
by which to fasten it on to the " this." And without such a 
link it must fall outside the series. 

We generally, it is true, take forcible detail and strong 
particularity as a sign of fact, and look for its place in the 
series of events. But, if the place is not found, the imagined 
fact is never secured to us. The visions of dreams may 
be very definite, but the content of those visions refuses to 
link itself to the series of events connected with perception, 



76 THE PRINCIPLES OF LOGIC BOOK I 

and so, if we cannot get rid of the ideas, at least we stamp 
them as mere illusions. 

If this were the place for an excursion into psychology, we 
should find some difficulties and many interesting questions. 
When once we have referred a content to the real, we generally 
tend to refer it again. We say that we know it happened at 
some time, though when we can not say. And we might be 
tempted perhaps to think that such ideas have greater strength 
or fuller detail than mere imaginations. This would be er 
roneous. It is not strength or detail which marks these ideas, 
but something so dim that we can not grasp it. It may be the 
general idea of reference to the " this," which, repelled by the 
content of the given " this," transcends it vaguely. It may be, 
on the other hand, some unconscious element of idea or feel 
ing, which serves to identify in an indefinite way the imagined 
with fact. For it is a mistake to suppose that these links 
with reality need be anything explicit. A feeling so obscure 
that we are not aware of it, and which perhaps no effort of 
attention would be able to distinguish from its vague totality 
of consciousness, may serve as the basis by which we sepa 
rate a truth from a fiction (33). We must remember again 
that the point of connection may be, so to speak, in our in 
ward selves, and not at all in the outward series. If a false 
hood imagined is in the end believed, it is not always because 
it gains some kind of direct connection with outward fact. 
In the end it may actually identify itself with the habitual 
feeling which we have of ourselves. And this common 
meeting-ground of illusion and truth serves often to confuse 
them together in our minds. But we can not here further 
pursue these discussions. 

37. To resume, It is not the mere symbolic use of ideas 
which distinguishes truth from bare imagination. For imagi 
nation is not confined to particular images. Just as in percep 
tion it is hard to say where inference first appears, and where 
the analytic judgment becomes synthetic, so in much imagina 
tion we shall find the presence of a discursive element. The 
idea of a circle, we might say and say falsely, was nothing 
but an image; but the idea of a chiliagon would show us at 
once that there is a point where our imagery fails. And it is 
obvious that ideas of abstract relations may be held before the 



CHAP. II FORMS OF JUDGMENT 77 

mind without any judgment. This, however, is a content 
which is wholly symbolic, and yet (where no hypothetical 
judgment comes in) it is purely imaginary. It is detached 
from the existence of the image in our minds, but it is not 
attached to another reality. 27 

38. We now perhaps are able to say what it is we mean 
by the idea of an individual (or, we had better say, of a par 
ticular) fact. We saw the futility of seeking to find this in 
the proper names of persons, for what they stand for is never 
confined to a single event. The idea of particularity implies 
two elements. We must first have a content qualified by 
" thisness," and we must add to that content the general idea 
of reference to the reality. In other words a particular must 
first be represented in a series ; this gives us the first element. 
But so far we do not get beyond mere " thisness ; " the 
members are exclusive, within the series, but the whole col 
lection is not unique. To get the complete idea of a par 
ticular fact we must make our series, so to speak, externally 
exclusive as well and thus particular. And we do not do this 
till we qualify it by the idea of reference to our unique 
reality. 

If we actually attributed the series to reality, we not only 
should have got the idea that we wanted, but also more. 28 We 
should have judged that our idea was true in fact. And in 
this case we do not wish to go so far. We desire to have the 
idea of uniqueness, but not to assert the reality of the idea. 

We possess, as we have seen ( 24) in the idea of "this," 
the idea of immediate contact with the real, and it is this idea 
we must add to our series. When we think of the series both 
as a whole, and as touching the real in a point of presentation, 
we have thought of it then as truly particular. But there we 
must stop. For if we went on to judge our idea to be true, 
we should have to find it a special place in the unique series 
which extends perception. And we saw that to use the idea 
of " this " as the symbol of another content in judgment, was 
quite impossible. So long, however, as we abstain from judg 
ment, we can attach the aspect of " this " to a content other 
than that which is really presented. 

This is what we mean by the idea of a particular. There 
is a difference when we come to an individual person. Our 



78 THE PRINCIPLES OF LOGIC BOOK I 

idea is there particular, since it has limits within a particular 
series. But it also involves a real identity persisting through 
out a change of events. And so it falls outside the class of 
mere synthetic judgments. 

39. Uniqueness is merely the negative side of the idea of 
" this." A content is unique when, although of a sort (and 
that means regarded from the aspect of content) it neverthe 
less is the same as no other, is the only one there is of its 
sort. Uniqueness implies the idea of a series, 29 and is then 
relative or absolute. It is relative when the series, which con 
tains the element which excludes the others, is itself not 
unique. In any universe our fancy constructs, a thing may be 
unique but only unique within that universe. We have, on 
the other hand, absolute uniqueness when the series is con 
nected with direct presentation. In that case the relations 
within the series fix against each other the elements it holds, 
and nothing can be fact without its appearing in that one 
series. But the real subject, which, in predicating uniqueness, 
excludes any other event of the kind, we must remember, is 
not the particular event as such and taken by itself. It is 
rather the real which appears in that particular and so ex 
cludes others. We have here a negative existential judg 
ment, for the nature of which we must consult our Third 
Chapter. 

40. After meeting many difficulties, some of which, I 
trust, may have been overcome, we have finished our account 
of the second division of singular judgments. We must pass 
to the third, the assertions not confined to an event or a num 
ber of events in time (7). But, before we proceed, let us 
pause for a moment, and, however dangerous the experiment 
may be, let us try to put before our very eyes a synthetic 
judgment. Let us call before our mind some series of pictures, 
like Hogarth s Progress of the harlot or rake ; but let us also 
imagine something beside. One picture in the series must be 
the reality, the actual person in a real room, and on the walls 
of this real room must be hung the series of earlier and later 
pictures. By virtue of the sameness in the quality of the man, 
as he is in the room and is in the pictures, we, neglecting the 
appearance in particular frames, arrange the whole series as 
his past and future. We transcend in this way the visible room 



CHAP. II FORMS OF JUDGMENT 79 

and the presented scene, and view the real life of the person 
extending itself as a series in time. 

But the man in the real room that we see, is body and 
bones and breath and blood, while his past and future, if we 
mean by reality a sensible fact, are nothing in the world but 
glass and wood and paint and canvas. It is the same with 
all our future and past. The events of memory and of 
anticipation are facts now in our minds, but they no more 
are the reality they represent than paint and canvas are a 
throbbing heart. No doubt they stand for reality, and we 
flatter ourselves that, if they can not be fact, at least they are 
true. True indeed they may be if truth means a natural and 
inevitable way of representing the real. But if by their truth 
we understand more than this; if we say that the reality is 
as it appears in our ideal construction, and that actually there 
exists a series of facts past present and future I am afraid 
that truth, if we came to examine it, would change into false 
hood. It would be false if measured by the test of perception, 
and it may be, if tried by another standard, it would be falser 
still. 

41. The life of a man can not be presented in any one 
scene, and our very illustration has gone farther than we 
thought. That life is not even a mere succession of serial 
events, but contains (so we think of it) a something the 
same, a real identity which appears in all, but which is not any, 
nor even every, event. We find ourselves brought to the third 
main class of singular judgments, 30 and are speaking of a sub 
ject which is not an event. These judgments are separated 
into two divisions, according as the individual with which they 
deal is related to some given period of time, or not to any 
time in particular. 

III. (i) In the history of a man or nation we have a 
content referred to the real, but to the real as it appears 
throughout one certain part of that series which is deter 
mined by relation to given perception, (ii) In the second 
division we must place any judgments we make about the 
Universe or God or the soul, if we take the soul to be eternal. 31 
Our ideas are here identified with the real that we find in per 
ception, but they do not not attach themselves to any one part 
of the phenomenal series. It may be said, of course, that such 



80 THE PRINCIPLES OF LOGIC BOOK I 

judgments are illusory. But, as we saw, that conclusion, if 
true, could only be established by a metaphysical enquiry we 
have no place for. The judgments exist, and logic can do 
nothing else but recognize them. 

This third and last class of singular judgments is distinct 
from the others. Its essence is that its ultimate subject is 
not the real, as it appears in the " this " or in any one event 
in the series. But the distinction is to a certain extent un 
stable. Just as analytic judgments are always tending to be 
come synthetic, so here it is impossible to separate sharply the 
first division of this class from synthetic judgments. On the 
one hand the continuity of the element of time strictly ex 
cludes a mere serial character. 32 In every judgment about 
events we unknowingly are asserting the existence of an iden 
tity. On the other hand an individual living in a series seems 
naturally to belong to that class of judgment which constructs 
a series. Since, however, when an individual is concerned, 
we explicitly recognize something real, enduring throughout 
the changes of events, it is better perhaps to keep up a dis 
tinction which in principle must be admitted to fluctuate. The 
example of an individual person took us from analytic to 
synthetic judgments. And it has served again to carry us on 
further. 

42. 3 3 We have now considered all the three classes of 
singular judgments, and have seen in what way they attribute 
an idea to the real which appears. We have already antici 
pated the account to be given of Existential judgments, and 
may deal with them rapidly. Confining ourselves here to those 
which are affirmative, we can say at once that the subject in 
all of them is the ultimate reality, either (a) as it appears in 
some part of the series determined by the "this," or (b) as it 
underlies the whole series of phenomena. When I say " A 
exists," or " A is real," the content A is in truth the predicate. 
We use it to qualify existence or reality, in one of the two 
senses we have now mentioned. 

The enquiry into existential propositions reduces to ab 
surdity the notion that judgment consists in ideas. If we 
add to the adjectival idea of A another adjectival idea of 
reality, then, failing wholly in reference to fact, we fall 



CHAP. II FORMS OF JUDGMENT 8l 

entirely short of judgment. But this is not all. The idea of 
reality, like the idea of " this," is not an ordinary symbolic 
content, to be used without any regard to its existence. 34 The 
idea of what is real, or of that which exists, is found as an 
element in that actual reality and actual existence which we 
encounter directly. It can not in judgment be removed from 
this, and be transplanted away to another reality. We have 
here the same obstacle which met us before ( 25-27). The 
idea cannot be predicated of anything except its own reality. 
For, to get the idea, you must take it by a distinction from 
what is given. If you then make it a predicate of anything 
not given, you have a collision, and your judgment disappears. 
But if, on the other hand, you predicate it of that which 
actually is given, your procedure is idle. Why employ an idea 
to assert reality when you have the fact, and when your ideal 
synthesis is a mere analysis of this given reality, and at 
tributed in the end to that as subject? " Real " is clearly the 
adjective of " reality," and we know no reality but what ap 
pears in presentation. The idea then, to be true, must be 
true of that reality. But, if so, we must have the subject 
before us in the shape of fact, and, if we did not, the idea 
would at once become false. For a more detailed discussion 
we may refer to 25-27. 

Nor would it repay us here to examine the somewhat 
surprising view which Herbart has advocated (vid. 75). 
Our enquiries in this chapter should have prepared us for the 
result that the ultimate subject is never an idea, and that the 
idea of existence is never a true predicate. The subject, in 
the end, is always reality, which is qualified by adjectives of 
ideal content. 

43. We cannot say there is a class of existential judg 
ments, for all singular judgments have by this time been shown 
to be existential. And, with this conclusion, we may pass be 
yond them to another branch of affirmative judgments. In 
these we no longer have to do with any particular facts or 
in any sense with separate individuals. They are universal in 
the sense of transcending what is singular. They are not 
" concrete " but " abstract," since, leaving things, they assert 
about qualities, alone or in synthesis. In this respect, we may 
remark in passing, there is no real difference between the 



82 THE PRINCIPLES OF LOGIC BOOK I 

" general " and the " abstract ; " for, taken in comparison with 
the particular thing, 35 the general idea is a mere abstraction. 

44. We have reached the common type of universal 
judgment; and the point in this which we notice at once, is 
that every such judgment is concerned with adjectivals. 36 
They assert a connection between elements of content, and 
say nothing about the place of those elements in the series of 
events. In " Equilaterial triangles are equiangular " all I affirm 
is that with one set of qualities you will have the other set, 
but I make no assertion about where and when. And " Mam 
mals are warm-blooded " does not tell me anything about this 
or that mammal. It merely assures me that, finding one at 
tribute, I shall find the other. 

The fact that is asserted in an abstract judgment is not 
the existence of the subject or predicate (6), but simply the 
connection between the two. And this connection rests on a 
supposal. The abstract universal, " A is B," means no more 
than " given A, in that case B," or " if A, then B." In short, 
such judgments are always hypothetical and can never be 
categorical. And the proper terms by which to introduce them 
are " given," or " if," or " whenever," or " where," or " any," 
or "whatever." We should beware of "all." 

45. For the use of "all," we have seen above (6), is 
most misleading and dangerous. It encourages that tendency 
to understand the universal in the sense of a collection, 27 which 
has led to so many mistaken consequences. We shall glance 
elsewhere at that extraordinary teaching on the subject of 
quantity, in which the traditional logic delights. And we shall 
see hereafter, when we come to inference, the absurd incom 
petence of the dictum de omni. For our present purpose we 
need criticize no further the attempt to understand the " all " 
collectively. Even if that use were justifiable in itself, it 
would be irrelevant; for a judgment where "all" means a 
real collection of actual cases, 38 belongs to a class we have al 
ready disposed of. If " all " signifies a number of individual 
facts, the judgment is concerned with actual particulars. And 
so it obviously is but one form of the singular judgment. 
" All A is B," will be an abbreviated method of setting forth 
that this A is B, and that A is B, and the other A is B, and 



CHAP. II FORMS OF JUDGMENT 83 

so on until the lot is exhausted. Such judgments fall clearly 
under the head of singular. 

But, when this class is banished to the preceding category, 
have we any universal judgments left us? We can not doubt 
that; for there are judgments which do not assert the exist 
ence of particular cases. We come at once upon the judg 
ments that connect adjectival elements, and that say nothing 
about the series of phenomena. These abstract universals are 
always hypothetical and never categorical.* 

46. At this point we must pause to encounter an objec 
tion. " The distinction," we may be told, " between categorical 
and hypothetical is really illusory. Hypothetical judgments 
can all be reduced to, and in the end are nothing but, a kind 
of categorical." If this were well founded, it would certainly 
occasion us serious difficulty. But I do not think we need much 
disturb ourselves. 

" If A is B it is C," we may be told, " is equivalent to The 
instances or cases of A that are B are also C, and this is 
surely a categorical judgment." I answer, if " the cases of A 
that are B " means the existing cases of A B, and no others, 
then the judgment no doubt is categorical, but it is not an ab 
stract universal. It is merely collective, and it most certainly 
does not mean what we meant by our hypothetical judgment. 
" If butter is held to the fire it melts " is no assertion about 
mere existing pats of butter. And when it is reduced to the 
form, " All cases of the holding of butter, &c.," it does not 
become any more categorical. " All cases " means here 
"Suppose any case." 

Indeed, if we steadily keep in view the difference between 
a simple assertion about fact and an assertion on the strength 
of and about a supposition, we may perhaps be puzzled, but 
we are not likely to be led far astray by these elementary mis 
takes. 

47. And with this remark I could leave the matter. But 

* The extensional theory of judgment and reasoning is dealt with 
elsewhere (Chap. VI. and Book II. Part II. Chap. IV.). We may here 
remark that, taking " A is B " to mean " the things that are A are the 
things that are B," the judgment must be singular, if an existing set 
of things be denoted, and will be universal and abstract if possible 
things are included as well. 39 



84 THE PRINCIPLES OF LOGIC BOOK I 

it is perhaps worth while, by another instance, 10 illustrate 
the futility of this attempt to turn hypothetical into categorical 
judgments. J. S. Mill in his Logic (I. 4, 3) approaches the 
subject with an air of easy superiority. " A conditional 
proposition is a proposition concerning a proposition." 

" What is asserted is not the truth of either of the proposi 
tions but the inferribility of the one from the other." " If A is 
B, C is D, is found to be an abbreviation of the following: 
The proposition C is D, is a legitimate inference from the 
proposition A is B. J: 

How this doctrine is connected with Mill s other views as to 
the import of propositions, an expert in Mill-philology no 
doubt could inform us. But, left to ourselves, we can only 
conjecture the doctrine he here intended to teach, (i) If he 
really meant "inferribility" then cadit qucestio. For at once 
the statement is not about what is, but what may be or might 
be. It is not simply about existing propositions, but clearly 
involves a supposal of some kind, and is therefore not reduced 
to categorical form. It is still Suppose you have got AB, then 
you may go legitimately to CD. (ii) But no doubt there is 
more than this verbal quibble. He tells us that one is an 
inference from the other. Does this mean (a) that both are 
actually asserted, and that I further assert that I really have 
argued to the second from the first ? Surely not that ; but then 
what else? (&) Can it mean that, without asserting either 
proposition, I hold them in my mind, and affirm their con 
nection? It may mean this. But then this process of taking 
up a statement without believing it, and of developing its con 
sequences, is in fact nothing else than a supposition. The 
connection asserted is not between realities, and the proposi 
tion is still hypothetical, (iii) But the extraordinary illus 
trations towards the end of the section point to another 
interpretation ; " The subject and predicate are names of propo 
sitions." Without, however, attempting the hopeless task of 
understanding, we may perhaps state the issue in the form 
of a dilemma. Either (a) one proposition, in the sense of 
a little heap of words, does, as a particular event in my head, 
now follow another such heap; or (&) it would follow, if 
the other were there. The second alternative is of course still 
hypothetical. In the former at last we have got to something 



CHAP. II FORMS OF JUDGMENT 85 

categorical, but nothing to which a hypothetical judgment 
(or indeed any judgment) could possibly be reduced. It would 
be an error too gross to merit refutation. 

Whatever else may be the meaning of the writer, we after 
all may remain sure of this. Either the categorical judgment, 
to which he professes to reduce the hypothetical, is not its 
equivalent; or else it contains, under some flimsy veil of 
verbal ambiguity, a supposition which is the condition of the 
judgment. 

48. Such universal judgments are all hypothetical, and 
with this conclusion we are landed once more in our former 
difficulties (6). Judgment, we saw, always meant to be true, 
and truth must mean to be true of fact. But here we en 
counter judgments which seem not to be about fact. For a 
hypothetical judgment must deal with a supposal. It appears 
to assert a necessary connection, which holds between ideas 
within my head but not outside it. But, if so, it can not be a 
judgment at all; while on the other hand it plainly does 
assert and can be true or false. 

We are not able to rest in this conclusion, and yet we can 
not take back our premises. Let us then try to look more 
closely at the problem, and ask more narrowly what is involved 
in these judgments. And, in the first place, we can not expect 
to succeed until we know what a supposal is. 

A supposition, in the first place, is known to be ideal, and 
known perhaps to diverge from fact. At a low stage of mind, 
where everything is fact (cf. Chap. I.), it could not exist. For 
the supposed must be known as an ideal content, and, in 
addition, it has to be retained before the mind without a 
judgment. It is not referred as an adjective, either posi 
tively or negatively, to the real. In other words reality is not 
qualified either by the attribution or the exclusion of it. But 
though it does not judge, a supposition is intellectual, for (as 
such) it excludes desire and emotion. And again it is more 
than mere imagination, for it is fixed by attention and pre 
serves, or should preserve, its identity of content (vid. Book 
III. Chap, III. 23, 24). It certainly is all this, and yet this 
is not all. For to think of a chimsera is not quite the same 
thing as to suppose a chimaera. 

A supposition means thinking for a particular end, and in 



86 THE PRINCIPLES OF LOGIC BOOK I 

a special way. It is not a mere attending to a certain meaning, 
or an analysis of its elements. It has a reference to the real 
world, and it involves a desire to see what happens. We may 
illustrate perhaps from other usages. " Say it is so for argu 
ment s sake," "Treat it as this and then you will see," are 
much the same as, " Suppose it to be so." A supposal is, in 
short, an ideal experiment. 40 It is the application of a con 
tent to the real, with a view to see what the consequence is, 
and with a tacit reservation that no actual judgment has taken 
place. The supposed is treated as if it were real, in order to see 
how the real behaves when qualified thus in a certain 
manner. 

You might say it is the adding the idea of existence to a 
given thought, while you abstain from judgment. But that I 
do not think would be satisfactory. For it is not the mere 
idea of existence that is used. What we use is the real that is 
always in immediate contact with our minds, and which in a 
variety of judgments we already have qualified by a certain 
content. And it is to this that we bring up another idea, in 
order to see what result will come of it. 

. 49. So far there is neither truth nor falsehood, for we 
have not judged. The operation, we may say, is so far 
"subjective." It is all our own doing, and all of it holds 
inside our heads, and not at all outside. The real is not 
qualified by the attribute we apply to it. But, so soon as we 
judge, we have truth or falsehood, and the real is at once 
concerned in the matter. The connection of the consequence, 
of the " then " with the " if," of the result of our experiment 
with its conditions, is the fact that is asserted, and that is true 
or false of the reality itself. 

But the question is how. You do not assert the existence 
of the ideal content you suppose, and you do not assert the 
existence of the consequence. And you can not assert the 
existence of the connection, for how can a connection remain 
as a fact when no facts are connected? "If you only had 
been silent you would have passed for a philosopher." But 
you were not silent, you were not thought a philosopher, and 
one was not, and could not possibly be, a result of the other. 
If the real must be qualified by the connection of the two, it 
seems that it will not be qualified at all. Neither condition, 



CHAP. II FORMS OF JUDGMENT 87 

nor result, nor relation can be ascribed to it ; and yet we must 
ascribe something, for we judge. But what can it be? 

50. When I go to a man with a fictitious case, and lay 
before him a question of conduct, and when he replies to me, 
* I should act in this way, and not in the other way," I may 
come from him with some knowledge of fact. But the fact is 
not the invented position, nor yet the hypothetical course of 
action, nor the imaginary relation between the two. The fact 
is the quality in the man s disposition. 41 It has answered to a 
trial in a certain way. But the test was a fiction, and the 
answer is no fact, and the man is not qualified by one or the 
other. It is his latent character that is disclosed by the 
experiment. 

It is so with all hypothetical judgment. The fact that is 
affirmed as an adjective of the real, and on which depends the 
truth or falsehood, does not explicitly appear in the judgment. 
Neither conditions nor result of the ideal experiment are taken 
to be true. What is affirmed is the mere ground of the con 
nection; not the actual existing behaviour of the real, but a 
latent quality of its disposition, a quality which has appeared 
in the experiment, 42 but the existence of which does not de 
pend on that experiment. "If you had not destroyed our 
barometer, it would now forewarn us." In this judgment we 
assert the existence in reality of such circumstances, and such 
a general law of nature, as would, if zve suppose some condi 
tions present, produce a certain result. But assuredly those 
conditions and their result are not predicated, nor do we even 
hint that they are real. They themselves and their connection 
are both impossible. It is the diminution of pressure and 
the law of its effect, which we affirm of the actual world 
before us. And of course that law is resolvable further 

(52). 

51. In all judgment the truth seems none of our mak 
ing. 43 We perhaps need not judge, but, if we judge, we lose 
all our liberty. In our relation to the real we feel under 
compulsion (4). In a categoric judgment the elements them 
selves are not dependent on our choice. Whatever we may 
think or say, they exist. But, in a hypothetic judgment, there 
is no compulsion as regards the elements. The second, in 
deed, depends on the first, but the first is arbitrary. It depends 



88 THE PRINCIPLES OF LOGIC BOOK I 

on my choice. I may apply it to the real, or not, as I please ; 
and I am free to withdraw the application I have made. And, 
when the condition goes, the result goes too. The compulsion 
extends no further than the connection, and yet it does not 
extend to the connection as such. The relation of the ele 
ments in a hypothetical judgment is not an actual attribute of 
the real, for that relation itself is arbitrary. It need not be 
true outside the experiment. The fact which existed before 
the experiment, and remains true after it, and in no way 
depends on it, is neither the elements, nor the relation be 
tween them, but it is a quality. It is the ground of the 
sequence that is true of the real, and it is this ground which 
exerts compulsion. 

52. This quality of the real is not explicit in the judg 
ment, and, in respect of that judgment, is occult or latent. We 
know it is there because of its effects, but we are not able to 
say what it is. We can not even tell, without further enquiry, 
that it is not the same as what we have asserted in another 
judgment, the elements of which, and also their relation, were 
very 44 different (cf. Chap. III. 19). And, when we push 
the investigation further, and ask, Are these qualities, that 
thus seem to lie at the base of our judgments, altogether 
latent, or only latent each in respect of its peculiar judgment, 
then we get at once into difficult questions. It is certain on 
the one hand that we can find the grounds of many such 
judgments, which thus have relatively become explicit. But 
this only serves to bring us nearer to the doubt, whether in the 
end they have ceased to be latent. Do we ever get to a ground 
of judgment which we can truly ascribe to the real as its 
quality? Or are we left with ultimate judgments, which are 
certainly true, but neither the elements nor relations of which 
are true of reality? Must we say, in the end, that the quality, 
which we know is the base of our synthesis, remains in other 
ways altogether unknown and is finally occult? We seem here 
to be asking, in another form, for the limits of explanation, 
and it would be the task of metaphysics to pursue an enquiry 
which must here be broken off. 45 

53- We have seen that, what hypothetical judgments 
assert, is simply the quality which is the ground of the con 
sequence. And all abstract universal, we have seen are 



CHAP. II FORMS OF JUDGMENT 89 

hypothetical. It may here be asked, Are the two things 
one? Are all hypothetical judgments thus universal? 

This might for a moment appear to be doubtful, since the 
real, to which application is made, is at times an individual. 
And for the purposes of this, and the following section, I will 
give some examples; "If God is just the wicked will be 
punished," " Had I a toothache I should be wretched," " If 
there were a candle in this room it would be light," "If it is 
now six o clock we shall have dinner in an hour," " If this 
man has taken that dose, he will be dead in twenty minutes/* 
It may surprise some readers to hear that these judgments are 
as universal as " All men are mortal : " but I think we shall 
find that such is the case. 46 

In the first place it is certain that in none of these judg 
ments is the subject taken to be actually real. We do not 
say above that a just God exists, or that I have a toothache; 
we only suppose it. The subject is supposed, and, if we 
consider further, we shall find that subject is nothing more 
than an ideal content, and that what is asserted is not any 
thing beside a connection of adjectives. The " that," the 
"this," the "I," the "now," do not really pass into the 
supposition. They are the point of reality to which we apply 
our ideal experiment, but they themselves are in no case sup 
posed. More or less of their content is used in the hypothesis, 
and passes into the subject. But, apart from themselves, their 
content can not possibly be called individual. 

54. This would hardly be doubtful, were it not for the 
ambiguity of all these assertions, a point to which we should 
carefully attend. " If he had murdered he would have been 
hanged," may perhaps assert nothing but the general connec 
tion of hanging with murder, and the " he " is irrelevant. But 
" if God is just the wicked will be punished," may perhaps 
not say that punishment would follow from any justice, but 
only from justice that is qualified by omnipotence. On the 
other hand, when you say " If this man has taken that dose, 
&c.," you do not tell me if his speedy death would happen 
because the dose would poison any one, or would only poison 
such a man as he is, or would not even poison such a kind of 
man, unless under present special conditions. And the other 
examples would all entangle us in similar ambiguities. The 



go THE PRINCIPLES OF LOGIC BOOK I 

supposition is not made evident, and reflection convinces us 
that, supposing we know the subject of the judgment, at all 
events we do not display our knowledge. 

55. And since this is so, since the adjectival content is 
not made explicit, since all we have is an indefinite reference 
to this or that case, we fall into the mistake of thinking it is 
the particular we have to deal with. But our real assertion, 
when we come to analyze it, never takes in the " that," or the 
" now," or the " this." It is always the content about which 
we assert. But, because we are not clear what that content is, 
and because we know it is to be found in the individual as 
supposed, we fire, so to speak, a charge of shot instead of a 
bullet, and take the individual as the point of reality to which 
our supposition is to be confined. In this way we give rise 
to the erroneous idea that the reality itself passes into the 
supposal. The fact, as we have seen, is that some of the 
content either is or makes part of the adjectival condition 
about which we assert. But, because that content has not 
been analyzed, we go to the individual to get it in the lump. 
The real judgment is concerned with nothing but the indi 
vidual s qualities, and asserts no more than a connection of 
adjectives. In every case it is strictly universal as well as 
hypothetical. 

56. We have found, thus far, that all abstract judgments 
are hypothetical, and in this connection we have endeavoured 
to show what a supposition is, and to lay bare that occult 
affirmation as to the real, which is made in every hypothetical 
judgment. Singular judgments we have already discussed, 
and we found that, be they analytic or synthetic, they all at 
first sight seem categorical. They do not merely attribute 
to the real a latent quality, which manifests itself in an unreal 
relation, but they qualify the real by the actual content which 
appears in the judgment. It is not the mere connection, but 
the very elements which they declare to exist. 

We have still remaining another kind of judgment (7), 
but, before we proceed, it is better to consider the result we 
have arrived at. That result perhaps may call for revision, 
and it is possible that the claim of the singular judgment to 
a categoric position may not maintain itself. 



CHAP. II FORMS OF JUDGMENT QI 



CHAPTER II (Continued) 

57- What is the position in which we now find our 
selves? We began with the presumption that a judgment, 
if true, must be true of reality. On the other hand we found 
that every abstract universal judgment was but hypothetical. 
We have endeavoured to reconcile these conflicting views by 
showing in what way, and to what extent, a conditional judg 
ment asserts of the fact. But singular judgments stand apart, 
and have claimed to be wholly categorical, and true of the 
reality; and hence they demand a position above that given 
to universal judgments. We must now scrutinize this pre 
tension. We must still defer all notice of those individual 
judgments which transcend the series of events in time. Con 
fining ourselves to judgments about the phenomenal series, let 
us proceed to ask, Are they categorical? Do they truly and 
indeed rank higher, and closer to the real world, than those 
universal judgments which we found were hypothetical? We 
shall perhaps do well to prepare our minds for an unwelcome 
conclusion. 

In passing from the singular to the universal judgment, we 
seem to have been passing away from reality. Instead of a 
series of actual phenomena connected with the point of present 
perception, we have but a junction of mere adjectivals, the 
existence of which we do not venture to affirm. In the one 
case we have what seem solid facts ; in the other we have noth 
ing but a latent quality, the mere name of which makes us 
feel uneasy. We have not quite lost our hold of the real, but 
we seem to have left it a long way off. We keep our con 
nection by an impalpable thread with a veiled and somewhat 
ambiguous object. 

But our thoughts may perhaps take a different colour, if 
we look around us in the region we have come to. However 
strange it may seem to us at first, yet our journey towards 
shadows and away from the facts has brought us at last to 



g 2 THE PRINCIPLES OF LOGIC BOOK I 

the wo-ld of science. The end of science, we all have been 
taught, is the discovery of laws; and a law is nothing but a 
hypothetical judgment. It is a proposition which asserts a 
synthesis of adjectivals. It is universal and abstract. And it 
does not assert the existence of either of the elements it 
connects. 47 It may imply this (6), but such an implication is 
not essential. In mathematics,* for instance, the truth of our 
statement is absolutely independent of the existence of either 
subject or predicate. In physics or chemistry the truth does 
not depend on the actual existence at the present moment of 
the elements and their relation. If it did so, the law might be 
true at one instant and false at the next. When the physio 
logist, again, tells us that strychnine has a certain effect on 
nerve-centres, he does not wait to enunciate his law until he is 
sure that some dose of strychnine is operating in the world ; nor 
does he hasten to recall it as soon as he has lost that assurance. 
It would be no advantage to dwell upon this point. It may be 
regarded now as a certain result, that the strict expression for 
all universal laws must begin with an " if," and go on with a 
" then." 

58. And from this we may draw a certain presumption. 
If the singular judgment is nearer the fact, and if, in leaving 
it, we have actually receded from reality, yet at least in sci 
ence that is not felt to be the case. And there is another pre 
sumption which may help to strengthen us. In common life 
we all experience the tendency to pass from one single case to 
some other instance. We take what is true at one time and 
place to be always true at all times and places. We generalize 
from a single example. We may deplore this tendency as an 
ineradicable vice of the unphilosophic mind, or we may recog 
nize it as the inevitable condition of all experience, and the 
sine qua non of every possible inference (vid. Book II.). 
But in either case, let us recognize it or deplore it, we still do 
not feel the passage we have made as an attempt to go from 
the stronger to the weaker, from that which is more true to 
that which is less. And yet, without doubt, it is a transition 
away from the individual to the universal and hypothetical. 

59. But a matter of this sort is not settled by presump 
tions. There are prejudices, it may be, that operate both 
ways. And we may be told, on behalf of the singular judg- 



CHAP. II FORMS OF JUDGMENT 93 

ment, that it is the fact that these judgments are categorical. 
For they do assert the actual existence of their adjectival con 
tent, and, attributing to the real an explicit quality, they are 
truer than any hypothetical judgment, if indeed they are not 
the only true judgments. Such, we take it, is the claim of the 
singular judgment, and it can not be denied that its claim in 
one respect is very well founded. It does assert the existence 
of its content, and does affirm directly of the real. But the 
answer we must make is that, although it does so assert and 
affirm, yet, when we leave the popular view and look more 
closely at the truth of things, the assertion and affirmation 
which it makes are false, and the claim it puts forward rests 
on a mistake. We must subject the pretensions of the singu 
lar judgment to an examination which we think may prove 
fatal. 48 

60. We need spend no time on the synthetic judgment. 
In transcending what is given by actual perception, we without 
any doubt make use of an inference. A synthesis of ad 
jectives is connected with the present by virtue of the identity 
of a point of content. By itself this synthesis is merely uni 
versal, and is therefore hypothetical. It becomes categoric 
solely by relation to that which is given, and hence the whole 
weight of the assertion rests on the analytic judgment. If that 
is saved, it will then be time to discuss its extension; but if, 
on the other hand, the analytic be lost, it carries with it the 
synthetic judgment. 

61. Let us turn at once to the judgments which assert 
within what is given in present perception. These seem 
categorical because they content themselves with the analysis of 
the given, and predicate of the real nothing but a content 
that is directly presented. And hence it appears that the ele 
ments of these judgments must actually exist. An ideal con 
tent is attributed to the real, which that very real does now 
present to me. I am sure that nothing else is attributed. I 
am sure that I do not make any inference, and that I do not 
generalize. And how then can my assertion fail to be true? 
How, if true, can it fail to be categorical? 

We maintain, on the other hand, that analytic judgments 
of sense are all false. There are more ways than one of 
saying the thing that is not true. It is not always necessary to 



Q4 THE PRINCIPLES OF LOGIC BOOK I 

go beyond the facts. It is often more than enough to come 
short of them. And it is precisely this coming short of the 
fact, and stating a part as if it were the whole, which makes 
the falseness of the analytic judgment. 

62. The fact, which is given us, is the total complex of 
qualities and relations which appear to sense. But what we 
assert of this given fact is, and can be, nothing but an ideal 
content. And it is evident at once that the idea we use can 
not possibly exhaust the full particulars of what we have 
before us. A description, we all know, can not ever reach to 
a complete account of the manifold shades, and the sensuous 
wealth of one entire moment of direct presentation. As soon 
as we judge, we are forced to analyze, and forced to dis 
tinguish. We must separate some elements of the given from 
others. We sunder and divide what appears to us as a sen 
sible whole. It is never more than an arbitrary selection 
which goes into the judgment. We say " There is a wolf," or 
" This tree is green ; " but such poor abstractions, such mere 
bare meanings, are much less than the wolf and the tree which 
we see; and they fall even more short of the full particulars, 
the mass of inward and outward setting, from which we 
separate the wolf and the tree. If the real as it appears is 
= abcdefgh, then our judgment is nothing but X = a, 
or X = dr-b. But a-b by itself has never been given, and is not 
what appears. It was in the fact and we have taken it out. 
It was of the fact and we have given it independence. We 
have separated, divided, abridged, dissected, we have muti 
lated the given.* And we have done this arbitrarily : we have 
selected what we chose. But, if this is so, and if every 
analytic judgment must inevitably so alter the fact, how can 
it any longer lay claim to truth ? 

63. No doubt we shall be told, " This is idle subtlety. 
The judgment does not copy the whole perception, but why 
should it do so? What it does say, and does reproduce, at all 
events is there. Fact is fact, and given is given. They do not 
cease to be such because something beside themselves exists. 
To maintain that There is a wolf is false, because an ab 
stract wolf is not given entirely by itself, is preposterous and 
ridiculous." 

* Cf. here Lotze s admirable chapter, Logik, II. VIII. 



CHAP. II FORMS OF JUDGMENT 95 

And I am afraid that with some readers this will end the 
discussion. But to those who are willing to venture further, 
I would suggest as encouragement that a thing may seem 
ludicrous, not because it is at all absurd in itself, but because 
it conflicts with hardened prejudice. And it is a prejudice of 
this kind that we have now encountered. 

64. It is a very common and most ruinous superstition 
to suppose that analysis is no alteration, and that, whenever 
we distinguish, we have at once to do with divisible existence. 
It is an immense assumption to conclude, when a fact comes 
to us as a whole, that some parts of it may exist without any 
sort of regard for the rest. Such naive assurance of the 
outward reality of all mental distinctions, such touching con 
fidence in the crudest identity of thought and existence, is 
worthy of the school which so loudly appeals to the name of 
Experience. Boldly stated by Hume (cf. Book II. II. Chap. I. 
5)5 this cardinal principle of error and delusion has passed 
into the traditional practice of the school, and is believed too 
deeply to be discussed or now recognized. The protesta 
tions of fidelity to fact have been somewhat obtrusive, but 
self-righteous innocence and blatant virtue have served once 
more here to cover the commission of the decried offence in 
its deadliest form. If it is true in any sense (and I will not 
deny it) that thought in the end is the measure of things, yet 
at least this is false, that the divisions we make within a 
whole all answer to elements whose existence does not depend 
on the rest. It is wholly unjustifiable to take up a complex, 
to do any work we please upon it by analysis, and then simply 
predicate as an adjective of the given these results of our ab 
straction. These products were never there as such, and in 
saying, as we do, that as such they are there, we falsify the 
fact. You can not always apply in actual experience that 
coarse notion of the whole as the sum of its parts into which 
the school of " experience " so delights to torture phenomena. 
If it is wrong in physiology to predicate the results, that are 
reached by dissection, simply and as such of the living 
body, it is here infinitely more wrong. The whole that is 
given us is a continuous mass of perception and feeling; and 
to say of this whole, that any one element would be what it is 
there, when apart from the rest, is a very grave assertion. We 



96 THE PRINCIPLES OF LOGIC BOOK I 

might have supposed it not quite self-evident, and that it was 
possible to deny it without open absurdity.* 

65. I should like to digress so far as to adduce two 
examples of error, which follow from the mistake we are 
now considering. When we ask " What is the composition of 
Mind," we break up that state, which comes to us as a whole, 
into units of feeling. But since it is clear that these units by 
themselves are not all the " composition," we are forced to 
recognize the existence of relations. But this does not stagger 
us. We push on with the conceptions we have brought to the 
work, and which of course can not be false, and we say, Oh 
yes, we have here some more units, naturally not quite the 
same as the others, and voila tout. But when a sceptical 
reader, whose mind has been warped by a different education, 
attempts to form an idea of what is meant, he is somewhat at 
a loss. If units have to exist together, they must stand in 
relation to one another; and, if these relations are also units, 
it would seem that the second class must also stand in relation 
to the first. If A and B are feelings, and if C their relation 
is another feeling, you must either suppose that component 
parts can exist without standing in relation with one another, 
or else that there is a fresh relation between C and AB. Let this 
be D, and once more we are launched on the infinite process of 
finding a relation between D and C-AB ; and so on for ever. If 
relations are facts that exist between facts, then what comes 
between the relations and the other facts ? The real truth is 
that the units on one side, and on the other side the rela 
tion existing between them, are nothing actual. 50 They are 
fictions of the mind, mere distinctions within a single reality, 
which a common delusion erroneonsly takes for independent 
facts. If we believe the assurance of a distinguished Pro 
fessor^ this burning faith in the absurd and the impossible, 
which was once the privilege and the boast of theology, can 
now not be acquired anywhere outside the sacred precincts 
of the laboratory. I am afraid it is difficult to adopt such an 
optimistic conclusion. 

66. And perhaps I may be pardoned if, by another illus- 

IIl! 9 F r thC gCneral validity of Anal ysis and Abstraction see Book 
fVid. Huxley, Hume, pp. 52, 69. 



CHAP. II FORMS OF JUDGMENT 97 

tration, I venture to show how entirely the mind which is 
purified by science can think in accordance with orthodox 
Christianity. 51 In the religious consciousness God and Man 
are elements that are given to us in connection. But, reflect 
ing on experience, we make distinctions, and proceed as above 
to harden these results of analysis into units. We thus have 
God as an unit on one side, and Man as an unit on the other: 
and then we are puzzled about their relation. The relation 
of course must be another unit, and we go on to find that we 
should like something else, to mediate once more, and go be 
tween this product and what we had at first. We fall at 
once into the infinite process, and, having taken up with poly 
theism, the length we go is not a matter of principle. 

67. To return to the analytic judgment. When I say 
" There is a wolf," the real fact is a particular wolf, not like 
any other, in relation to this particular environment and to 
my internal self, which is present in a particular condition of 
feeling emotion and thought. Again, when I say " I have a 
toothache," the fact once more is a particular ache in a certain 
tooth, together with all my perceptions and feelings at that 
given moment. The question is, when I take in my judg 
ment one fragment of the whole, have I got the right to 
predicate this of the real, and to assert " It, as it is, is a fact of 
sense"? Now I am not urging that the analytic judgment is 
in no sense true. I am saying that, if you take it as asserting 
the existence of its content as given fact, your procedure is 
unwarranted. And I ask, on what principle do you claim the 
right of selecting what you please from the presented whole 
and treating that fragment as an actual quality? It certainly 
does not exist by itself, and how do you know that, when put 
by itself, it could be a quality of this reality? The sensible 
phenomenon is what it is, and is all that it is; and anything 
less than itself must surely be something else. A fraction of 
the truth, here as often elsewhere, becomes entire falsehood, 
because it is used to qualify the whole. 

68. The analytic judgment is not true per se. It can not 
stand by itself. Asserting, as it does, of the particular 
presentation, it must always suppose a further content, which 
falls outside that fraction it affirms. What it says is true, if 



98 THE PRINCIPLES OF LOGIC BOOK I 

true at all, because of something else. The fact it states is 
really fact only in relation to the rest of the context, and only 
because of the rest of that context. It is not true except 
under that condition. So we have a judgment which is really 
conditioned, and which is false if you take it as categorical. 
To make it both categorical and true, you must get the con 
dition inside the judgment. You must take up the given 
as it really appears, without omission, unaltered, and un- 
mutilated. And this is impossible. 

69. For ideas are not adequate to sensible perception, 
and, beyond this obstacle, there are further difficulties. 52 The 
real, which appears within the given, can not possibly be con 
fined to it. Within the limit of its outer edges its character 
gives rise to the infinite process in space and time. Seeking 
there for the simple, at the end of our search we still are 
confronted by the composite and relative. And the outer 
edges themselves are fluent. They pass for ever in time and 
space into that which is outside them. It is true that the 
actual light we see falls only upon a limited area; but the 
continuity of the element, the integrity of the context, forbids 
us to say that this illuminated section by itself is real. The 
reference of the content to something other than itself lies 
deep within its internal nature. It proclaims itself to be 
adjectival, to be relative to the outside; and we violate its 
essence if we try to assert it as having existence entirely in 
its own right. Space and time have been said to be " prin 
ciples of individuation." It would be truer to say they are 
principles of relativity. They extend the real just as much 
as they confine it. 

I do not mean that past and future are actually given, and 
that they come within the circle of presentation. I mean that, 
although they can not be given, the given would be de 
stroyed by their absence. If real with them, it would not 
be given; and, given without them, it is for ever incomplete 
and therefore unreal. The presented content is, in short, not 
compatible with its own presentation. It involves a contra 
diction, and might at once on that ground be declared to be 
unreal. But it is better here to allow it free course, and to 
suffer it to develope by an impossible consequence its inherent 
unsoundness. 



CHAP. II FORMS OF JUDGMENT gg 

70. We saw that you can not ascribe to the real one part 
of what is given in present perception. And now we must 
go further. Even if you could predicate the whole present 
content, yet still you would fail unless you asserted also both 
the past and the future. You can not assume (or I, at least, 
do not know your right to assume) that the present exists 
independent of the past, and that, taking up one fragment of 
the whole extension, you may treat this part as self-subsistent, 
as something that owes nothing to its connection with the 
rest. If your judgment is to be true as well as categorical, 
you must get the conditions entirely within it. And here the 
conditions are the whole extent of spaces and times which 
are required to make the given complete. The difficulty is 
insuperable. It is not merely that ideas can not copy facts of 
sense. It is not merely that our understandings are limited, 
that we do not know the whole of the series, and that our 
powers are inadequate to apprehend so large an object. No 
possible mind could represent to itself the completed series of 
space and time; since, for that to happen, the infinite process 
must have come to an end, and be realized in a finite result. 
And this can not be. It is not merely inconceivable psycho 
logically ; it is metaphysically impossible. 

71. Our analytical judgments are hence all either false or 
conditioned. " But conditioned/ I may be told, " is a doubtful 
phrase. After all it is not the same as hypothetical. A 
thing is conditioned on account of a supposal, but on the 
other hand it is conditioned by a fact. We have here the 
difference between if and * because. 53 When a statement is 
true in consequence of the truth of another statement, they 
both are categorical." I quite admit the importance of the 
distinction, and must recur to it hereafter (Chap. VII. 10). 
But I deny its relevancy for our present purpose. 

The objection rests on the following contention. " Ad 
mitted that in the series of phenomena every element is 
relative to the rest and is because of something else, yet for 
all that the judgment may be categorical. The something 
else, though we are unable to bring it within the judgment, 
though we can not in the end ever know it at all and realize it 
in thought, is, for all that, fact. And, this being so, the state 
ment is true ; since it rests in the end, not at all on an if 



IOO THE PRINCIPLES OF LOGIC BOOK I 

but upon a because/ which, although unknown, is none the 

less real. Let the analytic judgment admit its relativity, let 

it own its adjectival and dependent character, and it surely 

saves itself and remains categorical." 

But even this claim it is impossible to admit. I will not 

raise a difficulty about the " because " which is never realized, 

and the fact which can never be brought before the mind. 

My objection is more fatal. In the present case there is no 

because, 54 and there is no fact. 

We are fastened to a chain, and we wish to know if we 

are really secure. What ought we to do? Is it of much use 
to say, " This link we are tied to is certainly solid, and it is 

fast to the next, which seems very strong and holds firmly to 
the next; beyond this we can not see more than a certain 
moderate distance, but, so far as we know, it all holds to 
gether"? The practical man would first of all ask, "Where 
can I find the last link of my chain? When I know that is 
fast, and not hung in the air, it is time enough to inspect the 
connection." But the chain is such that every link begets, 
as soon as we come to it, a new one ; and, ascending in our 
search, at each remove we are still no nearer the last link of 
all, on which everything depends. The series of phenomena 
is so infected with relativity, that, while it is itself, it can never 
be made absolute. Its existence refers itself to what is be 
yond, and, did it not do so, it would cease to exist. A last 
fact, a final link, is not merely a thing which we can not 
know, but a thing which could not possibly be real. Our 
chain by its nature can not have a support. Its essence ex 
cludes a fastening at the end. We do not merely fear that it 
hangs in the air, but we know it must do so. And when the 
end is unsupported, all the rest is unsupported. Hence our 
condition*** truth is only conditional. It avowedly depends on 
what is ^ not fact, and it is not categorically true. Not stand 
ing by itself, it hangs from a supposition; or perhaps a still 
worse destiny awaits it, it hangs from nothing and falls 
altogether. 

72- It will be said, of course, that this is mere meta 
physics. Given is given, and fact is fact. Nay we ourselves 
distinguished above the individual from the hypothetic judg 
ment, on the ground that the former went to perception, and 



CHAP. II FORMS OF JUDGMENT IOI 

that we found there existing the elements it asserted. Such a 
plain distinction should not be ignored, because it disappears 
in an over-subtle atmosphere. But I do not wish to take 
back this distinction. It is valid at a certain level of thought; 
and, for the ordinary purposes of logical enquiry, individual 
judgments, both synthetic and analytic, may conveniently be 
taken as categorical, and in this sense opposed to universal 
judgments. 

But, when we go further into the principles of logic, and 
are forced to consider how these classes of judgment stand to 
one another, we are certain to go wrong, if we have not raised 
such questions as the above. It is not enough to know that 
we have a ground of distinction. We must ask if it is a true 
ground. Is it anything more than a point to reckon from? 
Is it also fact? Does the light of presence, which falls on 
a content, guarantee its truthfulness even if we copy? Are 
the presented phenomenon, and series of phenomena, actual 
realities? And, we have seen, they are not so. The given in 
sense, if we could seize it in judgment, would still disappoint 
us. It is not self-existent and is therefore unreal, and the 
reality transcends it, first in the infinite process of phenomena, 
and then altogether. The real, 55 which (as we say) appears 
in perception, is neither a phenomenon nor a series of 
phenomena. 

73. It may be said " This is only the product of reflec 
tion. If we are content to take the facts as they come to us, 
if we will only leave them just as we feel them, they never 
disappoint us. They neither hang by these airy threads 
from the past, nor perish internally in a vanishing network of 
never-ending relations between illusory units. The real, as 
it simply comes to us in sense, has nothing of all this. It 
is one with itself, individual and complete, absolute and 
categorical." We are not here concerned to controvert this 
statement. We are not called on to ask if anything that is 
given is given apart from intellectual modification, if there is 
any product we can observe and watch, with which we have 
not already interfered. We have no motive here to raise such 
an issue; nor again do we rejoice in that infatuation for in 
tellect, and contempt for feeling, which is supposed to qualify 
the competent metaphysician. Nor will we pause to argue that 

2321. I H 



IO2 THE PRINCIPLES OF LOGIC BOOK I 

frustrated feeling itself heads the revolt against the truth of 
sense. It was a baffled heart that first raised the suspicion of 
a cheated head. 

You may say, if you like, that the real just as we feel it is 
true. 56 But, if so, then all judgments are surely false, and 
your singular judgment goes with the rest. For our present 
purpose we may admit your assertion, but, if it is meant as an 
objection, we answer it by asking the question, What then? 
Who is it who says this? Who counts himself so free from 
the sin of reflection as to throw this stone? Some man no 
doubt who has not an idea of the consequences of his saying; 
some writer whose pages are filled with bad analysis and 
dogmatic metaphysics ; some thinker whose passion for " ex 
perience " is mere prejudice in favour of his own one-sided 
theory, and whose loyal regard for the sensible fact means 
inability to distinguish it from that first result of a crude re 
flection in which he sticks. 

For the present we may assume, what metaphysics would 
discuss, that phenomena are what we can not help thinking 
them in the end, and that the last result of our thought is true, 
or all the truth we have. It is not the beginning but the end 
of reflection which is valid of the real ; or we are such at least 
that our minds are unable to decide for aught else. And we 
have seen that our thinking about the real, if we remain at 
the level of the analytic judgment, will not stand criticism. 
The result of our later and, we are forced to believe, our 
better reflection is conviction that at least this judgment is 
not true. To assert as a quality of the real either the whole 
or part of the series of phenomena, 57 is to make a false 
assertion. 

74. The reality is given and is present to sense ; but you 
can not, as we saw ( n), convert this proposition, and say 
Whatever is present and given is, as such, real. The present 58 
is not merely that section of the phenomena in space and time 
which it manifests to us. It is not simply the same as its 
appearance. Presence is our contact with actual reality; and 
the reception of the elements of sensuous perception as exist 
ing facts is one kind of contact, but it is not the only kind. 

In hypothetical judgments there is a sense in which the 
real is given; for we feel its presence in the connection of the 



CHAP. II FORMS OF JUDGMENT IO3 

elements, and we ascribe the ground to the real as its quality. 
Hypothetical judgments in the end must rest on direct 
presentation, though from that presentation we do not take 
the elements and receive them as fact. It is merely their 
synthesis which holds good of the real ( 50), and it is in our 
perception of the ground of that synthesis that we come into 
present contact with reality. I will not ask if this contact is 
more direct than that which supports the analytical judgment. 
But at all events we may say it is truer; since truth is what 
is true of the ultimate real. A supersensible ultimate quality 
is not much to assert, but at all events the assertion seems 
not false. 59 On the other hand the categoric affirmation of 
the analytic judgment of sense we know is not true. The 
content it asserts we know is not real. And, taken in this 
sense, there remains no hope for the individual judgment. 

75. There is no hope for it at all, till it abates its pre 
tensions, till it gives up its claims to superiority over the 
hypothetic judgment, and is willing to allow that it itself is 
no more than conditional. But it does not yet know the 
degradation that awaits it. It may say, " It is true that I 
am not categorical. My content is conditioned, and the be 
cause has turned round in my hands into if/ But at least I 
am superior to the abstract hypothetical. For in that the 
elements are not even asserted to have reality, whereas, sub 
ject to the condition of the rest of the series, I at least 
assert my content to be fact. So far at least I affirm existence 
and maintain my position." 

But this claim is illusory, for if the individual judgment 
becomes in this way hypothetical, it does not assert that its 
content has any existence. If it did it would contradict itself, 
and I will endeavour to explain this. 

The content a-b in the categoric judgment was directly 
ascribed to real existence. The abstract universal judgment 
a-b does not ascribe either a or b or their connection to the 
real; 60 it merely ascribes a quality x. The question now is 
Can you save the categoric a-b by turning it into a hypo 
thetical in which a-b is still asserted of existence, though 
under a condition, or must it become the universal a-b 
which ignores existence? In the latter case it would simply 
mean, " Given a, then b." But in the former it would run, 



IO4 THE PRINCIPLES OF LOGIC BOOK I 

" Given something else, then a-b exists." This illusory claim 
is not very pretentious, but I wish to show that it is suicidal. 

Drobisch (Logik, 56), following Herbart (I. 106), trans 
lates the judgment, " P exists," into " If anything exists any 
where, then P exists." I consider this translation to be 
incorrect; for it covertly assumes that something does exist, 
and hence is in substance still categorical. And if we apply 
this translation to the facts of sense, then what is really 
supposed is the completed series of other phenomena, and 
the translation must run thus, "If everything else exists, then 
P exists." But the assertion is now suicidal, for " everything 
else," we have seen above (70), can never be a real fact. 
The hypothetical assertion of existence 61 is therefore made 
dependent on a condition which can not exist. Now it is 
not true that the consequence of a false hypothesis must 
be false; but it certainly is true, when an impossible ground 
is laid down as the sole condition of existence, that in a 
roundabout way existence is denied. The individual judg 
ment, we saw, was false when taken categorically. And now, 
we see, when taken hypothetically, instead of asserting it 
rather denies, or at least suggests that denial may be true. 

76. The only hope for the singular judgment lies in 
complete renunciation. It must admit that the abstract, al 
though hypothetical, is more true than itself is. It must ask 
for a place in the same class of judgment and be content 
to take the lowest room there. It must cease to predicate 
its elements of the real, 62 and must confine itself to asserting 
their connection as adjectives generally, and apart from par 
ticular existence. Instead of meaning by " Here is a wolf," 
or " This tree is green," that " wolf " and " green tree " are 
real facts, it must affirm the general connection of wolf with 
elements of the environment, and of " green " with " tree." 
And it must do this in an abstract sense, without any reference 
to the particular fact. In a low and rudimentary form it thus 
tends to become a scientific law, and, entirely giving up its 
original claims, it now sets its foot on the ladder of truth. 
77- But it remains upon the very lowest round. Every 
judgment of perception is in a sense universal, and, if it were 
not so, it could never be used as the basis of inference. The 
statement goes beyond the particular case, and involves a 



CHAP. II FORMS OF JUDGMENT IO5 

connection of adjectives which is true without respect to 
"this" "here" and "now." If you take it as ascribing its 
ideal content to this reality, it no doubt is singular, but, if you 
take it as asserting a synthesis inside that ideal content, it 
transcends perception; for anywhere else with the same 
conditions the same result would hold. The synthesis is true, 
not here and now, but universally. 

And yet its truth remains most rudimentary, for the con 
nection of adjectives is immersed in matter. 63 The content is 
full of indefinite relations, and, in the first vague form which 
our statements assume, we are sure on the one hand to take 
into the assertion elements which have nothing to do with 
the synthesis, and, on the other hand, to leave out something 
which really helps to constitute its necessity. We say for 
example, " This body putrefies ; " but it does not putrefy 
because it is this body. The real connection is far more 
abstract. And again on the other hand it would not putrefy 
simply because of anything that it is, and without foreign 
influence. In the one case we add irrelevant details, and in 
the other we leave out an essential factor. In the one case 
we say, " The real is such that, given abc, then d will follow," 
when the connection is really nothing but a-d. In the other 
case we say, " The connection is a-b," when a is not enough to 
necessitate b, and the true form of synthesis is a (c)-b. 
Measured by a standard of scientific accuracy, the first forms 
of our truths must always be false. They say too little, or 
too much, or both; and our upward progress must consist in 
correcting them by removing irrelevancies and filling up the 
essential.* 

78. The practice of science confirms the result to which 
our long analysis has brought us; for what is once true for 
science is true for ever. Its object is not to record that com 
plex of sensible phenomena, which from moment to moment 
perception presents to us. It desires to get a connection of 
content, to be able to say, Given this or that element, and 
something else universally holds good. It endeavours to dis 
cover those abstract elements in their full completeness, and 
to arrange the lower under the higher. Recurring to a term 

* For explanation and illustration I must refer to Lotze s admirable 
chapter cited above. 



THE PRINCIPLES OF LOGIC BOOK I 

we used before, we may say its aim is to purge out " thisness," 
to reconstruct the given as ideal syntheses of abstract ad 
jectives. Science from the first is a process of idealization; 
and experiment, Hegel has long ago told us, is an idealizing 
instrument, for it sublimates fact into general truths. 

Both in common life and in science alike, a judgment is at 
once applied to fresh cases. It is from the first an universal 
truth. If it really were particular and wholly confined to the 
case it appears in, it might just as well have never existed, 
for it could not be used. A mere particular judgment does 
not really exist, and, if it did exist, would be utterly worth 
less (cf. Chap. VI. and Book II.) . 

79. It is time that we collected what result has come 
from these painful enquiries. If we consider the ultimate 
truth of assertions, then, so far as we have gone, the cate 
gorical judgment in its first crude form has entirely dis 
appeared. The distinction between individual and universal, 
categorical and hypothetical, has been quite broken through. 
All judgments are categorical, for they all do affirm about 
the reality, and assert the existence of a quality in that. 64 
Again, all are hypothetical, for not one of them can ascribe to 
real existence its elements as such. All are individual, since 
the real which supports that quality which forms the ground 
of synthesis, is itself substantial. Again all are universal, 
since the synthesis they affirm holds out of and beyond the 
particular appearance. They are every one abstract, for they 
disregard context, they leave out the environment of the 
sensible complex, and they substantiate adjectives. And yet 
all are concrete, for they none of them are true of any 
thing else than that individual reality which appears in the 
sensuous wealth of presentation. 

80. But, if we remain at a lower point of view, if we 
agree not to scrutinize the truth of judgments, and if we 
allow assertions as to particular fact to remain in the character 
which they claim for themselves, in that case our result will 
be somewhat different. 65 Abstract judgments will all be hypo 
thetical, but the judgments that analyze what is given in 
perception will all be categorical. Synthetic judgments about 
times or spaces beyond perception will come in the middle. 
They involve an inference on the strength of an universal, 



CHAP. II FORMS OF JUDGMENT 107 

and so far they must have a hypothetical character. They 
again involve an awkward assumption, for you can go to 
them only through the identity of an element in the several 
contents of a perception and an idea. As however, on the 
strength of this assumption, the universal is brought into con 
nection with the given, the " if " is so turned into a " be 
cause," and the synthetic judgment may be called categorical. 
The two classes, so far, will on one side be assertions about 
particular fact and on the other side abstract or adjectival 
assertions. The latter are hypothetical, and the first cate 
gorical. 

81 . We have all this time omitted to consider that class 
of judgment which makes an assertion about an individual 
which is not a phenomenon in space or time (41). Is it 
possible that here we have at last a judgment which is not in 
any sense hypothetical? Can one of these directly predicate 
of the individual real an attribute which really and truly 
belongs to it? May we find here a statement which asserts 
the actual existence of its elements, and which is not false? 
Can truth categorical be finally discovered in some such 
judgment as " The self is real," or " Phenomena are nothing 
beyond the appearance of soul to soul " ? 66 It would seem to 
us strange indeed if this were so, and yet after all perhaps it 
is our minds that are really estranged. 

But we can not here attempt to answer these questions. 
We can only reply when asked where truth categorical dwells, 
" Either here or nowhere." 



ADDITIONAL NOTES 

i " S P." This form I found of course in use, and I employed 
it in this volume where that seemed convenient. I neither did nor do 
attach importance to its use. In I, par. 3, "is not our judgment" 
should have been perhaps "need not be," and, lower down, after "was 
not " might better have come " perhaps." 

2 "Objectivity." What this means is that it is the object itself 
which is this or that. The " subjective " = the irrelevant. See the 
Index of this work. And cf. Appearance, p. 237, and Essays, the 
Index. 

3 " Existences of different orders." See here the Index, s. v. Ex- 



I0 g THE PRINCIPLES OF LOGIC BOOK I 

istence. And cf. Essays, Chap. Ill, and Index, s. v. real world. 
"Existence" and "exist" (like "fact") are used in the present work 
often in a wide sense. On the narrower sense, which limits " existence " 
to the temporal series of my "real world," cf. Appearance, p. 317, and 
Essays, Chap. XVI. 

* Unfortunately in this work, with regard to "reality," neither 
the view of Common Sense (whatever that is) nor any other view 
has been kept to consistently. Cf. Chap. II. 72 and Bk. III. Pt. II. 
Chap. IV. 

5 " Altering the series of either space or time." But in what world? 
In our own so-called "real world" only? Cf. Note 7. 

6 " Images." But see Chap. I, Note 8. And (a few lines lower 
down) " quite apart from " should certainly have been " without 
regard to." 

7 " Three great classes." These distinctions are all in the end 
untenable. See Bosanquet, K & R, Chap. I. All judgments without 
exception are conditional. See T. E. II, and cf. Appearance and 
Essays, the Indexes. On class (ii), the words "some facts of time 
or space " are of course qualified by the following words " which . . . 
perceive." For the third class cf. 41. And, for a correction of the 
footnote with regard to Kant, see the Note to Chap. VI, 28. 

8 " Is false &c." It is false in the sense that its opposite also is 
true. See the Index, s. v. Conditional. And cf. Essays, p. 232. 

9 For references as to the "real" and "grammatical" subject see 
Index, s. v. Subject. We must remember that there is no presump 
tion anywhere that these two are identical. See Bosanquet, K & R, 
163-4, 181 foil. 

10 On the " present " &c. cf . 74, and see Appearance and Essays, 
the Indexes s. v. Time. A view, such as that advocated, e.g., by Mr. 
Russell, I take (i) to deny the reality of apparent change, and (ii) to 
be incompatible with the fact of the appearance. 

11 " The whole sensible reality." But at the same time there always 
is selection. See the Index, s. v. Judgment. Cf. here Bosanquet, 
K & R, 164 foil. 

12 On proper names see Bosanquet, K & R, 73 foil., Logic y I, 47 foil. 

13 "There is always an inference." How far the judgment itself 
is here an inference is, however, a further question. See Essays, 
p. 369, and Index, s. v. Memory. 

14 " To attribute them" should have been "to attribute it or 
them." 

15 " The series itself," that is, as we have it before us. 

16 " Content " or " quality " means here anything distinguishable 
so as to be for us a content or quality. In saying that the " this " 
does not fall within the " what," we must add that it does not fall in 
the "that" either. For each of these is an abstraction. Again, where 
a quality is unique, it ceases to be so if you take it as distinct from 
its "that" for, if so, there may be another instar.ee. On Uniqueness 
&c. see further T. E. IV and V. 



CHAP. II FORMS OF JUDGMENT IOO, 

17 On these important points see Essays, Chap. VI. 

18 On the question raised here as to the idea of "this" see the 
reference given in Note 16. 

19 The one idea, so far as positive, is that of reality, or experience, 
as immediate. Under this one main head of immediacy fall the " now," 
" here," and " mine." It is under the last of these that we are concerned 
with Attention. 

"Immediate contact with the presented reality" (24), if taken 
as a definition, is, I think, wrong. " Contact " and " presentation " 
are further aspects not, in my judgment, belonging essentially or 
universally to immediate experience. See the references given in 
Note 16. But in the present volume I certainly did not always mean 
by " presentation " the outward or even the inward perception of 
an object. The reader, I fear, must be on his guard throughout 
against what is perhaps a careless use of this term. 

20 " Former discussion." See 10 foil. 

21 Reality is unique (a) negatively and (b) positively. The given 
"this" also offers itself as unique. But an examination shows that we 
here have but appearance. The "this," through its content, negates 
itself as unique, and is seen to involve transcendence and ideality. On 
these points see T. E. IV and V. 

22 " A completed series &c." except (that is) when viewed in 
relation to a limited purpose and idea which it realizes. 

23 " Identity." Cf. 80, and see Bk. III. I. Chap. III. 2. 

24 " Or has rather some point &c." But we must remember that 
the "point" may be some quality of the whole. To the reference 
given to Lotze should be added "and Med. Psych., p. 487 (published 
in 1852)". 

25 I had at this time, I think, no acquaintance, as yet, with Her- 
bartian psychology, or I should have noticed the doctrine that percep 
tions all survive below the conscious level, ready to emerge if and 
when the conditions serve. But I should have added " However, 
this problem of dispositions is solved ultimately (if it can be 
solved), what stands in the text holds good. For it is in the end 
only as an ideal construction that I can have before me the series 
of events past and future &c." Cf. Mind, O. S., 47, p. 363. For 
Memory, see Essays, the Index. 

26 On Imagination see Bk. III. I. Chap. III. 23, and Essays, the 
Index. 

27 The false doctrine of "mere ideas" recurs in this section. See 
Chap. I, Note 13. And, for " the image," see ibid., Note 8. 

28 " If we actually &c." We do and must " attribute the series 
to reality," though not to reality as present. If the reader will consult 
the account of Uniqueness and of the idea of " This," in T. E. IV and 
V, he will, I hope, see his way to correct the mistakes of the text. 

29 " Implies the idea of a series." This is very doubtful. 

30 See above, Note 7. 

31 "If we take the soul to be eternal." I did not mean "ever 
lasting." I was alluding to the yiew that the whole essence of the 



HO THE PRINCIPLES OF LOGIC BOOK I 

soul can not be identified with its appearance in one or more periods 
of time. 

32 " A mere serial character." The use of these words (I can now 
recall nothing) seems careless. Probably I meant " a mere discreteness 
in the events so that they do not exist in and by connection into one 
whole." 

33 42, 43. The division into (a) and (b), in 42, is clearly 
wrong, if only because it omits all the worlds of events which fall 
outside my " real " world. See Note 3. 

We may perhaps distinguish "Singular" judgments (i) about my 
" real " world, or (2) about some " imaginary " world of events. 
(3) "General" judgments might perhaps be those referring to some, 
if not all, of the above worlds. (4) Judgments become "abstract" 
when this reference is struck out. Whether we have (5) to recognize 
abstract worlds or regions, taken somehow to "exist," though sensible 
existence in time and space is struck out, I will not offer to discuss. 
There will remain (6) judgments taken otherwise than as falling 
under the above heads. But, for myself, I attach little importance 
to such distinctions, even if tenable. What is important is to keep in 
mind that every judgment is, in various ways and degrees, conditioned 
and conditional. 

Instead of using " existence " as one with " reality," it is far better, 
I think, to limit it to the sphere of events. But, if so, though all 
judgments will be "real," certainly not all will be "existential." See 
the Index. 

54 The difficulty as to the "symbolic" use of such ideas as "this" 
and " real " is dealt with in T. E. V. 

3(5 " The particular thing " should be " the particular or individual 
thing." 

36 " Adjectivals." The words "even where these are not taken so 
ostensibly " should have been added. 

37 On the Collective Judgment (cf . Bk. II. II. Chap. III. 3) my 
treatment is one-sided. It ignores the fact that this judgment asserts a 
connection of content within an aggregate of individuals taken as 
exhaustive. On the Collective and Generic Judgments the reader is 
referred to Dr. Bosanquet s Logic, I, 152 foil., and 209 foil. 

a8 " Collection of actual cases." "Actual" does not mean "given 
as present." 

s9 " Will be universal and abstract." This, I think, is wrong. See 
Chap. VI, i. 

40 " Ideal experiment." But (a) we must remember that there are 
no mere ideas. Every idea is referred to its own world as there 
real and true, and as, so far, not merely "in my head." And (b) 
the " reality," to which my idea is opposed, is not necessarily " fact " 
in the sense of belonging to my "real world." It itself may be 
"imaginary," though here, as against my idea, it is taken as real. 

Having then an idea, or rather a truth, holding in one region, 
we may be said to apply this to another region of reality with a 
view to observe the result. This other reality, as we have it, repels 



CHAP. II FORMS OF JUDGMENT III 

our idea, or admits its opposite, and hence, taken on one side, the 
result is doubt. But on the other side it is a judgment made subject 
to an x. We assert, that is, not S M P, but S(x) M P. 
M p ? W e say, is true, but, as to S M, we have not got that 
actually, and, further, we do not know what qualification of S is 
involved in the reality of S M. 

For the logical meaning of " If" the reader is referred to T. E. II, 
and to Dr. Bosanquet s Logic, the Index, s. v. Hypothetical. We 
can, I think, easily see its psychological nature and origin, if we take 
the case of means (M) to an end desired, a certain alteration, that is, 
of a given fact (S). I may have one or more ideas of these means, 
but there is something in S, as I have it, which repels them all. I, 
however, retain them because they are (a) relevant and interesting, 
and also (b) possible. They contain, that is, some of the conditions 
of S, as that is to be altered, and I do not know that there really are 
counter-conditions in S itself. On the other side I do not know, and 
I will not assume, that S does not contain these. Hence I refrain 
from action, and assert S M P subject to a doubt as to S M. 
I hold, in other words, S(x) M P as true. And here x means 
(a) that further conditions are involved, and that (b) as to the nature 
and effect of these I am more or less ignorant. 

The supposed (to pass to another point) is in one aspect (M P) 
quite certain and actual. It is in connection with S (as known) that 
M P is but possible. And I may add that, where S itself is taken 
as possible only, the supposed is here doubly possible. But, essentially 
and always, what is supposed is taken as possible. 

This statement may seem at first to be in conflict with plain facts, 
such as the example given on p. 87 (cf. Essays, pp. 37-40). I ma Y 
be told that possibility is here certainly excluded. I would on the other 
side, however, ask the reader to reflect whether certainty is not 
contrary to the very meaning of "If." And, since to my mind that 
point is clear, I conclude that any appearance to the contrary rests 
on what may be called linguistic or rhetorical artifice. I actually, 
that is, assert or deny some real connection, and so far there is no 
"If." But, for some unstated reason, I desire at the same time to 
suggest that things throughout might have been otherwise. And I 
convey at once my undoubting judgment and my doubtful suggestion 
by licentiously applying " if" to the undiscriminated compound. "The 
destruction of the barometer ( 50) caused the absence of warning 
and it need not have been so." And " since you are well (which 
you might not have been)" is the double meaning conveyed in "si 
vales bene est." We may notice further in this connection that it 
is common to refute an asserted S P by showing it as true only 
if the impossible is supposed. 

4 1 "The fact is the quality in the man s disposition." (i) It is 
so here, but even here a " disposition " apart from any circumstances 
is an impossible abstraction. Further (ii), if "disposition" is used 
to explain "conditional," then obviously, since the very meaning of 



H2 THE PRINCIPLES OF LOGIC BOOK I 

" disposition " involves a standing " if," the explanation is circular 
(see Appearance, Index, s. v. Dispositions), (iii) The objection to 
"quality" is that it seems merely to repeat (what we knew before) 
that things are so; and to admit (if we add "latent") that we do 
not know how (Cf. Appearance, p. 362.). 

42 " A quality which has appeared . . . experiment." This state 
ment (see above) may involve a vicious abstraction. 

43 There is much here that requires correction, (i) I surely, in 
the case of every categorical judgment, am not forced to make it. 
The " arbitrary " character of all judgment and inference is discussed 
in T. E. I and II. (ii) Logical compulsion means merely that the 
object is so, whatever else I am pleased to fancy. And if a hypotheti 
cal judgment did not say that much, it would be no judgment at all. 
(iii) And further, to make the result of the "experiment" disappear 
from the reality is in principle vicious. 

44 "Were very different." The "very" here is objectionable. See 
Chap. Ill, 13. 

45 With regard to the limits of explanation I will merely state 
here that except in a relative sphere where assumptions are made 
all judgments and all truth on my view involves what is inexplicable. 
There is in every case a certain amount of unknown condition (x). 
The question in any particular case will be as to the nature and amount 
in the end of this x. See Appearance, p. 581 and its Index, and that 
of Essays, s. v. Inexplicable. 

46 The conclusion drawn in 53-56 is, I think, sound on the whole, 
though in part perhaps inaccurate. Even in the case of a designated 
particular we can hardly say broadly that this falls outside the sup- 
posal. On the other hand certainly we fail to get this, as merely 
designated, within the supposal and the judgment. The judgment 
therefore will, more or less against our wish, turn out to be abstract 
merely and only conditional though neither in form. See Essays, pp. 
38-40, and the Index of that work, and of this, s. v. Designation. 

47 " It does not assert the existence." Yes, it does assert this and 
must do so. But what existence and where is in every case the ques 
tion. See on 2 and Chap. I, 10. 

48 For the doctrine that all judgments are conditional see Essays, 
Index, s. v. Judgment. 

49 Cf. T. E. I and IX, and Essays, pp. 299 foil. 

50 The real truth . . . actual." This is the doctrine for which 
I have now for so many years contended. See Appearance and Essays, 
the Indexes. Relations exist only in and through a whole which 
can not in the end be resolved into relations and terms. " And," 
"together" and "between," are all in the end senseless apart from 
such a whole. The opposite view is maintained (as I understand) 
by Mr. Russell, and was perhaps at last tacitly adopted by Prof. 
Royce. But, for myself, I am unable to find that Mr. Russell has 
ever really faced this question. See Essays, Index, s. v. Unity. 

51 In "orthodox Christianity," the "orthodox" was meant to be 
emphatic. 



CHAP. 11 FORMS OF JUDGMENT 113 

52 On the actual content of the " this " see T. E. IV and V, and 
the Index. 

53 On conditioned and conditional see T. E. II, and Essays, the 
Index. 

54 " There is no because," i.e. of the character which you assume 
and require. The argument here is, in my opinion, sound, but it is 
perhaps better put as follows. The condition, on which the judgment 
holds, is unknown, and it admits also the opposite of what is asserted. 
The judgment therefore, in its present form, is at once both true 
and false. See Essays, Index, s. v. Conditional. 

55 The "real." See on 4. 

56 " You may say &c." It is of course the English empiricist of 
1883 who is being addressed here. As to how far the criticism is now 
out of date, the reader must judge for himself. 

57 " The whole or part of the series of phenomena," i.e. as such. 

ss " The present." Cf. ii foil. 

59 " The assertion seems not false." On the other side, since it 
depends on an unknown condition, and since therefore its opposite 
also is possible, it has not absolute truth. In this point, and so far, 
it is like the " analytical judgment of sense." On the other hand it is 
higher and truer because, and so far as, its condition is less unknown 
and less dependent on mere " matter of fact." 

60 "Does not ascribe . . . real." This, we have seen (Note 3) 
is wrong. But, if " existence " meant my " real world " of events, it 
could stand. On the " quality " see Note 41. 

61 If "existence" (Notes 3 and 33) means my " real world," then to 
say of anything that its existence is implied in there being such a 
world, is, so far, unconditional assertion. But on the other hand, so 
far as this world itself is not absolutely real and true, the assertion 
becomes, so far, merely relative, and dependent on an unknown con 
dition. If you could say that P, as such, is implied in the real, that 
would make P true absolutely. 

To " the consequence of a false hypothesis &c.," we should, I think, 
add "unless by an abstraction the hypothesis is taken as merely false." 

62 It must cease to predicate real " should be " It must cease 
to predicate its elements, as such, of the perceived real." 

63 "Immersed in matter." For "matter of fact" see Essays, pp. 
377-8o. 

64 " Assert the existence . . . that " should be " assert their content 
of that." And "can ascribe ... as such" should be changed to 
"can ascribe to reality its content unconditionally." 

65 The division made in 80 is (we have seen) indefensible, if only 
because the "imaginary" is left out. See Note 33- And for the 
" awkward assumption " cf. 32. 

66 " Soul to soul." Cf. Note 31. And (lower down), to the question 
raised by "Either here or nowhere," the answer, I think, must be 
" in the end nowhere." But for the sense of this reply I must refer 
to my Appearance and Essays. 



CHAPTER III l 

THE NEGATIVE JUDGMENT 

I. After the long discussion of the preceding chapter, 
we are so familiar with the general character of judgment that 
we can afford to deal rapidly with particular applications. 
Like every other variety, the negative judgment depends on 
the real which appears in perception. In the end it consists 
in the declared refusal of that subject 2 to accept an ideal 
content. The suggestion of the real as qualified and deter 
mined in a certain way, and the exclusion of that suggestion 
by its application to actual reality, is the proper essence of 
the negative judgment. 

2. Though denial, as we shall see, can not be reduced to 
or derived from affirmation, yet it would probably be wrong 
to consider the two as co-ordinate species. It is not merely 
as we shall see lower down (7), that negation presupposes 
a positive ground. It stands at a different level of reflection. 
For in affirmative judgment we are able to attribute the 
content directly to the real itself. To have an idea, or a 
synthesis of ideas, and to refer this as a quality to the fact 
that appears in presentation, was all that we wanted. But, 
in negative judgment, 3 this very reference of content to reality 
must itself be an idea. Given X the fact, and an idea a b, 
you may at once attribute a b to X ; but you can not deny 
a b of X, so long as you have merely X and a b. For, in 
order to deny, you must have the suggestion of an affirmative 
relation. The idea of X, as qualified by a b, which we may 
write x (a b), is the ideal content which X repels, and is 
what we deny in our negative judgment. 

It may be said, no doubt, that in affirmative judgment the 
real subject is always idealized. We select from the whole 
that appears in presentation, and mean an element that we do 
not mention (Book III. I. Chap. VI. 12). When we point 
to a tree and apply the word " green," it may be urged that the 
subject is just as ideal as when the same object rejects the 

114 



CHAP. Ill THE NEGATIVE JUDGMENT HtJ 

offered suggestion "yellow." But this would ignore an im 
portant difference. The tree, in its presented unity with 
reality, can accept at once the suggested quality. I am not 
always forced to suspend my decision, to wait and consider 
the whole as ideal, to ask in the first place, Is the tree green? 
and then decide that the tree is a green tree. But in the nega 
tive judgment where " yellow " is denied, the positive relation 
of " yellow " to the tree must precede the exclusion of that 
relation. The judgment can never anticipate the question. 
I must always be placed at that stage of reflection which 
sometimes I avoid in affirmative judgment. 

3. And this distinction becomes obvious, if we go back 
to origins and consider the early development of each kind. 
The primitive basis of affirmation is the coalescence of idea 
with perception. But mere non-coalescence of an idea with 
perception is a good deal further removed from negation. It 
is not the mere presence of an unreferred idea, nor its unob 
served difference, but it is the failure to refer it, or identify 
it, which is the foundation of our first denial. The exclu 
sion by presented fact of an idea, which attempted to qualify 
it, is what denial starts from. What negation must begin, 
with is the attempt on reality, the baffled approach of a 
qualification. And in the consciousness of this attempt is 
implied not only the suggestion that is made, but the subject to 
which that suggestion is offered. Thus in the scale of reflec 
tion negation stands higher than mere affirmation. It is in 
one sense more ideal, and it comes into existence at a later 
stage of the development of the soul.* 

4. But the perception of this truth must not lead us into 
error. We must never say that negation is the denial of an 
existing judgment. For judgment, as we know, implies belief; 
and it is not the case that what we deny we must once have 
believed. And again, since belief and disbelief are incom 
patible, the negative judgment would in this way be made to 
depend on an element which, alike by its existence or its 
disappearance, would remove the negation itself. What we 
deny is not the reference of the idea to actual fact. It is the 
mere idea of the fact, as so qualified, which negation ex- 

* Compare on this whole subject Sigwart, Logik, I. 119 and foil. 
I do not, however, wholly accept his views. 



!l6 THE PRINCIPLES OF LOGIC BOOK I 

eludes; it repels the suggested synthesis, 4 not the real judg 
ment. 

5. From this we may pass to a counterpart error. If it 
is a mistake to say that an affirmative judgment is presup 
posed in denial, it is no less a mistake to hold that the predicate 
alone is affected, and that negation itself is a kind of affirma 
tion. We shall hereafter recognize the truth which this doc 
trine embodies, but, in the form it here assumes, we can not 
accept it. The exclusion by fact of an approaching quality is 
a process which calls for its own special expression. And 
when we are asked to simplify matters by substituting " A 
is Not-B " for " A is not B," we find an obvious difficulty. 
In order to know that A accepts Not-B, must we not al 
ready have somehow learnt that A excludes B? And, if so, 
we reduce negation to affirmation by first of all denying, and 
then asserting that we have denied, a process which no doubt 
is quite legitimate, but is scarcely reduction or simplification. 

6. There is a further objection we shall state hereafter 
( 16) to the use of Not-B as an independent predicate. But 
at present we must turn to clear the ground of another error. 
We may be told that negation " affects only the copula ; " and 
it is necessary first to ask what this means. If it means what 
it says, we may dismiss it at once, since the copula may be 
wanting. If the copula is not there when I positively say 
" Wolf," so also it is absent when I negatively say " No wolf." 
But, if what is meant is that denial and assertion are two sorts 
of judgment, which stand on a level, then the statement once 
again needs correction. It is perfectly true that these two 
different sorts of judgment exist. The affirmative judgment 
qualifies a subject by the attribution of a quality, and the 
negative judgment qualifies a subject by the explicit rejection 
of that same quality. We have thus two kinds of asserted 
relation. But the mistake arises when we place them on a 
level. It is not only true that, as a condition of denial, we must 
have already a suggested synthesis, but there is in addition 
another objection. The truth of the negative may be seen in 
the end to lie in the affirmation of a positive quality; and 
hence assertion and denial cannot stand on one level. 5 In " A 
is not B " the real fact is a character x belonging to A, and 
which is incompatible with B. The basis of negation is really 



CHAP. Ill THE NEGATIVE JUDGMENT 117 

the assertion of a quality that excludes (#). It is not, as we 
saw, the mere assertion of the quality of exclusion (Not-B). 

7. Every negation must have a ground, and this ground 
is positive. It is that quality x in the subject which is in 
compatible with the suggested idea. A is not B because A 
is such that, if it were B, it would cease to be itself. Its 
quality would be altered if it accepted B ; and it is by virtue of 
this quality, which B would destroy, that A maintains itself 
and rejects the suggestion. In other words its quality x and B 
are discrepant. And we can not deny B without affirming in A 
the pre-existence of this discrepant quality. 6 

But in negative judgment x is not made explicit. We do 
not say what there is in A which makes B incompatible. We 
often, if asked, should be unable to point out and to dis 
tinguish this latent hindrance ; and in certain cases no effort we 
could make would enable us to do this. If B is accepted, A 
loses its character ; and in these cases we know no more. The 
ground is not merely unstated but is unknown. 

8. The distinctions of " privation " and " opposition " 
(Sigwart, 128 foil.) do not alter the essence of what we have 
laid down. In a privative judgment the predicate " red " would 
be denied of the subject simply on the ground that red was 
not there. The subject might be wholly colourless and dark. 7 
But if " red " were denied on the ground that the subject was 
coloured green, it would be the presence of an opposite quality 
that would exclude, and the judgment would then be based on 
positive opposition. This distinction we shall find in another 
context to be most material (cf. Chap. VI. and Book III. II. 
Chap. III. 20) ; but, for our present purpose, it may be called 
irrelevant. In the one case as in the other, the subject is 
taken with a certain character; and by addition as well as by 
diminution that individual character may be destroyed. If 
a body is not red because it is uncoloured, then the adding-on 
cf colour would destroy that body as at present we regard it. 
We may fairly say that, if the predicate were accepted, the 
subject would no longer be the subject it is. And, if so, in 
the end our denial in both cases will start from a discrepant 
quality and character. 

9. It may be answered, no doubt, that the subject, as it 
is now and as we now regard it, is not the same thing as the 

2321.1 i 



Il8 THE PRINCIPLES OF LOGIC BOOK I 

subject itself. In the one case, the subject rejects a sugges 
tion through a quality of its own, in the other it may reject 
on the strength of our failure. But I must persist in denying 
that this objection is relevant. In both cases alike the subject 
is taken as somehow determined; and it is this determination 
which (whatever it comes from) does give the subject a 
positive character, which in both cases lies at the base of the 
denial. No subject could repel an offered suggestion simply 
on the strength of what it was not. It is because the " not- 
this " must mean " something else that we are able to make 
absence a ground for denial. We shall all agree that the 
nothing which is nothing can not possibly do anything, or be a 
reason for aught. 8 

These distinctions do not touch the principle we stand 
upon, but I admit they give rise to most serious difficulties. 9 
And, mainly for the sake of future chapters, it may be well if 
we attempt here to clear our ideas. And (i) first, when we 
have a case of " opposition," there the subject repels the offered 
predicate because it has in its content a positive quality, 
filling the space which the predicate would occupy, and so 
expelling it. If a man has blue eyes, then that quality of 
blueness is incompatible with the quality brown. But (ii), 
when we come to privation, two cases are possible. In the 
first of these (a) within the content of the subject there is 
empty space where a quality should be. Thus, a man being 
eyeless, in this actual content lies the place where his eyes 
would be if he had them. And this void can not possibly be 
a literal blank. You must represent the orbits as somehow 
occupied, by peaceful eyelids, or unnatural appearance. And 
so the content itself gets a quality, which, in contrast to the 
presence of eyes, may be nothing,* but which by itself has a 
positive character, which serves to repel the suggestion of 
sight. 

10. But privation can rest on another basis (&). The 
*I may mention that, though contrast can not always be taken 
as holding true of the things contrasted, yet for all that it may rest 
n a positive quality. Thus, even in the case of a word like blind 
ness we should be wrong if we assumed that the blind man is 
qualified simply by the absence of sight from the part which should 
furnish vision. His mind, we can not doubt, has a positive character 
which it would lose if another sense were added. 



CHAP. Ill THE NEGATIVE JUDGMENT 1 19 

content of the subject may contain no space which could pos 
sibly be qualified by the presence of the predicate. What 
rejects the predicate is no other determination of the con 
tent itself, but is, so far as that content itself is concerned, 
an absolute blank. It is difficult to find illustrations of this 
instance. If I say "A stone does not feel or see," it may 
rightly be urged " Yes, because it is a stone, and not simply 
because it is nothing else." But we can find an example of 
the privation we want in the abstract universal. The univer 
sal idea (cf. Sigwart, 130), if you keep it in abstraction, 
repels every possible extension of its character. Thus " tri 
angle," if you mean by it the mere abstraction, can neither 
be isosceles nor scalene nor rectangular; for, if it were, it 
would cease to be undetermined. We may invent a stupid 
reductio ad absurdum: This isosceles figure is certainly a 
triangle, but a triangle is certainly not isosceles, therefore . 

If we release the universal from this unnatural abstraction, 
and use it as an attribute of real existence, then it can not sup 
port such a privative judgment. For, when referred to reality, 
we know it must be qualified, though we perhaps can not state 
its qualification. Once predicate triangle of any figure, and 
we no longer can deny every other quality. The triangle is 
determinate, though we are not able to say how. It is only 
the triangle as we happen not to know it, which repels the 
suggestion of offered predicates. It is our ignorance, in short, 
and not the idea, which supports our exclusion of every sug 
gestion. 

ii. In a judgment of this kind the base of denial is 
neither the content of the subject itself, nor is it that content 
plus a simple absence; for a simple absence is nothing at all. 
The genuine subject is the content of the idea plus my psycho 
logical state of mind. The universal abstraction, ostensibly 
unqualified, is determined by my mental repulsion of qualities. 
And the positive area which excludes the predicate really lies 
in that mental condition of mine. My ignorance, or again my 
wilful abstraction, is never a bare defect of knowledge. It is 
a positive psychological state. And it is by virtue of relation 
to this state, which is used as content to qualify the subject, 
that the abstraction, or the ignorance, is able to become a 
subject of privation. We shall see that, in this form, the 



120 



THE PRINCIPLES OF LOGIC BOOK I 



universal may more truly be called particular (Chap. VI. 
35) ; for it is determined and qualified, not by any develop 
ment of the content, but simply by extraneous psychological 
relation. 10 

12. The various kinds of negative judgment follow 
closely the varieties of affirmation. The immediate subject 
may be part of the content of present perception (" This stone 
is not wet ") ; or it may be found in some part of the series of 
space, or again of time, which we do not perceive (" Marseilles 
is not the capital of France," " It did not freeze last night "). 
Again what is denied may be a general connection ("A metal 
need not be heavier than water"). In this last case it is of 
course the unexpressed quality at the base of the hypothesis 
(Chap. II. 50) which the real excludes. 11 But, in all negative 
judgment, the ultimate subject is the reality that comes to us 
in presentation. We affirm in all alike that the quality of 
the real excludes an ideal content that is offered. And so 
every judgment, positive or negative, is in the end existential. 

In existential judgment, as we saw before (Chap. II. 42), 
the apparent is not the actual subject. Let us take such a 
denial as " Chimaeras are non-existent." " Chimaeras " is here 
ostensibly the subject, but is really the predicate. It is the 
quality of harbouring chimaeras which is denied of the nature 
of things. And we deny this because, if chimaeras existed, 
we should have to alter our view of the world. In some 
cases that view, no doubt, can be altered, but, so long as 
we hold it, we are bound to refuse all predicates it excludes. 
The positive quality of the ultimate reality may remain occult 
or be made explicit, but this, and nothing else, lies always at 
the base of a negative judgment. 

13. For logical negation can not be so directly related to 
fact as is logical assertion. 12 We might say that, as such and 
in its own strict character, it is simply " subjective : " it does 
not hold good outside my thinking. The reality repels the sug 
gested alteration; but the suggestion is not any movement of 
the fact, nor in fact does the given subject maintain itself 
against the actual attack of a discrepant quality. The process 
takes place in the unsubstantial region of ideal experiment. 
And the steps of that experiment are not even asserted to 
exist in the world outside our heads. The result remains, and 



CHAP. Ill THE NEGATIVE JUDGMENT 121 

is true of the real, but its truth, as we have seen, is something 
other than its first appearance. 

The reality is determined by negative judgments, but it 
can not be said to be directly determined. The exclusion, as 
such, can not be ascribed to it, and hence a variety of ex 
clusions may be based on one single quality. The soul is not 
an elephant, nor a ship in full sail, nor a colour, nor a fire- 
shovel; and, in all these negations, we do make an assertion 
about the soul. But you can hardly say that the subject is 
determined by these exclusions as such, unless you will main 
tain that, after the first, the remainder must yield some fresh 
piece of knowledge. You may hold that " all negation is deter 
mination," if you are prepared to argue that, in the rejection 
of each new absurd suggestion, the soul exhibits a fresh side 
of its being, and in each case performs the special exclusion 
by means of a new quality. But it seems better to say that 
nothing is added by additional exclusions. 13 The develop 
ment and application of these may proceed ad infinitum, but 
the process is arbitrary and, in the end, unreal. The same 
quality of the soul which repels one predicate, repels here all 
the rest, and the exclusion itself takes place only in our heads. 

I do not mean to deny that a thing may be qualified by 
the exclusion of others, that the real character of a fact may 
depend on what may be called a negative relation. What I 
mean to say is that the negative judgment will not express 
this. It asserts that a predicate is incompatible, but it does 
not say that either the predicate, or the incompatibility, are 
real facts. If you wish to say this you must transcend the 
sphere of the negative judgment. 

14. We must not, if we can help it, introduce into logic 
the problems of the " dialectical " view. 14 It may be, after all, 
that everything is just so far as it is not, and again is not just 
so far as it is. Everything is determined by all negation ; for 
it is what it is as a member of the whole, and its relation to all 
other members is negative. Each element in the whole, itself 
the whole ideally while actually finite, transcends itself by 
mere self-assertion, and by mere self-emphasis brings forth 
the other that characterizes and negates it. If everything thus 
has its discrepant in itself, then everything in a sense must be 
its own discrepancy. Negation is not only one side of reality, 



I2 2 THE PRINCIPLES OF LOGIC BOOK I 

but in the end it is either side we please. On this view it 
would be doubtful if even the whole is positive ; for it is just 
so far as by position it disperses itself in its own negation, and 
begets from its dispersion the opposite extreme. It is doubt 
ful if we may not transform the saying that " Everything is 
nothing except by position," into " Everything by position is 
its proper contrary, and nothing by position is all and every 
thing." 

If this is so, there would remain no quality which is 
simply positive; and logical negation, in another sense than 
we have given it above, becomes the soul and, we sometimes 
are inclined to think, the body of the real world. But we are 
not called upon to discuss this view (cf. Chap. V.), for our 
result will stand in any case, I think, in its principal outline. 

A mere logical negation, 15 it is fully admitted by the dia 
lectical method, need not express a real relation. And, this 
being so, it seems the better course to consider it by itself 
as merely subjective, and to express the real implication of 
exclusives by an affirmative judgment, which sets forth that 
fact. What denial tells us is merely this, that, when we bring 
the discrepant up, it is rejected. Whether what repels it is 
entirely independent, or whether it has itself produced or 
solicited what it excludes, is quite irrelevant. And it is still 
more irrelevant to ask the question if the first rejection is 
merely coquettish, and will lead in the end to a deeper sur 
render. This all goes beyond what denial expresses, for that, 
merely by itself, is not asserted beyond our minds. 

The dialectical method, in its unmodified form, may be 
untenable. It has, however, made a serious attempt to deal 
with the relation of thought to reality. We can hardly say 
that of those eminent writers who are sure that logic is the 
counterpart of things, and have never so much as asked them 
selves the question, if the difference and identity, with which 
logic operates, are existing relations between actual phenomena. 

15. To resume, logical negation always contradicts, but 
never asserts the existence of the contradictory. To say " A 
is not B " is merely the same as to deny that " A is B," or 
to assert that " A is B " is false. And, since it can not go 
beyond this result, a mere denial of B can never assert that 
the contradictory Not-B is real. The fact it does assert is the 



CHAP. Ill THE NEGATIVE JUDGMENT 123 

existence of an opposite incompatible quality,* either in the 
immediate or ultimate subject. This is the reason why the sug 
gested A B is contradicted ; and it is only because this 
something else is true, that the statement A B is rejected 
as false. But then this positive ground, which is the basis of 
negation, is not contradictory. It is merely discrepant, oppo 
site, incompatible. It is only contrary. In logical negation the 
denial and the fact can never be the same. 

1 6. The contradictory idea, if we take it in a merely 
negative form, must be banished from logic. If Not- A 
were solely the negation of A, it would be an assertion with 
out a quality, and would be a denial without anything positive 
to serve as its ground. A something that is only not some 
thing else, is a relation that terminates in an impalpable void, 
a reflection thrown upon empty space. It is a mere nonentity 
which can not be real. And, if such were the sense of the 
dialectical method (as it must be confessed its detractors have 
had much cause to suppose), 18 that sense would, strictly 
speaking, be nonsense. It is impossible for anything to be 
only Not-A. It is impossible to realize Not-A in thought. 
It is less than nothing, for nothing itself is not wholly negative. 
Nothing at least is empty thought, and that means at least my 
thinking emptily. Nothing means nothing else but failure. 
And failure is impossible unless something fails; but Not-A 
would be impersonal failure itself ( n). 

Not-A must be more than a bare negation. It must also 
be positive. It is a general name for any quality which, when 
you make it a predicate of A, or joint predicate with A, 17 
removes A from existence. The contradictory idea is the 
universal idea of the discrepant or contrary. In this form it 
must keep its place in logic. It is a general name for any 
hypothetical discrepant; but we must never for a moment 
allow ourselves to think of it as the collection of discrepants. 

17. Denial or contradiction is not the same thing as 
the assertion of the contrary; but in the end it can rest on 
nothing else. 18 The contrary however which denial asserts, 
is never explicit. In " A is not B " the discrepant ground is 
wholly unspecified. The basis of contradiction may be the 
assertion A-C or A-D, C and D being contraries of B. But 
*0n the nature of incompatibility see more, Chap. V. 



I2 4 THE PRINCIPLES OF LOGIC BOOK I 

again it may perhaps be nothing of the sort. We may reject 
A-B, not in the least on the ground of A, but because A 
itself is excluded from reality. The ultimate real may be 
the subject which has some quality discrepant with A-B. For 
contradiction rests on an undetermined contrary. It does not 
tell us what quality of the subject excludes the predicate. 
It leaves us in doubt if the subject itself is not excluded. 
Something there is which repels the suggestion; and that is 
all we know. Sokrates may be not sick because he is well, or 
because there is now no such thing as Sokrates. 

18. Between acceptance and rejection there is no middle- 
point, and so contradiction is always dual. There is but one 
Not-B. But contrary opposition is indefinitely plural. The 
number of qualities that are discrepant or incompatible with 
A, can not be determined by a general rule. It is possible of 
course to define a contrary in some sense which will limit the 
use of the term; but for logical purposes this customary 
restriction is nothing but lumber. In logic the contrary should 
be simply the discrepant. Nothing is gained by trying to 
keep up an effete tradition. If a technical distinction can 
not be called necessary, it is better to have done with it. 

19. Contradiction is thus a " subjective " process, which 
rests on an unnamed discrepant quality. It can not claim 
"objective" reality; and since its base is undetermined, it is 
hopelessly involved in ambiguity. In " A is not B " you know 
indeed what it is you deny, but you do not say what it is you 
affirm. It may be a quality in the nature of things which is 
incompatible with A, or again with B. Or again it may be 
either a general character of A itself which makes B impos 
sible, or it may be some particular predicate C. That "a 
round square is three-cornered," or that " happiness lies in 
an infinite quantity," may at once be denied. We know a 
round square, or an infinite number, are not in accordance 
with the nature of things. But " virtue is quadrangular," or 
" is mere self-seeking," we deny again because virtue has no 
existence in space, and has another quality which is opposite 
to selfishness. 

" The King of Utopia died on Tuesday " may be safely 
contradicted. And yet the denial must remain ambiguous. 
The ground may be that there is no such place, or it never 



CHAP. Ill THE NEGATIVE JUDGMENT 125 

had a king, or he still is living, or, though he is dead, yet he 
died on Monday. This doubtful character can never be re 
moved from the contradiction. It is the rejection of an idea, 
on account of some side of real fact which is implied but 
occult. 

20. We may conclude this chapter by setting before our 
selves a useful rule. I think most of us know that one can 
not affirm without also in effect denying something. In a 
complex universe the predicate you assert is certain to exclude 
some other quality, and this you may fairly be taken to deny. 
But another pitfall, if not so open, yet no less real, I think 
that some of us are quite unaware of. Our sober thinkers, 
our discreet Agnostics, our diffident admirers of the phenome 
nal region I wonder if ever any of them see how they com 
promise themselves with that little word " only." How is it 
that they dream there is something else underneath appear 
ance, and first suspect that what meets the eye veils some 
thing hidden? But our survey of negation has taught us the 
secret, that nothing in the world can ever be denied except on 
the strength of positive knowledge. I hardly know if I am 
right in introducing suggestive ideas into simple minds; but 
yet I must end with the rule I spoke of. We can not deny 
without also affirming; and it is of the very last importance, 
whenever we deny, to get as clear an idea as we can of the 
positive ground our denial rests on. 



ADDITIONAL NOTES 

1 This chapter contains some serious erors. I have since accepted 
in the main Dr. Bosanquet s account of negation. See his K & R and 
Logic. I have briefly discussed the whole matter in T. E. VI. 

2 "That subject," i.e., as in one with a selected determination. See 
Chap. !,ii and 12. 

s The abstraction of the idea from all " reference " is not defensible. 
See on Chap. I, 10. There is always some region in which an idea is 
real. It is only where the perceived world is taken as the one real 
object, that other worlds are merely subjective" (13). 

As to whether affirmation and denial are co-ordinate, we ^may 
say that in the end they are so, because the conscious use of ideas 
as ideas implies both a positive and negative aspect. But denial can 
be called more "reflective," in the sense that we become aware of 
it later. We must retain an excluded idea before we can know it 



126 THE PRINCIPLES OF LOGIC BOOK I 

as excluded. The beginning of affirmation, we may say, is an object 
before me changed ideally so as to lead to action. The beginning 
of negation is the exclusion of an ideal change in the object this 
exclusion not being retained by the mind, though action is thereby 
prevented. By "action" (I should add) is not meant necessarily 
action which is "practical." Thus it is not true that we have a 
separate suggestion and then consciously apply it. The attempt to 
identify may at first appear to us not as an attempt, but simply as 
the actual exclusion, where not the actual qualification. It is when we 
hold the suggestion, while excluding it from our perceived and selected 
object, that we first have denial in the proper sense of the word. 

4 The " suggested synthesis " (here and lower down) needs correc 
tion in the sense of the foregoing Note. 

5 It is true that a excludes b because it is a. It is true that there 
is a ground and a Why, and that in the end you can not make this 
Why explicit. But the same holds good also of b, as distinct from 
and so as negative of a. On the other hand this two-sided negation 
is at first implicit only and does not appear. You begin positively 
(as we saw above) with a designated object (Ro) qualified further 
ideally. It is only later and through reflection that, instead of such 
an object, Ro (ab), we arrive at a world qualified everywhere by 
distinctions, at once connected with and opposed to one another, and 

R 
so can write our object as / \ 

a b 

6 1 have, here and everywhere, altered " disparate " where in the 
original text it was used wrongly for " discrepant." I am quite unable 
to account for this mistaken use, which, I am sorry to add, recurs 
frequently, and for the sake of the reader has been now throughout 
corrected. 

7 "Colourless and dark." If "dark" meant "visibly dark" 
which I do not think it did mean there would be a mistake here. See 
Bosanquet K & R, p. 247. 

8 On the subject of Incompatibility the reader is referred to Ap 
pearance, Appendix, Note A, and to Bosanquet s Logic. 

9 These distinctions are (i) exclusion by a specified incompatible; 
(ii) exclusion of a quality from a space in a subject where that 
quality is looked for; (iii) exclusion from an assumed space taken 
as empty on the ground of absence, i.e. of my failure to find the 
quality there. If you were to drop the assumption made here, and 
were to reject the empty space, as being either meaningless or itself 
for some known reason excluded, the above exclusion would become 
sound. But at the same time it would cease to rest upon failure 
and mere privation. What on the other hand damns the privative 
judgment, as ultimate, is its assumption, based on mere ignorance, 
of an empty space in the character of the Universe. Where however 
you know positively that the Universe is in a certain respect deter- 
minable further, there your failure to find a particular qualification 



CHAP. Ill THE NEGATIVE JUDGMENT 127 

(a) is a ground for denial, just so far as you have reason to think 
your knowledge complete. But see the Notes on Chap. VII, 13 and 
28, and see T. E. VII. And cf. Appearance and Essays, the Indexes, 
s. v. Privation. 

10 " Extraneous psychological relation " should be perhaps " a dis 
tinction turned into a separation and made an exclusion on a mere 
extraneous psychological ground." 

11 " The unexpressed quality." See on Chap. II, 50. 

12 " Fact " here should be " perceived fact." And negation is " sub 
jective " in the sense that mere negation, mere exclusion, is an ab 
straction and is by itself really nothing at all. Cf. 15-19. Otherwise 
negation is not "subjective," though it is more "reflective" than is 
affirmation (2). 

13 " Nothing is added by additional exclusions." It is true that the 
abstract negation takes no account of the " how," which therefore, 
so far, may be the same. But to go beyond this is wrong (Chap. I, 
52). SeeT. E. VI. 

14 " Dialectical view." But, apart from this, in logic we may and 
must insist that Reality has to be regarded as a disjunctive totality, 
as the positive unity of diversities each of which is one and is not 
the others. In our intellectual world we must take every element as 
within a whole, and as qualified by its relations in that whole, and, 
further, as qualified by them internally. By "internally" is meant 
that the element itself, and not merely something else, is qualified. 
Hence everything will imply its relations both positive and negative. 
On the other hand we must not say of anything that it is nothing 
beyond its implications even though what else it is we are unable 
in the end to state. The problem of identity and diversity is, I agree, 
not in the end soluble (see Essays, pp. 240, 264). And our whole 
world, as merely intellectual, is not ultimately real. 

15 " A mere logical negation." The mere must be emphasized. 

16 " Much cause " should perhaps be " some cause." 

17 "Or joint predicate." In a sense it never is anything but a joint 
predicate. See Appearance, Appendix, Note A. 

18 The main point is this, that denial means exclusion from and 
by the real. Mere denial, however, rests on abstract exclusion, which, 
as abstract, is really nothing. Actually the real excludes because the 
real is qualified incompatibly, and may be so in a variety of senses, the 
whole of which variety is ignored by the abstract denial. See on 13. 



CHAPTER IV 

THE DISJUNCTIVE JUDGMENT * 

I. The disjunctive judgment may fairly complain that 
by most logicians it is hardly dealt with. It is often taken 
as a simple application of the hypothetical, and receives the 
treatment of a mere appendage. It is wonderful in how many 
respectable treatises not the smallest attempt is made to 
understand the meanings of " if " and of " either or." 

The commonest way of regarding disjunction is to take it 
as a combination of hypotheses. This view in itself is some 
what superficial, and it is possible even to state it incorrectly. 2 
" Either A is B or C is D " means, we are told, that if A is 
not B then C is D, and if C is not D then A is B. But a 
moment s reflection shows us that here two cases are omitted. 
Supposing, in the one case, that A is B, and supposing, in the 
other, that C is D, are we able in these cases to say nothing 
at all ? Our " either or " can certainly assure us that, if A is 
B, C-D must be false, and that, if C is D, then A-B is false. 
We have not exhausted the disjunctive statement, until we have 
provided for four possibilities, B and not-B, C and not-C. 

2. But however complete may be the cases supposed, 
disjunctive judgments can not really be reduced to hypothet 
ical. Their meaning, no doubt, can be given hypothetically ; 
but we must not go on to argue from this that they are 
hypothetical. The man who illustrated everything else has 
touched this point too in the Gentlemen of Verona: 

Speed. But tell me true, will t be a match? 

Launce. Ask my dog: if he say, ay, it will; if he say, no, it will; 
he shake his tail and say nothing, it will. 
Speed. The conclusion is then that it will. 

Launce. Thou shalt never get such a secret from me but by a 
parable (Act II. Scene v.). 

It is indeed by an indirect process, and by making secret 
a categorical judgment, that hypothetical can express dis 
junction. 



128 



CHAP, IV THE DISJUNCTIVE JUDGMENT I2Q 

I do not mean that the " either or " is purely categorical. 
I mean that to some extent at least it is categorical, and 
declares a fact without any supposition. In " A is b or c " 
some part of the statement is quite unconditional. It asserts 
a fact without any " if " at all. And when pressed with the 
objection, " But you can not deny that it is reduced to a com 
bination of supposals," we need not take long to practise an 
answer. A combination of hypothetical surely does not lie 
in the hypothetical themselves. It lies in the mind which 
combines them together, and surveys the field which together 
they exhaust. It is nonsense to say you are able to " reduce " 
a statement to elements of a certain character, when these 
elements, if taken merely by themselves and without a 
peculiar mode of union, are able to express nothing like the 
statement. 3 The basis of disjunction, the ground and founda 
tion of your hypotheticals, is categorical. 4 

3. There is, no doubt, some difficulty about the categor 
ical nature of disjunctive judgments. " A is b or c; " but this 
mode of speech can not possibly answer to real fact. No real 
fact can be " either or." It is both or one, and between the 
two there is nothing actual. We can hardly mean to say that 
in fact A is b or c. On the other hand, we are far from 
expressing simple ignorance. If we merely said " I do not 
know if A is b, and I do not know if A is c" that would not 
be equivalent to the original statement. And that we make 
an assertion can be shown in this way. If the subject of our 
predicate " either or " were proved not to exist, our state 
ment would be false. It is clear not only that the subject 
has existence, but that it also possesses some further 
quality. 5 

The distinction of the apparent and the ultimate subject, 
which we had to make in our former discussions, must not 
here be forgotten. " A is either b or c " need not always imply 
that A is a fact. For example, I may say that "either A 
exists or does not exist." The subject here is the nature of 
things, and this either repels the content A or is qualified by 
it. But still the assertion remains categorical. Throughout 
the rest of the chapter I shall take A to stand for the real 
subject, and the reader must remember that in every case 
the apparent subject may belong to the predicate, and that what 



130 THE PRINCIPLES OF LOGIC BOOK I 

is asserted respecting A may only be true of the ultimate sub 
ject. 

And the same remark applies to such examples as " Either 
A is B or C is D." The subject in this case is not A or B or 
again C or D. The subject is the real, which is qualified by 
the predicate A-B or the predicate C D. 

4. The assertion in " A is b or c " is not that A is b or c. 
What then do we affirm? We say in the first place that A 
exists. In the next place we certainly give it some quality. 6 
What quality do we give it? If it can not be either b or c, 
can it possibly be something that falls between them ? No, for 
that would be neither. For instance, grey is not white or 
black, and it excludes both colours. The predicate of A, while 
neither b nor c, must not be a quality exclusive of either. It 
must then be a quality common to both, which is not yet 
either, but is further determinable as one or the other. 

5. If we like to call this basis x, then "A is x " is 
categorically true. We may in some cases have distinguished 
x and given it a name, but in other cases it is unnamed and 
implicit. " Man, woman, and child," have a common basis in 
" human being." In " white or black " the quality " coloured, 
and coloured so as to exclude other hues," is the attribute 
asserted. " In England or America," " alive or dead," com 
mit us to the statements " somewhere not elsewhere " and 
" organized being." And so, if we call a man " bad or good," 
we say at least he is a moral agent. There is no exception to 
the truth of this rule. Even existence and non-existence have 
so much in common that, in any sense in which we can use 
them, they imply some kind of contact with my mind. We 
have seen (Chap. III.) that there is no pure negation. So, 
in every disjunction and as the ground of it, there must be 
the assertion of a common quality, the sphere within which 
the disjunction is affirmed. 

6. But x is not any universal whatever which happens to 
be common to b and c. It is particularized further. It excludes 
the opposite of each of these qualities, and can not be the nega 
tive of " b or c" It is affirmed as fully determined not outside 
the region which is covered by be. But since b and c, as 
predicates of A, are incompatible, it can not be both of them. 
The conclusion remains that it must be one. " One single 



CHAP. IV THE DISJUNCTIVE JUDGMENT 13! 

element of the region enclosed by be " is the predicate common 
to b and c. And this predicate it is which, in disjunction, we 
categorically assert of A. 

So much is fact and no hypothesis ; but this by itself would 
not be the assertion " b or c." The disjunctive judgment is 
not wholly categoric. Being sure of our basis, the quality x t 
upon this universal we erect hypotheses. We know that b 
and c are discrepant. We know that A is particularized 
within b and c, and therefore as one of b and c. It can not be 
both, and it must be some one. 7 So much is the fact. To 
complete the disjunction we add the supposal, "If it is not 
one it must be the other." If A is not b, it must be c; and it 
must be b, if it is not c. This supposal completes the " either 
or." Disjunctive judgment is the union of hypotheticals on 
a categoric basis. 

7. We shall return to consider this process further, but 
at present we may pause to correct a mistake. It has been 
doubted if alternatives are always exclusive. 8 " A is b or c" 
it is said, may be taken to admit that A is possibly both. It 
may either be be or b or c. And, no doubt, in our ordinary 
disjunctive statements we either leave the meaning to be 
gathered from the context, or really may not know what it is 
that we mean. But our slovenly habits of expression and 
thought are no real evidence against the exclusive character 
of disjunction. " A is b or c " does strictly exclude " A is both 
b and c." When a speaker asserts that a given person is a 
fool or a rogue, he may not mean to deny that he is both. But, 
having no interest in showing that he is both, being perfectly 
satisfied provided he is one, either b or c, the speaker has not 
the possibility be in his mind. Ignoring it as irrelevant, he 
argues as if it did not exist. And thus he may practically be 
right in what he says, though formally his statement is down 
right false ; for he has excluded the alternative be. 9 

And it is not always safe to be slovenly. It may be a 
matter of vital moment to make our disjunction accurate and 
complete, and to know if we mean " A is b or c" or " A is 
be or b or c." About the commonest mistake in metaphysics 
is the setting up of false alternatives. If we either admit be 
as a predicate when b and c are discrepant, or exclude be 
when b and c are compatible, we are liable to come to most 



132 THE PRINCIPLES OF LOGIC BOOK I 

false conclusions. And the very instance we have quoted above 
should read us a lesson. It is false that the alternative 
" either rogue or fool " does never exclude the possibility of 
both. It is a common thing to make this mistake. When 
we try to guess a man s line of conduct, we first lay it down 
he is fool or rogue, and then afterwards, arguing that he is 
certainly a rogue, we conclude that his conduct will be de 
liberately selfish. But unfortunately the man has been a fool 
as well, and was not in any way to be relied on. It is often im 
possible to speak by the card, but still inaccuracy remains 
inaccuracy. And, if we do not mention the alternative " or 
both," when held to our words we certainly exclude it. 

If we mean to say " A is b or c or again be" the process 
of the judgment is very simple. A exists and is further 
determined. It is determined within the region be. A ex 
cludes all qualities which are incompatible with b and c and 
again with be. Within be fall b and c and again be, and 
nothing else falls there. And since these are discrepant, A 
is but one of them. So far the fact, and then come the 
hypotheses. If A as determined excludes b and c it must be 
be; if it excludes c and be it is b; if it excludes b and be it is c. 
The number of discrepants is of course irrelevant to the 
nature of the process. 

8. But the inaccuracy we have noticed has a natural 
foundation. We are accustomed to use " or " with an impli 
cation, and at times we forget whether " or " stands alone or 
must be taken as so qualified. I will briefly illustrate. If, in 
drawing up a rule, I lay down that " the number of tickets 
being limited, each person shall be entitled to a red ticket or 
a white one," it is at once understood that the alternatives are 
incompatible. A ticket means here obviously one at most. 
But, if I say " No one shall be entitled to pass within this 
enclosure except the possessor of a white or red ticket," I 
should hardly be taken to exclude the man who was qualified 
by both. A ticket means here one at least. And it becomes 
very easy to misunderstand, and to suppose that " or " in each 
of these cases has a different force. 

But in both cases " or " means precisely the same. In the 
second, as in the first, it is rigidly disjunctive. But in the 
second of our instances "or" does not stand alone. It is 



CHAP. IV THE DISJUNCTIVE JUDGMENT j^ 

qualified by an unexpressed " if not " or " failing that." And 
this implication makes a vital difference. 

9. The alternatives which are offered are not red and 
white. I am not to be admitted, given white or red. The 
entitling conditions (so far as they are contemplated) are 
firstly " white," and then " red, white failing " or " red with 
out white ; " and it can hardly be maintained that these con 
ditions are compatible. For, if white is there, then red can not 
make good the failure of white, and the red, that is specified 
as excluding white, can not by any means admit its presence. 
What you mean to say is, Suppose white is there, then cadit 
quastio; but, if white is not there, red will answer the pur 
pose. And you express your meaning by assigning two 
alternatives, " white present " on the one hand, and, on the 
other hand, " red coupled with the absence of white." And 
this practically provides for every possibility. 

The logical objection which may be raised against it is not 
that its "or " is partly conjunctive, for this, as we have seen, is 
a pure mistake. The disjunction is faulty not because it is 
conjunctive, but because it is incomplete. It ignores the 
possibility of the co-existence of red and white, and in form 
it might be construed as excluding it. But the reason is 
obvious. You are never forced to consider separately this 
individual possibility, since you can always treat it as a 
simple case of the presence of white. If "white" really 
means " white with or without red," and " red " means " red 
on the failure of white," and if the absence of both is fully 
provided for, then the disjunction is absolutely complete and 
exhaustive. And these alternatives (i) white with or without 
red, (ii) red without white, and (iii) failure of both, are 
absolutely incompatible. 

10. And this I think is the answer to an argument 
brought forward by Professor Jevons (Principles, p. 73). 
Against the exclusive character of alternatives he urges an 
indirect argument. If that were so, he objects, the negative 
of such a term as " malleable-dense-metal " could not be 
" not-malleable or not-dense or not-metallic." There would be 
seven distinct alternatives, and this would be absurd. 

I must remark, in the first place, that I wholly fail to see 
the absurdity. If you mean to exhaust the cases which ex- 

2321.1 K 



134 THE PRINCIPLES OF LOGIC BOOK I 

elude the term " malleable-dense-metal," the absurdity would 
lie in their number being less than what follows from the 
number of possible combinations. But if you mean to say 
that, if "or " is exclusive, you can not deny the term which is 
offered unless you set out all the cases which exclude it, then 
this is just the mistake we have been considering. In " not- 
malleable or not-dense or not-metallic" the disjoined are in 
compatible, but the full possibilities are not set out. You 
must understand with each " or " the implication of " failing 
that." " Not malleable " does not mean the isolated presence 
of non-malleability. It is not one possibility: it is a class 
that covers several. It means the absence of malleability, 
whether the subject is metallic or not-metallic, dense or not- 
dense. You may fairly object that combinations are ignored, 
or else that the term " not-malleable " is ambiguous, since it is 
used to cover a number of cases. But these technical objec 
tions would have little importance, and they do nothing to 
show that " or " does anything but rigidly disjoin. 

ii. Despite my respect for Professor Jevons, I can not 
admit any possible instance in which alternatives are not 
exclusive. I confess I should despair of human language, if 
such distinctions as separate " and " from " or " could be 
broken down. And, when I examine the further evidence 
produced, it either turns on the inaccurate modes of expres 
sion we have lately discussed, or consists in what I must be 
allowed to call a most simple confusion. We are told that 
the expressions " wreath or anadem," or again " unstain d by 
gold or fee " (Jevons, p. 70), show that " or " may sometimes 
be non-exclusive. But this is quite erroneous. The alterna 
tives are meant to be rigidly incompatible. The distinction is 
however not applied to the thing, but simply to the names. If 
we suppose that the terms are quite synonymous, then " wreath 
or anadem" means "you may call it by either name you 
please." The thing has two titles, one of which is at your 
service. I hardly think Professor Jevons would assert that we 
are asked to use both names at once. So, if " fee " is not 
meant to be distinct from " gold," the assertion is that there is 
no stain arising from the thing you may term indifferently 
gold or fee. The idea of your wanting to say both at once is 
quite ignored. 



CHAP. IV THE DISJUNCTIVE JUDGMENT 135 

I will try to make the matter clearer by inventing a piece 
of imaginary dialogue. A. Who is the greatest Roman poet? 
B. His name is Virgil. A. What, not Vergilius? B. Yes, 
Virgil or Vergilius. A. I understand : he has two names. I 
will call him henceforth " Vergilius- Virgil," and then I shall be 
safe. B. Excuse me: in that case you must be wrong. You 
may call him by either of the names you please, but not by 
both of them at once. 

It is not worth while to multiply illustrations. In every 
instance that can be produced, we have either a loose mode of 
common speech, or else the " or " denotes incompatibility, 
whether that lie in the simultaneous use of alternative names, 
or in the facts themselves. 

12. The mere statement, of course, may fail to tell us 
which of these incompatibilities is before us. And no one can 
deny that alternatives are often presented in a very inac 
curate way. It is an excellent thing in all these questions 
to refer to the common usages of language, but we must 
remember that in those usages, besides what one calls " un 
conscious logic," there also may lurk mere looseness and care 
lessness. It may not be amiss to illustrate the mistake we 
have just been discussing, by a parallel ambiguity in the 
hypothetical judgment. It is, of course, the established doc 
trine that, while you may argue from ground to consequence, 
you can not demonstrate from consequence to ground. 10 And, 
although from a metaphysical point of view this doctrine is 
certainly open to doubt, still for logical purposes it is suffi 
ciently valid. But yet, by appealing to loose expressions, 
we might show that the ground is the only ground, and can 
therefore be inferred from the presence of the consequence. 
Sigwart has called attention to these cases (Logik, I. 243 ; and 
Beitrage, 59). "If you run hard you will catch him," is 
often an indirect way of saying, " You will not catch him 
unless you run hard." But such mere loose phrases are no 
valid reason for impugning the doctrine that, unless this fact is 
specially stated, the condition is not given as a sine qua non. 
When the context shows that our expressions are not to be 
strictly interpreted, we are at liberty to take " eitheror " as 
compatible, and " if " may be the same as " not unless." But 



136 THE PRINCIPLES OF LOGIC BOOK I 

we should remember that what a thing can pass for may differ 
widely from what it really is. 

13. It is time we left these misleading errors to return to 
the discussion of the matter itself. The detail of the process 
in disjunctive judgments can not fully be dealt with till we 
come to inference. But here we may partly prepare the 
ground. 

In the first place, as we shall see in the following chapter, 
disjunction does not rest on Excluded Middle. The latter is 
merely a case of disjunction. 

" A is b or c " asserts, as we saw, that A exists and pos 
sesses a quality. That quality, further, falls within be. It is 
affirmed to be what is common to both, and it is stated also to 
be further determinable within be. In other words, it excludes 
all discrepant with both b and c. 

We have seen this above, and the point I wish here to 
bring forward is the following. How do we know, and how 
can we know, that there is not something discrepant with be 
and yet compatible with A? All rests upon this; and what 
does this rest on? 

We must answer, for the present, that it rests on our 
impotence. 11 There is no great principle on which we can 
stand. We can not find any opposite of b or opposite of c 
which is not also an opposite of A; and we boldly assume 
that, because we find none, therefore there is none. The con 
clusion from impotence may itself seem impotent, but, as 
we shall hereafter see, there remains some doubt if it may not 
in the end be taken as the ground and the sole ground we have 
for believing anything (Book III. II. Chapter III.). 

14. We may state the whole matter once more thus. " A 
is b or c" may be expressed by (i) If A is b it is not c, and 
If A is c it is not b, (ii) If A is not b then it is c, and If A 
is not c then it must be b. The first two hypothetical state 
ments are erected on the knowledge that b and c as predicates 
of A are incompatible, or that Abe can not possibly exist. 

The second pair are based on the assumption that, because 
we do not find a predicate of A which excludes b or c, there 
fore there is none. Every opposite of b or of c, that we find, 
is an opposite of A. Hence there remains this result; within 
the limit of A there is no not-fc but c, and no not-c but b: and 



CHAP. IV THE DISJUNCTIVE JUDGMENT 137 

A must have some further quality. This is the ground for our 
second two hypotheticals. 

So we see the essence of disjunctive judgment is not got 
by calling it a combination of supposals. It has a distinctive 
character of its own. It first takes a predicate known within 
limits, and defined by exclusion, and then further defines it 
by hypothetical exclusion. It rests on the assumption that we 
have the whole field, and by removing parts can determine 
the residue. It supposes in short a kind of omniscience. Its 
assertion again, if not quite categorical, is certainly not quite 
hypothetical. It involves both these elements. And it implies, 
in addition, a process of inference which will give us cause 
for reflection in the future. 



ADDITIONAL NOTES 

1 On the subject of Disjunction the reader is referred to Dr. 
Bosanquet s Logic. I fully accept his main view; but, before pro 
ceeding in consequence to point out some errors made in this volume, 
I will add a few remarks which may perhaps assist the reader. 

Disjunction means "or," and, viewed psychologically, "or" stands 
for Choice. Hence it may be useful to consider here how choice 
arises. Where something is desired, where there are various ways 
of realizing this end, and where I find that I can not have all of 
these as a whole and at once and where, by this negation, action 
has been suspended the result may be choice. And, in choosing, I 
accept one way while rejecting the rest. Or, again, I foresee, let us 
say, that an event affecting me must actually happen, and that, so far, 
there are no two ways, but that, as to how the event will happen and 
affect me, the ways are various. And let us add that I perceive that 
these diverse modifications, while impossible all at once, are otherwise, 
each of them, more or less in my power. Here, as above, after suspend 
ing action I identify myself in choice with one of these modes, while 
rejecting the rest. And obviously the "or" thus contained in choice 
is exclusive; and any other view as to "or" would, here at least, 
conflict with plain fact. 

We may note further that in choice the alternative need not 
merely be dual. The incompatibles that are each possible may be 
clearly more than two. And this plurality in the " or " holds, I would 
add, not merely psychologically and in choice, but equally belongs to 
the "or" of logical disjunction. The necessary duality of disjunction 
in the sense that the incompatibles, which are each possible, can not 
be taken as more than two is to my mind a view which, so far, is 
contrary to fact. 



THE PRINCIPLES OF LOGIC BOOK I 

What is true here is that when, and so far as, in choice or other 
wise, you identify yourself with one possibility, the residue tends to 
be regarded or at least treated, so far, as not even possible. It is 
taken for our purpose, we may say, in the lump and as all one, and 
so, we may add, is taken but as one only. But in the above attitude 
(to speak strictly) there is really no question of number, since what 
is rejected is viewed merely from the side of its general quality. 

Having now noticed the character of " or " as we find it in choice, 
I will go on to deal briefly with the origin and nature of logical dis 
junction. Before this arises we have found that Reality, as this or 
that recognizable object, has various qualities. We have passed, that 
is, beyond the stage of an immediate unity of one and many. We 
have reached a level where the distinguished many are recognized as 
diverse, and yet, as each and also the rest, belonging somehow to the 
one object. And the object possesses this diversity, so far, all together 
and at once. The qualities thus seem simply conjoined and are called 
compatible. But we go on to discover, in the same or in some other 
object, qualities not found thus together, and we call these, so far, 
incompatible. The object may have now one and now another, but 
never has at once both or all. On the other side (here is the point) 
the object has these qualities. It has them, now one and now 
another, according to the conditions. It has them, that is, not simply, 
but according as it itself is made diverse, so as itself to enter into 
and become this one qualification while rejecting the others. And, 
since we find that this holds good also with regard to these other 
incompatibles, the object is now qualified by them all, but qualified 
disjunctively. While on one hand the object is all, it is on the other 
hand each singly and each exclusively according to the diverse con 
ditions. 

Such in outline, we may say, is the origin of Disjunction, and its 
intellectual importance and necessity can not well be overestimated. 
But we are led none the less to look beyond it to a higher and more 
ultimate stage, where we return to Conjunction in a different sense 
and at a higher level. In a complete and perfect system, where all 
conditions were filled in, the real Universe would have all its de 
terminations at once, all as connected and each as qualifying the others 
and the whole. And here negation would disappear except as one 
aspect of positive and complementary distinction. But for us this 
ultimate stage of the intellect remains an ideal, in the sense that it 
can not in detail and everywhere be attained completely. 

This ideal, I must add, in no way justifies the doctrine that in 
logic " or " can anywhere have a sense which is not exclusive. In 
other words so far as " or " ceases to exclude both " or," and 
disjunction with it, have so far ceased as such to exist. See below, 
on 7. 

2 " To state it incorrectly." I can not now recall the origin of this 
remark, which seems at best negligible. For the possibility of reduc 
tion to two hypothetical see Bosanquet, K & R, p. 208. 



CHAP. IV THE DISJUNCTIVE JUDGMENT 139 

31 " It is nonsense." Certainly (I must insist) it is so. We may 
illustrate by the attempt to reduce relational wholes, and even per 
haps all facts, to relations and terms. 

4 "The basis ... is categorical." This, however, is subject to a 
qualification, for which see Bosanquet, Logic (Ed. II), I, 328. 

5 It is of course not true that disjunction assumes the existence 
of its subject (cf. Chap. V, 23), if that means "existence in my real 
world." The subject may be hypothetical or otherwise "imaginary." 
But there is in the end an Ultimate within which all disjunction falls 
and which has no negative. 

6 The use of "quality" here is objectionable. See on Chap. II, 50. 

7 " It can not be both and it must be some one." If " some one " 
means " one only," this would anticipate the disjunction. It should 
mean " must be, so far, within the field of both while not both." The 
disjunction implied in "one only" requires hypothetical to complete 
it and make it explicit. The same requirement, though not in the 
same sense, holds, I think, of our knowledge that b and c are in 
compatible. 

8 I am more than ever convinced that the view which takes " or " 
as not always exclusive is utterly untenable, except perhaps by way of 
of a mere convenient artifice. On the whole question, and for a refuta 
tion of technical objections, see Bosanquet, Logic (Ed. II), Vol. I, 
pp. 355 foil. The subject is now perhaps exhausted, but I will allow 
myself to add one or two remarks. 

(i) The evidence from psychology seems to me to be all on one 
side. " Or " answers to choice, and choice seems nonsense if it means 
that you can have all at once. And this consideration ought, I submit, 
to carry great weight. 

(ii) The fallacy of " false alternative," I would further remind 
the reader, may be said perhaps to dominate our lives. But how could 
this be so, if "or" were not taken instinctively as everywhere exclu 
sive? And the fallacy does not lie in our assuming this as true. It 
lies, on the other hand, in our forgetting constantly the actual nature of 
our subject. We may say that (apart from exceptional cases) in every 
judgment made in life the real subject is other than that which is 
formulated. It is really that which is "understood" for the purpose 
in hand, which limited purpose, not being made explicit, is easily 
ignored or forgotten. Thus, in " A is b or c," the A which we mean 
is A qualified and limited by our special object and interest. It is of 
and within this qualified A that our " b or c " holds. And it is when 
we ignore or forget this, and when we go on to take A simply and 
unrestrictedly in the sense of " A anyhow," that the fallacy everywhere 
tends to arise. But this tendency, with its false result, points, I submit, 
to our unfailing reliance on the exclusiveness of "or." 

The arguments against its exclusiveness seem to me plausible only 
when this unexpressed qualification of A is ignored. In our actual 
use of " or," A means an A not only where the possibility of Abe is 
excluded, but also where it is tacitly set aside as irrelevant to our 



I4O THE PRINCIPLES OF LOGIC BOOK I 

purpose. And, when we remember this, the case against exclusiveness, 
to my mind, disappears. 

(iii) If we keep to mere "or," then "or" is both exhaustive and 
exclusive; and, if we are to argue against the second of these characters, 
we must also argue against the first. After stating that A is & or c, we 
may receive the answer "yes or both" without any feeling that our 
statement has been denied. But, on just the same principle, we may 
accept a suggested addition of "or d" not as a correction but as a 
complement. And yet to argue from this that disjunction is not taken 
as exhaustive would, if plausible, be erroneous. The " or d " is ac 
cepted because, and so far as, A did not mean "A pure and simple." 
It in fact meant, for our purpose, something like " A, whatever else A 
elsewhere may be." Hence a correction and a replacement of A by 
a wider subject is (we feel) not called for here by the addition of 
"or d." And thus the actual disjunction is really exhaustive, just as 
on the same principle (we saw above) it was really exclusive unless, 
that is, the disjunction in both cases has ceased, as such, to exist, and 
has really given way to some lower or higher mode of assertion. 

9 " His statement is ... false." And it therefore, I presume, can 
lead formally to the equally false result " He is either wise or honest " 

(Keynes, Formal Logic, p. 280, note). This, if correct, I take to 
confirm the doctrine of my text, which doctrine, I venture to think, 
here and elsewhere, Dr. Keynes has failed to understand. 

10 "The established doctrine." The doctrine is, however, in the 
end untenable. See Bosanquet, Logic I, Chap. VI. I have fully 
accepted his view; see Appearance, Index, s. v. Cause, and T. E. X. 
Apart from this, the instance in the text may serve to illustrate the 
ambiguity of ordinary language. 

11 For privation and impotence as a ground of knowledge see on 
Chap. Ill, 9. So far as our knowledge is completely systematized, 
privation, of course, so far ceases to exist. 



CHAPTER V 

THE PRINCIPLES OF IDENTITY, CONTRADICTION, EXCLUDED 
MIDDLE, AND DOUBLE NEGATION. 

i. After discussing negative and disjunctive judgments, 
we may deal at once with the so-called " Principles " of Iden 
tity, Contradiction, and Excluded Middle; and we will add 
some remarks on Double Negation. 

The principle of Identity is often stated in the form of a 
tautology, " A is A." If this really means that no difference 
exists on the two sides of the judgment, we may dismiss it 
at once. It is no judgment at all. As Hegel tells us, it sins 
against the very form of judgment; for, while professing to 
say something, it really says nothing. It does not even assert 
identity. For identity without difference is nothing at all. 
It takes two to make the same, and the least we can have is 
some change of event in a self -same thing, or the return to 
that thing from some suggested difference. For, otherwise, to 
say " It is the same as itself " would be quite unmeaning. We 
could not even have the appearance of judgment in " A is A," 
if we had not at least the difference of position in the different 
A s ; and we can not have the reality of judgment, unless some 
difference actually enters into the content of what we assert. 

2. We never at any time wish to use tautologies. No 
one is so foolish in ordinary life as to try to assert without 
some difference. We say indeed " I am myself," and " Man is 
man and master of his fate." But such sayings as these are 
no tautologies. 1 They emphasize an attribute of the subject 
which some consideration, or passing change, may have 
threatened to obscure ; and to understand them rightly we 
must always supply " for all that," " notwithstanding," or 
again, " once more." It is a mere mistake to confuse what 
Kant calls " analytical judgments " * with tautologous state 
ments. In the former the predicate is part of the content of 
the conception A, which stands in the place of, and appears as, 

*This is not the sense in which I have used "analytical." p. 48. 

141 



!42 THE PRINCIPLES OF LOGIC BOOK I 

the subject. But in every judgment of every kind a synthesis 
is asserted. The synthesis in Kant s analytical judgment holds 
good within the sphere of the conception ; and the real subject 
is not the whole of A, but is certain other attributes of A 
which are not the attribute asserted in the predicate. In " All 
bodies are extended " what we mean to assert is the connection, 
within the subject "bodies," of extension with some other 
property of bodies. And even if " extended " and " body " 
were synonymous, we still might be very far from tautology. 
As against some incompatible suggestion, we might mean to 
assert that, after all misapprehension and improper treatment, 
the extended is none the less the extended. And, again, we 
might be making a real assertion of a verbal nature. We 
might mean that, despite their difference as words, the mean 
ing of " body " and " extended " was the same. But mere 
tautology with deliberate purpose we never commit. Every 
judgment is essentially synthetical. 

3. The axiom of Identity, if we take it in the sense of a 
principle of tautology, is no more than the explicit statement 
of an error. And the question is, would it not be better to 
banish irrevocably from the field of logic such a source of 
mistake? If the axiom of Identity is not just as much an 
axiom of Difference, then, whatever shape we like to give it, 
it is not a principle of analytical judgments or of any other 
judgments at all. On the other hand, perhaps something may 
be gained if a traditional form can get a meaning which con 
veys vital truth. Let us try to interpret the principle of Iden 
tity in such a way that it may really be an axiom. 

4. We might take it to mean that in every judgment we 
assert the identity of subject and predicate. Every connection 
of elements we affirm, in short all relations and every differ 
ence, holds good only within a whole of fact. 2 All attributes 
imply the identity of a subject. And taken in this sense the 
principle of Identity would certainly be true. But this perhaps 
is not the meaning which, for logical purposes, it is best to 
mark specially. 

5. There remains a most important principle which, 
whether it be true or open to criticism, is at least the sine qua 
non of inference. And we can not do better than give this the 
name of principle of Identity, since its essence is to emphasize 



CHAP. V THE PRINCIPLE OF IDENTITY 143 

sameness in despite of difference. What is this principle? It 
runs thus : " Truth is at all times true," or, " Once true always 
true, once false always false. Truth is not only independent 
of me, but it does not depend upon change and chance. No 
alteration in space or time, no possible difference of any event 
or context, can make truth falsehood. If that which I say is 
really true, then it stands for ever." 

So stated the principle is not very clear, but perhaps it 
will find acceptance with most readers. What it means, how 
ever, is much more definite, and will be much less welcome. 
The real axiom of Identity is this : What is true in one context 
is true in another. 5 Or, If any truth is stated so that a change 
in events will make it false, then it is not a genuine truth at all. 

6. To most readers this axiom, I have little doubt, will 
seem a false statement. For the present it may stand to serve 
as a test if our previous discussions (Chap. II.) have been 
understood. If every judgment in the end is hypothetical, 
except those not directly concerned with phenomena if each 
merely asserts a connection of adjectives, in this sense that 
given A then B must follow we see at once that under any 
conditions it will always be true. And we shall see here 
after that in every inference this result is assumed as a prin 
ciple of reasoning, and that we can not argue one step with 
out it. 

7. We saw that such judgments as " I have a toothache," 
in their sensuous form, are not really true. They fail and 
come short of categorical truth, and they hardly have attained 
to hypothetical. To make them true we should have to give 
the conditions of the toothache, in such a way that the con 
nection would hold beyond the present case. When the judg 
ment gave the toothache as the consequent coming according 
to law from the ground, when the judgment had thus become 
universal, and, becoming this, had become hypothetical, then 
at last it would be really true, and its truth would be uncondi 
tional and eternal. 

I know how absurd such a statement sounds. It is impos 
sible, I admit, however much we believe it, not to find it in a 
certain respect ridiculous. That I do not complain of, for it 
is not our fault. But it is our fault if the common view does 
not seem more ridiculous. I say that " I have a toothache " 



144 THE PRINCIPLES OF LOGIC BOOK I 

to-day. It is gone to-morrow. Has my former judgment 
become therefore false? The popular view would loudly pro 
test that it still is true, for I had a toothache, and the judg 
ment now holds good of the past. But what that comes to is 
simply this. The judgment is true because answering to fact. 
The fact alters so that it does not answer; and yet the judg 
ment is still called true, because of something that does not 
exist. Can anything be more inconsistent and absurd? If the 
change of circumstance and change of day is not a fresh con 
text which falsifies this truth, why should any change of 
context falsify any truth? And if changed conditions make 
any truth false, why should not all truth be in perpetual flux, 
and be true or false with the fashion of the moment ? 

8. We shall discuss this question more fully hereafter 
(Bk. II. Part I.), but may here anticipate a misunderstanding. 
To ask " Does space or time make no difference " is wholly to 
ignore the meaning of our principle. We ask in reply, " Does 
this difference enter into the content of A? If it does, then 
A becomes perceptibly diverse, and we confessedly have left 
the sphere of our principle. But, if it does not so enter, then 
the truth of A is considered in abstraction from spaces and 
times, and their differences are confessedly irrelevant to its 
truth. We thus meet the objection by offering a dilemma. 
You have abstracted from the differences of space and time, 
or you have not done so. In the latter case your subject itself 
is different; in the former case it is you yourself who have 
excluded the difference. 

We may indeed on the other side be assailed with an ob 
jection. We may be asked, "What now has become of the 
identity? Has it not disappeared together with the differ 
ences? For if the different contexts are not allowed to enter 
into the subject, how then can we say what is true in one con 
text is true in another? It will not be true in any context at 
all." But we answer, The identity is not contained in the judg 
ment " S P," since that takes no kind of account of the dif 
ferences. 4 The identity lies in the judgment, " S P is true 
everywhere and always." It is this "everywhere" and "al 
ways " that supply the difference against which S P becomes 
an identity. The predicate attributed to the real belongs to it 
despite the difference of its diverse appearances. We do not say 



CHAP. V THE PRINCIPLE OF CONTRADICTION 145 

the appearances are always the same, but the quality keeps its 
nature throughout the appearances. And with this reply we 
must here content ourselves. 

9. When we come to discuss the nature of inference we 
shall see more fully the bearing of the principle. It stands 
here on the result of our former enquiries, that every judg 
ment, if it really is true, asserts some quality of that ultimate 
real which is not altered by the flux of events. This is not the 
place for metaphysical discussion, or we might be tempted to 
ask if identity was not implied in our view of the real. For if 
anything is individual it is self -same throughout, and in all 
diversity must maintain its character. 

THE PRINCIPLE OF CONTRADICTION. 

10. Like the principle of Identity, the principle of Con 
tradiction has been often misunderstood. And in the end it 
must always touch on a field of metaphysical debate. But, for 
logical purposes, I think it is easy to formulate it in a satisfac 
tory way. 

It is necessary before all things to bear in mind that the 
axiom does not in any way explain, that it can not and must 
not attempt to account for the existence of opposites. 5 That 
discrepants or incompatibles or contraries exist, is the fact it is 
based on. It takes for granted the nature of things in which 
certain elements are exclusive of others, and it gives not the 
smallest reason for the world being such in nature and not 
quite otherwise. If we ever forget this, the Law of Contra 
diction will become a copious source of illusion. 

II. If the principle of Contradiction states a fact, it says 
no more than that the discrepant is discrepant, that the exclu 
sive, despite all attempts to persuade it, remains incompatible. 
Again, if we take it as laying down a rule, all it says is, " Do 
not try to combine in thought what is really contrary. When 
you add any quality to any subject, do not treat the subject 
as if it were not altered. When you add a quality, which not 
only removes the subject as it was, but removes it altogether, 
then do not treat it as if it remained." This is all the meaning 
it is safe to give to the axiom of Contradiction; and this 
meaning, I think, will at once be clear, if we bear in mind our 
former discussions. The contrary is always the base of the 



146 THE PRINCIPLES OF LOGIC BOOK I 

contradictory, and the latter is the general idea of the contrary. 
Not-A for example is any and every possible contrary of A 
(Chap. III. 16). 

12. We have to avoid, in dealing with Contradiction, the 
same mistake that we found had obscured the nature of Iden 
tity. We there were told to produce tautologies, and here 
we are by certain persons forbidden to produce anything else. 
" A is not not-A " may be taken to mean that A can be nothing 
but what is simply A. This is, once again, the erroneous asser 
tion of mere abstract identity without any difference. It is 
ordering us to deny as a quality of A everything that is differ 
ent from A, and in this sense not-A. But differents and dis- 
crepants should never be confused. The former do not exclude 
one another; they only exclude the denial of their difference. 
The discrepant with A can never be found together with A in 
any possible subject, or be joined to it in the relation of subject 
and attribute. 6 The different from A does not exclude, unless 
you attempt to identify it with A. It is not A generally, but 
one single relation to A, which it repels. 

As we saw before, there is no logical principle which will 
tell us what qualities are really discrepant. Metaphysics, in 
deed, must ask itself the question if any further account can 
be given of incompatibility. It must recognize the problem, 
if it can not solve it. We might remark that no thing excludes 
any other so long as they are able to remain side by side, that 
incompatibility begins when you occupy the same area; and 
we might be tempted to conclude that in space would be found 
the key of our puzzle. But such other experiences as that 
assertion and denial, or pain and pleasure, are incompatible, 
would soon force us to see that our explanation is insufficient. 
But in logic we are not called upon to discuss the principle, 
but rest upon the fact. Certain elements we find are incom 
patible; and, where they are so, we must treat them as such. 

13. There is no real question of principle involved in 
such different ways of stating the axiom as " A is not not-A," 
" A is not both b and not-b" " A can not at once both be and 
not be." For if A were not-A, it would be so because it had 
some quality contrary to A. So also, if A has a quality b, it 
could only be not-b by virtue of a quality discrepant with b. 
And again, if A both were and were not, that would be be- 



CHAP. V THE PRINCIPLE OF CONTRADICTION 147 

cause the ultimate reality had contrary qualities. The charac 
ter in which it accepted A, would be opposite to the quality 
which excluded A from existence. Under varieties of detail 
we find the same basis, repulsion of discrepants. 

A simple method of stating the principle is to say, " Denial 
and affirmation of the self -same judgment is wholly inad 
missible." And this does not mean that if a miracle in psy 
chology were brought about, and the mind did judge both 
affirmatively and negatively, both judgments might be true. 
It means that, if at once you affirm and deny, you must be 
speaking falsely. For denial asserts the positive contrary of 
affirmation. 7 In the nature of things (this is what it all comes 
to) there are certain elements which either can not be con 
joined at all, or can not be conjoined in some special way; 
and the nature of things must be respected by logic. 

14. If we wish to show that our axiom is only the other 
side of the Law of Identity, we may state it thus, " Truth is 
unchangeable, and, as discrepant assertions alter one another, 
they can not be true." And again, if we desire to glance in 
passing at the metaphysical side of the matter, we may remind 
ourselves that the real is individual, and the individual is har 
monious and self-consistent. It does not fly apart, as it would 
if its qualities were internally discrepant. 

15. Having now said all that I desire to say, I would 
gladly pass on. For, notwithstanding the metaphysics into 
which we have dipped, I am anxious to keep logic, so far as is 
possible, clear of first principles. But in the present instance 
the law of Contradiction has had the misfortune to be flatly 
denied from 8 a certain theory of the nature of things. So far 
is that law (it has been contended) from being the truth, that 
in the nature of things contradiction exists. It is the fact that 
opposites are conjoined, and they are to be found as discrepant 
moments of a single identity. 

I need hardly say that it is not my intention compendiously 
to dispose in a single paragraph of a system which, with all its 
shortcomings, has been worked over as wide an area of ex 
perience as any system offered in its place. My one idea here 
is to disarm opposition to the axiom of contradiction, as it 
stands above. 9 But I clearly recognize that, if not-A were 



148 THE PRINCIPLES OF LOGIC BOOK I 

taken as a pure negation, no compromise would be possible. 
You would then have to choose between the axiom of contra 
diction and the dialectical method. 

I will say, in the first place, that whatever is conjoined is 
therefore ipso facto shown not to be discrepant. If the ele 
ments co-exist, cadit qucestio; there is no contradiction, for 
there can be no contraries. And, saying so much, I feel 
tempted to retire. But yet with so much I shall hardly escape. 
" Have not we got," I hear the words called after me, " have 
we not got elements which any one can see negate one another, 
so that, while one is, the other can not be; and yet have we 
not got very many conceptions in which these discrepants 
somehow co-exist ? It is all very well to say, * then not con 
trary ; but try them, and see if they are not exclusive." 

It is plain that I must stand and say something in reply. 
But I think I shall hardly be so foolish as to answer, " These 
conceptions of yours are merely phenomenal. Come to us and 
learn that knowledge is relative, and with us give up the 
Thing-in-itself." For without knowing all that would be 
poured on my head, I can guess some part of what I should 
provoke. " You say give up the Thing-in-itself ? Why that 
is all that you have not given up. You profess that your 
knowledge is only phenomenal, and then you make the law of 
Contradiction valid of the Absolute, so that what it excludes 
you are able to know is not the Absolute. That is surely in 
consistent. And then, for the sake of saving from contradic 
tion this wretched ghost of a Thing-in-itself, you are ready to 
plunge the whole world of phenomena, everything you know 
or can know, into utter confusion. You are willing to turn 
every fact into nonsense, so long as this Thing-in-itself is 
saved. It is plain, then, for which you really care most. And 
as for * relativity/ it is you yourselves who violate that prin 
ciple. Your turning of the relative into hard and fast con 
traries is just what has brought you to your miserable pass." 
I confess I should hardly care to subject myself to all these 
insults; and I had rather Mr. Spencer, or some other great 
authority whoever may feel himself able to bear them, or 
unable to understand them should take them on himself. 

If I chose to turn and provoke a contest, I know of 
another weapon I might use. I might say, " Your conceptions 



CHAP. V THE PRINCIPLE OF CONTRADICTION 149 

4- 

are partial illusions. They are crude popular modes of repre 
senting a reality whose nature can not be so portrayed. And 
the business of philosophy is to purify these ideas, and never 
to leave them until, by removal of their contradictions, they 
are made quite adequate to the actual fact." But, after all, 
perhaps I could only say this for the sake of controversy, and 
controversy is what I am anxious to avoid. And for this end 
I think that some compromise may perhaps be come to. With 
out calling in question the reality of negation, and the identity 
of opposites, are we sure that we can not understand that 
doctrine in a sense which will bear with the axiom of Contra 
diction? This axiom is not like the principle of Identity. It 
is a very old and most harmless veteran; and for myself I 
should never have the heart to attack it, unless with a view 
to astonish common-sense and petrify my enemies. And in 
metaphysics we can always do that in many other ways. 

What I mean is this. 10 Supposing that, in such a case as 
continuity, we seem to find contradictions united, and A to be 
b and not-b at once, this may yet be reconciled with the axiom 
of Contradiction. A we say is composed of b and not-b; for, 
dissecting A, we arrive at these elements, and, uniting these, 
we get A once more. But the question is, while these elements 
are in A, can they be said, while there, to exist in their fully 
discrepant character of b and not-b? I do not mean to sug 
gest that the union of contraries may be that misunderstanding 
of the fact which is our only way to understand it. For, if I 
felt sure myself that this were true, I know it is a heresy too 
painful to be borne. But, in the object and within the whole, 
the truth may be that we never really do have these discrep- 
ants. We only have moments which would be incompatible if 
they really were separate, but, conjoined together, have been 
subdued into something within the character of the whole. If 
we so can understand the identity of opposites and I am not 
sure that we may not do so then the law of Contradiction 
flourishes untouched. If, in coming into one, the contraries 
as such no longer exist, then where is the contradiction? 

But, I fear, I shall be told that the struggle of negatives is 
the soul of the world, and that it is precisely because of their 
identity that we have their contradiction. It is true that the 
opposition which for ever breaks out leads to higher unity in 

2321. x L 



I5O THE PRINCIPLES OF LOGIC BOOK I 

which it is resolved ; but still the process of negation is there. 
It is one side of the world which can not be got rid of, and it is 
irreconcileable with the non-existence of discrepants in a single 
subject. Each element of the whole, without the other, is 
incompatible with itself ; but it is none the less incompatible 
with the other, which for ever it produces or rather becomes. 

I am after all not quite convinced. If the law of Contra 
diction is objected against because, in isolating and fixing the 
discrepant, it becomes one-sided, is it not quite possible that, 
in denying the law, we have become one-sided in another 
way? If the negation itself, while negative on one side, is on 
the other side the return from itself to a higher harmony if, 
that is to say, the elements are not discrepant without each at 
once, by virtue of its discrepancy and so far as it is discrepant, 
thereby ipso facto ceasing to be discrepant, then surely, in 
denying the law of Contradiction, we ourselves have fixed one 
side of the process, and have treated the contrary as simply 
contrary. The contrary which the law has got in its head, is 
the contrary that entirely kills its opposite, and remains tri 
umphant on the field of battle. It is not the contrary whose 
blows are suicidal, and whose defeat must always be the doom 
of its adversary. It is incompatibles fixed as such, it is dis 
crepants which wholly exclude one another and have no other 
side, that the axiom speaks of. But dialectical contraries are 
only partially contrary and it is our mistake if we keep back 
the other side. And if an opponent of the law reminds me 
that the existence of these two sides within one element is just 
the contradiction, that in the b which is contrary to not-& 
the implication of not-b makes it self-contradictory, then I 
must be allowed to say in reply that I think my objector has 
not learnt his lesson. The not-& in b is itself self-discrepant, 
and is just as much b: and so on for ever. We never have 
a mere one-sided contrary. 

But it is one-sided and stationary contraries that the axiom 
contemplates. It says that they are found, 11 and no sober 
man could contend that they are not found. No one ever 
did maintain that the dialectical implication of opposites could 
be set going in the case of every conjunction that we deny. 
It can hardly be maintained that there are no discrepants, 
except these contraries which at the same time imply each 



CHAP. V THE PRINCIPLE OF EXCLUDED MIDDLE 151 

other. And the law of Contradiction does not say any more 
than that, when such sheer incompatibles are found, we must 
not conjoin them. 

Its claims, if we consider them, are so absurdly feeble, it is 
itself so weak and perfectly inoffensive, that it can not quarrel, 
for it has not a tooth with which to bite any one. The 
controversy, first as to our actual ability to think in the way 
recommended by Hegel, and secondly as to the extent to which 
his dialectic is found in fact, can not only not be settled by an 
appeal to the axiom, but falls entirely outside its sphere. 
Starting from the fact of the absolute refusal of certain ele 
ments to come together, and wholly dependent upon that fact, 
so soon as these elements do come together the axiom ceases 
forthwith to be applicable. It is based upon the self-con 
sistency of the real, but it has no right to represent that con 
sistency except as against one kind of discrepancy. So that, if 
we conclude that the dialectic of the real would in the end 
destroy its unity, that has nothing to do with the axiom of 
Contradiction. Like every other question of the kind, the 
validity of dialectic is a question of fact, to be discussed and 
settled upon its own merits, and not by an appeal to so- 
called " principles." And I think I may venture to hazard the 
remark, that one must not first take up from uncritical 
views certain elements in the form of incompatible discrepants, 
and then, because we find they are conjoined, fling out against 
the laws of Contradiction and Excluded Middle. They, such 
as they are, can be no one s enemy; and since no one in the 
end can perhaps disbelieve in them, it is better on all ac 
counts to let them alone. 

PRINCIPLE OF EXCLUDED MIDDLE. 12 

1 6. The axiom that every possible judgment must be 
true or false, 13 we shall see is based on what may be called a 
principle. It is however doubtful if the axiom itself should 
receive that title, since it comes under the head of disjunctive 
judgment. We must not imagine that our axiom supplies the 
principle of disjunction. It is merely one instance and applica 
tion of that principle. 

17. If we recall the character of the disjunctive judg 
ment, we shall remember that there we had a real, known to 



152 THE PRINCIPLES OF LOGIC BOOK I 

be further determined. Its quality fell (i) within a certain 
area; and (ii) since that area was a region of discrepants, the 
real was determined as one single member. On this basis 1 * 
we erected our hypotheticals, and so the " either or " was 
completed. 

Excluded Middle shows all these characteristics. In it we 
affirm (i) that any subject A, when the relation to any 
quality is suggested, is determined at once with respect to 
that predicate within the area of position and negation, and 
by no relation which is incompatible with both. And (ii) we 
assert that, within this area, the subject is qualified as one 
single member. And then we proceed to our " either or." 

18. Excluded Middle is one case of disjunction: it can 
not be considered co-extensive with it. Its dual and con 
tradictory alternative rests on the existence of contrary 
opposites. The existence of exclusives without reference to 
their number is the ground of disjunction, and the special case 
of assertion and denial is developed from that basis in the 
way in which contradiction is developed from exclusion. 
Common discrepant disjunction is the base, and the dual 
alternative of b and not-b rests entirely upon this. 

19. Excluded Middle is one kind of disjunction : and we 
must proceed to investigate the nature of that kind, (i) Dis 
junction asserts a common quality. In "b or not-b" the 
common quality asserted of A is that of general relation to b. 
(ii) Disjunction asserts an area of incompatibles. Affirmation 
or denial of b is here the area within which A falls. The 
evidence that it does not fall outside and that all the dis 
crepants are completely given, may be called my impotence 
to find any other. 15 (iii) Disjunction attributes to the subject 
A one single element of the area. And this part of the process 
does not call here for any special remark. 

20. We find however, when we investigate further, a 
point in which the axiom of Excluded Middle goes beyond 
the limits of disjunctive judgment. It contains a further 
principle, since it asserts a common quality of all possible 
existence. It says, Every real has got a character which 
determines it in judgment with reference to every possible 
predicate. That character furnishes the ground of some 
judgment in respect of every suggested relation to every 



CHAP. V THE PRINCIPLE OF EXCLUDED MIDDLE 153 

object. Or, to put the same more generally still, Every element 
of the Cosmos possesses a quality, which can determine it 
logically in relation to every other element. 

21. This principle is prior to the actual disjunction. It 
says beforehand that there is a ground of relation, though it 
does not know what the relation is. The disjunction proceeds 
from the further result that the relation falls within a dis 
crepant sphere. We thus see that, on the one hand, Excluded 
Middle transcends disjunction, since it possesses a self-de 
termining principle which disjunction has not got. On the 
other hand, in its further development, it is nothing what 
ever but a case of disjunction, and must wait for the sphere 
of discrepant predicates to be given it as a fact. 16 

22. The disjunction is completed by the fact that, when 
any predicate is suggested, the quality of every element is a 
ground of either the affirmation or the denial of the predicate. 
It compels us to one and to one alone ; for no other alternative 
can possibly be found. 

And here the opposition, directed before against the axiom 
of Contradiction, must again be confronted. It is false, we 
are told, that A must either be c or not-c. We have often to 
say " both," and sometimes " neither." But I think perhaps 
the discussion at the end of the foregoing chapter will have 
strengthened us to persist. I fully admit that often, when 
challenged to reply Yes or No, it is necessary to answer " Yes 
and No" or "Neither." But, I venture to think, that is 
always because the question is ambiguous, and is asked from 
the standpoint of a false alternative. 17 " Is motion continuous? 
Yes or no." I decline to answer until you tell me if, by saying 
Yes, I am taken to deny that it is also discrete. In that case 
perhaps, instead of saying Yes, I should go so far as to 
answer No. There may be a middle between continuity and 
discretion; there can be none between continuous and not- 
continuous. 

The ground of the objection to the Excluded Middle is, 
I am bold enough to think, fallacious. Given not fixed dis- 
crepants but dialectical opposites, the existence of these 
together in one single subject does not give us the right to a 
negative judgment. One can not be made use of as the 
positive ground on which to build the denial of the other. 



154 



THE PRINCIPLES OF LOGIC BOOK I 



One does not wholly remove the other, and, failing to do so, 
it is not qualified as a logical contrary. For it is only the 
discrepant which destroys its opposite that can serve as the 
base of a negative judgment. And, failing the denial of one 
quality through the other, the answer must be that both are 
present, and the denial of either is wholly excluded. But I 
fear it is hard altogether on this point to effect a compromise. 
If the negative of b is ever simply not-&, and if this is the 
other which is implicated with b in one subject A, then I 
grant the Excluded Middle disappears. But, I think, in this 
case it will carry along with it enough to ruin what is left 
behind. And I must leave the matter so. 

23. The Excluded Middle, as we saw before, is a 
peculiar case of the disjunctive judgment; and I think this 
insight may serve us further to dispel some illusions which 
have gathered round it. 

In the first place we must not think it is a formula, by 
applying which we can magically conjure elements of know 
ledge from the unknown deep. It is nonsense to say that it 
gives us a revelation that any subject must have one of two 
predicates. For, even if we do not make a logical mistake and 
really have got contradictory qualities, that is still not the 
right way to put the matter. Denial is not the predication of 
a contradictory ; and all that Excluded Middle tells us is that, 
given any possible element of knowledge, you must be right in 
either affirming or denying any suggestion that is made about 
that. 

We learnt, in our chapter on the Disjunctive Judgment, 
that this judgment must assume the existence of its subject, 18 
though that subject may not be the grammatical subject. And 
when, in the case of Excluded Middle, we are told it will 
guarantee us the truth of either b or not-& as a predicate of A, 
we naturally ask, " But what guarantees to us the existence of 
A ? " And we get no answer. Things in themselves either 
are b or are not b. Undoubtedly so, but what is the real sub 
ject of this statement? It perhaps after all is not " Things-in- 
themselves," but is ultimate reality, which may totally reject 
the whole offered synthesis. In this case we shall at once be 
able to say that Things-in-themselves are not anything at all 
in the real world, though, considered as illusions, they no doubt 



CHAP. V THE PRINCIPLE OF EXCLUDED MIDDLE 155 

have qualities. On the other hand, if Things-in-themselves 
are taken as such to have existence, then that is not proved 
by our Excluded Middle, but is a sheer assumption on which 
we base it and which it presupposes. 

24. But when we are told, " Between the true and the 
false there is a third possibility, the Unmeaning" 19 (Mill, 
Logic, II. vii. 5), we must answer, " Yes, an unmeaning pos 
sibility, and therefore none at all." The doctrine that proposi 
tions need neither be true nor yet be false because they may be 
senseless, would introduce, I agree, " a large qualification " 
into the doctrine of the Excluded Middle. But I am inclined 
to think that this " qualification " might be larger than it seems 
to be, and might be operative perhaps beyond the limits so 
sparingly assigned to it. But surely, on the one hand, it is 
clear that a proposition which has no meaning is no proposi 
tion ; and surely again, on the other hand, it is clear that, if it 
does mean anything, it is either true or else false. And when 
a predicate is really known not to be " one which can in any 
intelligible sense be attributed to the subject " is not that 
itself ground enough for denial ? 20 But logicians who actually 
(Mill, loc. cit.) are ready to take divisible finitely and divisible 
infinitely as contradictories, are justified in expecting extra 
ordinary events. Suppose these terms to be absolutely incom 
patible, that would hardly bring them under Excluded Middle, 
unless we are prepared to formulate the axiom thus: When 
ever predicates are incompatible, then, although there be three 
or more possibilities, it is certain that one of these two possi 
bilities must always be true. But perhaps this " qualification " 
might tend to create more difficulties than it solves. 

25. If we turn from these somewhat elementary mis 
takes, and consider the amount of actual knowledge vouch 
safed to us by the Excluded Middle, I hardly think we shall 
be much puffed up. We must remember that, even if we are 
able to assert about such a subject as Things-in-themselves, 
we must always be on our guard against an error. We may 
be affirming about the meaning of a word, or about a mere 
idea in our heads, and may confuse these facts with another 
kind of fact (p. 42). But, even supposing we keep quite 
clear of this mistake, yet when we come to negative judgments 



THE PRINCIPLES OF LOGIC BOOK I 

there is ambiguity, unavoidable and ceaseless, about the 
positive ground of the denial. We may penetrate so far into 
hidden mysteries as perhaps to be privileged solemnly to avouch 
that Things-in-themselves are not three-cornered, nor coloured 
rose-red, nor pock-marked nor dyspeptic. But what does this 
tell us? What more should we know, if we spent our breath 
and wasted our days in endless denials of senseless sugges 
tions? If the ground of negation remains the same, 21 each 
particular denial asserts nothing in particular (Chap. III. pp. 
121, 124). 

26. 22 Confined to its limits the Excluded Middle is 
rigidly true. But you may easily assert it in a shape which 
would exhibit a parallel falsehood to those we considered in 
examining the Principles of Identity and Contradiction. 
" Everything," we might say, " is either simply the same as 
any other, or else has nothing whatever to do with it." 

Once again, in conclusion, I must call attention to the 
positive principle which underlies the Excluded Middle. We 
assume that every element of knowledge can stand in some 
relation with every other element. And we may give this, if 
we please, a metaphysical turn, though in doing so we go 
beyond the equivalent of the Excluded Middle. We may say, 
If the real is harmonious and individual, it must exist in its 
members and must inter-relate them. 

27. I may notice by way of appendix to this subject a 
somewhat subtle argument of Professor Jevons, which I regret 
to state I am unable to understand. He argues * that to say 
" A = B or b " must be incorrect. For the negative of " B or 
b " will be Bb, and by consequence a, the negative of A, must 
itself be Bb. And the objection to this is that Bb = o. But 
because " every term has its negative in thought," therefore the 
negative of A can not be = o, and the premise " A = B or b " 
is thus indirectly proved false. Professor Jevons proceeds to 
draw from this a general conclusion that any judgment, in the 
form " A = B or b" is necessarily erroneous, and that we 
must write instead of it " A = AB or A&." 

Though I fully agree with this last result, yet Professor 
Jevons reasoning, as I understand it, appears to me unsound, 

* Principles, p. 74. For the meaning of Professor Jevons sym 
bols I must refer to his work. 



CHAP. V THE PRINCIPLE OF EXCLUDED MIDDLE 157 

and I can not reconcile his conclusion with his process. I will 
take the latter point first. It appears to be right to judge 
" A = AB or Ab" But what is the negative ? I suppose the 
negative is AbE, and we must conclude that a = AbE. But 
the term AbE most clearly = o. So that, after all, we are 
left with a conclusion which proves the falsity of our 
premise. 

The result is thus out of harmony with the argument, but 
for all that the result is perfectly true. It is true that we can 
not say " A = B or b" and I will proceed to show why this 
must be true. We must take it that A has a determinate 
quality; but what is merely B or & is anything whatever. Eb 
being nothing, what is simply not-Eb will therefore be any 
thing. And, as A is something definite, " A = anything " will 
of course be false. The sphere " B or b " is wholly un 
limited. 

This confirms the doctrine we have above adopted (p. 123). 
If you take not-B as the bare and simple negation of B, it is 
nothing at all. And if you keep to this sense, then " A = 
not-B " could not be true. The true meaning of not-B is any 
indefinite general quality which does exclude B. And, so 
long as A is something definite, A can not be this. I am 
inclined to think from the presence of x (Principles, pp. 94, 
95) that Professor Jevons would agree with this doctrine. 

But the conclusion, which Professor Jevons uses as false, 
is not only quite true, but is the necessary result of the true 
doctrine he accepts. Taking A as the genuine subject 23 that 
lies at the base of the disjunction, then " a = nothing " must 
follow at once, since " A is B or not-B " does assume and 
postulate that A is real. If a were anything but non-existent, 
you could not use A as the base of a disjunction. What is 
wrong is not this conclusion or its premises, but the mistaken 
idea about the negative which Professor Jevons has em 
braced. 

I confess I am not sure if I apprehend him rightly, but he 
seems to argue that the non-existent is not thinkable, and 
hence, because the negative of everything is thinkable, you 
must never have a negative which is non-existent. Now I 
admit that, if " existence " is used in the widest possible sense, 
this argument is tenable. The unreal, the impossible, and 



158 THE PRINCIPLES OF LOGIC BOOK I 

the non-existent will every one of them exist, provided they 
are thinkable. And, since even nothing itself 24 in this sense 
exists, it is obvious the whole argument thus disappears. 

But, if it does not disappear, and if existence be taken 
in anything like the sense of reality, the argument becomes 
vicious. We have no right to assume that the contradictory 
of an idea which is true, must itself be real. Take for in 
stance the idea of " reality " itself. I could not even admit that 
in thought all ideas are qualified by their negations. I should 
doubt if the highest term we arrive at can be said to have an 
opposite even in thought, although by an error we are given 
to think so. But to hold that what contradicts the real must 
be real, is a logical mistake which I cannot venture to attribute 
to Prof. Jevons. 

I may end with the remark that it would be entertaining 
and an irony of fate, if the school of " Experience " fell into 
the cardinal mistake of Hegel. Prof. Bain s " Law of Rela 
tivity," approved by J. S. Mill, has at least shown a tendency 
to drift in that direction. " Our cognition, as it stands, is 
explained as a mutual negation of the two properties. Each 
has a positive existence because of the presence of the other 
as its negative" (Emotions, p. 571). I do not suggest that 
Prof. Bain in this ominous utterance really means what he 
says, but he means quite enough to be on the edge of a preci 
pice. If the school of " Experience " had any knowledge of 
the facts, they would know that the sin of Hegel consists, not 
at all in the defect, but in the excess of " Relativity." Once 
say with Prof. Bain that " we know only relations " ; once 
mean (what he says) that those relations hold between posi 
tives and negatives, and you have accepted the main prin 
ciple of orthodox Hegelianism. 



28. It is obvious that duplex negatio affirmat. To say 
" It is false that A is not B " is equivalent to the positive 
assertion, " A is B." But this is not because the added negation 
barely negates the original judgment. For if that were all, we 
should be left with nothing. If mere not-A is simply zero, 
then not-not-A is, if possible, less. And we must not say that 



CHAP. V DOUBLE NEGATION 159 

negation presupposes a positive judgment, which is left in pos 
session when the negative is negated. For we saw before 
(Chap. III. 4) that this positive judgment is not presup 
posed. 

29. The real reason why denial of denial is affirmation, 
is merely this. In all denial we must have the assertion of a 
positive ground; and the positive ground of the second denial 
can be nothing but the predicate denied by the first. I can 
not say " It is false that A is not b" unless I already possess 
the positive knowledge that A is b. 2Q And the reason of 
my incapacity is that no other knowledge is a sufficient 
ground. 

30. I will briefly explain. We know well by this time 
that, in judging A not to be b, I presuppose a quality in A 
which is exclusive of b. Let us call this y. I now desire to 
deny my judgment, and need, as before, some quality as the 
ground of my new denial. Let us take some quality other 
than b. Let this quality s be exclusive of y, and let us see 
what we have. We have now A^ with the exclusion of y which 
excluded b. But that leaves us nowhere. We can not tell 
now if A is b, or is not b, because z itself, for anything we 
know, may also exclude b f just as much as y did. What, in 
short, we have got is our own private impotence to deny " A 
is b " ; but what we want is an objective ground for declaring 
such a denial to be false. 

The same result holds good with any other quality we 
can take, excepting b itself. The only certainty that b is not 
absent is got by showing that b is present. For the possible 
grounds of the exclusion of b being quite indefinite, you can 
not get rid of them by trying to exhaust the negations of b. 
You could only do that if the number of possibilities with 
respect to A had already been limited by a disjunctive judg 
ment. And this is not here the case. 

Suppose, for instance, we have the judgment that " Ulti 
mate reality is not knowable," and we wish to assert that this 
judgment is false. We expose the ground on which it is based, 
and go on to show that this ground is not valid. Our pro 
ceeding, no doubt, may be perfectly admirable, but all that it 
gives us is the right to doubt the original judgment, and to 
deny the truth of the basis it stands on. If we wish to deny 



I6O THE PRINCIPLES OF LOGIC BOOK I 

the original judgment, we can not do that by refuting our 
antagonists. We must show ourselves that reality is know- 
able. The ground for the denial of " A is not b" must lie in 
"Aw b." 27 

31. I will endeavour to remove a possible source of mis 
apprehension. It might be urged that in practice the denial 
of a judgment can always be denied by something other than 
the judgment itself. Thus, for instance, " It did rain yes 
terday," may be false, because it snowed or because it was 
fine. But each of these can be denied on the ground of the 
other. The result of our double negation of " it rained," 
might be either " it snowed," or again " it was fine " : and we 
might return to " it rained," by virtue not of a double but of a 
triple denial. 

But this objection would rest on a misunderstanding. It 
is perfectly true that, in denying " it rained," I must imply 
and make use of some discrepant quality. It is, once more, 
true that what I have in my mind, and should assign as my 
reason, may be either " it snowed " or again " it was fine." 
But it is a mistake to conclude that the denial really rests upon 
either the one of these or the other. Whatever you might 
have had in your mind, no logic could force you to allow that 
your denial had committed you to either " it snowed " or " it 
was fine." What we use in denial is not the whole discrepant : 
it is that part of the discrepant which answers our purpose. 
The denial asserts no more than the existence of so much 
quality as is enough to exclude the judgment " it rained." 
This universal " so much " is possessed by either " it 
snowed " or " it was fine," and this you can not banish by 
anything short of the judgment " it rained." In other words, 
if you say " it did not rain," you are at once committed to a 
positive " because," but you are committed to nothing but 
an unspecified quality. The evidence for this quality no doubt 
in the end must be found in the presence of a contrary asser 
tion, but the mere contradiction does not affirm this or any 
particular contrary. It affirms merely some contrary, and you 
get rid of this only by the judgment " it did rain." We find 
here once more the constant ambiguity, which we have seen 
(Chap. III. 19) makes the use of negation so precarious. 
It is so difficult to work with double denial that I hardly can 



CHAP. V DOUBLE NEGATION l6l 

expect in the present volume to have supplied no example of 
the error I condemn.* 

* Mr. Venn, I think, has certainly done so. 28 When I had the 
pleasure of reading his Symbolic Logic, I congratulated myself on the 
fact that I had already written the present and all the preceding 
chapters. I have not found occasion in consequence to alter anything 
of what I had written, but I should like to use one of his principal 
doctrines to exemplify the fallacious use of the negative. I have added 
this discussion as a mere appendix, for it hardly carries the subject 
further. It is due to myself to defend my own views against a counter 
theory from a writer of established and merited reputation. 

After calling attention to the ambiguity of affirmative universals, 
the doubt, that is, if they affirm the existence of their grammatical 
subject, Mr. Venn, if I understand him rightly, asserts that at all 
events the negative is not ambiguous (p. 141). I will not here enquire 
if in other places he is compelled to recognize that the opposite of this 
assumption is true. At all events the foundation he here seems to 
build on is the assertion that negatives have only one meaning. " It 
comes to this therefore that in respect of what such a proposition 
affirms it can only be regarded as conditional, but that in respect of 
what it denies it may be regarded as absolute" (142). The affirmation 
of xy is always ambiguous, since x may not be actual; but the denial of 
x not-y is perfectly clear. And upon this basis he seems to build his 
doctrine. 

Now the reader of this volume will know that a negation is always 
ambiguous. We may consider this as settled, and I will not re-discuss 
the general question. I will first call attention to the seeming absurdity 
of Mr. Venn s doctrine. He teaches in effect that, although you do not 
know what a statement means, you can always tell what you mean by 
denying it. And he ought to hold that the ambiguity of a judgment at 
once disappears, if you deny it and then deny your denial. This course 
has not generally been found so successful. 

But it is better to show the actual mistake. And we will preface our 
criticism by setting down some elementary truths. You can not argue 
from the assertion of possibility to the assertion of actuality, but you 
can always argue from the denial of possibility to the denial of actual 
ity. To deny possible x (you must of course not take "possible" as 
"merely possible") is by implication to deny actual x. Now the simple 
application of this commonplace doctrine is that, if you are given a 
connection xy and do not know whether it is possible or actual, at all 
events, if you deny its possibility, you may be very sure that you also, 
and as well, have denied its actuality. This is literally (unless I mis 
understand him) the whole principle which Mr. Venn unconsciously 
proceeds upon, and the idea that it could lead to any great result, or 
to a better understanding of hypothetical, seems somewhat strange.^ 

I can not be quite sure of his exact procedure, but I think it is this. 



l62 THE PRINCIPLES OF LOGIC BOOK I 

The affirmative judgment both affirms and denies. Mr. Venn will not 
say that what it affirms is mere possibility, but he quietly assumes that 
what it denies is impossibility. (If he does not do this, he makes a 
simpler mistake to which I will return.) That is to say, he tacitly and 
without any justification assumes that x not-;y asserts the impossibility 
of xy; and it is solely by denying this arbitrary fixture that the positive 
xy becomes unambiguous. But if he wishes to restrict the affirmative 
judgment to the minimum sufficient to deny the denial of possibility, 
surely it would be better to say at once, "The affirmative judgment 
does not assert more than bare possibility." He would so have done 
openly and in an intelligible manner the very thing he has in effect 
done, indirectly and most objectionably, by going round through two 
denials. The procedure could in no case have become more arbitrary. 

I will put the same thing otherwise. With affirmative judgments 
possibility is the minimum: with negative judgments impossibility is 
the maximum. Now it is uncertain (we may so interpret Mr. Venn) 
if the affirmative xy asserts the maximum (actuality) or the minimum 
(possibility), but it is certain that it unambiguously denies the nega 
tive. But, if the negative becomes unambiguous because it is arbi 
trarily fixed at its maximum degree (impossibility), then surely it is 
clear that we thereby, and ipso facto, are fixing the affirmative at its 
minimum degree. For so far at least as the affirmative denies and is 
not ambiguous, it is so because its minimum is enough. And the 
fallacy is simple. This minimum is not enough unless the negative is 
fixed at the maximum. Suppose not-xy to mean " xy does not exist," 
then " xy is possible" ceases to deny this: for, although xy may not 
exist, it still can be possible. Again if xy meant " xy is actual," then 
"xy is impossible" (or, again, "if x then no y") is not its contra 
dictory, and goes a long way beyond its denial. In short, since not-*y 
means either d-e facto non-existence or else impossibility, it seems 
absurd to assert that the denial of this is not ambiguous. And if you 
mean to fix the meaning of the negative arbitrarily, it seems absurd 
to shrink from doing the same by the positive. 

In conclusion, if we suppose that not-;ry is really meant to assert 
non-existence, that is to deny the actuality of xy, then the error is 
palpable. You first say you do not know whether xy asserts existence 
or possibility, and yet you say it denies the non-existence of xy. But 
possibility, not affirming existence, of course can not deny non-exist 
ence, and the whole process disappears unless you rapidly shuffle from 
one term to the other. 

This hidden equivocation soon begins to bear fruit in the curious 
reasoning which immediately follows (p. 143). If I do not misappre 
hend Mr. Venn, he tries to make a passage from bare possibilities to 
a positive existential judgment. I confess his metaphysics take away 
my breath ; and I am bound the more to admire his audacity as he 
somewhat poses as abjuring "transcendentalism," and likes to take 
things " in a perfectly matter of fact way." But let us see what this 
way is. We suppose four possibilities, (i) x with y, (ii) x not-y, (iii) 



CHAP. V DOUBLE NEGATION 163 

y not-*, and (iv) not-* not-y. We have first a conditional assertion 
of xy, and this destroys (ii). We have next a similar assertion of yx, 
and this destroys (iii). We have therefore, after this second asser 
tion, but two possibilities, (i) and (iv). 

" Before, the positive possibilities were three in number, now they 
are reduced to two ; for it is implied that everything must be either 
both x and y or neither of the two. Carrying this process one step 
further, we see that three such " [i.e. conditional] " propositions would 
be requisite to establish unequivocally the existence of any one of 
the four classes. If we expunge xy" [i.e. not-* not-;y] "also, we are 
then reduced at last to an assertion of existence, for we have now 
declared that xy is all, viz. that within the sphere of our discussion 
everything is both * and y" (p. 143). 

Now, so far as I can see, we may understand this process in two 
different ways, but on either understanding the argument is vicious. 
The first way is to take our possibilities as holding within an exhaus 
tive disjunction. As Mr. Venn says, we know " that everything must 
be either xy, or * not-y, or y not-*, or not-* not-;y" (142). The 
disjunction will rest here on a positive existential proposition, and 
the inference will be quite correct. But the objection is that, on 
Mr. Venn s theory, we can hardly assume that we have such a dis 
junction. At least I do not understand why the assertion, Everything 
is one of four possibilities, should be able to be taken in its positive 
meaning. We surely are bound, if we wish to be unambiguous, to 
take it as denying. And if you take it as denying, it does not prove the 
conclusion. It asserts that what is not one of four possibilities is non 
existent (or impossible), but it does not say that anything exists. 
The possibility of everything is all that is asserted, and from this the 
argument will not take you to more than the sole possibility of xy. 
If you start with nothing but possibilities, you can not cross from a 
bare possibility to actual existence simply on the ground that the other 
possibilities have sunk into nothingness. At least I am sure " tran- 
scendentalists " especially would be interested in learning Mr. Venn s 
"matter of fact way" of accomplishing this exploit. 

We thus see that the reasoning can not be based on an affirmative 
existential disjunction. And without this foundation it is thoroughly 
unsound. Not-* not-y is to be suppressed by a conditional judg 
ment, and in its dying struggles is to establish xy as "an assertion of 
existence." I will not ask what the conditional proposition could be. 
"If anything exists then xy exists" might answer the purpose; but 
it would not do so unless it were really unconditional, and covertly 
contained the very assertion that " xy is actual." And this I think 
is the alternative to which we are brought: we either completely 
abandon and throw over our doctrine of the superiority of the nega 
tive, and avowedly start with an affirmation of existence; or else 
we prove the existence of xy through a double denial which assumes 
the conclusion in order to extract it. 

We may verify the presence of the same ambiguity in the ex- 



164 THE PRINCIPLES OF LOGIC BOOK I 

traordinary assertion that contrary judgments, such as "All x is y" 
and "No x is y," can be compatible (145). It is not worth while to 
enter into a discussion of this matter. They are of course compatible 
if you allow yourself to play on their ambiguity; but how in that case 
they can be said to be contrary I have no conception. " The interest 
ing and unexpected application" is to me, I confess, not anything 
beyond a confused example of a well known doctrine concerning the 
relations of possibility and existence. But I confess besides that, I 
have never been much used " to discuss the question in a perfectly 
matter of fact way." 

I need not mention what seem to me other mistakes of much the 
same kind. And, beside these, there are some statements in connection 
with the hypothetical judgment with which I do not agree, but for 
which, I think, my treatment of the subject has provided sufficiently. 
I am sorry to be forced, both here and again (Chap. VII.), to empha 
size my difference with Mr. Venn. And by way of compensation I 
should like, if he will allow me, to offer a suggestion. If Mr. Venn 
had not such a horror of "metaphysics" and "transcendentalism," if 
he was a little less resolved to be " matter of fact," and " discuss the 
question entirely on scientific or logical ground," I fancy he would 
have come somewhat nearer a solution of the problems it is his merit 
to have undertaken. At any rate I suspect his idea of science might 
have been expanded, and some prejudices as to "matter of fact" 
have been somewhat loosened. He would certainly have imbibed a dis 
like for artifices, and such a scruple against entertaining commodious 
fictions, as in itself would have saved him from a succession of serious 
logical mistakes. 



ADDITIONAL NOTES 

1 On the idea of a term being related to itself see Essays, Index, 
s. v. Terms. 

2 "Within a whole of fact." "Fact" is of course to be under 
stood here in the widest sense. 

a All truth must abstract, and, so far as it is truth, it can not 
be made false from the outside. How far any truth which abstracts 
can be wholly true, I have discussed elsewhere. See Appearance and 
Essays f the Indexes. 

4 "In the judgment S P." Add "of which we were speaking." 
And, after "becomes an identity," add "and so enters as an element 
into a fresh S P." In the next sentence the "it" (in "belongs to 
it") is to be emphasized. 

5 What the reader should keep in mind is the following. Differ 
ences are all incompatible if you attempt simply to identify them. 
They are again all compatible if and so far as they are merely con 
joined. Wherever there is conjunction there is something more in 
the conjoined whole than mere identity, so that here the whole, as 



CHAP. V DOUBLE NEGATION 

simply identical, does not attempt to enter into each diversity. The 
whole, however, if it is to be made intelligible, must become dis 
junctive. The aim of disjunction (see Chap. IV, i) is to replace the 
conjunctive unity by the discovery and statement of conditions. As 
to why certain conjunctions are possible in fact, while others are not 
so logic does not enquire. The question of detail belongs here 
mainly, I think, to psychology. On the above see Appearance, Appen 
dix, Note A, and Bosanquet s Logic, II, Chap. VII. 

6 "The discrepant with A ... attribute." This sentence should 
run, "The incompatible with A is what is not a mere joint predicate 
with A in any subject, nor is joined to it ... attribute." 

7 " For denial . . . affirmation." In this sentence " the " should 
be " a." 

8 " From a certain theory." " From " is here, I think, rightly used 
in contradistinction to " by." 

9 The main point here is as follows, Incompatibles exist, and no 
one denies this fact. And, so far as they exist, the Law of Con 
tradiction holds. The real question is as to the limits within which, 
and the conditions under which, incompatibles are found and can 
be justified. How far in other words is the truth of contradiction, 
as such, only relative and more or less of an appearance? What, 
as I understand it, the Dialectical Method is concerned to deny is 
merely the absolute, utter and final, truth of fixed incompatibles. On 
the whole matter see my Appearance, Index, s. v. Contradiction. 

10 " What I mean, &c." The point here is that, where you have 
differences in A, A is never mere and bare A. Cf. on 10. 

11 " Stationary contraries " . . . " are found." Yes, but as an 
appearance only. See Note 9. 

12 On the principle of Excluded Middle, while once more referring 
the reader to Bosanquet s Logic, I will add a few words. This prin 
ciple presupposes a disjoined world of incompatibles, and its truth 
is but relative and limited to Reality taken in the character of such 
a world. So far as the real is otherwise, as being either below or, 
again, above the level of disjunction, the principle does not hold. 
If we accept the view that no truth is quite true and no error merely 
false a view advocated in my Essays and Appearance we must admit 
that Excluded Middle, however necessary and important, is not true 
absolutely. 

In rejecting it as the principle of disjunction, I meant to deny that 
disjunction stands upon it in the shape of a ready-made base. We 
may on the other hand take it as containing the abstract form of 
disjunction. It is disjunction made all-embracing and dual by group 
ing all the incompatibles, save only one, under their negative aspect, 
with the result that nothing is left beyond assertion or denial. The 
leaving the other members of the whole thus artificially blank, is of 
course a grave shortcoming. For, merely in the shape of such an 
abstraction, these other members are not real positively, and so are 
not real at all. Knowledge is not advanced by the exhaustiveness 

2321. i M 



1 66 THE PRINCIPLES OF LOGIC BOOK I 

of disjunction effected formally through an artificial duality. Its real 
object is to discover in concrete detail the full connection of its 
elements. 

Excluded Middle is, however, in a sense more fundamental, and 
goes, we may say, further than mere disjunction. For it asserts the 
actual being of the disjunctive world. We affirm in it that Reality 
is a region where "either or" holds, and that everything is so de 
termined as to fall within this sphere everything, that is, so far as 
it is not self -contradictory or otherwise senseless. (For the connec 
tion between these two ideas see T. E. VIII.) But, as was remarked 
above, we have here a relative truth which is taken wrongly if made 
absolute. 

I may add that the principle that every idea is attributed to Reality, 
and is therefore in some sense real, has no special connection with 
Excluded Middle. And the same thing holds again of the corollary 
that, where all possibles but one are excluded, the one left is actually 
real. 

13 " True or false." See, however, the preceding Note. 

14 "On this basis." But see on Chap. IV, 6. 

15 " My impotence." See on Chap. Ill, 9. 

16 "Must wait" . . . fact." But it is better, I think, to take 
Excluded Middle as assuming, not only connection everywhere through 
out the Universe, but also that special kind of connection which 
holds between incompatibles. See Note 12. 

17 " False alternative." But, if we say this, surely we must mean 
that Excluded Middle has been assumed to hold outside its own lim 
ited sphere, and that hence it does not hold everywhere. Again, in 
the next paragraph, " fallacious " can not, I think, stand. But I agree 
that it is certainly possible, and sometimes easy, to object wrongly to 
the legitimate and necessary use of Excluded Middle. 

18 "The existence of its subject." But see on Chap. IV, 3. 

19 Mill s misuse of " contradictories " can be excused, I presume, 
as a mere slip; but his doctrine of a "third possibility" seems really 
something worse. He takes the possibility with regard to an offered 
judgment that it is senseless, and therefore no actual judgment; and 
he then places this itself as a possibility under the judgment as actual, 
and as itself falling between the two other possibilities of truth and 
falsehood. Cf. Bosanquet, Logic, I, 352 (Ed. II). 

Conceivably all that Mill meant was to warn us that an unmeaning 
idea or judgment is none, and so must not be used. But, if so, his 
meaning, I submit, was expressed by a serious blunder. The writer 
whom he criticizes, we may also do well to remind ourselves, made 
use of the word "judgment" rather than "proposition." 

20 "Ground enough for denial." It would be better, for "denial," 
to substitute "rejection with a denial of possibility." 

21 " Ground of negation remains the same." We should add " or 
at least is not known." See on Chap. Ill, 13. 

22 For this section, as also for 20, see Note 12. 



CHAP. V DOUBLE NEGATION 167 

23 Taking A as the genuine subject." "Genuine" is to be em 
phasized. See on Chap. IV, 3. And, again, for " reality " and " exist 
ence," see on Chap. II, 2. 

2 * "Even nothing itself." For "nothing" see Essays, the Index, 
and T. E. VII. 

25 " Double Negation." There is a serious mistake in these pages. 
The whole subject has, I think, been made clear in Bosanquet s Logic, 
I, PP. 302-7. Cf. his K & R, pp. 230 foil. 

The main point here is this. Double negation holds where the 
alternatives are limited to two, and it does not hold otherwise. And 
in denial we have always this dual alternative. 

The error in my treatment is as follows. I did not see that (as 
Dr. Bosanquet has shown) all denial sets up an exhaustive dual dis 
junction (Cf. T. E. VI). Judgment divides the world, we may say, 
into the selected and the residual Reality, and in denial what is ex 
cluded must qualify the latter. Having so an " either or "when 
we have denied our denial the affirmative only is left. 

So much for my mistake; but, apart from this, my discussion did 
well, I think, to insist on an important truth. Since all denial rests 
on a positive ground, though this is not stated in and by the denial, 
we may hence be led into error. We may make the ground of 
negation, as we happen to have that in our minds, an essential part 
of the denial. We covertly, that is, in "A (x) is not b" explicate 
the x, and treat this, in the form e.g. of c, as being the sole ground 
of our denial. We thus turn " A (x) is not b " into " A (c) is not b," 
and so without right come back from the denied absence of b to the 
presence of c. For instance, having decided to wait because the 
ground will not be dry, and, having then the denial that there has 
been rain, I may rush to the conclusion that the ground will be ({ drv 
forgetting snow or dew. I have turned " not after rain," into " dry," 
by taking wrongly the simple denial as qualified. 

26 " Positive knowledge." We must add " direct or indirect." " It 
is false that the ground will not be dry " rests on the exclusion, how 
ever arrived at, of every state incompatible with dryness. 

27 " A is b." " Or " (we should add) " in the knowledge that what 
excludes b does not belong to A, but is (where it is anything) some 
thing merely accidental. 

28 I now regret the asperity of this criticism. Dr. Venn probably 
had no idea of his challenge and of the provocation which he gave. 
And how far he ought to have been aware of this, I have now 
certainly no wish to discuss. 



CHAPTER VI 

THE QUANTITY OF JUDGMENTS 

I. If in considering an idea you attend to its content, 1 
you have its intension or comprehension. Its extension may be 
taken in two different senses. It is an instance or instances, 
ideal or actual. 2 It refers ultimately to the real, but it may 
directly signify (a) any other more concrete idea which con 
tains the intension, or (b) any individual of which the inten 
sion can be predicated. Thus if " horse " signifies the attributes 
possessed by a horse, it is taken in intension. If it signifies any 
other idea which includes " horse," e.g. cart-horse or race-horse, 
it is taken in extension. And again, it is otherwise taken in 
extension if it is used for individual horses.* 

2. We have come again upon a distinction which is now 
familiar. An idea is symbolic, and in every symbol we sepa 
rate what it means from that which it stands for. A sign 
indicates or points to something other than itself ; and it does 
this by conveying, artificially or naturally, those attributes of 
the thing by which we recognize it. A word, we may say, never 
quite means what it stands for or stands for what it means. 
For the qualities of the fact, by which it is recognized and 
which correspond to the content of the sign, are not the fact 
itself. Even with abstracts the actual case of the quality is 
hardly nothing but the quality itself. The idea and the reality 
are presumed to be different. 

It is perhaps an ideal we secretly cherish, that words 
should mean what they stand for and stand for what they 
mean. And in metaphysics we should be forced to consider 
seriously the claim of this ideal. But for logical purposes it 
is better to ignore it. It is better to assume that the meaning 
is other than the fact of which the meaning is true. The fact 
is an individual or individuals, 3 and the idea itself is an univer 
sal. The extension can not be reduced to intension. 

* If it were used for possible horses, it would be taken in sense (a). 
Cf. pp. 171, 179, 186. 

168 



CHAP. VI THE QUANTITY OF JUDGMENTS 169 

3. The difference may be expressed by the terms " de 
notation " and " connotation." These phrases have found 
favour with the English public, and the indiscriminate use of 
" connotation " marks one kind of superior person. 4 But they 
serve no useful purpose in logic. They are unnecessary and 
objectionable. 5 They have no advantage over the terms in 
general use, and they have in addition a positive vice. To 
" connote " is to " imply " ; and the meaning of a word is not 
its implication. With the names of individuals the meaning 
may perhaps be said to be " connoted," but with adjectives 
such as " red," and abstracts such as " redness," what is 
" connoted " is clearly not at all the attributes but the indi 
vidual reality. Nothing but ambiguity can arise from such 
perversions. If you will use a word which signifies implica 
tion, to convey what more usually is the direct meaning, you 
must expect the confusion which your unfortunate choice has 
already to some extent occasioned. 

4. Hand in hand with this slovenly terminology there 
goes a superstition we have in part refuted (Chap. II. 17). 
We are told that words may be " non-connotative." They 
may signify, we are told, a subject only or only an attribute. 
Both of these assertions must be rejected. No word such as 
" whiteness " stands simply and solely for the abstract quality.* 
It means this directly; but it indirectly points to an implied 
individual, an actual case of whiteness. And still less can be 
said for the doctrine we have already refuted. The name of 
an individual must carry with it and imply certain attributes, 
or else its attachment to that individual becomes a psycho 
logical impossibility. It is mere want of thought which allows 
us to suppose that a sign can mean nothing and yet stand for 
something. 

5. It would be as easy to prove that a word may mean 
nothing and may also stand for nothing. And it may be 
useful, perhaps, at this point to digress. We have seen that 
all propositions are "real" (p. 42). Verbal propositions be 
come manifestly real, if you write them " The meaning of S is 
P." But there is a class of judgments where the subject has 
*A11 ideas imply a reference of their content to the real (p. 3), 
and hence to the individual. We may notice besides that abstracts 
imply within their content a supporting subject. They are doubly 
adjectival. 6 



170 THE PRINCIPLES OF LOGIC BOOK I 

got no definite meaning, and is not a perfect sign. If we take 
such a statement as " magistri is the genitive case of magister" 
we might be tempted to assert that some words are devoid of 
both extension and intension. 

"Theophilus is Greek," " Theophilus is dear to God," 
" Theophilus has the measles." The last of these informs us 
of the disease of a man. The second tells us the meaning of 
a name. The first assures us that a word is a member in a 
system of signs, but it seems to give us nothing which that 
word stands for and nothing that it means. If a sign were 
something with a definite signification, then we could not say 
that all words are signs. We may know of a sound no more 
than this, that it is a sign. It stands for something, but we 
do not know what ; and it means something also, but what we 
do not know. 

And we are not at the end. This last remnant of ordinary 
extension and intension is doomed to vanish. I may treat the 
word as a common noise. " Why did you make that noise 
Theophilus when you saw that man? Theophilus is not a 
pleasant sound." We have here no signification and no 
meaning, nor have we any longer a word. But even here 
in a rudimentary form we have the sides of extension and 
intension. We may distinguish two elements that are blended 
in Theophilus. Even here it is universal, and is the product 
of abstraction and generalization. The sound that I should 
know under all its differences, of varying tone, of the person 
uttering, and of places and times, is one side of the whole. 
The other is this particular utterance and other possible par 
ticular utterances. The elements still co-exist at this early 
stage of their evolution. We can never separate the one from 
the other except by a mistake. 

6. Let us dismiss for ever the term " connotation," and 
try to keep clear of the errors it beacons. We may pass to a 
doctrine of another kind, not so misleading but equally idle. 
Extension and intension, we are told, are related and must be 
related in a certain way. The less you happen to have of 
the one, the more you therefore must have of the other. 
This statement has often passed itself off as both true and 
important. 1 confess that to me it has always seemed either 
false or frivolous. 7 



CHAP. VI THE QUANTITY OF JUDGMENTS 17! 

(a) If we take extension to mean that number of real 
individuals of which the meaning is true, then it is ludicrously 
false that an increase of the extension is a decrease of the 
meaning. The logician who, impelled by the practical syl 
logism, begets a child, does not find his doctrine verified by 
the fact. The conclusion, which appears from the union of 
the premises, no doubt may surprise him and add to his 
experiences, but it may not diminish the " comprehension " 
with which he hears the word child. His new-born instance 
may destroy his definition of the genus homo as animal risibile, 
but the content it shears off will be largely made good by 
other attributes. He may say, what he never thought to 
have said, All children are scourges. 

It is obvious that fresh instances may increase the inten 
sion by the discovery of attributes essential but overlooked. 
The doctrine understood in this sense is false. And if you 
write " possible " for " actual " individuals, still diminution of 
the meaning need not add to the number. If possible means 
that which is presumed to exist, we may remark that the com 
plex may be possible in fact just as much as the simple; the 
simple indeed by itself may be impossible. But if possible 
means what can be produced by artificial and arbitrary think 
ing (p. 203), we have now obviously left the sense of exten 
sion we have been dealing with. The extension has ceased to 
lie in the individuals ; 8 it has become those groups of attributes 
in which analysis can find the meaning. 

7. But (b) even if we give this sense to extension, the 
doctrine is not true. If you compare ideas, the narrower mean 
ing does not always have the wider application. Take a 
simple instance. The idea of the visible has, we may all 
admit, a fuller meaning than the ideas of that which can be 
tasted or smelt. But the latter have not got any greater 
extension. Everywhere, if you take adjectives or combina 
tions of adjectives, which are co-ordinate and which can not be 
subsumed the one under the other, the doctrine ceases to have 
any bearing. Since the greater emptiness has not been got by 
further abstraction, there is no reason why the adjective which 
has less content should be predicable of a greater number of 
kinds. 

And if for marks and combinations of marks we sub- 



1/2 THE PRINCIPLES OF LOGIC BOOK I 

stitute laws or modes of combination, the same thing holds 
good. If these laws do not stand the one under the other, 
but simply fall under a common head, then you have no right, 
on comparing these laws, to expect the emptier to be the more 
wide and the wider to be more empty. 

8. There undoubtedly is some truth in the doctrine, but 
that truth does not come to much more than this. If you take 
adjectival marks or laws, and choose to arrange them in the 
form of a pyramid; if you place at the bottom, and as the 
stones of your lowest layer, all those ideas which have noth 
ing subordinate; if you form the second and superimposed 
layer by subtracting the differences from two of these stones, 
and by placing the residue left by the operation on the top of 
the pair; and if you so proceed to pile layer upon layer, so 
as to form a mass which grows narrower with each tier if all 
this is done, then it is geometrically true that the higher you 
go up the fewer stones you will find, and the lower you go 
down the more stones you will have. And since you have 
gone up by leaving out differences, it is obvious that the nar 
rower the pyramid becomes the more stones will each single 
stone have to stand upon, and the more there will be of which 
it can be predicated. This is undeniable, but what does it come 
to? It comes to this, that if you arrange your material in a 
certain geometrical figure, then it will have certain geometrical 
properties. That is true, but it seems to me quite frivolous. 

9. It is true, I admit, that if B must be C, then, sup 
posing A should ever be B, it will also be C. But, if you offer 
me this as a truth about A, I can hardly affect to feel very 
grateful. It looks to me more like a truth about B. You 
begin to establish a claim to gratitude when you show me also 
that A is B, or is likely to become so. And this is the real 
question at issue. If you arrange ideas in a certain way they 
will have the qualities of that arrangement. Who doubts it? 
What first may be doubted is the possibility of so arranging 
all ideas ; and what may next be doubted is the wisdom of the 
arrangement. If it is not the natural relation of the material, 
if it is forced and arbitrary, then the truth you offer me may 
after all be sterile. It may have little or nothing to do with 
the actual matter in hand. 

If you confine yourself to the ideas of adjectivals, then 



CHAP. VI THE QUANTITY OF JUDGMENTS 173 

(though I will not undertake to maintain it) I think that with 
more or less of regularity you may effect your pyramidal 
arrangement; but I think you much over-estimate its value. 
If reasoning were always the subsumption of a stone on a 
lower tier under a stone belonging to a higher layer, then 
your construction would begin to serve as a machine and 
would even live; your ladder would grow green and blossom 
as the tree, not of pedantry, but of knowledge. But reasoning 
is really not always subsumption, and with the cutting off that 
root of delusion your tree shows dead, and breaks before the 
breath of actual existence. The importance ascribed to your 
arrangement of ideas comes from a fundamental mistake 
(See Book II. Part I. Chap. II.). 

10. And there remains an objection we can not discuss 
but must not pass over. If you do not confine yourself to 
the ideas of adjectives and their combinations, what then? 
Take ideas of individuals. If you have ideas of smaller 
wholes, enclosed in and subordinated to larger wholes, will 
it there be true that the wider the synthesis the emptier it 
becomes? Are universals always more abstract than particu 
lars? Is it certain that the idea of a state has less content 
than the idea of any one of its citizens? Are we sure that 
the soul is more of an abstraction than any particular psychical 
event? Is the idea of God assuredly less full than the idea 
of a molecule? And if we consider the idea of synthetical 
unity, it does not appear that the higher and wider function 
of synthesis need have less attributes than a subordinate func 
tion. If we entertain the belief that syntheses are possible 
which are not the abstraction from lower syntheses, but are 
the individuations of these lower abstractions, then the doc 
trine which has showed itself to be idle once more becomes a 
positive error. 

This objection, I am aware, will not press very heavily. 
There are few readers not so wise in their own esteem as to 
convict this suggestion of folly or madness. 9 It would belong 
to metaphysics to lay folly at the door of its true possessors. It 
is sufficient here for our logical purpose to have pointed out an 
objection, disregarded and despised, but in itself not despicable. 

Apart from this possible ground of dissent, and confining 
ourselves to the consideration of marks and the modes of 



174 THE PRINCIPLES OF LOGIC BOOK I 

their union, we may sum the matter so. The law of the 
relation of extent to intent is not a law of ideas themselves; 
it is a law of pyramidal arrangement; and that arrangement 
in the case of ideas, where it is possible, is not of importance. 
It may fairly be relegated to our logical lumber-room. 

ii. The question which is next to claim our notice is 
still concerned with Extension and Intension. 10 If we leave 
mere ideas and go on to judgments, it has been asked whether 
these make a statement in respect of the extension of their 
elements, or the intension, or both. And this is a topic we 
can not quite pass over, as it presents us with several dangerous 
illusions. I will begin by the assertion that every proposition 
can be read in whichever of these ways we prefer. I will then 
show, in the first place, how all can be interpreted in extension, 
and will prove the same, secondly, with respect to intension. 

12. Every judgment makes a double affirmation, or a 
single affirmation which has two sides. It asserts a connec 
tion of different attributes, with an indirect reference to an 
identical subject; or it directly asserts the identity of the 
subject, with an implication of the difference of its attributes. 
If you prefer to consider the identity of the subject (im 
mediate or ultimate), you read the judgment in extension. 
If again you emphasize the connection of the differences, you 
take the judgment intensionally. It is not true that every 
judgment is naturally read in both of these ways. It is true 
that all judgments can be read correctly in either manner, and 
read legitimately. 

If you take the proposition " Dogs are mammals," then 
this means either that, where anything is a dog, the same 
individual thing will be a mammal ; or that, given in anything 
the attribute dog, you will certainly have with it the at 
tribute mammal. And it is possible to interpret every judg 
ment in this self -same way. 

13. Dismissing for the present the intensional reading, 
let us consider interpretation in Extension. We find here the 
presence of misleading errors. It is a common doctrine that 
when we read in extension we assert inclusion in a class or 
collection. We are told that in " Dogs are mammals " no 
attribute is really affirmed of dogs; the assertion is that the 



CHAP. VI THE QUANTITY OF JUDGMENTS 175 

things called dogs are included within the class of mammals. 
I can discover little in this current theory but error and 
confusion. 

It sounds at least palpable, when we hear of enclosing 
within a class. But try to handle it, and at once your grasp 
is closed upon mist and unreality. The class, if it is to be 
real at all, must be, I presume, an aggregate or collection of 
individuals; and this must exist either in my head or else 
outside it. The latter alternative can hardly be meant. There 
is no actual physical aggregation which answers to every 
general name. For every single mark would be the ground of 
such an aggregate, and I can not suppose that any one believes 
that these strange complications of groups or herds actually 
exist in rerum natura. 

14. " The class is mental. It is no group of things. It 
is our own private way of putting images together within our 
own minds." But, at the risk of seeming to affect singularity, 
I am bound to assert that within my own mind I can not find 
these classes. By a class I suppose you mean a group of 
images which actually exist; but when I come to the facts 
and look into my mind, and survey what is there when I hear 
the word " mammals " or " triangles " or " cats," I scarcely ever 
am able to find an actual group. The idea that " mammals " 
is the name of a flock of mammal-images, herded together in 
my mental field, and that among these I can see the little 
pack of dogs, and all the cats sitting together, and the rats, 
and the rabbits, as well as the elephants, all marked with 
curious references and cross-references to heads " quadruped " 
and " carnivorous " and " placental " and Heaven knows what 
else I do not think that this looks like the fact. 

15. These flocks and herds are pure mythology, they are 
nothing real. But let us suppose that they really exist. Enter 
taining fables, we may unawares embrace a truth. Let 
" mammals " be a group of mammal-images ; and let " dogs " 
be a mental pack of dog-images ; and let the judgment " Dogs 
are mammals " be the inclusion of the former within the 
latter. But what does this mean? 

If I look at the mammals I either know which mammals 
are dogs, or this is hid from me. (a) Suppose that I know it. 
The inclusion then means that a certain definite number of 



176 THE PRINCIPLES OF LOGIC BOOK I 

my present mammal-images are also dogs, and that these are 
surrounded or mixed up with the residue of mammal-images 
which are not dogs. The judgment asserts a spatial relation 
in my mind of the dog-mammals to the mammals which are 
rats and cats and rabbits and the rest. But such juxta 
position, let it be ever so actual in my imagination, is clearly 
not what we meant by our judgment. I wanted to say some 
thing real about dogs ; but this local relation fabled in my head 
does not even pretend to represent external existence. 

(b) And if I do not know which mammals are dogs, the 
case is not altered. I regard my mental conglomeration of 
mammals, and fail to distinguish the dogs from the cats. I 
can not say which image is a dog-image, but I know that the 
dogs are every one there. They are inside the mammal-fold 
and not outside. The mammals range over a mental park, and 
all the dogs are on this side of the paling. But that again 
is not what I meant to assert. The local position of my canine 
images with respect to the enclosure which bounds my mam 
mals, is not the idea which I meant to convey by " Dogs are 
mammals." 

1 6. These interpretations are fictions that is one objec 
tion. But it is followed by another they are unprofitable 
fictions. They are not only baseless: they also are useless. 
They do not read the whole proposition in extension. If the 
extension means the objects called mammals, then in neither 
case is " mammals," in this sense, the predicate. In saying 
" Dogs are enclosed by mammals," I do not say that " Dogs 
are mammals." A group of objects is one thing; a spatial 
relation, indefinite or definite, to that group of objects is 
clearly another thing. And, what is more, that relation is an 
attribute of dogs. The local relation is not the things them 
selves, and it certainly is predicated as qualifying dogs.* If 
the ostensible predicate has been taken in extension, the propo 
sition has in part been read intensionally ; for it has asserted 
an attribute of the subject. The inclusion within the class 
has no meaning, if the class is the mere individuals themselves, 
and the copula simply asserts them of the subject. But if the 
judgment affirms a spatial relation to some of those individuals, 

* I do not say the spatial relation of A to B is nothing but an 
attribute of A. Still it is such an attribute. 



CHAP. VI THE QUANTITY OF JUDGMENTS 177 

or the area they all occupy, or the fence that confines them, 
then what the judgment really affirms is an attribute. 

17. If we keep to extension we must keep to the ob 
jects, and it is these we must try to predicate of the subject. 
In " Dogs are mammals " we must try to assert " some mam 
mals " of dogs. What is affirmed must be identity. The 
dogs and dog-mammals are all the same thing. (Cf. Chap 
I- 17.) 

If they were wholly the same there would be no difference. 
They could not then be at all distinguished, and both sides 
of the judgment would fall together. The judgment would 
disappear. Hence a difference must exist ; and what we mean 
to say must come to this, that, Though the dogs and dog- 
mammals are the same, yet for all that what? Here we have 
to join issue. 

For all that, we may say, they are sometimes inside the 
mammal-enclosure and sometimes outside, and that is the 
difference. The dog-mammals sometimes are packed by 
themselves, and go wandering off in the mental distance, and 
at other times their images, compelled by some secret influ 
ence, consort with all whose blood flows warmly. But this 
strange mythology would not answer to our meaning. We 
never intended to say that the dogs could exist indifferently 
on each side of a hedge which grows in our minds. 

1 8. " The dog-mammals and the dogs are all the same, 
and yet for all that their names are different. You have a 
set of individuals which obviously in themselves are simply 
themselves. The difference asserted is the difference of their 
two signs * mammal and dog. That surely is a very pal 
pable thing, and, in saying Dogs are mammals/ we mean to 
assert that certain definite indivisible objects have got two 
names. It happens that they have been christened twice, or 
christened with two names, and this is the real heart of your 
mystery." 

The explanation possesses the merit of simplicity. It is 
perhaps too simple for sophisticated mortals. Belief in it will 
not " come with observation," but demands a new birth from 
the world of fact into the world of faith. Philosophy has not 
revealed it, and not many wise are likely to accept it. The 
creed of nominalism is no theme for argument. To those 



178 THE PRINCIPLES OF LOGIC BOOK I 

who believe that assertions about things assert nothing but 
names, the universe has long ago given up its secrets, and 
given up everything. 

19. The first interpretation asserts that the individuals, 
notwithstanding their sameness, cross and recross the mam 
mal-fence. The second asserts that, although they are the 
same, their names are different. The first interpretation is a 
fiction ; the second ignores the fact to be interpreted. Neither 
expresses the meaning of the judgment; and both in the end 
do predicate attributes. The change of position with respect 
to a herd or the pale that encloses it, is a spatial attribute. 
The possession of one or two or three names is again an 
attribute. The subject is not two different names; it has 
them. One name is not the other; it co-exists with it. One 
thing as distinguished is not the other thing; both have a 
quality which is the same. On the nominalist interpretation 
the actual predicate is not taken in extension. The interpre 
tation is not only ludicrously false, but, if we take it as true, it 
still asserts an attribute of the subject. 

The natural and the true interpretation of " Dogs are 
mammals " is that dog and mammal are different attributes, 
and that these differences co-exist within the same things ; or 
again, that, though the things are certainly the same, for all 
that they possess two different attributes, dog and mammal. 
But this natural interpretation involves the abandonment of 
the theory of inclusion within the predicate. 

20. And if you understand extension in a different sense, 
the result is the same. The class of mammal may be taken 
to contain, not only the collection of individuals which are 
mammals, but also the kinds of thing which are mammal. 
" Dog is one kind, and the judgment includes it among all the 
other kinds." It is doubtful what this means, but, whatever 
it means, the extension is not affirmed as a predicate. If I 
have in my mind a known or unknown aggregate of kinds, 
and say that dog is in the midst of this aggregate, then I 
assert of dog a spatial relation to a set of elements or the area 
they occupy. But this relation is surely an attribute. If 
again I mean that dog is an unit which, taken in addition 
with other units, amounts to the sum which I call " mammal," 
then I assert a relation to the other units, and a further 



CHAP. VI THE QUANTITY OF JUDGMENTS 179 

attribute that results from this relation. If I mean that dog 
possesses mammal, and that other kinds, known or unknown, 
do so, or that dog is like these other kinds in possessing 
mammal, then again I assert an attribute of dog, the having 
an attribute, and the identity in this respect with some other 
kinds. 

These interpretations are all forced and unnatural. They 
none of them are really what I have in my mind when I say 
" Dogs are mammals." Inclusion is not what I mean to 
assert. But, if I assert it, then my predicate is an attribute. 
The whole or part of the extension of mammals is not the 
real predicate. The predicate is that which I either affirm or 
deny of the subject, and a thing is not the same as a relation 
between itself and something else. 

21. If you say, " The dogs, with other things, make up a 
certain amount we know as mammals," then this contribution 
to a certain number is an undeniable attribute. If you say, 
" The dogs share a quality mammal with a heap of other 
things," this again is an attribute. If you suppose dogs and 
mammals to be two different lots in two adjoining folds, and 
if you pull up the mental hurdles which separate them, then 
you can not say, " The dogs are in the mammals," unless you 
are prepared to embrace a marsupial or some other such 
hypothesis. They are related locally to the other mammals or 
to the area or fence within which all mammals are circum 
scribed. And this local relation is an attributive predicate. 

The mythology you invoke is not strong enough to save 
you, and, if you throw yourself into the arms of Nominalism, 
then you have not only an account of the fact which is 
absurdly insufficient, but the difference of names is still an 
attribute. 

And if, in the end, to escape from your difficulties, you say 
"The class is no real collection in my head or out of it. It 
is a name that stands for the possible objects that have a 
certain attribute," then the answer is simple. If the class is no 
longer an aggregate or collection, it has become little else than 
a mere description. " Dogs are included in a possible group of 
things which are mammals," " Dogs are of the description 
mammal," " Dogs possess the attribute mammal " what is 
the difference between these three assertions? I ask you, is 



ISO THE PRINCIPLES OF LOGIC BOOK I 

there any, and if so, what? To include real dogs among mere 
possibilities can hardly be the end you have in view. 11 You 
must mean, " The dogs possess this attribute, and by virtue of 
this attribute are related to other possible mammals." The 
last part of the sentence calls for interpretation. " Dogs," we 
must read it, "are not only mammals but, supposing anything 
else to be mammal, then we may argue a relation between this 
thing and dogs." What relation? Surely not juxtaposition; 
that is too preposterous. The relation meant must surely rest 
on nothing whatever but the joint possession of the attribute. 
The inclusion in the class of possible mammals means nothing 
but the having the attribute mammal, and in addition, a 
hypothetical relation of identity with anything else of the 
same description. We predicate two things, in the first place 
a quality, and then a relation to possible objects supposed to 
have the same quality. Both of these predicates are attributes, 
and the last is an addition which may be superfluous. It is 
a mistake to think that the phrase " possible " will help us 
anywhere into anything but bad metaphysics. And the fa 
vourite prey of this delusion is the men who think themselves 
above metaphysics. 

We may briefly sum up this matter thus. The only way 
to read the whole judgment in extension 12 is to take it as 
asserting a relation of identity between different individuals. 
Two individuals are one though their attributes differ. 13 This is 
simply the other side of the judgment that different attributes 
are interrelated within the same individual. To take the sub 
ject as included in the predicate is in the first place to sub 
stitute fiction for fact, and in the next place is to predicate 
an attribute and is not to read the whole judgment in ex 
tension. But if the subject alone be taken in its extension, 
then what is asserted is obviously a connection of attributes 
within an individual or individuals. 

22. 14 Every judgment can be read in extension. Al 
though some present two or more subjects in relation, yet all 
can be reduced to the affirmation of a connection of content 
within one subject. In " A is to the right of B," the whole 
presentation is the subject, and the spatial relation of A to B 
is an attribute of that. In " Caesar is sick," the same person is 



CHAP. VI THE QUANTITY OF JUDGMENTS l8l 

said to be sick as well as Caesar. And in " Dogs are mam 
mals," there are certain things which are declared to be both. 
In this sense of extension every proposition can be read ex- 
tensionally. 

We have now to ask if every judgment can be taken in 
intension. Can not only the predicate, but also the subject be 
reduced to mere content? Do they all assert a connection of 
attributes? And this question at first sight may be answered 
in the negative. In " Caesar is sick," we certainly have a 
junction of adjectives, but it will be said, " We have some 
thing else beside. There is the individual of whom these 
qualities are predicated ; and. this individual is finite and deter 
mined. Admitted that in every intensional judgment you have 
a reference to the ultimate reality, and that this reality is 
individual, yet the ultimate subject does not affect the judg 
ment. 15 It is given undetermined except so far as it is deter 
mined by the judgment : and hence it does not interfere with 
the connection of the adjectives. But when you have a finite 
subject, then that subject interferes. In Caesar is sick, the 
judgment is not true unless you make it of this one Caesar. 
You can not get rid of the individual person, and, while he 
remains, he prevents your reading the judgment in intension." 

23. We have already cut the ground from under this 
objection by proving that every such judgment is hypothetical 
and strictly universal (Chap. II.). If the subject is taken as an 
existing individual or set of individuals, then no doubt the 
judgment is categorical, and can not possibly be read inten- 
sionally. " All these six sheep have got the rot," " William 
invaded England," " I have a headache " : if " these sheep," or 
" William," or " I," are taken as sensible individuals in the 
series of time, then that character enters into the assertion, 
and we can not reduce it to a hypothetical synthesis of ad 
jectives. But then our analysis in Chapter II. has shown us 
that the reduction is demanded. When we press for the final 
truth of the judgment, the particular subject becomes an 
unspecified condition of the content. The Assertion is thus 
hypothetical. It conjoins mere adjectives, though what it 
conjoins is vague and undetermined. The true subject of 
the judgment is, not this or that finite person or thing, but 
the ultimate reality. All the qualities of the ostensible sub- 

2321.1 N 



l82 THE PRINCIPLES OF LOGIC BOOK I 

ject pass into the condition of a universal connection of 
attributes. It would be idle to repeat the painful enquiries 
which have established this result. It stands or falls with our 
second chapter, and while it stands it carries the conclusion 
that every judgment can be read in intension. 

24. Thus, when the ostensible subject is a particular 
phenomenon 16 or collection of phenomena, no ordinary means 
will reduce the judgment. To take it in intension we must 
apply the drastic treatment we discussed in Chapter II. But 
in other instances the remedy is more obvious, and is easier 
to administer. " Some trespassers must be prosecuted," 
" Some English citizens are to be hung," " In some impossible 
cases right would be wrong." These assertions would, I pre 
sume, be called particular, but none of them need refer to 
this or that phenomenon. The " some " may mean " under 
some condition." It may describe the attribute, not point to 
the individuals. 

There are cases where " some " most clearly does not 
indicate this or that particular or set of particulars. " Some 
crimes are deserving of capital punishment," " In some dis 
eases the patient should be secluded " : we mean here that, 
given a crime or disease of a certain sort which we do not 
specify, then something else would in that case follow. The 
judgment couples mere attributes with attributes. It does not 
assert the existence of this or that crime or disease. It is 
hypothetical, and is naturally read at once in intension. 17 

25. " Some " again may mean an unknown number. 
" Some English citizens will be hung next year," may mean, 
not one sort, but one unspecified quantity of English citizens 
will suffer this fate. A particular event is here asserted, and 
the proposition must in the end be reduced by the method 
laid down in Chapter II. But the event it foretells has al 
ready in part been stripped of particularity. The forming a 
number, or contributing to an amount, is an universal at 
tribute : it is a general adjective, and to this extent the subject 
has been already purified. When read in intension the judg 
ment runs thus, " Given certain conditions, part unspecified, 
part specified as the attribute of English citizen and the at 
tribute of amounting to a certain number, then" etc. 

It is an elementary mistake to suppose that number 18 



CHAP. VI THE QUANTITY OF JUDGMENTS 183 

confers particularity and destroys intension. And the error 
reveals a deep foundation of bad metaphysics. Number is 
surely nothing but an attribute. And how can the addition 
of an universal quality force us to take a judgment merely in 
extension? How can it even help towards such a result? 
You may say, perhaps, that nothing is numbered save actual 
phenomena, but such an assertion would be incompatible with 
fact. " In the single case of two men being three men, four 
men would be six men" this is, I presume, an hypothetical 
judgment. Not only can you take it as connecting attributes, 
but I do not see how you can take it otherwise. 19 It is idle to 
object that the subject is really the imagined example, where 
two is three, and that this example is a particular event. For 
it is nothing of the sort. It is a supposed condition which, 
if it existed, would really be single, but does not exist and 
will never be anything real at all. 

26. The idea that a numerical subject is particular van 
ishes as soon as we confront it with facts. The numerical 
character is nothing but a character. It is nothing but an 
adjective, and no adjective or accumulation of adjectives will 
make anything else than an abstract universal. Suppose that 
a phenomenon is capable of division in fact or in idea. Its 
divisibility is a general quality, which other phenomena might 
also possess, and which would not difference one from the 
other. To be regarded as a collection of units summed by 
means of addition to a certain quantity, is an attribute not 
special to any single phenomenon: it can in no sense bestow 
uniqueness. And again, if the subject is taken as a quan 
tity which stands in a certain fractional relation to another 
quantity, it is absurd to think that, on the strength of these 
mere qualities, you leave universals and get to existence. 20 
" If a penny is thrown one thousand times, half the number of 
throws will most probably give head " : we have here a purely 
intensional judgment. There is nothing contained in it but 
bare universals: there is nothing but hypothetical junctions of 
adjectives. Of course, if you say, " This penny in half its 
throws will now give heads," the case is altered : but the num 
bers have not changed it. The subject is particular, not be 
cause it is numerical, but because it is not so, because over 
and above it has now been taken as a particular fact. It must 



184 THE PRINCIPLES OF LOGIC BOOK I 

be reduced by the method laid down in Chapter II. But so far 
as it is numerical it is already reduced, and is already nothing 
whatever but attributes. 

27. We may pass on to consider another superstition. 
If the intension signifies the meaning of a word, and the ex 
tension is the number of actual objects of which the meaning 
can be truly predicated, then both extension and intension 
are relative to our knowledge, and naturally fluctuate with 
altering experience. For instance, " mammal " is a term whose 
meaning has changed and will change. We can fix no limit 
to the possible information the word may convey, for we do 
not know how many attributes in the end may be found to 
be implied in the quality of giving suck. And the number of 
objects we denominate " mammal " is of course not stationary. 
Such considerations may seem too obvious to be ignored, but 
their neglect has given rise to a serious mistake. 

In certain judgments, where the predicate is not of the 
" essence " of the subject, we are warned that an intensional 
reading is impossible. " All American citizens know the name 
of their President," is, we are told, to be taken in extension 
(Venn, Symbolic Logic, p. 395 ). 21 It can not connect one set 
of attributes with another set of attributes, because the con 
nection it asserts is accidental. But the mistake here is 
obvious. If I know every single American citizen, so as on 
this knowledge to make my assertion, I surely must know by 
the selfsame process that the attribute I assert exists in each. 
After I have noticed each single citizen, it is one of his at 
tributes and part of his meaning to know the name of his 
President, and, before I have done so, I can say nothing at 
all. If the extension is increased, so also is the meaning. And 
the objection that, if the mark were part of the intension of 
" American," we should assert it of American citizens in the 
future as well as at present, may at once be dismissed. If 
the subject stands also for " all Americans in the future," then 
the attribute becomes at once part of their meaning. But, 
if the subject is confined to the present time, then the mark is 
the meaning of "present Americans," and you have no right 
to apply it beyond. 

The judgment is particular, not in the least because it is 
" accidental," but because American citizens are facts in time. 



CHAP. VI THE QUANTITY OF JUDGMENTS 185 

It would be just as particular if I changed it into " American 
citizens are Americans." And of course if the citizens meant 
by the subject are neither real men, nor real images, but mere 
possibilities, the judgment is hypothetical at once, and we 
need not have recourse to Chapter II. to effect its reduction. 

28. This same mistake lay at the foundation of the doc 
trine (4) that proper names have no " connotation." 22 The 
meaning is not fixed, and this leads to the idea that no mean 
ing exists. The simple enquiry "Is the denotation fixed?" 
leads at once to the result that, here as everywhere, intension 
and extension fluctuate together. 

Both are relative to our knowledge. And the perception 
of this truth is fatal to a well-known Kantian distinction. A 
judgment is not fixed as " synthetic " or " analytic " : its 
character varies with the knowledge possessed by various 
persons, and at different times. If the meaning of a word 
were confined to that attribute or group of attributes with 
which it set out, we could distinguish those judgments which 
assert within the whole one part of its contents from those 
which add an element from outside (p. 142) ; and the distinc 
tion thus made would remain valid for ever. But in actual prac 
tice the meaning itself is enlarged by synthesis. What is added 
to-day is implied to-morrow. We may even say that a synthetic 
judgment, so soon as it is made, is at once analytic. Kant 
has really no need of this unfortunate division, which he 
seems to have inherited. The real question which he means 
to ask is, What kind of synthesis does each judgment contain, 
and what in each synthesis is the principle of unity? 23 

29. To sum up the result 24 a proposition is read in- 
tensionally, when both subject and predicate are taken as 
attributes hypothetically related. Whenever the ostensible 
subject is no individual or collection of individuals the 
judgment is naturally understood in intension. Where the 
subject is one or more actual phenomena, the judgment can 
not be interpreted naturally as a hypothetical connection of 
attributes. But although not natural, this interpretation is 
legitimate, and is also necessary. When we leave first appear 
ances and ask for truth, we find that any phenomenal judg 
ment, whose subject refuses to be taken as content, is a 
judgment which is false (Chapter II.). 



l86 THE PRINCIPLES OF LOGIC BOOK I 

The error we must avoid is the idea that a class is a 
mere aggregate of individuals. 25 Such aggregates in my head 
or outside my head are barren mythology : they do not really 
exist. And if we mean by a class a possible aggregate of 
possible * individuals, we have no longer any collection. For 
possibilities occupy no place in the series of events connected 
with perception. They are not actual individuals, but merely 
ideal. A possible horse is anything which might conceivably 
possess the qualities, first of general uniqueness, and then of 
equine nature (Chap. VII.). Thus if the class means the 
attribute with reference to a hypothetical collection, to in 
clude in the class is to predicate an adjective. It is to assert 
an attribute, and through that attribute to assert a relation of 
identity and difference with any other instance. 

30. We have by this time had perhaps more than enough 
of the quantity of judgments, and yet there is a question we 
have not fully cleared up. The distinctions " universal," 
" particular," and " singular," fall under quantity, and it may 
be well that we should more definitely state here the meaning 
in which we take these terms. The common logic, we shall 
all remember, ranks singular and universal judgments to 
gether, and opposes the particular to both of these. A par 
ticular judgment is a judgment which fails to take the subject 
explicitly and avowedly in the whole of its extension; and 
other judgments are considered universal because in them you 
have all of the subject. This arrangement we shall not pro 
ceed to discuss. It is sufficient for the technical use of the 
syllogism, and it is perhaps in itself not so foolish as it seems 
to be. We need not however pause to examine it. We may be 
satisfied if we succeed in making clear our own interpretation. 

31. The subject is not only beset with ambiguities, but 
it tends at each moment to cross the border and to enter the 
field of metaphysics. I am afraid it is impossible for me here 
to defend the interpretation which I have adopted. I must 
content myself with trying to exhibit clearly the doctrine which 
seems metaphysically true, and which agrees with the logical 
results we have arrived at. 

*I suppose we do not always mean "judged possible." Cf. p. 4 
note. 



CHAP. VI THE QUANTITY OF JUDGMENTS 187 

We may realize some difficulties which obscure the sub 
ject, if we state them in the form of thesis and antithesis. 
(i) Nothing that is real is universal, (ii) All that is real is 
universal, (iii) Nothing that is real is particular, (iv) Most 
that is real is particular. I believe in the truth of all these 
propositions, and will endeavour to show that they are not in 
conflict. But first it is better to advocate each. 

32. (i) Nothing that is real is universal. Indeed, how 
should it be? What is real is substantial and exists by itself: 
it is individual. But the universal is nothing whatever but an 
adjective. It is an epithet divorced, a shadow which apart 
from its body is nothing, and can not exist. 

(ii) Everything that is real is universal. How can it be 
otherwise? For what exists must be individual, and the indi 
vidual is no atom. It has an internal diversity of content. 
It has a change of appearance in time, and this change brings 
with it a plurality of attributes. But amid its manyness it 
still remains one. It is the identity of differences, and there 
fore universal. 

(iii) And so we see that No real is particular. For if 
particular, then not individual, and if not individual, then 
non-existent. The particular is atomic. It excludes all dif 
ference. It is itself and nothing beyond itself. And that self 
is simple : it is so far as it is nothing else. The true particular 
in respect of quality is shut up in one quality; relations it 
can not be said to have; in respect of time it has no con 
tinuance, and in space it can not occupy extension. Its exist 
ence in space is nothing but a point, in other words, is nothing 
spatial. Such a particular is of course not to be verified in 
experience. It is a metaphysical ens rationis, an abstract 
universal 26 which can not be real. 

(iv) And it can not be real because, if not all, at least 
Most reality must be particular. 27 For in existence the indi 
viduals which are real are finite. To some extent at least 
they are defined by their limits. It is because they repel 
other things that they are what they are. Exclusion by 
others, and exclusion of others, enters into their substance; 
and where this is there is particularity. 

33. It is obvious here that in thesis and antithesis words 
have been used with different meanings. And this result we 



l88 THE PRINCIPLES OF LOGIC BOOK I 

desired to establish. The abstract universal and the abstract 
particular are what does not exist. The concrete particular 
and the concrete universal both have reality, and they are 
different names for the individual. 

What is real is the individual; and this individual, though 
one and the same, has internal differences. You may hence 
regard it in two opposite ways. So far as it is one against 
other individuals, it is particular. So far as it is the same 
throughout its diversity, it is universal. They are two dis 
tinctions we make within it. It has two characters, or aspects, 
or sides, or moments. And you consider it from whichever 
side you please, or from the side which happens for the pur 
pose of the context to be the emphatic or essential side. Thus 
a man is particular by virtue of his limiting and exclusive rela 
tions to other phenomena. He is universal because he is one 
throughout all his different attributes. You may call him 
particular, or again universal, because, being individual, he 
actually is both, and you wish to emphasize one aspect or 
side of his individuality. The individual is both a concrete 
particular and a concrete universal ; and, as names of the whole 
from different points of view, these both are names of real 
existence. 

34. The abstract universal and abstract particular are 
both unreal, because neither are names for the individual. 
They take the two aspects or characters of the whole, and, 
turning them into independent existences, then assert their 
reality. But one side of a whole can not stand by itself 
except in our heads. It is nothing but an adjective, an internal 
distinction which we try to take as substantial fact. We can 
all see that this holds good of abstract universals. The 
oneness or identity of a man, we know, is not found when we 
search the series of mental phenomena. But the same is true 
of the abstract particular. If you take atoms seriously, and 
deny their extension, you find at once you are dealing with 
something which can not be fact. Mere exclusion in space of 
other spaces is nothing real. A reality in space must have 
spatial diversity, internal to itself, and which it does not ex 
clude. And this holds again with psychical atoms. For, as 
observed, they have internal multiplicity, duration in time, 
quality, and degree; and as anything else they could not be 



CHAP. VI THE QUANTITY OF JUDGMENTS 189 

observed. An atom which really was particular, which was 
not divisible at least in idea, could not possibly be fact. It is 
one aspect of fact torn away from the rest, and is nothing in 
itself and apart from the act which tears it away. 

35. The abstract particular and the abstract universal are 
mental creations, which, if taken as fact outside our heads, 
are different examples of the same mistake. Both are dis 
tinctions within a whole, hardened into units that stand by 
themselves. And not only do they spring from the same 
mistake, but we may even say that they are the same error. 
The abstract triangle in and by itself is found to exclude all 
further predicates (cf. p. 119). Determined by that division 
and consequent exclusion which gave it its origin, it has be 
come particular. And the particular itself, because produced 
by mental separation, is really no more than an adjective 
divorced, or abstract universal. The dialectical method has 
laboured to show that, here as everywhere, insistence upon a 
onesided view brings out by negation the opposite onesided- 
ness. The universal, the more we emphasize its character, 
divides itself the more from the whole. We make its being 
depend on exclusion, and it turns in our hand into its logical 
contrary. The particular again, excluding others, and being 
so far as it merely excludes, is its own negative relation to 
other particulars. It falls beyond itself into a series of units 
pervaded by an universal identity, and itself has there become 
its own opposite. In this speculative movement, if we take it 
in the character it claims for itself, 28 I neither myself profess 
belief nor ask it from the reader. But I think we may go so 
far as this, that in the end the individual is real, and that ab 
stract universal and abstract particular are distinctions taken 
within that reality, which a mistake has afterwards turned into 
divisions and hardened into units. If we do not admit that 
each is a moment which, by negation of itself, affirms the other 
and begets the whole, we may certainly say that each has 
sprung from the same mistake, and is an illusion of the 
self-same kind. And we may muster courage, perhaps, to 
profess that the individual is the identity of universal and 
particular. 

36. We must keep in view the following distinctions. 
We have first the abstract universal and particular, and 



IQO THE PRINCIPLES OF LOGIC BOOK I 

neither of these can exist in nature. 29 On the other side we 
have the individual, and the individual is the only thing which 
is real. But where this real is finite it may be taken from two 
points of view : it is concrete particular or concrete universal. 
In so far as it is a finite individual which excludes all others, 
so far it is a relative particular. But because it includes a 
diversity of content, it is therefore also a relative universal. 

There is here, I confess, a doubtful point I am forced to 
.leave doubtful. It might be urged that, if you press the 
enquiry, you will be left alone with but a single individual. 
An individual which is finite or relative turns out in the end 
to be no individual; individual and infinite are inseparable 
characters. Or again, it might be said, the individual is 
finite, and there can not be an absolute individual. Meta 
physics, it is clear, would have to take up these questions, and 
in any case to revise the account which is given in this chapter. 
But that revision must be left to metaphysics ; and for the pur 
poses of logic we may keep the distinctions already laid down. 
We have (i) the real, supposed to fall into (a) absolute indi 
vidual or concrete universal, (b) relative individual or con 
crete universal or concrete particular; and (ii) the unreal, con 
sisting (a) of the abstract universal, and (b) of the abstract 
or absolute particular. 

37- We may now attempt to lay down what we mean by 
universal judgments. Such a judgment is one whose subject 
is universal. And it is obvious that here we have more than 
one meaning. An universal judgment may be (i) absolute, 
or (ii) relative. 

(i) In the first case we have again two divisions. Such a 
judgment may (a) be abstract, or again (b) may be concrete. 
If (a) the judgment is abstract, the ostensible subject will of 
course be an attribute. The statement will truly be hypo 
thetical, 30 since the actual subject is non-phenomenal reality. 
The ordinary kind of universal judgment such as " The angles 
of a triangle are equal to two right angles " is, as we have seen 
(Chap. II.), of this description. And it is universal for two 
reasons. The grammatical subject is an abstract universal: 
while the actual subject, the ultimate reality, is a concrete uni 
versal and is also absolute. This is the first and more ordi 
nary kind of judgment which we are able to call absolutely 



CHAP. VI THE QUANTITY OF JUDGMENTS IQI 

universal. But (b) it is necessary to mention another sort. 
Any statement made concerning a reality which is not con 
sidered finite will also be an absolute universal judgment. 
Nothing will fall outside the subject, and the predication will 
be categorical. I do not say that such judgments are prac 
ticable; but they are logically possible, 31 and must be provided 
for. 

38. (ii) A judgment is relatively universal where the 
subject is a finite individual or collection of individuals. It is 
universal, because the subject is the identity of its own internal 
diversity. In " Caesar is sick," Caesar is not affirmed to be 
nothing but sick: he is a common bond of many attributes, 
and is therefore universal. But this judgment is relative, 
because Caesar is one man among other men ; and, if you take 
him so, he himself is particular. 

39. 32 A judgment which is absolutely particular can not 
exist. It would have a subject completely shut up and con 
fined in the predicate. And such a judgment, if it came 
into being, would not be a judgment. For it obviously would 
say nothing else of the subject or predicate than themselves. 
" This is this " may be taken as the nearest example. 

A relative particular judgment is one where the subject 
is this or that singular or collection. It is the same as the 
relative universal judgment, but is taken from another side of 
its nature. The subject excludes all other individuals, and so 
is particular; but within itself it has a diversity, and so is 
universal. It possesses attributes other than the predicate, 
and may be taken within another context. It thus serves as a 
middle term in reasoning, as is shown in the third of the 
syllogistic figures. 

40. We have seen before (Chap. II. 45) that no logical 
difference separates the singular and collective judgments. 33 
It is ridiculous to think that if one individual is not universal, 
you reach universality by adding on others. The number 
of units is quite irrelevant, since, however many they become, 
each remains a singular. And this or that collection of indi 
viduals is as hard a particular as any individual found in the 
collection. Nay, from this point of view, the single individual 
himself turns out to be a mere collection. Considered logi 
cally they are both alike. Excluding others, they are relative 



IQ2 THE PRINCIPLES OF LOGIC BOOK I 

particulars. Common to all their internal diversity and iden 
tical throughout it, they both alike are relative universals. 

41. No judgment has or can have a subject shut up 
within the limits of one single predicate. If we remain at the 
popular point of view, and admit those judgments where the 
subject is nothing but a finite phenomenon or set of phenomena, 
yet even these judgments are universal relatively. The sub 
ject will serve as a middle in reasoning. It is hence the iden 
tity of differences, and it could not be that if it were only 
particular. Every judgment is thus universal, and in the end 
they all may be said to be universal absolutely. For, if we 
exclude the possibility of non-phenomenal finite individuals, 
we have shown (Chap. II.) that every judgment to be true 
must predicate of the absolute individual, either hypothetically 
or categorically. And the former of these cases must, in the 
end, be reduced to the latter. The finite subject changes in 
our hands into a heap of mere adjectival conditions, and, since 
these conditions can never be complete, the statement loses its 
categorical force. But becoming hypothetical it predicates 
indirectly a latent quality 3 * of the ultimate reality, and so once 
more is categorical, true categorically of the absolute 
subject. 

42. All judgments are thus alike universal, but it can 
not be said they are universal equally. If the subject of one 
judgment is a whole which includes the subject of another, 
the first is certainly the more universal. And again, if we take 
two abstract judgments, they are both hypothetical, but the 
one may assert a more abstract connection than is affirmed in 
the other. The purer hypothesis, the one most set free from 
irrelevant conditions, will be also more true. It will predicate 
in a higher sense of the universal subject, and therefore may 
be called the more universal. But if the connection, although 
less concrete, is not more pure, we must then not call one 
judgment more universal than the other, unless we qualify uni 
versal by abstract. 35 

43. I will repeat in conclusion the distinctions it is right 
we should keep in mind. The real is individual. The merely 
universal or merely particular are unreal abstractions. Con 
crete universal and concrete particular are the individual from 
different points of view. But we could not say that an abso- 



CHAP. VI THE QUANTITY OF JUDGMENTS IQ3 

lute individual was really particular, since it would have no 
relation to anything outside. 

Particular judgments, if taken categorically, are precisely 
the same as relative universal. The phenomenal individual, 
or collection of individuals, is the identity of diverse relations 
and qualities. Universal judgments are relative or absolute. 
If relative, they are the same as particular judgments. If 
absolute, they are either hypothetical or categorical. In the 
first the ostensible subject is an abstraction: in the second it 
must be the ultimate reality. Particular categorical judgments 
may all be reduced to abstract or hypothetical universals, and 
these again to categorical universals. In the end all truth, if 
really true, is true of the ultimate non-phenomenal fact. 



ADDITIONAL NOTES 

1 " Its content," i.e. in abstraction from its reference. 

2 " Ideal or actual." By "actual " I evidently meant here " existing 
in our " real world." But the " ideal " instance, though not in this 
sense " real," must be taken as an individual or particular. The ex 
tension always means the particular object or objects to which the 
meaning is applicable. We may note that the word " any " implies 
always, if strictly used, a number of individuals (Cf. Essays, p. 286). 
The statement, in the footnote to this page, as to "possible horses" 
is wrong. It forgets that the " imaginary " also is " real " and can 
be individual. Cf. on Chap. II, 45, note. 

3 " The fact is &c." The " fact," however, may be " imaginary." 

* "The indiscriminate use person." This detestable misuse as 
well as that of "distinctly" for "clearly" or " undoubtedly "seems 
now gone out of fashion. 

5 " Unnecessary and objectionable." Dr. Keynes (Formal Logic) 
has not induced me to alter my opinion. He is, I presume, right in 
saying that what Mill meant by "connotation" was merely "conven 
tional meaning"; and I very possibly also in some other point may 
not have represented Mill s view fairly. But that his innovation was 
useless and objectionable I remain convinced, and why it should 
not be quietly buried, Dr. Keynes, I think, has failed to show. For 
the meaning of Proper Names I refer the reader to Bosanquet s 
Logic, I, pp. 50-1. 

6 Cf . here Bosanquet, Logic, I, 47. 

7 "False or frivolous." Cf. p. 486. The doctrine clearly, except 
within certain limits, is false. But to call it everywhere worthless is, 
on the other hand, to fall into error. Subsumption (9) has its own 
value. See Bosanquet, Logic I. 55 foil. 



194 THE PRINCIPLES OF LOGIC BOOK I 

8 " Has ceased to lie in the individuals." But see Note 2. 

9 " There are few readers." This perhaps, even in 1883, was an 
exaggeration. 

10 On the subject of 11-29 see further T. E. III. 

11 " To include real dogs &c." should be " to include dogs, perhaps 
real, &c." 

12 " The only way . . . extension." I do not, by " in extension," 
mean " merely in extension " ; for this on my view is not possible. 

13 "Two individuals . . . differ." We should add, "And, where 
you have only one individual, you can still, by more or less of vio 
lence, bring it under the above head. For, dividing it by a distinction, 
you can so make the one individual into two." 

14 Sections 22 foil, require correction. No judgment can on my 
view be read merely in intension (see Note 10). Any passage in the 
text therefore, which seems to imply that possibility, should be 
amended. In 22, par. 2, the words " reduced to mere content " are 
ambiguous and misleading. Though nothing but " content " enters into 
a judgment, the question as to the reference and the extension remains 

(cf. Notes i and 2). 

15 How far and in what sense "the ultimate subject" does, and 
does not, enter into the judgment is discussed elsewhere (see on 
Chap. I, 12). It is true that, so far as the judgment depends 
on Designation, it remains conditional (see Index, s. v. Designation). 
But to pass from this to the assertion of a mere conjunction of ad 
jectives is at least misleading. What in the text I really was 
attacking is the position of any one who takes the content of the 
judgment as depending on individuals or particulars, known merely 
by Designation so as to preclude an intensional reading of the 
judgment. Anything beyond this was to overshoot the mark, if not 
to fall into error. On Designation see the Index, s. v., and Appear 
ance and Essays, the Indexes. On "the ultimate subject" see on 
Chap. I, 12. 

16 " A particular phenomenon " should have been " a merely par 
ticular &c." 

17 " Naturally read at once in intension," but not merely inten- 
sionally, however much the emphasis falls on the intension. The 
words " It is hypothetical " are again misleading here, as is also the 
reference to " existence," if that means " existence in my real world." 

18 " Number." The mark here is once again overshot. I was really 
concerned to deny that mere "numerical" sameness and difference 
is possible, and that particulars, diverse in this sense, and so unique, 
can enter into a judgment and so exclude an intensional reading. 

19 "How you can take it otherwise." (Cf. the "impossible cases" 
of 24.) These words should be corrected in accordance with what 
has been laid down in previous Notes. And so again with "nothing 
of the sort." There is aways an extensional side in judgment, how 
ever much this side may be wrongly emphasized or misinterpreted. 

20 "And get to existence," i.e. in such a sense as to exclude an 
intensional reading. 



CHAP. VI THE QUANTITY OF JUDGMENTS 195 

21 It is, I think, unnecessary to ask if I here represent Dr. Venn s 
contention fairly. If "all American citizens" means "all that now 
exist," the extensional aspect, I can agree, is naturally emphasized, 
though the statement becomes, I presume, obviously false. But in any 
case the intensional aspect of the judgment is there. I would add 
that the use of " hypothetical " and " hypothetically " (in 27 and 29) 
would better have been here avoided. Cf. Note 17. 

22 " Proper Names." See Note 5. 

23 Kant is not a writer whom I can suppose myself to understand, 
but my criticism seems, at least in part, to be unfair both in the foot 
note to Chap. I, 7 and also here. However insufficient his answer, 
Kant did not, I presume, neglect " the real question " as to the nature of 
the synthesis within the idea, and as to how far, and by what right, 
this limited synthesis can be transcended. 

On the real importance of the distinction between the essential 
and the accidental, see Bosanquet, K & R, pp. 59 foil. 

24 The statement here is far less correct than that in 12. After 
"actual phenomena" add "real or imaginary." And, after "judg 
ment which is false," add " In any case, even where we refer to one 
or more particulars and the emphasis is on the extension, the inten 
sional aspect is still there." 

25 On Class see Essays, pp. 283 foil. A class is an aggregate, but 
is also more. The mere aggregate is that which here and everywhere 
is mythical. 

" Possible individuals." The statement here is, at the least, mis 
leading. Possible horses, as actually imagined, are real individuals, 
though, except as psychical events, they do not enter into my "real" 
world. The footnote here repeats an error for which see Note 2. 
" Possible horses," again, are not the same as the possibility of horses, 
which latter is, itself as such, hardly a particular fact, except, once 
more, in the sense of a psychical event. 

"A relation of identity, &c.," should have been "a relation of 
identity with, and difference from, every &c." For the Collective 
Judgment see Chap. II, 45. 

26 " An abstract universal." Though this statement is correct, it 
might have been better to have said merely " an abstraction." 

2. 7 "Most reality." All reality, that is, except the Universe itself. 
In the next sentence, and again lower down, "existence" is not to 
be confined merely to " my real world." See Chap. II, Note 3. And 
(in 33, line 4) to "what does not exist" we should add "as such." 
For everything conceivable has existence in some sense. 

2 " Character it claims for itself," should be, I think, " character 
so often claimed for it." 

29 "Exist in nature" should be "as such be real." And, in the 
following paragraph, "as such" should again be added to "and (ii) 
the unreal." 

so " Hypothetical." Here (in 37 (0, and again in 41) "con 
ditional " would be a better term to use, if either term is required. 



IQ6 THE PRINCIPLES OF LOGIC BOOK I 

31 "Logically possible." But even here the judgment will be sub 
ject to a condition. See Essays, pp. 228 foil., and T. E. II. 

32 1 have in 39-41 assumed that merely external relations are 
impossible or at least would be useless. 

33 " No logical difference." This seems to be unnecessary, and is 
incorrect (see on Chap. I, 45). And the sentence "Nay . . . collec 
tion," though true, seems to be here more or less parenthetical. 

34 " A latent quality." See on Chap. I, 50. 

35 This 42 seems wanting in clearness, and I can not recall what 
exactly was in my mind when I wrote it. It appears to contemplate 
first (i) the case of two concrete wholes, and to lay down that the 
one which includes the other, or (we should add) is, generally, the 
more inclusive, is the more universal. We have next (2) the case 
of two abstract judgments, one of which is higher than the other 
(as being more general, and also "purer," in the sense of containing 
fewer unanalyzed, and perhaps irrelevant, conditions. The former 
judgment is therefore more universal as really covering and including 
more ground. Then we have (3) apparently two cases. In one of 
these (a) the judgment should be more universal in the sense of No. 2, 
but fails really to be so, because, though in a more general sphere 
and, in this sense, more abstract it contains as much or even more 
internal irrelevancy than is found in the other. Or (b) we have 
the case of a judgment which holds in a narrow, and so abstract, 
region, and therefore does not really cover more or even as much 
ground as is covered by a less " pure " and more concrete, but in 
effect wider, judgment. 

We should here remember that, if our knowledge were completely 
systematic, these distinctions, at least in part, would cease to hold. 
But, as things are, our pure and abstract knowledge is really, though 
not ostensibly, conditioned by that enormous mass which it fails to 
explain and comprehend, and so really to include. Hence the knowl 
edge (say) of a mathematician may in one sense be far narrower 
and less universal than the knowledge (say) of a biologist. The 
above remarks may perhaps serve to explain, and, where necessary, 
to correct the text of 42 in detail. The subject is perhaps too difficult 
to admit of any brief statement. 



CHAPTER VII 

THE MODALITY OF JUDGMENTS* 

i. Modality is not an alluring theme. I should be glad 
to plead the fragmentary nature of the present work as an 
excuse for passing it by in silence. But for the sake of clear 
ness it is necessary to make an excursion into the subject, 
neglecting those parts of it which do not seem to concern us 
here. 

We must begin by stating an erroneous view. Modality 
may be supposed to affect the assertion in its formal character, 
and without regard to that which is asserted. We may take 
for instance a content S P, not yet asserted, and may claim 
for modality the power of affirming this content S P, un 
altered and unqualified, in several ways. S P, it is sup 
posed, may be asserted, for instance, either simply or prob 
lematically or apodeiktically, and may yet remain throughout 
S P : and thus, though the content is unmodified, the asser 
tion is modal. 

2. This doctrine rests on a misunderstanding. There 
are no degrees of truth and falsehood. 1 If S P is fact, it 
can not be more than fact : if it is less than fact, it is nothing 
at all. The dilemma is simple. S P is affirmed or it is not 
affirmed. If it is not affirmed, it is not judged true at all. If 
it is affirmed, it is declared to be fact, and it can not be more 
or less of a fact. There clearly can be but one kind of judg 
ment, the assertorical. Modality affects not the affirmation, 
but what is affirmed. It is not mere S P that is asserted 
modally : it is another content, a modified S P. In other 
words, you do not say that the mere idea S P holds good 
in fact ; you first say something else about S P, and it is 
then this new and different idea which really is asserted. 

3. Modality in this sense, it has been rightly observed, 
has no natural limits. There are endless ways of modifying a 
judgment so as to make a fresh judgment. You may take 
* Cf. Sigwart, Logik, pp. 189 and following. 

2321.1 W 



198 THE PRINCIPLES OF LOGIC BOOK I 

the idea of a judgment S P and express any attitude of 
your mind towards it. You may say " I make it," or " wish to 
make it," or " fear to make it," or " can not make it," or " am 
inclined to make it," or " am forced to make it." All these are 
simple assertorical statements about my condition of mind. 
They have a psychological not a logical bearing, and may at 
once be dismissed. 

4. The different ways in which we can stand to a judg 
ment S P are a matter for psychology rather than for logic. 
Logical modality must be limited to that which seems to affect 
the idea S P, and to affect it in its relation to the world of 
reality. If we say, " I wish S P were a fact," this once 
more is a psychological mode. The content S P is not 
here first modified and then attributed to the ultimate subject. 
Neither itself nor anything we can call a modification of itself, 
pretends to be either true or false. The judgment in fact is 
concerned with nothing but my mental attitude. 

Either logic has nothing to do with modality, or modality 
affects S P from the side of truth and falsehood. The ideal 
content must be referred to or else denied of reality. But the 
reference or denial itself is simple, and can not be modified. 2 
What therefore must in some way be modified is the content 
itself. Not S P but a transformed and conditioned S P 
is the assertion made by logical modality. 

5. The modes of S P which logic has to consider are 
three in number. In each case we assert, we refer some idea 
to ultimate fact, we begin the judgment by saying, " It is true," 
but we go on to fill up the blank in each case by a different 
idea. It is true that S P is actual, or is possible, or again 
is necessary. The idea pronounced true is " actual S P," or 
"possible S P," or "necessary S P." These modes we 
retain for consideration, dismissing all others. But our choice 
is not really so arbitrary as it seems. We have here in a 
veiled and hidden shape the distinction of categorical and 
hypothetical assertion. The possible and the necessary are 
special forms of the hypothetical ; and between the assertorical 
and the categorical there is no difference whatever. 3 

I shall begin by asking (i) the general meaning which in 
logic we assign to the predicates possible, necessary, and real. 
I shall then point out (ii) that the possible and the necessary 



CHAP. VII THE MODALITY OF JUDGMENTS 199 

have no real existence. But on the other hand I shall show 
(iii) that these modal assertions, though as such and in them 
selves they are not true of fact, must always rest on a basis of 
assertion which is true or false of actual reality. 

6. (i) We need not ask what we mean by (a) asser- 
torical judgment. It is judgment categorical or unconditioned. 
" S P is real," attributes S P, directly or indirectly, to the 
ultimate reality. And on this point we have nothing to add 
to the explanations already given in Chapter II. The asser- 
torical judgment may be dismissed from our thoughts. To 
draw a difference between a categorical judgment on the one 
hand, and on the other a judgment which asserts reality, is 
plainly impossible. The assertorical is simply the categorical, 
taken in contrast with the possible and the necessary. 

7. And these are nothing but phases of the hypothetical. 
What may be and what must be involve a supposition. Neither 
is declared to be actual fact: they both are inferred on the 
strength of a condition, and subject to a condition. 

(b) It is easy to give the general sense in which we use the 
term necessity. A thing is necessary if it is taken not simply 
in and by itself, but by virtue of something else and because 
of something else. Necessity carries with it the idea of media 
tion, of dependency, of inadequacy to maintain an isolated 
position and to stand and act alone and self-supported. A 
thing is not necessary when it simply is; it is necessary when 
it is, or is said to be, because of something else. 

And where necessity is " internal," this meaning is re 
tained. 4 For it is not the totality which in this case is necessi 
tated. There is a diversity of elements contained in the whole, 
and these elements are divided into that which constrains and 
that which follows. In an unseparated world there could be no 
necessity. 

8. In a work on metaphysics the word " because " 5 would 
lead us straight to some fundamental difficulties, which will 
meet us again in our concluding Book. Is there any because 
outside of our heads ? Is it true that one thing is by means 
of another, and because of another? Or are we forced to 
admit that every fact, while it is no doubt and is also perhaps 
together with others, is not an adjective depending on these 
others, has no real bond that fastens it to its environment, 



2OO THE PRINCIPLES OF LOGIC BOOK I 

nor is subject to any alien influence? The objection would 
assail us : " One fact is and another fact is/ so much is true ; 
but One fact is and so another fact is/ must always be false. 
It is giving reality to mere ideal connections." And, if we 
escaped this objection, we should find another lying in wait for 
us. " You may say that one reality is the cause of another, 
and you may, if you please, add to this that the second is 
because of the first. But, if you venture to convert this asser 
tion, and assume that whenever you have a because you have 
also a cause, you fall into error of the worst description. A 
cause is real, a because is ideal; you may have the one and 
do often have it, where the other is impossible. They do not 
always co-exist; and where they do co-exist, they do not 
always coincide; and where they coincide, they are not identi 
cal. They are not the same thing: they are not even two 
different faces of the same thing. They are nothing but coun 
terparts, two parallel series which have no common points 
but possess some terms which have a constant relation " 
(Book III.). 

9. In a work of this kind we can not grapple with the 
problems offered us. We must here admit the objection and 
retire before it. We must admit that in logic " because " does 
not stand for a real connection in actual fact ; 6 we must allow 
that necessity is not a bond between existing things. For 
logic what is necessary is nothing beyond a logical conse 
quence. Necessity is here the force which compels us to go 
to a conclusion, if we start from premises. The " because " 
expresses an ideal process of mental experiment, which gives 
as its result a certain judgment. It does not guarantee the 
truth of this judgment, if you take it by itself. It does not 
guarantee the truth of the data which the process starts from, 
and on which it operates. A necessary truth may be, and 
commonly is, categorical, but, so far as its necessity goes, it is 
hypothetical. It ceases to be hypothetical only when it ceases 
to be merely necessary. 7 

10. I admit it is not the same thing to affirm " // M is P 
then S is P," and " Since M is P therefore S is P." 8 And the 
difference is obvious. In the latter case the antecedent is a 
fact, and the consequent is a fact: they are both categorical 
(Chap. II. 71). In the former case the antecedent may be 



CHAP. VII THE MODALITY OF JUDGMENTS 2OI 

false and the consequent impossible. But the necessity in each 
case is one and the same. S P must be true, if you take 
M P, and take S M, and draw the conclusion. That 
is all the necessity it is possible to find. The knowledge that 
S M M P are both true, and that S P is a statement 
which holds of fact, falls outside the necessity and does not 
increase it. The hypothetical result becomes categorical by 
an implied addition. And the hypothetical connection may 
not even then become categorical. The bond of necessity is a 
logical passage, and to say that this logical passage itself exists 
in fact demands an assumption which can not be hazarded in 
the face of objections. In logic we must be content to say 
that, if the premises are categorical, the result is categorical. 
We can not add that this result is necessary, unless for a 
moment we treat the data as hypotheses, and mean no more 
than // S MM P are given, then S P must follow. 

ii. We are able to urge a two-fold argument to show 
that necessity is hypothetical. We can reason from principle, 
and again from usage. The argument from principle 9 we may 
repeat as follows. Logical necessity is an ideal process, and 
you can not assume that either ideas or process are facts. 
Even if the ideas exist in fact, and exist in corresponding 
sequence, you can not assume that in this sequence your process 
exists. Your ideal operation works with ideas, and, so far 
as you know, it works only with ideas. The idea may be more 
than a mere idea, but it is as an idea that it goes into the 
experiment. And a mere idea is no more than a mere sup- 
posal. The result, so far as necessitated, is therefore so far 
not categorical. This we may call the argument a priori. 

And we have in addition an argument from usage. A 
necessary judgment, a statement introduced with " It must be 
so," may assert what not only fails to be actual but is plainly 
impossible. " If two were three then four must be six " pre 
sents us with a truth which is compulsory. The result must 
follow ; it is necessary truth ; but it does not follow in actual 
existence, and could not follow there, since both antecedent 
and consequence, and their actual junction, are impossibilities. 
It is not true that apodeiktic modality strengthens our asser 
tions. It serves rather to weaken them.. If S is P, there 
is an end of doubt. If S must be P, we know indeed that, 



2O2 THE PRINCIPLES OF LOGIC BOOK I 

given something else, we can be sure of S P, but we are 
certain of no more. The apodeiktic mode either leaves our 
doubts, or removes them only by the covert assertion of the 
condition of S P. Where the necessary asserts strongly 
it borrows its strength from a concealed assertorical. I will 
conclude this section in Sigwart s words. " There is a common 
idea that the apodeiktic judgment stands for something higher 
than the assertorical. It is believed that, if we start from the 
problematic judgment and ascend to the apodeiktic, we steadily 
increase the certainty of our knowledge, and add to the worth 
and dignity of our assertions. This idea must be relinquished. 
All mediate certainty must stand in the end on immediate 
knowledge: the ultimate premises of every proof can not be 
proved. The usages of life stand in comic discrepancy with 
the emphasis we lay upon apodeiktic certainty. The sayings 
1 It must be so/ It must have so happened, are judgments 
apodeiktic: but the confidence they express has most modest 
limits." (Logik, I. 195.) 

12. (c) A necessary truth is a truth which results from 
assumed conditions. 10 If we imply, as we very commonly do, 
that those conditions are actual, then the result is categorical. 
But, though the necessary may be real, its necessity is hypo 
thetical. What have we now to say about possibility? When 
S P is possible, does that mean that S P would exist as 
fact, if something else were fact? Is possibility in short a 
form of hypothetical necessity? 

It sounds strange when we hear that the possible falls 
under the head of the necessary. But it is at least as surpris 
ing to learn that the necessary may be impossible or non 
existent; and this we already know to "be the case. On such 
subjects as these our first impressions may be worth very little. 

The possible is that which is known or assumed to be the 
consequence of certain conditions. So far the possible is one 
with the necessary, where it is implied that the antecedent is 
real. But it differs in this point ; for S P to be possible 
all the conditions which make S P necessary must be sup 
posed, but only a part of them need be assumed to exist. It 
is implied that a part of the antecedent exists, but as to the 
other part we are left in ignorance. Thus the partial existence 
of the conditions of S P is the differentia which separates 



CHAP. VII THE MODALITY OF JUDGMENTS 203 

the species " possible " from the genus " necessary." Take 
a judgment such as this, Given abed then E must follow. 
Add to it the judgment, or the supposition ( 15), that ab 
exists, while cd is not known to exist, and we get the possible. 
E is now a possibility. We have an assumed fact ab, we also 
have ideal conditions c and d, assumed to be compatible with 
ofc/ 1 but not taken to exist. We have a hypothetical judgment, 
Given abed, we should have E. And from this, by the as 
sumption that ab exists, we pass to " We may in fact have E." 
In other words, ab is the " real possibility " of the possible E. 
It is known to be real, or at least is treated as if it were so 
known ( 15). 

13. Everything possible must be really possible. It must 
stand on a reality assumed to exist, and taken as part of that 
sum of conditions which would make S P an actual fact. 
Possibility apart from or antecedent to the real world is utter 
nonsense. 

But the basis of fact may vary indefinitely. S P is 
possible in the highest sense when the detailed conditions 
which make it necessary are fully known, and a part of these 
detailed conditions is also taken to exist. 12 This highest sense 
sinks by slow degrees to the lowest of all, where " possible " 
stands for "not known to be impossible." Here we do not 
know what special conditions give S P. Our basis of fact 
is nothing but the assumption that the nature of the world 
admits S P. 13 Because reality does not in our knowledge 
exclude S P, we take reality as one existing condition of 
S P, and we assume not only that the rest may be found, 
but also that they are compatible with reality. In this lowest 
and barest sense of possibility it is really wrong to call S P 
possible. It is better to say, We do not know that S P is 
impossible.* 

Between these extremes come many degrees. In the hypo 
thetical judgment about S P we may not know the special 
conditions of S P, but we may know a smaller or greater 
amount of them, and, where we are ignorant, we may have 
more or less reason to make an assumption. And in respect to 
the partial existence of these conditions, our knowledge admits 

*We rest our assertion on a privative judgment. Cf. Chap. IIL 
8, and p. 213. 



2O4 THE PRINCIPLES OF LOGIC BOOK I 

of many stages, and we make assumptions with grounds that 
may vary almost indefinitely. We should gain nothing here 
by dwelling on these varieties, and prefer to give some simple 
illustrations. 

14. Are disembodied spirits possible? Let us agree to 
take the most unfavourable view for the sake of argument. 
We have no direct experience of the existence of such spirits, 
and the question is whether we can call them possible. We 
know no conditions which would give the result. We have no 
reason to think such imagined conditions compatible with the 
real nature of things. 14 On the other hand we can not reject 
the idea as impossible, since we have no right to affirm " It is 
incompatible with the nature of things." We should content 
ourselves with saying, " Your proposed assertion is not cer 
tainly false, but there is no ground for thinking it true. Our 
ignorance is forced to admit a * bare possibility/ but it gives 
not the very smallest reason for entertaining that idea as real. 
And such bare possibilities, we have seen, are none; they 
are * idle frivolities, that have no place in the minds of reason 
able men/ " 

The case we have given is, as we have given it, an ex 
ample of the lowest sense of " possible." Let us go a step 
higher. " It is possible that some of the planets are inhabited." 
We have here the hypothetical judgment that under certain 
conditions life would result ; and to some extent we know these 
conditions, while we supplement our ignorance by assumptions 
for which we have reasonable ground. These special condi 
tions again are in various planets known to exist in part and in 
different amounts. Our judgment that this or that planet may 
be tenanted thus varies through different degrees of possibility, 
according to the amount of this partial existence. 

But now take the assertion " That coin may have given 
head." Here we know, on the one hand, special conditions 
which must exhibit head, and we know on the other hand that 
part of these conditions really exists. This is possibility in its 
highest form. 

15. We have noticed that possibility may stand not on 
fact but on supposition. If a coin had three sides, then it 
would be possible that neither head nor tail should be upper 
most. There is here no vital change in the meaning of 



CHAP. VII THE MODALITY OF JUDGMENTS 2O5 

" possible." For the real basis is supposed to exist, and the 
possible is subject to the supposition. But we should not here 
say that S P is possible ; we can not strictly go beyond " It 
would be possible." It is possible, if by a fiction of thought 
you treat the unreal as if it were real, or the unknown as if 
it were known. We must distinguish such hypothetical from 
actual possibility. For, just as we more commonly imply that 
the necessary exists, so we imply and must ordinarily even be 
taken to assume that the ground of the possible is actual fact 
and not merely supposed. 15 

1 6. We have now discussed the meanings of " possible " 
and " necessary," so far as to see that both are forms of the 
hypothetical. And with this conclusion we have anticipated 
the result of our second enquiry, Does logical modality exist 
in fact? 16 

(ii) We saw long ago that hypothetical judgments, as such, 
are not true in rerum natura. Neither the subject, nor the 
predicate, nor again the connection, need exist in fact. What 
is true of fact is the quality that forms the base of that con 
nection. The junction itself may be non-existent and even 
impossible. We shall verify this result in the possible and the 
necessary. 

17. (a) We have seen that what must be is never neces 
sary save on the hypothesis of some condition. We have seen 
that this antecedent, and the consequence which follows, may 
claim no existence and may have no possibility. 17 The neces 
sity in these cases, if we mean the necessary connection of the 
elements, does not exist outside our ideas; it is not true of 
fact. 

And again, when the antecedent and with it the conse 
quence have actual existence, and appear in a relation which 
is clearly the counterpart of logical necessity, the same result 
holds. We saw that the difference between the cause of 
knowledge and the cause of existence staggers our assump 
tions. And even when the two seem to us to coincide, how 
can we assume that they are ever identical ? It is a great thing 
to say that what is true in thought must hold in fact. But 
it is something more to maintain that thinking and existence 
appear as two sides of a single reality, and to insist that every 
logical process must be found in fact, and that all real con- 



2C>6 THE PRINCIPLES OF LOGIC BOOK I 

nection is, if we could see it, a logical process. We shall recur 
to these questions in a later Book. For the present we may 
repeat that, if such a doctrine is tenable in metaphysics, it 
can not be supported in a logical treatise. The objections it 
calls forth, if they could be disposed of, could be disposed of 
only by a complete revolution of our current doctrine as to 
mind and things. 18 

For logic the necessary must remain the hypothetical. 
Facts for logic must be facts that are and that never must be. 
The real connection which seems the counterpart of our logical 
sequence, is in itself not necessary. It is necessary for us, 
when in ideal experiment we retrace the process of actual fact. 
But, at least in logic, we must not assume that our ideal rela 
tion is the bond of existence. The ideal compulsion of logical 
necessity is as strong where the premises are known to be 
false, and the antecedent can not be believed to exist, as where 
we start from categorical truths and pass from them to a cate 
gorical conclusion. If in both these cases there is logical 
necessity, how can we ever be safe in assuming that such 
necessity is found in existence? 

1 8. (b) And when we pass from the necessary to the 
possible, our conclusion remains. The possible, as such, exists 
nowhere at all but in the heads of men. 19 The real is not 
possible unless for a moment you think of it as unreal. When 
the possible becomes real it ceases at once to be a mere possi 
bility. For metaphysics I will not deny that the possible might 
bear another meaning. But for logic, wherever a fact appears, 
a possibility vanishes. It is not merely that the possible is 
confined within the limits of human thinking. It can not 
exist outside the domain of human doubt and human ignorance. 

We have seen that to say " S P is possible," means, 
" S P would follow under certain conditions, some at least 
of which are not known to be present." And at this stage of 
our enquiry, we may say at once that the sequel of such a 
hypothetical judgment can not be taken to have actual exist 
ence. The antecedent is not fact, the connection is not fact, 
and the consequence is not fact. Or, if they are fact, their 
" factual " character must be either unknown or put out of 
our minds, when we treat them as possible. If we knew the 
reality we should make no supposals; or, if we made them, 



CHAP. VII THE MODALITY OF JUDGMENTS 2O? 

we should know that they were made and, as such, did not 
exist. 

19. Common usage enforces our conclusion. The accused 
obviously is guilty or is not guilty (Sigwart, 228). But we 
say " It is possible he may be either." That is grossly false, 
if you take it as asserting about the fact. A fact is not and 
can not be an alternative. The possible existence of both 
guilt and innocence is relative to our knowledge ; it exists only 
in our heads, and outside them has no meaning. A ship has 
sailed from Liverpool for America, and we say " It may have 
arrived in New York, or again it may be at the bottom of the 
sea." If you make this statement of the actual fact, it can not 
be true. It is not possible that a ship should be in two places 
at once. It must actually be somewhere; and, being actually 
there, it is not possibly elsewhere, nor even possibly where it 
is. The possibility is nothing beyond a supposition founded 
on our real or hypothetical ignorance. Outside that ignorance 
and that supposition it is not anything at all. 

20. 20 We have now shown in the first place that 
" necessary " and " possible " are both hypothetical. We have 
seen in the second place that, at least for logic, they do not 
exist, as such, in the world of fact. It remains to show that, 
although " subjective," they must rest on a basis of categorical 
assertion about reality. 

(iii) We have only to recall the doctrine we reached in 
our Second Chapter, to perceive at once the truth of this con 
clusion. We saw there that all judgment in the end was 
categorical. The basis of the hypothetical must be fact, and 
without that basis the judgment would be false. 

(a) We need give ourselves no pains to verify this result 
in the case of necessity. We have seen that " S P is a 
necessary truth" means "S P follows from something 
else." This something else need not be fact, and, where it is 
fact, that can not be assumed to make any difference to the 
ideal connection. We can not say " In fact S P really is a 
necessary consequence as such." But, the connection being 
hypothetical, it on the other hand demands a basis which is 
categorical. All necessity affirms a real ground explicit or 
implicit. It thus so far has actual existence, not in itself, but 
indirectly and simply in its ground (Chap. II.). 



2O8 THE PRINCIPLES OF LOGIC BOOK I 

21. When we come (b) to the possible, we are tempted 
to think it has less actuality than belongs to the necessary, 21 
since a part of its conditions remains unspecified. But, un 
less we imply that the antecedent of the necessary exists in 
fact, such a comparison would be illusory. In neither case can 
we assume that antecedent or consequent exists; and when 
we pass from what must be to what only may be, the ground 
of the judgment seems in either case to be equally real. 

In the merest hypothetical possibility we have an assertion 
about actual fact. We affirm the necessity of S P following 
from abed, conditions a part of which is supposed. And in 
this we attribute the base of that connection to ultimate reality. 
But in an ordinary assertion of possibility we imply the exist 
ence of a part of abed, and thus make another statement about 
fact. What we do in a case of so-called bare possibility again 
is this. We first, on the strength of a privative judgment 22 
( 13), conclude that the conditions are compatible with 
reality. We then get the existence of a part of these unspeci 
fied conditions by taking the real (because it is compatible) 
as a joint condition. Thus reality, taken in some unknown 
character and passing into the conditions, gives partial exist 
ence unknown to the antecedent; while the same reality, in 
another character, then guarantees the hypothetical sequence 
of S P. We thus in the end (whatever we may think of 
them) have two categorical assertions. 

In " A disembodied spirit is possible " we start by denying 
that it is impossible. This judgment rests, first, on the as 
sumption that the real has an actual unknown quality, which, 
in the second place, if you take it together with other unspeci 
fied conditions, makes a hypothetical antecedent from which 
" disembodied spirit " follows as a consequence. As the 
ground of this second judgment we have to attribute another 
unknown quality to the real to serve as the basis of the hypo 
thetical connection. We have thus two assertions about the 
nature of things. 

22. Let us now take an instance of rational possibility. 
If we say " It is possible A holds the ace of trumps," we know 
there are conditions which would give this result. Such or 
such an arrangement of the pack, such or such adjustments of 
the muscles in the person who cuts and the person who deals, 



CHAP. VII THE MODALITY OF JUDGMENTS 2OO, 

must give the ace to A. The ground of this judgment consists 
in mechanical and other laws, in accordance with which the 
result would follow. These laws we regard as qualities of the 
real, and this is one of our assertions. We next affirm that 
an event has happened, viz. the dealing of the pack, which 
presents in fact a certain part of our antecedent; in other 
words, which gives reality to our supposed conditions to a 
certain point and within a limit. The antecedent is not actual 
in that full and especial form which gives the ace to A, but 
it is there in that outlined and partial character which gives 
the ace to some one player. 

Everywhere, where we say that S P is possible, we 
assert a real possibility of S P. We must assume a fact 
which actually is, though it is not S P. And we assume that 
this fact would under some conditions give us S P. That 
is, we categorically assert the ground of an hypothetical judg 
ment; and again we categorically assert the existence of a 
fact which forms part of the antecedent. These two positive 
assertions can everywhere be found in the most guarded state 
ment about an actual possibility; and the former is required 
for mere hypothetical possibility. 

We have now accomplished the third task we set before us. 
We have shown that the necessary as well as the possible has 
a basis in fact and depends upon experience. A modal judg 
ment has to make an assertion about reality. But the judg 
ment itself expresses a truth which is not a fact. Modality is 
but hypothetical, and hypothetical connections exist only in 
our thoughts. 

23. There are various points in connection with the sub 
ject which claim our attention. We are accustomed to hear 
of " capacities " and " faculties," and to use such phrases as 
"potential energy," with but little regard for their actual 
meaning. The "potential" is regarded as something real, 
stored up outside existence, which hereafter may emerge in 
the world of fact. This deplorable piece of effete metaphysics 
takes a leading place in popular versions of the truths^ of 
physics. Potential energy of course as such has no real exist 
ence. It is merely the consequence in a hypothetical judgment 
where the conditions are not all taken as actual. It would-be 
better to say, " Though there is no energy, there is something 



210 THE PRINCIPLES OF LOGIC BOOK I 

actual which exists as the real possibility of energy." But 
even this correction leaves a residue of error. 

In strictness of speech a real possibility of S P can not 
exist as such. 23 It should mean that reality which, if you 
place it in an ideal construction, developes S P as a conse 
quence. Itself is fact, and the attribute at the base of the 
hypothetical judgment again is fact: but that judgment with 
its elements can not be taken as fact. We are met by this 
dilemma. Apart from the judgment the real is mere fact and 
has no potentiality ; but within the judgment the reality itself 
has ceased to be real. It has taken its place in a mental con 
struction. Unless you are prepared to make ideal elements 
determining forces in the processes of nature, you can not 
properly believe in real possibilities. And I think, upon any 
metaphysical theory, it would be better to find some other 
expression. 

24. But I shall hear : " Conditions are surely real. 24 
Before life began its conditions could be present. And the 
real possibility being a condition, as such you must allow it to 
exist." In the above I see nothing but the same mistake. A 
condition as such can not be said to exist. A condition is an 
element in a hypothetical judgment and, outside that judgment, 
it is no condition. If you say, " A exists and is an actual 
condition of B," you are speaking inaccurately. What real 
bond corresponds to your phrase? B is not in existence, and 
if the other conditions do not appear, it will not exist. And 
yet you say, " A is one of its conditions." If you wish to be 
accurate you should say, " A is something which, if taken from 
existence and placed within an ideal construction, mentally 
gives rise to B." All beyond is unwarranted. 

A condition ex vi termini does not as such exist; and to 
define the cause as " the sum of the conditions " is to commit 
a serious metaphysical mistake. It is saying, " The reality 
which gives rise to reality is made up by adding mere ideas 
together." * But the cause must be fact, and its effect must 

* Of course the word sum again is open to criticism. It implies a 
theory of the union of the elements, which certainly can not be taken 
for granted. But to clear up this point a long digression would be 
wanted. There are some remarks on causation in Book III. II. 
Chap. II. 



CHAP. VII THE MODALITY OF JUDGMENTS 211 

be fact. We should do better to call the cause the meeting of 
elements which, in the moment of their union, begin a process 
which issues in the change we call the effect. An actual union 
of actual elements is the cause. Each element by itself and 
apart from this union is not even a condition. It becomes a 
condition when you place it ideally in union with others. But, 
in order to do that, you must make it an idea. In its character 
of condition it must so far cease to be fact. 

I am far from suggesting that the want of accuracy I have 
just been noticing is always error. The phrases " potential " 
and " condition " and " possibility " may be harmless and 
useful. We ought all to be able to employ them safely. But 
I fear that too often the case is otherwise. Too often they 
prove mere engines of illusion, drowsy sops thrown down to 
make reason slumber. If we believe in something that neither 
is nor is not, but rules some strange middle-space between 
existence and nothingness, let us at least have courage to 
profess our opinion. Do not let us use words in using which 
we take refuge from doubt in blind ambiguity. 

25. It was blind ambiguity and little beside that lay at 
the root of a controversy we remember. Amongst those who 
vexed themselves and others with disputes on the " Perma 
nent Possibilities of Sensation," 25 how many adopted the 
obvious course of asking what lay hid in this spell ? We know 
now that a real possibility means something which, in itself 
and in fact, is no possibility, but must be something actual. 
It is a veritable fact which actually exists; and to this we 
must add here the idea of permanence. I suppose this means 
that our actual fact has, against something else, at least a 
relative duration and freedom from change. But now what is 
this real or, I should say, these reals, which do not change, and 
which an attribute of the reality guarantees to produce the 
consequence of sensation, so soon, that is, as you have trans 
formed them into ideas, and placed them within ideal con 
structions? Are they real things, as distinct from sensations, 
or, if not, what are they? I do not say that the asking this 
question is enough to explode the theory of J. S. Mill. I will 
say that the answer to it, however it is answered, must alter 
at least the statement of that theory, and change at least some 
of the points in dispute. 



212 THE PRINCIPLES OF LOGIC BOOK I 

I must be pardoned for seeing in another use of this delu 
sive phrase an ambiguity which threatens the conclusion. If 
there are difficulties in the way of making pleasure, in the 
sense of atomic and momentary feelings, the end of life, can 
we be said to escape them if we say Happiness is the end, and 
if Happiness is defined as a permanent possibility of pleasant 
feeling? We are met by the objection, If the end is pleasure 
then it surely must lie in actual pleasure. But if it lies in 
actual pleasure, it can hardly lie in mere possible pleasure. 
Either the end is pleasure present and actual, such pleasure 
again as has a quality (itself also pleasure) which guarantees 
a hypothetical result of ideal pleasure, and this present pleasure 
is also permanent either this, I say, or Hedonism is given up, 
for something not pleasure is made the end. Here again I 
must venture to make the remark that the answer to the objec 
tion must modify at least the statement of the doctrine. 26 

26. We may turn from these criticisms to a positive 
result laid down by Sigwart (182, 227), and which our dis 
cussion of possibility should have served to make clear. The 
particular judgment, in the end and really, we found to be 
nothing but a hypothetical in which the conditions remained 
imperfect (Chap. II.). In the problematic form of judgment 
we once again encounter the particular. The one is the other 
under a disguise which disappears before our scrutiny. The 
particular judgment " Some S is P " is the same as the judg 
ment " S may be P." The assertion that S does actually exist 
is not contained in the particular judgment, 27 any more than 
it is in the problematic. " Some S is P " asserts no more than 
that, S being given in ideal connection with other conditions, 
of which conditions some part is assumed or supposed to be 
actual, then P will follow. And this is precisely the sense of 
" S may be P." Both are imperfect hypothetical judgments, 
and both are founded on a basis of fact believed in or sup 
posed ( 15). 

27. Reality in itself is neither necessary, nor possible, 
nor again impossible. These predicates (we must suppose in 
logic) are not found as such outside our reflection. 28 And to 
a knowledge and reflection that had command of the facts 
nothing ever would be possible. The real would seem neces 
sary, the unreal would seem impossible. 



CHAP. VII THE MODALITY OF JUDGMENTS 213 

The impossible is that which must be unreal. 29 We might 
call it, if we chose, one kind of the necessary. When we say 
of S P that it can not exist, we do not merely mean that in 
ideal experiment the suggestion of S P directly vanishes. 
We suppose for a moment that S P is real. Then on that 
hypothesis we see that the conditions from which alone S P 
would follow are directly or indirectly incompatible with the 
real. The real, if changed in ideal construction so as to afford 
the conditions of S P, is changed in such a way as to cease 
to be itself. The alteration removes some attribute that we 
assign to the real ; and this attribute, in our reflection, by means 
of its exclusion of other possibilities, thus generates the im 
possible and becomes the necessary. 

Impossibility and necessity are correlative ideas. They 
emerge together. The real does not seem necessary until it 
has excluded what is incompatible, and reasserted the attribute 
which is the ground of the exclusion. 30 Because of this attri 
bute nothing else can be, and the attribute must be because 
nothing else is. The unreal again is not impossible until we 
have seen, not merely that it fails, but that its supposed success 
would destroy what is, and what must be because its opposite 
is excluded. 

28. These ideas suggest a number of difficulties. In a 
later book we must return to one of them, and may content 
ourselves here with a brief indication. The impossible we see 
must always imply a positive quality, known or assumed to 
belong to the real. If X is impossible, this means and must 
mean that an actual X would remove by its presence some 
positive attribute we take to be real. 

This bears on a point which already has engaged us 
( 13, 21). The possible may be taken as anything whatever 
which is not real nor yet impossible. 31 We objected to this 
process, as frivolous in its result and insecure in its method. 
The method is insecure, since it passes from the absence of 
known incompatibility to the assumption of compatibility. 
We take X to be compatible, if the real, as we know it, will 
pass unabridged into a set of conditions which give X as a 
consequence. Again, so far as we know, X is not incompatible, 
when the suggestion of X as an attribute of the real calls 
forth no answer affirmative or negative. And the doctrine 

2321. I p 



214 THE PRINCIPLES OF LOGIC BOOK I 

we object to passes direct from want of incompatibility to 
compatibility. In the one case X is possible, since it follows 
from conditions a part of which is supplied by the real. But 
in the other case we can say nothing about reality, unless we 
make an enormous assumption. 

29. We offer our suggested X to the real, and the real 
is passive: X is not excluded. This privative judgment, if 
we wish to understand it, must be reduced to an ordinary 
negative where a positive quality in the subject rejects. What 
is the positive quality here? It is the mental presence of the 
real with such and such attributes. Now even the smallest 
addition to these present attributes is an alteration of the real, 
as we have it in our minds, against which it asserts itself in 
the character it bears at the actual moment. In other words, 
the base of our assertion that X is not rejected by the real, is 
the assumption that the real differs in no point from the real 
as at this moment it is present. 

Now it is one thing to say " Whatever I judge true holds 
good of reality," and another thing to say " What I fail to 
judge true is absent from reality." And there is this very 
great difference between them. In the first case we assume 
that, whatever else may be, at least so much is true. In the 
second we go so far as to say that what we have in our minds 
is co-extensive with reality. But, if we hold to this, we ought 
to go further. What the real does not exclude is not possible, 
it is actual and necessary (pp. 118-19). And if we shrink 
from this assertion, ought we to maintain that X is even 
possible ? 

30. The mistake is apparent. A privative judgment (as 
we saw in Chapter III.) is not true of a subject, if that subject 
is confined to something without the sphere of the predicate. 
It then becomes obviously frustrate and unmeaning. You can 
not predicate absence unless you predicate the positive space 
from which the absent is lacking (Chap. III.). We shall find 
that this holds good of ultimate reality. To say of it, " It is 
without the rejection of X," is to say of it something which 
has no meaning unless, so to speak, the place left empty by 
this mere privation is occupied by a positive attribute. We 
ought to be able to say There is a quality the presence of 
which guarantees, or goes to guarantee, the absence of the 



CHAP. VII THE MODALITY OF JUDGMENTS 215 

exclusion of X. But this quality would obviously be either 
the presence or compatibility of X. It is on the ground of this 
presence or compatibility that we ought to assert the possibility 
of X. For otherwise we fall into circular argument. 

I will give an illustration. Suppose I were to say that an 
isosceles triangle with three unequal angles is certainly pos 
sible, and possible because it is not impossible. The universal 
triangle, so far as I am supposed to know it, tells me nothing 
about the nature of the isosceles. 32 On the privative judgment 
that the universal triangle does not reject my idea,, I call it 
possible. Is not this absurd ? It is absurd, because a privative 
judgment, where the subject is left entirely undetermined in 
respect of the suggestion, has no kind of meaning. Privation 
gets a meaning, where the subject is determined by a quality 
or an environment which we have reason to think would give 
either the acceptance or the rejection of X. But, if we keep 
entirely to the bare universal, we can not predicate absence, 
since the space we call empty has no existence. 

31. Or if our privative judgment has a meaning, then it 
has a false meaning (Chap. III.). It rests on a confusion 
between the universal and its psychological existence. We 
take the idea, as we find it existing within our minds as a 
psychical event, and then confound the determination it so gets 
with its logical qualities. We say Here is a fact, and we can 
not find that it does reject X. But the answer is simple. In 
the first place we have the reductio ad absurdum. Since the 
real has a quality on the ground of which it must accept or 
decline every possible suggestion (Chap. V.) ; and since the 
real here ex hyp. does not decline, it therefore must accept. 
X is not possible, it is actual and necessary. In the next place 
we directly deny the premise. In your experiment you have 
not got the reality, and you ought to know that you have not 
got it. If you wish to determine your empty universal so as 
to get an answer in regard to X, you have nothing to do with 
the psychological setting of this universal. The psychical 
environment is not the space which, in respect to X, must be 
full or empty. It is quite irrelevant and must be discarded. 
You must fill out your idea by adding to its content. When 
the content is supplied to such an extent that, in saying, " Re 
jection of X is still absent/* you mean that some of the condi- 



2l6 THE PRINCIPLES OF LOGIC BOOK I 

tions of X are already present when you mean that there are 
qualities which do affect the prospects of X, that a part of that 
attribute, which when complete will accept or reject X, is 
already there and that part is favourable then I admit you 
may found possibility on your privative judgment. 33 The com 
plaint I make is that your proceeding is frivolous. You have 
in your hands the positive ground on which your judgment is 
based directly, and you choose to proceed in a way which is 
indirect and in this case circular (Chap. V. 28). 

We should never trust a privative judgment until we have 
seen its negative form. We should never trust a negative 
judgment until we have seen its affirmative ground. We 
should not take our impotence as a test of truth, until we at 
least have tried to discover the positive counterpart of that 
failure. The observance of these rules might preserve us from 
errors which sometimes are dangerous. 

The relation of necessity and impossibility to our mental 
impotence is a subject which would carry us beyond the present 
volume. We shall add some remarks in our concluding Book. 
In the present chapter we have yet to see how modality is the 
passage from judgment to reasoning. But, before we indicate 
that transition, we must rapidly deal with a most important 
application of modality, so far at least as to show its connec 
tion with our general view. 

32. If Logic professed to supply a method for the dis 
covery of truth, the logician could not mention the theory of 
Probability 34 without shame and confusion. The fruitful 
results of the modern rival would offer themselves in damag 
ing contrast with the sterility of the old and privileged veteran. 
And, where a true view of the claims of logic makes this con 
trast impossible, the logician, it may seem, has no right to 
trespass within the limits of another science. The objection 
is heightened when the writer on logic confesses himself un 
acquainted with mathematics. He may appear in this case to 
be talking about things of which he knows nothing. 

But the objection rests on a misunderstanding. The prin 
ciples on which probabilities are reckoned, the actual basis and 
foundation of the theory, are not themselves mathematical. 
Before mathematics can deal with the subject some assump- 



CHAP. VII THE MODALITY OF JUDGMENTS 2I/ 

tions are necessary; and, though these assumptions can be 
justified by their results, it is desirable to examine them simply 
by themselves, to see what they are and whether they are true. 
An enquiry of this sort, by whomsoever it is made, is a logical 
enquiry. 

33. Probability, we know, has to do with possibilities. 
And starting from this, at the point we have reached, we 
can go at once to an important result. No statement we make 
about probabilities can, as such, be true of the actual facts. 
This is half the truth, and we must not forget it. But it is not 
more than half, nor is it even the half best worth remembering. 
It is just as true that an assertion about chances does make an 
affirmation about reality. Every hypothetical judgment, we 
have seen, must rest upon some categorical basis. The con 
clusions we have adopted enable us to say without further 
enquiry, Any theory which calls the doctrine of chances merely 
" objective," or merely " subjective," is certainly false. It 
is a vicious alternative which, if it were sound, would upset 
general results we have found to be true, and which is con 
trary to the special facts of the case. 

34. I shall return hereafter to the consideration of this 
root-mistake, but it is better to begin with a statement of the 
truth. We are to omit the subject of probability in general, 
and confine ourselves to the particular instance of that which 
is called mathematical probability. And the point which first 
presents itself to our notice, is the necessity of limiting the 
possibilities. Before we can advance a single step we must 
have the whole of the chances before us. This exhaustive 
survey may rest on knowledge or on arbitrary assumption, but 
it is always presupposed. The calculation of chances, in a 
word, must be based on a disjunctive judgment, and the hypo 
thetical assertions, which represent the chances, take place 
within the bounds of that judgment. But disjunction, as we 
know (Chap. IV.), implies a categorical foundation. This 
basis of fact is the condition of our assertions about the 
chances. 

35. Take a simple instance. A die has been thrown 
without our knowledge, or is now about to be thrown before 
us. As a previous step to reckoning the chances we must 
make some categoric statements. We must be able to say, 



2l8 THE PRINCIPLES OF LOGIC BOOK I 

The die will fall (or has fallen), and will fall beside in a 
certain way. It must have one side up, and this, whatever else 
it is, will at least be not other than all these six sides. It must 
have a quality determined as what is common to the six, and 
not determined as what will be none of them. On this cate 
gorical foundation all the rest is based, and without it there is 
no possibility of advance. 

This result has a most important application. There is no 
probability before all reality. There is none which does not 
stand on a basis of fact assumed or actual, and which is not a 
further development of that basis. 

36. We have seen the foundation of our disjunctive 
judgment. What is it that completes it? It is of course the 
setting out of exclusive alternatives. These alternative possi 
bilities are given us in the various hypothetical judgments 
which we are able to make as to the number on the face which 
we know is lying uppermost, or which will so lie. We have 
now a disjunctive judgment, enclosing an exhaustive statement 
of exclusive possibilities. But we have not yet got to mathe 
matical probability. To reach this a further step is to be made. 
We must take the possibilities all to be equal, or, if they are 
not equal, we must make them comparable. 

37. The possibilities must all be equally probable. What 
does this mean? It means that there is no more to be said 
for one than there is for another. The possibilities are 
each a hypothetical result from certain conditions ; and these 
results are equal, when, in the first place, they follow each 
from no more than one single set of conditions, and when 
in the second place, I attach no more weight to any one 
set than I do to the others. When, in short, I have no more 
reason for making one hypothetical judgment than I have 
for making any other, they are possible alike and equally 
probable. 

X must be a or b or c. X qualified by certain conditions 
would be a, if qualified by other conditions would be b f and so 
with c. If in my knowledge I have any ground 35 for taking X 
in one set of conditions rather than in another, then a, b, and c 
are not equally likely. If such a ground is absent, then they 
are equal. Again, if X will give a with a single set of con 
ditions, and b or c with more than one set, the chances are 



CHAP. VII THE MODALITY OF JUDGMENTS 219 

different in the different cases. 36 Otherwise they are the 



same. 



38. If the separate alternatives are not found equal, then 
we must either give up our attempt to reckon chances, or must 
find some common unit of value. We must analyze one possi 
bility, and find, perhaps, that its final result is really two; or 
that, though the final result is one, it will follow from two or 
three sets of conditions, and hence can stand for two or three 
units. In these cases there were two hypothetical judgments 
which we joined in one. Again, if we can not divide the 
greater, we may join the smaller. By considering two or 
more alternatives as one, we raise the whole to a unit of 
higher value. 

39- Where we have a disjunction the alternatives of 
which are equally likely, or are reduced to alternatives which 
are equally likely, we can state the chances. Since we have 
the same ground to think every possibility true, the probability 
of each is just the same quantity. In our knowledge they 
divide the actual fact between them equally. The reality then 
we represent as unity, and each alternative possibility we 
represent by a fraction, of which the denominator is the number 
of equal alternatives, and the numerator is one. Against our 
belief in the general fact we have nothing to set. Against 
any one of its developments we have to set the whole of the 
others. 

40. Take the instance of the die. We know it will fall 
in a certain way. So much is categorical, and we have now to 
determine the further possibilities. What are the conditions 
from which in each case our hypothetical results proceed? 
They are first the general character of the fall, those positive 
and negative general conditions from which comes a fall with 
one of the six faces up, and no more than one. Do these 
furnish a ground for making one fall more likely than others? 
Clearly they do not. 

The general conditions, which we have considered so far, 
are known to exist. The fact must take place in such a way 
that these conditions will be realized. But, beside this known 

* Wolff has expressed the principle very well, " Probabilior est pro- 
positio, si subjecto predicatum tribuitur ob plura requisita ad veritatem, 
quam si tribuitur ob pauciora." 



22O THE PRINCIPLES OF LOGIC BOOK I 

element, there are a number of circumstances about which we 
are in doubt. The particular throw must be the result of one 
particular position of the die, the contraction of particular 
muscles in the thrower, and the character of the surface which 
receives the fall. The number of different sets of conditions 
which would lead to the result, is very great, and in part per 
haps unknown. 37 Still this makes no difference. They are all 
at least known or assumed to be compatible with the reality, 
and they lead indifferently to any one of the six results. 
With respect to each face we have exactly as much reason 
to think it uppermost, as we have to think any other face 
uppermost. The chances are equal; and since they are six, 
and since they divide the sphere of a single unity, they are 
each one-sixth. We have a certain reason to expect one face, 
say for instance four, but we have the same reason five times 
over not to look for four. 

41. Now suppose one face loaded. The final possibilities 
are still six in number, but their value is not equal. There are 
more sets of conditions, which would lead to the loaded face 
being downwards, than sets which would bring the opposite 
face into the same position. I have thus more reason to look 
for one than I have to expect the rest. My task is now 
to get a fresh unit by breaking up some or all of the 
possibilities. If I succeed in this, the whole will again be 
divided into fractions expressing the respective chances, but 
these fractions will be unequal. The units of reason to 
look for each face will be more in one case and less in 
another. 

42. The above is, I think, the entire foundation of 
the doctrine of chances. It is perfectly simple and entirely 
rational. It need not appeal as a warrant for its existence to 
those splendid successes which make it indispensable. Rightly 
understood its principles by themselves are abundantly clear 
and beyond all controversy. 

We have no cause and no right to follow the theory even 
into its first and most simple applications, but we can not 
pass over an important point. Where we can not determine 
numerically the conditions of different possibilities in a way 
that is direct, we can proceed indirectly. For example, in 
the case of a loaded die, I may have no data for calculating 



CHAP. VII THE MODALITY OF JUDGMENTS 221 

the chances, since I may not have accurate knowledge of the 
conditions. But I can go to the result in another way. I 
can throw the die a number of times, and, setting down the 
numbers for every face, can then in view of an unknown throw 
state the fractions in accordance with the relations of these 
numbers. But this inverse process implies no appeal to a 
different principle. 

Let us perceive its nature. I assume that I have no reason 
whatever to think the unknown throw, which I wish to deter 
mine, different from the rest. I therefore take it as simply the 
same. But I can not take it as the same as any one, 38 for then 
it must be different from others. It is therefore the same in 
its general character, with possible alternatives which fall 
within the data supplied by the actual series. It remains to 
reduce these possibilities to fractions. 

We are obliged to reason from effect to cause. If a known 
cause A would produce a given effect, and if we have no 
reason whatever to believe in any other cause, 39 we assume we 
can go from the effect to A. The effect we are considering is 
a certain series, and the question is, Do we know the one cause 
which would produce that series? 

I hardly think we do. However long and however regular 
the series may be, we can never say that there is one and but 
one disposition of elements, which leads and must lead to the 
series we have seen. And if we could say this, and assume 
beside that the unknown throw will follow from this deter 
minate cause, then there would no longer be any probability 
in the case. The whole thing would be understood and cer 
tain. But we obviously do not know this one special cause 
which would produce our series. We can determine no more 
than its general character. It must be such a cause as would 
give a series possessing certain numerical relations. And we 
assume that an arrangement of which we can say, " It is the 
real possibility, with respect to any throw, of chances disposed 
in those numerical relations," is such a cause. It is therefore 
probable that the series is the effect of this cause. And since 
(by another assumption) we have no reason to believe in any 
other cause, it is certain that the series has resulted from this 
cause. And since again we assume that the unknown throw 
has a general character the same as that possessed by the 



222 THE PRINCIPLES OF LOGIC BOOK I 

series, we proceed without any further hesitation to reckon its 
chances directly. 

43. We may notice in passing that, if we had to suppose 
that the series might arise from some other cause, beside the 
one we have already mentioned, a further complication would 
be at once introduced. 40 But this we need not consider; for 
the most simple case of inverse or inductive probable reasoning 
proceeds as above, and is sufficient to show the principle 
employed. And we may notice again that there are assump 
tions involved, which we shall have to discuss in a following 
section. We may here remark that, if we are not satisfied 
with a probable conclusion, if we go on to assert that the series 
has actually been produced by a cause of a certain character, 
which will operate again in the unknown throw, our assump 
tion is doubtful, if it is not false. But, to resume, however 
this point may be decided hereafter, the nature of our reason 
ing on chances is the same in inductive as it is in deductive 
probability. The chances of the new throw represent the pro 
portion of our grounds for belief. The fact that these grounds 
have been supplied by a series, and the reduction of that 
series to its actual or probable cause, makes no difference to 
the principle. What grounds have we got for determining the 
throw that is to take place? Those grounds which as causes 
have determined the known series. What are those grounds? 
They are those from which we go to the series in hypothetical 
judgments. What is the nature of these? We do not know 
them exactly, but, so far as known, we can arrange them as 
units, and groups of units, which stand to one another in 
certain relations. But grounds for belief, which stand to one 
another in numerical relations, are what we mean by the 
chances of the throw. 

44. From this hurried account of the general nature of 
what has been called the Logic of Chance, we pass to the 
removal of erroneous ideas. It is evident, in the first place, 
that probability does not affirm about the fact as such. The 
event may be past and absolutely fixed, but our alternatives 
continue to be truly asserted. But, on the other hand, if the 
chances are not facts, are they nothing at all but our belief 
about facts? Is probability simply the quantity of the belief 
we happen to possess? No, that once more would be in- 



CHAP. VII THE MODALITY OF JUDGMENTS 223 

correct. We need not trouble ourselves to discuss the mean 
ing assignable to "quantity of belief," for the whole idea 
must be banished at once. The amount of our belief is 
psychological, the probability of a fact is always logical. No 
matter what it is we happen to believe in, whether it exist or 
do not exist, our belief itself is unaffected. But an asser 
tion about chances must be true or false. It depends on fact 
and refers to that, though it is not true or false of the special 
fact in question. 

45. We have not contradicted ourselves. Probability 
tells us what we ought to believe, what we ought to believe on 
certain data. These data are assertions about reality, and the 
conclusion as to what we ought to believe results from a com 
parison of our grounds for belief. Since these grounds are 
the conditions of hypothetical judgments, the judgments again 
must be true or false, and they rest upon categorical bases. 
In these two points, (i) the general ground of the disjunction, 
and (ii) the special grounds of the alternatives, probability is 
true or false of reality. We call it " objective." 

On the other hand probability is " subjective." If I say 
"The probability of S P is y 1 ^," this may be true although 
S P is impossible. It is true to-day, and to-morrow it is 
true that the chance is -jfo, and the next day |. The belief 
must change with my varying information, and it is true 
throughout these variations, and is true though every one of 
them is an error. How can this be " objective "? It seems to 
lack the very differentia of truth. 

The solution is obvious. Within the probability 41 what is 
true or false is not the premises but the conclusion I draw 
from them. Given certain assumptions, there is only one way 
of stating the chances. Given certain grounds for belief or 
disbelief, there is only one correct inference to the fractional 
result. This result is neither " subjective " nor " relative," 
if those phrases mean that it might be different with different 
men. From certain data there is but one conclusion, and, if 
this is different in different heads, then one or both of these 
heads is mistaken. Probability is no more " relative " and 
" subjective " than is any other act of logical inference from 
hypothetical premises. It is relative to the data with which 
it has to deal, and is not relative in any other sense. It starts 



224 THE PRINCIPLES OF LOGIC BOOK I 

with certain assumptions about the nature of the fact, and it 
tells us what, if we are ready to take these assumptions as 
true, we ought to believe in consequence. If this is not to 
be " objective " and necessary, then farewell for ever to both 
these phrases. 

Probability as such is not true of the fact, but it always 
has a reference to fact. It is concerned with certain special 
deductions from the basis of propositions which are true or 
false in fact. 42 It certainly is confined to those deductions. 
But it possesses, when kept within its own limits, truth abso 
lute and unquestionable and that never can vary. 

46. Probability is neither simply " subjective " nbr yet 
simply " objective." This vicious alternative is the first of 
the errors we have to dismiss. It is allied to another elemen 
tary mistake, which must next engage us. 

It is mere misunderstanding which supposes that chance 
involves a series, and that the logic of probability is essentially 
concerned with statistical frequency. It is mere error which 
finds the necessary meaning of " The probability of S P is 
i," in " Once in a series of four events S P will be true." 
This mistaken theory contains some truth, but has taken one 
part of the truth for the whole. 

47. Is the series real or is it imaginary? Let us first take 
it as real, as something that exists, has existed, or will exist. 
Must the judgment " The chance of S P is J," refer always 
and essentially to an actual series? The assertion would be 
preposterous. The event S P may be hypothetical. It may 
have a probability of J on the ground of assumptions which 
we know are not true. Where is then the real series? The 
event again may be unique. The chance of my dying before 
I am forty is, say, ^. Does this mean that if I die three 
times, one case will realize the possibility? The event once 
more need not be an event. It need be nothing which ever 
could happen in time, and we should deceive ourselves if we 
gave it that name. " It is even chances that the soul is noth 
ing but a function of the body " : the probability is J. " It is 
one to two that God is a person " : the probability is -J-. " It is 
one to ninety-nine that the will is free " : the probability is you-* 

* Of course I do not mean these fractions as an expression of my 
opinion. 



CHAP. VII THE MODALITY OF JUDGMENTS 225 

It may be said, no doubt, that the figures are illusory, and that 
we can not find any unit of value; but I hardly think this 
objection can stand. Admit that the case is highly improbable, 
it still is possible that in the mind of some man the grounds, 
present for and against such judgments as these, might be 
reduced to a common denominator. How can we deny it ? and, 
if we do not deny it, what becomes of our series? 

48. The series clearly can not be real. Let us take it as 
imaginary. The question is then, Is such a fictitious imagi 
nary series the proper way in which to represent probability? 
Can we say, It is my meaning, or the only true way in which 
to render my meaning? This, I think, would be an absurdity. 
It will not stand a serious examination. 

Probability can indeed be always represented by a fictitious 
series. " It is two to one he is guilty " may be rendered by 
saying, " Two times out of three a verdict on such evidence as 
this would be right." Even when the possibility is unique, we 
yet can abstract from that quality and say, " Men such as I am 
would die before forty two times out of three." Nay, even 
when we leave events altogether behind us, we still can keep 
up this mode of expression by a fictitious series. Imaginary 
judgments here become the events. " It is even chances the 
soul is a bodily function " may be translated by " In making 
such judgments as this a man would be wrong through one 
half of the series and right through the other half." 

But is such a way of putting our meaning the real and 
essential idea we entertain ? When we wish to be correct, are 
we forced so to speak? It always is possible, but is it always 
necessary? Is it always even natural? And then there re 
mains a question in reserve, Is it not incorrect? 

49. Let us begin with its possibility. Why can we 
always express the chances by making use of a fictitious series? 
For this reason. When the grounds from which we reckon 
are considered as causes, we are accustomed to suppose that 
their issue in a series of phenomena will exhibit the same 
numerical proportions that our fractions possess. If so, then 
on one side the causes (or cause) of the series and, on the 
other side, the series itself will answer to each other. We say 
what we have to say of the cause, indifferently, either by 
stating its effects, or by setting out the reasons it gives us to 



226 THE PRINCIPLES OF LOGIC BOOK I 

expect one effect and not another. This is natural enough 
where the fictitious series is imagined to be real. It is not so 
natural with unique events, where the series strikes us as 
specially manufactured to express the chance. It is still less 
natural where the possibility itself is not an event, and the 
series is nothing but the series of judgments. But even here 
it still is possible. Since psychologically the grounds are 
causes (p. 545), since, in other words, the logical reasons 
which necessitate the result are what produces the fact of the 
judgment, I can imagine, if I please, a series of judgments, and 
say, Since these numerically answer to the reasons I have, 
therefore such a numerical part will be true. The expression 
by a series is here quite unnatural, but it still is possible. 

50. The issuing of a certain series is only one way of 
putting probability. It is sometimes a natural way; it is 
sometimes a not unnatural way; it is sometimes most un 
natural. But it is never the right way ; it is never more than 
a manner of statement; it is never the real meaning and in 
tent. Even when I start from an actual series, I must leave 
it before I can get to probability. I must go to its cause by 
what is called a method of reduction, by an inductive hy 
pothesis. And I can not simply define this cause as that which 
either has issued, or will issue, in a certain series. I can not 
do the first, for that would be certainty and not probability. 
And I can not do the second without an assumption which I 
am unable to justify. 

It is obvious, in the first place, that to take a series, and 
to say " The cause which has produced this series has pro 
duced this series " is merely frivolous. On the other hand, if I 
add " will produce this very same series on other occasions," 
that is not frivolous, but is either irrelevant or else unjustifi 
able. If it means " In another case where the conditions are 
not discrepant, the same cause will be followed by the same 
effect," that assertion is true but is quite irrelevant, because 
merely hypothetical. For in an actual fresh case I do not 
know the fresh conditions, and, if I did, I do not know what 
the old cause specially is. I do not know the actual cause (or 
causes) of the former series. I do not know that these are 
present again in the unknown case. I do not know what 
conditions the fresh case brings ; and, if I did, I might be 



CHAP. VII THE MODALITY OF JUDGMENTS 227 

unable to deduce the result from the complication of elements. 
In short I can not go from a given series to an unknown 
series or an unknown case. To reason directly is of course 
impossible, and I can not reason indirectly through the cause, 
because I do not know the actual cause in one case or the 
other. Its general character, to a certain limit, I do know in 
one case, and assume in the other, but this general character 
does not imply a series, and the individual cause itself I do 
not know and so can not use. 

The upshot of this is that within probability you really 
have not got the effects on one side and the cause on the other. 
If then you give as the essence of probability the produc 
tion of a series with certain marks, you go beyond what your 
data will warrant. For your actual series has now 43 ceased to 
be taken as a series of events produced in time. It has degene 
rated into a set of conflicting reasons, possibilities as to an 
event of a certain sort, which in default of detailed information 
I use in order to determine my judgment. My probabilities 
do not represent a series as such. I now have nothing what 
ever but conflicting grounds for belief and expectation, grounds 
for belief as to any fresh case or number of cases that have the 
general character of my series. And these fractional reasons, 
which are all I can work with, are the same in any one new 
instance as in any number of new instances. Thus the sup 
posed differentia of an imagined series, in the first place, 
would add nothing to the probability which already exists apart 
from the idea of any series. But, in the second place, if it 
does add, and if it goes on to say that the series must have a 
character answering to the expectation, then it adds what is 
false. 

51. And with this we come to an obstinate illusion. 
There is a common idea that, if you know the chances of any 
set of events, you really know the character of the actual events 
which are to take place. It is supposed that the series will 
correspond to the fractions. For instance, if we take the case 
of a die, the chance of any one face is J-, and from this we 
argue, " In a series of throws each face will be seen in one- 
sixth of the run." But we have no right to any such assertion. 
Not knowing the cause, knowing only a part while part is 
hidden, we can say no more than that onr information leads 



228 THE PRINCIPLES OF LOGIC BOOK I 

us to expect a certain result. It is monstrous to argue that 
therefore that certain result must happen. It is false reason 
ing a priori, and a posteriori the facts confute it. It is not 
found in experiment that actual runs do always, or often, 44 
correspond exactly to the fractions of the chances. That cor 
respondence is after all the most probable event, but to make 
it more is a fundamental error. 

52. I shall return to the truth contained in this error, 
but at present we must try to get rid, if we can, of the error 
itself. We may expect an objection. " Experiment," it will 
be said, " does not disprove the assertion that is made. That 
assertion is not that in a finite series the numbers will come 
right. They will come right only if we go on long enough, 
and in the long run." But what is this " long run " ? It is 
an ambiguity or else a fiction. Does it mean a finite time? 
Then the assertion is false. Does it mean a time which has 
no end, an infinite time? Then the assertion is nonsense. An 
infinite series is of course not possible. It is self-contradic 
tory; it could not be real. And to say that something will 
certainly happen under impossible conditions, is far removed 
from asserting its reality. The affirmation that an event may 
be assumed to take place in an infinite series, and not outside 
it, would, in the mouth of any one who knew what he meant, 
be a suggestion that the event may not take place at all. 45 

53. I hope I need not protest that I am hardly so foolish 
as to attempt to offer an ignorant objection to the use of 
infinities and infinitesimals within the sphere of mathematics. 40 
I would rather say nothing at all on this matter than appear 
as presuming to doubt the validity of processes employed 
by the greatest men in the exactest of sciences. But I shall 
not so be misunderstood. An objection to the use within cer 
tain sciences of certain ideas must be taken within the limits 
of those sciences. But the use of these ideas outside their 
science carries with it no authority, and, so long as the general 
meaning is understood, may be criticized by men who are igno 
rant of the science in which the ideas give brilliant results. It 
is so with infinity. Outside mathematics an infinite number 
is an idea that attempts to solder elements which are abso 
lutely discrepant. It could not exist until the world, as known 
in our experience, was utterly shattered and transmuted from 



CHAP. VII THE MODALITY OF JUDGMENTS 22Q 

the roots. I could not find an illustration I would sooner 
use to express impossibility. And it is this idea which, out 
side mathematics, is presented to us in the error we are 
combating. Mr. Venn, for whose powers I feel great respect, 
and from whose Logic of Chance we all can learn, holds that 
in the long run every chance will be realized. This " long 
run," he tells us, is an infinite series (p. 146), and (unless I 
very much misunderstand him) he goes on to call it a " physi 
cal fact" (p. 163). His book is much injured by this terrible 
piece of bad metaphysics. He has translated a mathematical 
idea into a world where it becomes an absurdity. 

54. We must everywhere protest against the introduction 
of such fictions into logic, and protest especially where the 
ideas are not offered in the shape of fictions. The formula 
of the " long run " must be banished from logic, and must 
carry with it a kindred illusion in the imbecile phrase, " if 
you go on long enough." " The event," we are told, " will 
answer to the chances." But it does not answer. "Oh, it 
will, if you only will go on long enough. You toss a coin 
and, the chances being equal, if you only go on long enough, 
the number of heads and tails will be the same." But this is 
ridiculous. If I toss the coin until the numbers are equal, of 
course they will be equal. If I toss it once more then, by the 
hypothesis, they become unequal I might just as well say, 
" If I only go on long enough the events will certainly not 
answer to the chances." 4T Your formula is false or else tauto- 
logous. If it means " Suppose the numbers are equal, and sup 
pose I then stop, the numbers will be equal," that is surely 
tautologous. But if it means the numbers will turn out equal 
in an infinite series, then that is false, for such a series is im 
possible.* 

55. But let us turn from the error and see the truth 
which lies hid beneath it. It is false that the chances must 
be realized in a series. It is however true that they most 
probably will be, and true again that this probability is in 
creased, the greater the length we give to our series. What 

* Cf. Lotze, Logik, 437. I may remark that if the formula meant, 
" The series is sure to cross and re-cross the point of equality," then, 
in the first place it would be false, since there is no certainty; and, in 
the second place, such an oscillation is not equality. 

2321. i Q 



23O THE PRINCIPLES OF LOGIC BOOK I 

reason have we for holding these two beliefs? (i) Why do 
we think that the series will probably answer to the fractions ? 
(ii) Why do we think that in a longer series the correspondence 
is more likely? 

(i) Probability, we have seen, is not essentially concerned 
with any series. It is based upon grounds which, even if we 
consider them as real, may not be causal in the sense of pro 
ductive of events in time. They may be causes cognoscendi 
and not essendi. 48 It is when our grounds are grounds for 
belief as to the nature of an agency, which is to produce events 
in time, that we are able to consider them as causal elements. 
And this is the case we have to suppose. 

We know that a series is to be thrown with a single die. 
Let us first take one throw. That will have a cause, and the 
cause is only partially known. We know that it is complex 
and consists of many elements. Of these elements, so far as 
they are distinctly known, five parts are hostile to any single 
face and but one part favourable. The unknown residue, so 
far as it determines the case, is quite unknown; and, though 
it is not indifferent and though it can not be so, yet within 
our knowledge we must take it as indifferent. In the cause 
of the single throw there are therefore, beside the unknown 
factors, one sixth part of the agencies favourable to each face. 

Now take the whole series. That series, before I throw it, 
is as certain and fixed as though I had thrown it already. 
But here again I do not know the causes. About one part I 
know nothing in detail, and so I must take it as being in 
different, although I am sure it is not so in reality. Of the 
rest of the agencies, which I suppose, one sixth is favourable 
to each face, and five sixths hostile. What conclusion can I 
draw as to the nature of the series? Will one agency pro 
duce that result which we suppose it would produce, did the 
others not intervene? Will in each case of the series the sup 
posed majority of agents prevail? We have no means of 
knowing. The series, absolutely fixed, is fixed by what we 
do not comprehend. We must take the possibilities, and 
the possibility for which there is most ground is the likeliest. 
There is less ground to think that in a series of six throws 
one face will be absent, and one twice present, than that 
all should show once. 49 In the latter case we do but make 



CHAP. VII THE MODALITY OF JUDGMENTS 231 

ignorance a ground for complete indifference. In the former 
case we give a preference without any kind of warrant. It is 
not that each face has any sort of claim to come uppermost 
once. It is that no face has more claim than another to show 
itself twice. This is why we think the most likely series, or 
the least unlikely, will be that which corresponds to our 
fractions. 

56. (ii) But why, it may be asked, does the length of 
the series increase this probability? Does the greater length 
add any new ground to those we have for believing in the 
correspondence of the events with the chances? No, it does 
not add any. Does it decrease any ground we had before for 
thinking the opposite? Yes, it does do that; and it does it, I 
think, in the following way. The unknown residuum in the 
cause of each throw was assumed to be indifferent. But it was 
not at all assumed to be passive. It supplies the determining 
element in the cause. It decides for one face, though we do 
not know for which face it decides. Now how does it de 
cide? Does it act regularly and in strict rotation, or is it ir 
regular? That we do not know; but, taking the possibilities, 
we believe that those in favour of irregularity are more than 
those in favour of rotation. It is therefore most probable that 
our series will turn out to be irregular. But, since we know no 
reason to prefer any one face, we can not say that any pro 
portion other than strict equality is the most probable. How 
are these assertions to be reconciled? Very easily in this 
way. Owing to the assumed indifference of the causal residue 
the faces will probably appear in their right numbers; but, 
because of its irregularity, their appearance will probably be 
irregular, and irregular to an extent to which we can assign 
no limit. To combine these attributes it is necessary to sup 
pose that the whole series will be most probably regular, but 
will contain periodic irregularities. The greater the irregu 
larity becomes, the less grows the chance of a final regu 
larity, unless the series is proportionately lengthened. There 
fore, since we can fix no limit to the irregular sequence of the 
faces, we conclude that, the longer the series becomes, the 
greater becomes the probability of a regular result. And this 
is a rational, and necessary conclusion from our imperfect 
data. 



232 THE PRINCIPLES OF LOGIC BOOK I 

57. It is true that, if you make a series longer, you de 
crease the chance of irregularity. It is true that, if per 
impossibile the series were so long that, in comparison with 
its length, every possible abnormal run was a period which 
other periods might easily balance in the completed cycle if, 
I say, per impossibile this phantom could be real, it is true 
that the above chance of irregularity would vanish. If we as 
sume that what we do know gives us reason to believe in a 
series correspondent to our fractions; if we next assume, by 
virtue of a fiction, that the unknown residue gives no reason 
to believe in an unbalanced irregularity, then on these assump 
tions we may go to a conclusion, and we have no ground to 
disbelieve the statement that the series will exhibit the relations 
of the chances. But the first assumption is based on ignorance, 
and the second is based on a known impossibility. 50 If we 
mean to speak about a series of events that could ever happen, 
we can say but this. It is certain there will be a series, each 
throw of which will give a single face. It is possible that in 
a series of any length but one single face should appear 
throughout. No arrangement is impossible. It is most prob 
able that the events will answer to the fractions, but against 
that probability there still remains another consideration, the 
chance arising from the possible irregularity of one part of the 
causal elements. This fraction is diminished by each increase 
of the series, but it does not disappear and it can not disappear. 

58. We do not know that in the long run the events 
will correspond to the probabilities. We do not know that, 
if we go on long enough, every chance will be realized. It is 
mere superstition which leads us to believe in the reality of 
the fiction which gives birth to these chimaeras. When I see 
the demonstrations, offered to gamblers against a bank, which 
prove to them that in the long run they can not but lose, I say 
to myself, On which side do I see the darker illusion? And I 
answer, On both sides the illusion is the same. For what is 
the root of the gambler s " system "? Is it not his belief that 
independent events are affected by each other? But this 
belief is a strict deduction from the premises offered him. If 
he really must lose, if there really is a cycle in which the 
chances must all be realized, then, let him observe the begin 
ning of the cycle, and mark the irregularities, and he surely 



CHAP. VII THE MODALITY OF JUDGMENTS 233 

must win. Since to equalize the numbers the end of the 
cycle must balance the beginning, he can speculate on that 
balance and his " system " is right. " Oh, but it is wrong, for 
the series is not finite. It is only after an infinite duration of 
play that the balance is struck. It is absurd to say he can be 
sure of winning." But is it not then equally absurd to say 
that he is sure to lose? If you mean he must have lost by the 
end of his life, you have just admitted your assertion to be 
false. If you mean he must have lost when he has got to the 
end of infinite time, confess that your meaning is something 
like nonsense, and that the gambler is right in imagining that 
you, as a rational man, must mean something else. The 
truth is that your common assumption is false. There is no 
must about it. The chances consist of grounds for belief in 
the nature of a series no event of which is known. And all 
they tell us is this: that we have more reason to expect one 
thing than we have to expect another, and that the increased 
length of the series proportionately decreases a reason for 
doubt, which never quite vanishes. 

5Q. 51 I must not be suspected of a desire to intrude into 
mathematics if, in this connection, I venture to remark on a 
well-known paradox. I am to toss a coin, and to go on toss 
ing so long as I throw heads and nothing but heads. I am to 
receive 2 if I throw head once ; if I throw head twice I am 
to win 4; for three successive heads I get 8, and so on 
accordingly. The series is supposed to have no limit except 
the appearance of a tail. And the question arises, how much 
am I to pay for the privilege of one single trial ? The answer 
given is, An infinite sum; for it is possible I may throw an 
infinite series of nothing but heads (vid. De Morgan, Proba 
bilities, p. 99). The reasoning on which this conclusion seems 
to rest is exceedingly simple, and I need hardly say that I do 
not doubt its perfect validity within mathematics. And I think 
I see that no other answer can possibly be given. Unless an 
arbitrary limit is fixed, I may be allowed to say in all humility 
that I think I understand that, if this possibility has any 
value at all, then the worth of my chance is either incalculable 
or else is infinite. If this answer is given me by a special 
science, I dutifully receive it as true within that science. 
But if I am told that in actual fact the result is true, I 



234 THE PRINCIPLES OF LOGIC BOOK I 

must be allowed to protest. I must be permitted to remark 
that the reasoning is absurd and the result is nonsense. I do 
not mean merely that it is absurd if we take it as a practical 
precept, because a man can not live for ever, and all the 
money in the world is finite. I mean that it is a theoretical 
absurdity. It is not true ideally any more than really. Since 
an infinite sum is an impossibility, the infinite series can not 
possibly be thrown. There is no chance whatever. There is 
no fraction at all. It is nothing I could win. It is nothing 
I can expect. It is nothing for which I can reasonably pay. 
The result is a deduction from premises known to be false 
and impossible. 

It is idle to answer that the problem is " stated in the 
ideal form " (Venn, ibid. p. 137). There is a difference surely 
between ideals which as such do not exist, because they are 
abstractions, and ideals which are downright self-contradic 
tions. It is one thing to say, " There is a connection between 
abstract elements, so that when one of these is found as a 
real quality we shall have the other," and another thing to 
continue this assertion, when we know that the first of these 
elements is self-contradictory and could not possibly be any 
quality of reality. In this latter case what is true of fact can 
not be the consequence of an impossibility, but only the basis 
of the hypothetical judgment. Neither antecedent nor con 
sequent is taken as real or even as possible. But in a com 
mon abstract judgment the antecedent is taken as at least 
a possible quality of the world. 52 Mr. Venn perhaps would 
question this difference between an abstraction and an im 
possibility, and would perhaps assert that an infinite series is 
really possible. In any case I must be allowed to protest 
against the invasion of logical reason by mathematical fic 
tions. If an infinite series is thought possible, we should be 
told how it can be possible. If it is not thought possible, it 
should not be offered us as if it were. 

60. There are other points in the theory of chances 
which have logical interest, but we have no space to discuss 
them here. We have said enough to make clear the relation 
in which that theory stands to our general principles. We 
have to avoid the fiction of the infinite long run, and the 
vicious alternative of " objective " and " subjective," and the 



CHAP. VII THE MODALITY OF JUDGMENTS 235 

false assumption that the essence of chance involves a series 
of events in time. If we keep clear of these pitfalls, the truth 
is by no means difficult to reach, and we hope above to have 
stated it clearly in its general form.* 

61. There is an aspect of modality we have neglected 
to notice. The omission was intentional, and the mention of 
this aspect has been reserved for the present place. There is 
an old doctrine which connects universality with necessity, 
and that doctrine is true. The necessary we saw was the 
ideal consequent, and such a consequent can not come except 
from an ideal antecedent. You never can say " B follows 
from A," " is because of A," " must be, given A," unless A is 
present in a determinate form. A must be a content without 
any mixture of mere sensuous conditions. 53 It must be 
ideal, abstract, and so universal. If the ancient doctrine on its 
logical side may suffer some loss, since necessity becomes for 
logic hypothetical, yet it stands all the firmer. The " because " 
can not couple anything but universals. 

62. We may notice an error which creeps in with this 
truth. 5 * The antecedent in necessity must be universal, but it 
need not be more universal than the consequent. Where we 
say " because " we do not always appeal to anything more 
abstractly general than that which follows from our reason. 
" A must be equal to B, because C is equal to both B and A," 
" A must be removed by one foot from C, since B, which 
touches both in a certain manner, is one foot long." The 
consequence is not less general than the antecedent, and we 
deceive ourselves in thinking it always must be so. 

No doubt in the cases where you say " because " you may 
find what we call the principle of the sequence, and that of 
course must be more abstract than the actual consequent. 
But the principle is not the antecedent itself. It is the base 
of the general connection, not the sufficient reason of the 
particular consequent. There is no more need for the con 
sequent to be more concrete than the antecedent, than there is 
for the effect to be more special than the cause. These ideas 
are nothing but kindred illusions (Book III. Chap. II.). 

*The books from which on this subject I have learnt most are 
Lotze, Logik; Sigwart, Logik; Wundt, Logik; Jevons, Principles of 
Science; Venn, Logic of Chance; De Morgan, Probabilities. 



236 THE PRINCIPLES OF LOGIC BOOK I 

63. We shall have to return hereafter to this point, but 
have been right to anticipate here the conclusion. We have 
indeed begun some time back to anticipate the conclusions we 
have to reach in the following Books, since already unaware 
we have entered their territory. Silently before in the second 
Chapter, and now almost explicitly we have made the transi 
tion from judgment to inference. In both the latter kinds 
of modality we reason openly. The possible is that which 
we argue would follow from certain premises, part of which 
are taken as true. The necessary is that which we infer must 
follow, if its grounds are premised. It was in this sense 
that possibility was one kind of necessity. In both alike we 
deal with conclusions, reasoned results from given data. In 
logic we find that a necessary truth is really an inference, and 
an inference is nothing but a necessary truth. This is the 
secret which we hardly have kept, and with the discovery of 
which we may pass at once to our Second Book. 



ADDITIONAL NOTES 

doctrine . . . falsehood." This statement needs correc 
tion. It is true that there are no degrees of the fact of logical 
assertion (cf. Chap. I, 15 (rf)). It is true that you can not alter the 
logical mode of asserting S P without altering S P itself. On the 
other hand it is not true that you can abstract the assertion from the 
asserted content See Bosanquet, Logic, I, 363 foil. On the doctrine of 
degrees of truth I may refer the reader to my Appearance and Essays. 

2 " The reference or the denial itself," i.e. taken in abstraction as 
a mental fact. 

3 " The possible . . . whatever." This sentence must be corrected. 
It is better, once more here, to substitute " conditional " for " hypo 
thetical." Further, both " conditional " and " categorical " should be 
taken as falling under " necessary." The merely categorical is the 
lowest form of necessary (Chap. II, 75 foil.) On the whole subject 
see Bosanquet, Logic (loc. cit.), and K & R, pp. 114 foil. 

4 "Where necessity is internal &c." So far as the totality is a 
system which is because of its internal necessity, and is viewed in 
that character, the above statement will not hold. 

5 " Because." On " because " see T. E. II. 

6 " We must admit fact." This, I think, is wrong. Logic, I agree, 
should abstain from dealing with the ultimate problem. But on the 
other hand logic most certainly should not admit and assume that its 
"because" is not real. To regard logical implication as merely 



CHAP. VII THE MODALITY OF JUDGMENTS 237 

" ideal " is an error. See T. E. I. And we must remember that " fact," 
like "existence," is ambiguous. See on Chap. II, 2 and 4. 

7 " When it ceases to be merely necessary." " Merely " here seems 
misleading. The "necessity" itself is in any case not hypothetical. 
Cf. 12. 

8 On the difference between " if " and " because " see T. E. II. 
This 10 is largely erroneous. It wrongly identifies " reality " and 
" fact," and it wrongly assumes the existence of judgments which really 
are not mediated. See ibid. 

9 " The argument from principle." This surely is vicious. There 
are no "mere ideas" (see on Chap. I, 10). Logic must assume that 
the ideal is real somehow and somewhere. The idea that did not 
qualify Reality would certainly fail to be an idea. 

As to the " argument from usage " I agree that " must " can be 
used to weaken an assertion. But this is where we have an implica 
tion that our " because " is only partial and is so defective. In an 
immediate certainty (e.g.) we are sure that we are right somehow 
though the " how " is not specified. At times, again, we specify the 
"how" in order to throw doubt on it. We mean that we have this 
reason, and no more than this. Cf. Bosanquet, Logic I, 379, and 
K & R, pp. 122 foil. As to the " ultimate premises " which are 
known immediately, such things I consider to be illusions. 

10 F or " conditions " see on 24. 

11 "Assumed to be compatible." These words (Cf. 13, 14, and 
21 ) were overlooked by some critics, who in consequence objected to 
my account on the ground that I had overlooked the possibility of 
incompatible conditions. But on the contrary my account assumes, 
not only that I have all the conditions, one part of which is taken 
as actual, but also that the rest are, in my knowledge, not incom 
patible. This point, however, should have been brought out more 
clearly, as it was later in Appearance, Index, s. v. Possible. 

12 " Taken to exist " should be " taken to be actual." 

13 "Our basis of fact &c." But we must remember that, for an 
idea to be an idea at all, it can not, so far, be unmeaning. We have 
therefore with every idea an assertion that it possesses, so far, the 
character of Reality, and further is real somehow. No possibility 
can rest fundamentally on mere privation. The assumption that, be 
yond the above, an idea is possible further, may, however, in a sense, 
be so grounded. Cf . on Chap. Ill, 9- What is certainly wrong is to 
use " possible," where we are simply ignorant as to impossibility abso 
lute or relative. See Appearance, Chaps. XXIV and XXVII. For the 
meaning of "possible" cf. T. E. XI and the Index of the present 
volume. 

14 "We have no reason &c." This must be corrected. For in the 
first place (i) if the idea has a meaning it, so far, is real. And (ii), 
if there are any facts which suggest a further reality, we have in these 
surely an additional ground. The "most unfavourable view," to be 
rational, would have, I think, to rest on the positive knowledge that 



238 THE PRINCIPLES OF LOGIC BOOK I 

body and mind are in themselves, directly or indirectly, inseparable. 
The following words, " are idle frivolities . . . men," are almost 
certainly a quotation, and are so marked. But I can not recall the 
source. 

15 ]7 or t m m supposed." This statement goes too far. The cor 
rect account of " hypothetical possibility " is, I think, as follows. If 
you take the actual (or fully grounded), to which the possible is 
anywhere opposed, and degrade this actual to possible your first 
possibility becomes then possible at a further remove. Or (it is the 
same thing) take a possibility as actual and then, in consequence, 
(on and against this) an even less grounded possibility may be 
doubly or possibly possible. Cf. T. E. XI. 

16 For this question see Note 6. 

17 " May claim no existence . . . possibility." But, since it must 
be thinkable, it must also to a certain point be real and possible. 
See preceding Notes. 

18 " Complete revolution," which revolution I consider necessary. 

19 By " men " I meant here " finite beings." And the same remark 
applies lower down to " human." In 18 foil, we should bear in mind 
the following. The ordinary abstract judgment does not deal ostensibly 
with possibles, since it assumes a world in which these are actual. 
And it is better not to call it "hypothetical," since the attitude of 
supposal is not there. We need not, again, take the supposed as 
possible, though clearly, if in no sense it were so logically for us, 
we could not in fact suppose it. 

The possible, as the partly grounded, is negative of a limited 
known reality, in the sense that not all of the possible is there. A 
part falls beyond and is actual only in another world. Thus the 
possible belongs to both of these worlds at once. But it is not 
a member of the first limited world, because it is only that in part 
and also is more. And hence alternative possibilities (r 1 , r 2 , r 3 ) are 
all possible, though they can not all at once simply qualify our limited 
reality. Thus the possible and the actual may or may not exclude 
one another. The assertion, e.g. that the actual Universe is not possible 
is ambiguous. And it is false if it means to go beyond the denial of 
mere possibility, and to suggest that the "more" must, in every sense 
and everywhere, exclude the " less." Cf. T. E. XL 

I shall return ( 28) to the dangerous error which takes " possible " 
as the contradictory of "impossible." Cf. ibid. 

20 Sections 20 foil, need correction throughout, but I need not 
repeat everywhere in detail what has now been laid down in general. 

21 " Less actuality than . . . the necessary." But obviously, if and 
so far as the " necessary " is taken as the " fully grounded," this is the 
case. 

22 "Privative judgment." This must be corrected. See above on 
13, 14. " Bare possibility " is that which is general as against that 
which is possible here or there. Or it is that which possesses no more 
than the least amount of the character required for possibility. 



CHAP. VII THE MODALITY OF JUDGMENTS 239 

23 On " real possibility," and on the " potential " see Appearance 
and Essays (the Indexes), and cf. the Index of this work. 

24 On Ground and Conditions cf. T. E. II. This section (24) is 
in part wrong because it once more ignores the various orders of 
reality (see Chap. II, Note 3). The conditions are the diverse elements 
of a grounded whole, and therefore are, in some sense and somewhere, 
actually real. Where in a limited "actual" you have a part of the 
above totality taken as there present this limited reality is the "real 
possibility "of the rest, though the rest is not actually there present, 
or at least is not taken as being so. In what follows, on "the 
cause," I had in mind, I presume, the cause taken as mere existing 
fact. But some correction is required here. See Bosanquet K & R, 
pp. 20-1. 

25 " Permanent Possibilities." Cf. Appearance, pp. 124-5. 

26 I was not denying here that the Hedonistic End can be formu 
lated correctly. I was merely giving another instance where the use 
of the same delusive phrase takes the place of thought. 

27 " The assertion &c.," that is, " apart from designation." See 
the Index, s. v. Designation. 

28 "These predicates reflection." But see Note 6. Further, with 
regard to the statement, "And to a knowledge . . . possible," we 
must ask, How far and in what sense would perfect knowledge 
contemplate unreality at all? It would do so, I presume, only so far as 
it remained discursive knowledge, and then only so far as the un 
reality is relative. 

In the next paragraph for "directly vanishes" "simply and 
directly" would, I think, be better. 

29 "On the Impossible see Appearance (Index), and T. E. VII. 
The impossible must of course have enough meaning to be what 
might perhaps be called " possibly possible." 

30 " The real does not ... incompatible." Under " incompatible " 
here will fall the case of the absence of some predicate. In the next 
sentence the words "Because . . . else is" go, I think, certainly 
beyond the first appearance of necessary impossibility. All that, so 
far, is present there, seems to be re-assertion with an exclusion on the 
ground of a " must." 

si On Privation cf. Note 13. And see T. E. VII and VIII and 
Appearance (Index). The main point here is this that a mere 
absence or exclusion is nothing at all. " Possible " and " impossible " 
are hence not mere contradictories. If the impossible is not possible 
enough to have a meaning, it is logically nought. Total absence of 
compatibility with the Real means sheer nothingness. The real ques 
tion is as to further compatibility, and whether we have positive 
reason, and if so, how much, to assume that, if there were "incom 
patibility," that would appear. In other words a mere failure to 
exclude is logically nothing, and so again is all mere exclusion whether 
of what has sense or is senseless. 

The doctrine of 28-9 is, I think, right in the main though some 



24O THE PRINCIPLES OF LOGIC BOOK I 

correction is needed. For "pass unabridged" (28) see Note n. 
For the rest, no suggestion, if it is a logical suggestion, can be 
meaningless and elicit no answer at all from Reality. Whether an 
utterly meaningless suggestion is possible as a psychological fact it 
would be idle here to ask. In logic the suggested must have a 
meaning, and must to some extent be real, and the question will be 
as to its further reality. Here, if we have but one possibility, that 
is real. If, on the other hand, we have counter-possibilities, the 
question will be as to the value to be attached to each of these upon 
positive grounds. 

Apart from this, the doctrine of 29 seems correct. We have a 
vicious identification of the real, as it is, with the real as we find 
it now mentally present; and we have a vicious conclusion that, if 
there were incompatibility, I should know of it. The reductio ad 
absurdum seems also correct. If anything is possible, then, if there 
is no counter-possibility, it is necessary and real. 

32 " The universal . . . nothing." " Nothing " here should be 
" nothing special." And, in the next sentence, " The universal tri 
angle " should be qualified by "thus held in abstraction." Cf. Chap. 
Ill, 10. 

33 On the doctrine of 31 see above, Note 31. The statement " then, 
I admit . . . judgment" is, we have seen, incorrect, unless we under 
stand what follows to deny the privative character of the foundation. 

34 On Probability cf. Bosanquet, Logic, Chap. VIII. 2. 

35 Instead of " any ground " " any further ground " would be 
more accurate. 

36 The reason of course is that in the latter case b (for instance) 
becomes a common heading of b 1 b 2 &c. 

37 1 think that " perhaps " should here be omitted. 

38 " The same as any one " would better have been " the same 
as any particular one." 

ao " Cause" is taken here not as pure cause (where there is 
reciprocity between cause and effect), but in that looser sense which 
admits " plurality of causes." See T. E. X and Index s. v. Cause. 

40 The " other cause " might, e.g. be loaded dice or some art in 
the thrower. The question thus raised is answered by considering 
the comparative probability of each " cause " ; and no new principle 
is involved here. 

41 i n " Within the probability " " within " is to be emphasized. 

42 In " true or false in fact " we must here, once more, give a wide 
sense to "fact" (see Chap. II, Note 3). What in probability is "sub 
jective" is in short merely the amount of my ignorance and knowledge. 

43 The word " now " should be omitted, as it might be wrongly 
taken in reference to "go beyond." 

44 The words " or often " can not, I think, stand. For, even if they 
were true, they would be superfluous. 

45 By " be a suggestion " what I meant was " be at least a sugges 
tion. 



CHAP. VII THE MODALITY OF JUDGMENTS 24! 

46 Cf . 59. I should also have said that I do not pretend to 
know the sense in which within mathematics the word "infinite" is 
taken. But, so far as I have been able to understand the meanings 
in which, outside mathematics, some mathematicians wish to use 
the term I am clear that these are self-contradictory. 

With regard to " an infinite number," see Bosanquet, Logic, II, 
pp. 161 foil. He points out that it involves the fallacy of counting 
where you have nothing in particular to count, where, that is, you 
count in abstraction from any presupposed whole. This objection 
is in principle the same as that usually urged, which insists on the 
necessary external determination, and consequent internal incomplete 
ness, of any mere counted sum. If you are led in principle beyond 
any whole which you take, that is really the same thing as counting 
without any whole. 

If I may be permitted a word of criticism on the later work of 
Prof. Royce, I would add that whether by the study of mathematics 
he really was carried over to a better world of ideas I am quite 
unable to judge. But the passage by that Lethe, where he crossed, 
led him (so far as I see), here and elsewhere, simply to forget that 
way of understanding (good or bad) which he once shared with those 
who still are able to remember what they learnt. 

47 By aiming at an unnecessary reductio ad absurdum, and also 
perhaps by a misunderstanding of Lotze, I was led here to injure a 
good case by a superfluous and serious blunder. This was noticed 
by Dr. Bosanquet, K & R, pp. 108 foil., and Logic, I, 108 foil. If 
the series is broken off at such a point that it can not exactly coincide 
with the ratio, to take this as being in any sense a deviation is plainly 
wrong. See Bosanquet, Logic I, 350. 

48 Essendi should have been fiendi. 

49 The statement here seems at least wanting in clearness. It would 
be better after "all should show once" to proceed as follows. "It 
is not that each face has a claim to show itself once, or that no face 
has a claim to appear twice. It is that there is less ground for the 
presence than for the absence of deviation from the ratio. This is why 
we think &c." 

50 The words "But the first assumption . . . impossibility" need 
some correction. They should, I think, have been "But the first 
assumption is based on partial ignorance, and the second, as to the 
unknown residue, is not true. We have some reason here to expect 
irregularity, and we find nothing here about a balance." 

51 On 59 cf. the Note on 53- 

62 The sentences " But ... the world," and the two preceding 
sentences are partly incorrect (see on 17). But, since the ques 
tion here is as to existence in fact, the conclusion remains unaffected 

53 "Without any mixture of" should be "freed, so far, from." 
And, in the next sentence, for "so universal," it would be better to 
write "in this sense universal." I should have added here that 



242 THE PRINCIPLES OF LOGIC BOOK I 

necessity has no meaning outside a whole which is a concrete universal. 
Lower down " hypothetical " should, once more, be " conditional." 

54 1 am unable to remember against what doctrine or writer I 
was arguing here, and I can not even say that the error noticed 
exists outside of some misapprehension of my own. See Bosanquet, 
K 6- R, pp. 209 foil. 



BOOK II I NFERENCE 

AT the end of our First Book we made a transition to the 
subject of our Second. Modality took us from judgment to 
reasoning. An inference is either a result or a process. If 
we take it as a result, we saw that it is the apprehension of a 
necessary truth. If we take it as a process, it is simply the 
operation which leads to that result. A truth judged true 
because of something else, and the going to a truth from 
the ground of a judgment or supposition x are what we mean 
by conclusion and reasoning. And this starting-place being 
reached, our right course may seem plain. We should first 
make quite clear the general character of inference, and should 
exemplify this by the necessary detail. And then we might 
proceed at our ease to remove the erroneous doctrines which 
cumber the ground. 

There is an objection to this way of dealing with the sub 
ject. The reader would find his difficulties increased. I do 
not indeed know, after my first Book, if at this stage I have 
any actual reader ; but I am sure, if I have one, that he is not 
eager to make a great effort. We have perhaps nothing in 
front of us so hard to cross as what we have passed over, and 
yet we shall find there are obstacles enough. It is better to 
make a gradual advance. Instead of going at once from the 
facts to the truth, and from that to the removal of erroneous 
theories, I shall aim at reaching an easy vantage-ground, from 
which we may disperse the mass of mistakes which bar our 
progress and harass each movement. This will be the object 
we shall try to gain first. Secure in our rear, we may then 
proceed upon the final position. 

243 



244 THE PRINCIPLES OF LOGIC BOOK II 

We must therefore in the first of the two following Books 
be content with a truth which is only partial. We must 
assume that in every valid inference no less than three terms 
are given to the reasoner. We shall hereafter see that this 
assumption is not tenable, but it will serve as a basis from 
which to operate. It may be a high thing to have no order 
of convenience, to follow the development of the subject 
matter, and to let the reader follow if he can. But it is an 
end more possible, and perhaps not much lower, to help the 
reader by any means whatever to a better understanding. 

The arrangement of this Book as well as its basis must be 
considered arbitrary. I shall begin by setting down some 
characteristics of inference which perhaps are likely to be 
accepted by all. And to these I shall add a few examples of 
actual reasoning. I shall then proceed to deal with some 
mistakes, confining myself in the main to the syllogism. In 
the next place I will point out that inference consists in an 
ideal construction. And fourthly I will state some principles 
of synthesis by which we operate to effect that construction. 
One essential factor in valid inference will then be indicated, 
and will be seen to rest on a serious assumption ; and we shall 
further show that in every inference at least one premise must 
be universal. Having reached this point we shall conclude our 
First Part, and take a fresh departure; and throughout the 
rest of this Second Book we shall be engaged in the work of 
clearing the ground. We shall have to criticize in general 
the alleged Association of Ideas, and especially the Associa 
tion of Similars. We shall briefly dispose of the supposed 
way of arguing from particulars to particulars ; and shall show 
by an examination of J. S. Mill s Canons that his Inductive 
Logic is theoretically invalid. After this, having declined to 
enter on a discussion of Mr. Spencer s doctrine, we shall end 
with a review of Professor Jevons theory of Equational Logic. 
The position we shall have reached, and the negative results 
we shall have been forced to gain, will have served to prepare 
us for a completer view. 

ADDITIONAL NOTE 

!" Judgment or supposition." Cf. p. 245, footnote. But to take 
"supposition" as excluding "judgment" is wrong. There are no 
"mere ideas." See on p. 4. 



PART I 
THE GENERAL NATURE OF INFERENCE 

CHAPTER I 

SOME CHARACTERISTICS OF REASONING 

i. When we first consider the subject of reasoning we 
seem to have nothing but a conflict of opinion. But a second 
glance reveals some agreement. There are three characteristic 
features of inference as to which in our hearts we are really 
at one. I do not mean that we should not deny them if our 
theories required it, but we should do so unwillingly and with 
a sense of compulsion. The first of these is a negative mark. 
There is a difference between reasoning and mere observa 
tion ; if a truth is inferred it is not simply seen, and a conclu 
sion is never a mere perception. The latter may seem to be 
given to us bodily, but the former involves some other ele 
ment. It may indeed be thrust upon us, we may be compelled 
and constrained to make it, but we can not passively take it in. 
The fancies we cherish in respect of perception desert us as 
soon as we come to inference. The external fact or the reflec 
tion it throws off can violently break into and enter our minds, 
or the reality can stamp our yielding substance with its image 
and superscription. But we can hardly apply these ideas to 
a conclusion, for we feel that in this there is something that 
repels them. An inference can not wholly come in from with 
out or be passively received. It is not mere vision, it is more 
than observation. 

2. There is another mark which a conclusion possesses. 
It is not a mere fragment or isolated unit; it does not exist 
in and by itself, but is the result of a process. It rests upon 
a basis, and that basis is something we already know.* In 
inference we advance from truth possessed to a further truth ; 

* For the sake of clearness I here ignore the hypothetical character 
of inference. 

2321.1 245 



THE PRINCIPLES OF LOGIC BOOK II. Pi. I 

and the conclusion would never be reached at all if it were 
not for knowledge already attained. It is therefore dependent 
and in a sense adjectival. 

3. But there is another attribute which a conclusion has 
got. It must convey some piece of information, and must tell 
us something else than the truths it depends upon. We have 
no inference at all, we have simply a frivolous show and 
pretence, if taking something we already know we assert the 
whole or part of this once more, and then say, " I have rea 
soned and got to a conclusion." An inference must be more 
than a vain repetition, and its result is no echo of senseless 
iteration. It is not mere observation yet it gives us something 
new. Though not self-existent it is more than a shadow. 
To those who delight in discrepant metaphors we may bring 
conviction when we so express ourselves : The truth which is 
seen in the mirror of inference has not wandered in through 
the window-pane of sense, nor yet is it merely a reflection 
cast by an article of furniture already in the mind. 

4. Except in the interest of a preconceived theory, I 
think that these statements, at least so far, will not be denied. 
But I can hardly hope that the examples of reasoning I am 
about to produce will all escape unchallenged. Yet I shall not 
defend them, for I do not know how. They are palpable 
inferences, and the fact that they are so is much stronger than 
any theory of logic. 

(i) A is to the right of B, B is to the right of C, therefore 
A is to the right of C. (ii) A is due north of B, B due west 
of C, therefore A is north-west of C. (iii) A is equal to 
(greater or less than) B, B is equal to (greater or less than) C, 
therefore &c. (iv) A is in tune with B, and B with C, there 
fore A with C. (v) A is prior to (after, simultaneous with) 
B, B to C, therefore A to C. (vi) Heat lengthens the 
pendulum, what lengthens the pendulum, makes it go slower, 
therefore heat makes it go slower, (vii) Charles I. was a 
king; he was beheaded, and so a king may be beheaded, (viii) 
Man is mortal, John is man, therefore John is mortal. We 
shall go from these facts to ask how far certain theories 
square with them. 



CHAPTER II 

SOME ERRONEOUS VIEWS 

i. The task before us in the present chapter is the re 
moval of certain mistaken ideas. And the first to go must 
be the major premise. We saw, at the end of the foregoing 
Book, that the necessary truth need be no more particular 
than the truth it depends on, and that logical necessity does 
not always come from the application of universals * to some 
thing less universal. But if so, there need not be always a 
major; and the examples we have given put this beyond 
doubt. 

In (viii) our old friend is still to be found, but in (vi) and 
in (vii) you will hardly be able to distinguish him from the 
minor, and in all the rest he has totally vanished. You may 
say that in (iii) we really argue from " Things equal to the 
same are equal to each other," and I do not doubt you will 
find believers. But if such reasoning is reasoning from an 
axiom, how did people reason before axioms were invented? 
And if without axioms it is impossible to infer, I wonder 
where all the axioms can have come from (cf. Book II. Part 
II. Chap. I.). But if we take an example like number (i), will 
any one show me the major there? "A body is to the right 
of that which that, which it is to the right of, is to the right 
of." I know this major, because I have just manufactured 
it; but you who believe in major premises and who scores of 
times must have made the inference, confess that you never 
saw this premise before. 

We must either admit that a major is not necessary, or 
else we must say that my examples are not inferences because 
they have no major. In either case an effete superstition will 
be doomed. 

Begotten by an old metaphysical blunder, nourished by a 
senseless choice of examples, fostered by the stupid conserva 
tism of logicians, and protected by the impotence of younger 

247 



248 THE PRINCIPLES OF LOGIC BOOK II. PT. I 

rivals, this chimaera has had a good deal more than its day. 
Really dead long since I can hardly believe that it stands 
out for more than decent burial. And decent burial has not 
yet been offered it. Its ghost may lie quiet when it sees that 
the truth, which lent it life, can flourish alone (cf. Book III.). 
2. The major premise, we have seen, is a delusion, and 
this augurs ill we may think for the syllogism. Our suspicion 
is well founded, for the syllogism itself, like the major premise, 
is a mere superstition. It is possible, no doubt, as in our 
seventh example, to have a syllogism which has either no 
major premise, or at all events no minor. And it is unques 
tionably true that in many arguments a major premise is 
actually used. Nor will I deny that some three fourths of our 
valid arguments can be got within the forms of Barbara 
Celarent. But yet after all the syllogism is a chimsera, for it 
professes to be the model of reasoning, and there are reason 
ings which can not by any fair means be conformed to its 
pattern. In whatever sense you interpret it, it turns out 
insufficient; and in certain cases it will turn out worse. Let 
us examine the principles of reasoning it lays down. 

3. If we take first the axiom of inclusion in extension as 
it finds expression in the maxim De omni &c., we are forced to 
say that this principle is unsound. It sins against the third 
characteristic of inference (Chap. I. 3), for it does not really 
give us any new information. And, as has been long ago 
remarked, it embodies a petitio; for if, asserting the premise 
" All men are mortal," I understand by the subject each 
single man, then I either am aware that John is mortal, or if 
not my major must be withdrawn. The major premise has 
asserted something of each member of a collection, and the 
minor and conclusion do but feebly re-echo one part of this 
statement. But that is no inference. 

We might try to understand the assertion differently. We 
might say that what " All men " really means is the collection 
or class and not each one member. But, if so, we fall blindly 
into a second pitfall. John s personality perhaps has no unity, 
but he can hardly be called a collection of men, and our 
syllogism now fails through quaternio terminorum. It per 
haps fails too through falsity of the major. 2 

The dictum de omni thus turns out vicious. But if it were 



CHAP. II, SOME ERRONEOUS VIEWS 249 

sound it would not be sufficient, for it does not cover all valid 
reasonings. 

4. There is another mode of interpreting the major. 
" All men are mortal " may be said to assert the identity of 
the subjects in " men " and " some mortals ; " and " John is 
man and therefore mortal " assures us that the subject, which 
we distinguish as John, is identical with a member of the class 
of men and also of mortals. But we know already how this is 
to be read. 3 The identity of the subject is another way of 
affirming the conjunction of diverse attributes. The fact we 
have got is either the co-existence in one single subject of the 
attribute mortal with the rest of John s attributes, or else the 
possession by a single thing of the several names " John," 
" man," and " mortal " (cf. Book I. Chaps. I. and VI.). And 
interpreted in this way, though the inference is valid, it will 
not fall under the dictum de omul. 

5. We may illustrate the above from complete induction. 
I may show that all planets move in an ellipse by counting 
and observing each single planet. But in what sense am I 
then said to perform an inference? I say "therefore all 
planets move in an ellipse," but I know already that every 
single planet does so move. If there were any planet which I 
could not so qualify I could not go on to therefore all planets. 
Does the " therefore " simply reiterate the " because "? Then 
there is clearly no inference. Does the conclusion assert that 
the collection, or class, itself moves through space in an 
elliptical manner? If this were true the premises would not 
prove it. But perhaps it means that, if anything is a known 
planet, it must have a course which will be found elliptical. 
We are free to forget that the individuals we know do move 
in ellipses. We have firmly established a connection of at 
tributes, so that hereafter, given any single individual which 
we barely perceive to be a known planet, we can go at once 
from the base of that attribute to elliptical movement. But 
the conclusion here does not rest on enumeration complete or 
otherwise; it proceeds from and rests upon a distinguished 
connection of attributes (Book I. Chap. VI. and Bk. II. II. 

Chap. III. 3)- , <T7 . 

We may sum up the matter thus. If you say Each 
individual has a certain attribute and therefore each has it, 



250 THE PRINCIPLES OF LOGIC BOOK II. PT. I 

that is absurd. If you say " therefore the collection has it," 
that is invalid. If you say " Anything belonging to the col 
lection has it and therefore this has it," then that is valid, but 
the " anything belonging " stands for an attribute. Com 
plete induction shares the fortunes of the syllogism. 

6. The principle of inclusion within class extension is not 
merely insufficient, but unless we interpret it as a connection of 
attributes it is intrinsically vicious. Let us see if we can find 
any other view which will come to the rescue and will save 
the syllogism. " What stands," says Kant, " under the condi 
tion of a rule stands under the rule." It is thus he interprets 
" nota notes est nota rei ipsius" If you have an universal 
connection of two attributes, then, given one in a subject, you 
must also have the other. 

It is evident that this principle of reasoning is valid, but it 
will not cover the whole of the ground; for, confined to the 
category of subject and attribute, it fails wherever you pass 
beyond. The subject no doubt is in some way qualified by 
whatever can be asserted about any of its attributes, but it is 
idle to expect a result from this where we are not concerned 
with subject and attributes. " A is prior to B and B to C, and 
therefore A is prior to C," but what here am I to call the 
"condition of the rule" or the "nota" or "attribute"? I 
can not take B as the attribute of A, and if I look for that 
attribute in " prior to B," I fall at once into quaternio termi- 
norum, since the second premise has got B simply. 

And even when we keep to subjects and qualities, there 
are inferences which the principle will not justify. The syllo 
gistic third figure can hardly be supposed to exemplify the 
axiom which Kant has adopted. Not only is the category 
of subject and attribute (as commonly applied) unable to 
cover the whole field of reasoning, but within that category it 
is a further mistake to insist on the necessity of a major 
premise. 

7. It is evident that the syllogism can not be saved or 
can only be saved in such a way as to be syllogism no longer. 
The one chance there is of preserving the syllogism is for us 
to take our stand upon the third figure. c< The attributes of 
one subject are interrelated " will then become the axiom of 
inference. We have seen (4) that all syllogisms in exten- 



CHAP. II SOME ERRONEOUS VIEWS 251 

sion can be interpreted according to this axiom, since the 
identity of the subject was the other side of that relation of 
attributes which we wished to assert. And it is evident again 
that all relations of attributes can be regarded as based in a 
subject. We shall see hereafter (Part II. Chap. IV) that Sub 
stitution of Similars can be taken as syllogism within the third 
figure; and I will go yet further. There is and there can be 
no inference whatever which may not be reduced under the 
head of the axiom, since everything which in any way is con 
joined can be taken as related within some subject (Book III. 
Chap. VI. 33,34). " 

We may see hereafter how this reduction is effected. For 
our present purpose it is enough to remark that in many cases 
it can not be performed without processes which would hor 
rify the conservative logician, and which gain no end worth the 
violence they use. Unless " subject and attribute" are used 
in a way which is quite unknown to the traditional logic, the 
axiom fails of universal validity, for it does not apply to any 
of those relations which two or more subjects bear to each 
other. " Two pianos are in tune with one fork and therefore 
the one is in tune with the other." But in this instance, unless 
the terms are manipulated freely, you will not show one sub 
ject with its attributes. 

8. It is obvious, if we fairly consider the examples which 
have been adduced at the end of Chapter I., that the syllogism, 
if it keep its traditional form, is in great part impotent. And 
I confess I do not know what policy will seem good to the 
friends of the syllogism. They may boldly accept the violent 
alternative of excluding all examples which they can not deal 
with. But I think we may say that such a course as this 
would be nothing short of a confession of bankruptcy. If a 
savage may know the road that will take him from A to B, 
and the road that will take him from B to C, and yet may not 
know, and may be unable to find out, the way he should go 
from A to C (cf. Spencer, Sociology, I. 91), I do not see bow 
it can be denied that he is ignorant because he is incapable of 
an operation. 5 And if that operation is not an inference, I can 
not see why anything else should be inference. The plain and 
palpable facts of the case will, I think, be too hard for the 
friends of the syllogism. And if they embrace another alterna- 



252 THE PRINCIPLES OF LOGIC BOOK II. PT. I 

tive, and find their amusement in the manufacture of majors, 
which would never have been seen if the arguments had not 
come first, then I think once more that the end must be near. 
So barren a shift will be the dying effort of a hard-run and 
well-nigh spent chimsera. 

But there is, as we saw, another alternative; it may per 
haps be thought possible to save the syllogism by first reform 
ing it. Throw the major premise overboard, and call anything 
a syllogism which can be brought into the form of elements 
related within one whole. But if the friends of the syllogism 
resolve on this policy, I think they are friends it might pray 
to be saved from. It is better to bury a delusion and forget 
it than to insult its memory by retaining the name when the 
thing has perished. And it is better to profess that delusion 
openly than ostensibly to abandon all but the name, and then 
covertly to re-instate the errors it once stood for. When a 
mistake has lasted some two thousand years I am ready to 
believe that it must contain truth, but I must believe too that 
the time is come when that truth should be able to stand by 
itself. We can not for ever with eyes fast closed swallow 
down the mass of orthodox rubbish in which that truth has 
wrapped itself up. And if the time has not come for extracting 
the kernel, the time has come for rejecting the shell. 

9. But if the principle of the syllogism is not the axiom 
of reasoning, can we find any other which will stand the test? 
We shall see hereafter that the logic of " Induction " is no 
more satisfactory. We shall allude to the doctrine of Mr. 
Spencer, and review the theory of Substitution which has 
found an advocate in Professor Jevons. For the present it 
will suffice to mention a principle adduced by Mr. Spencer, 
and which has succeeded in gaining the authority of Wundt. 
" Things related to the same are related to each other " is 
the axiom, we are told, of all valid reasoning. " Where judg 
ments are placed in relation to one another by means of con 
ceptions they possess in common, the other conceptions, which 
the judgments possess but do not possess in common, must 
stand themselves too in relation to one another, and that rela 
tion is expressed in a new judgment." (Wundt, Logik, I. 
282.) 

We may confine ourselves to the simpler formula. 



CHAP. II SOME ERRONEOUS VIEWS 253 

" Related to the same are related to each other " is wide 
enough to cover the examples we have given. We shall cer 
tainly hereafter have occasion to question if it is wide enough 
to cover all possible examples (Book III. Part I. Chap. I.). 
But though I may object to it hereafter as being too narrow, 
I must object to it here because it is too wide. It is a principle 
of falsehood as well as of truth ; " A runs faster than B and 
B keeps a dog (C)," "A is heavier than B and B precedes 
C," " A is worth more than B and B is on the table (C)," or 
" A is like B and B is like C." You may doubtless extract 
some kind of inference out of these premises, but you can 
hardly go from them to any definite and immediate relation 
between A and C. 6 

10. It is true no doubt that, if A and C are both related 
to a common term B, we know that some relation must exist 
between them, since both must be elements in one world of 
knowledge. But unfortunately we knew thus much before, 
and independent of the relation of both in particular to B. 7 

And again in defence of the axiom it may be said, In " A is 
like B and B is like C " the terms are not related to a common 
third term. B resembles A perhaps in one point and resembles 
C in another different one, and so it is with the other examples. 
It is not in so far as B keeps a dog that A outstrips him, it is 
not the B which has a place in time which is heavier than A, 
B is on the table in one capacity and is worth more than A in 
an other and different one. Thus the terms related are not 
related to the same, and, if they were, they would be related 
to each other. 

The defence I have invented points towards the truth, and 
yet it is vitiated by a fatal mistake. It is true to say that in 
every relation there must always be an underlying identity; 
that relations, such as those of space and time, presuppose a 
common character in the things they conjoin. And it is there 
fore true that, if a third term C stands first in spatial relation 
with A and again in temporal relation with B, its character in 
those two relations is different. Hence, if two relations are 
of different classes, the term common to each will so far not 
be the same. 

But this line of argument, if we follow it out, will make an 
end of all kinds of relation (cf. Chap. VI. 6). To say that, 



254 THE PRINCIPLES OF LOGIC BOOK II. PT. I 

when A is related to B, it is related so far as B is nought else 
but its relation to A, is quite suicidal. And, if we will not say 
that, and if already B is something different from its relation 
to A, on what ground can we refuse it a right to another 
relation with C, when at all events it has one point in which 
it differs from A? Let us try to see clearly; the terms of 
a relation must always be more than the relation between 
them, and, if it were not so, the relation would vanish. "A 
is equal to B," but if B were mere quantitative identity with 
A, we should have no equality ; there would be nothing but A. 
" A is the same as B or different in quality," but if A and B 
were not both different and the same, then the terms and the 
relation would all disappear together. " A is north of B or 
prior to C ; " but if A, B, and C were no more than mere 
naked positions in space or time, they would not be even that, 
and their relations would sink to utter nothingness. There 
always must enter into the relation something more than the 
actual relation itself. And this being admitted, if you deny 
that the B, which for instance is spatially related to C, is the 
same as the B which has a relation in time with A, you must 
be taken to assert that in the relation A B the character of 
B is perfectly simple, and that B is nothing but that which 
constitutes its relation in time. But, if so, it is nothing which 
can be related, and the axiom can find no possible application. 
The mistakes, which arise from a too wide axiom, may 
indicate the truth that related to the same are not related to 
each other unless they are related under certain conditions. 
We shall return to this point in Chapter IV., and the following 
Chapter will endeavour to convey some general idea of the 
nature of inference. 



ADDITIONAL NOTES 

1 " Given universals " would be better here than " universals." 

2 On the "Collective Judgment" and on "Class" see the Index. 
The "falsity of the major" refers to the ambiguity involved in the 
above ideas. On Complete Induction and Counting see Bk. II. II. 
HI. 3. 

3 " But we know . . . read." It would be better to say " But we 



CHAP. II SOME ERRONEOUS VIEWS 255 

know already how this identity of diverse subjects is here to be read." 
See on Bk. I. VI. n. 

4 See i of the next Chapter. 

5 " If a savage &c." The case, as stated, is so extreme as to be 
perhaps abnormal, but as an illustration it may stand. 

6 " Definite and immediate " should be " fresh and special." See 
again as in Note 4. 

7 After " in particular to B " add as follows. " Further, when 
we have got to know that A and B, B and C, are related in a par 
ticular whole which is before us this mere knowledge, that A and 
C are both together as members of that whole, will not be the con 
clusion that we seek We presumably are looking for some further 
and special relation between A and C, other than their mere co-pres- 
ence within one subject." 



CHAPTER III 

A GENERAL IDEA OF INFERENCE L 

I. Every inference combines two elements; it is in the 
first place a process, and in the second place a result. The 
process is an operation of synthesis; it takes its data and by 
ideal construction combines them into a whole.* The result 
is the perception of a new relation within that unity. We start 
with certain relations of elements; by virtue of the sameness 
of two or more of these elements we unite their relations in 
one single construction, and in that we perceive a fresh rela 
tion of these elements. What is given to us is terms conjoined ; 
we operate on these conjunctions and put them together into 
a whole ; 2 and the conclusion is the perception of two terms in 
relation, which were not related before the operation. Thus 
the process is a construction and the result an intuition, while 
the union of both is logical demonstration. 

2. Demonstration in logic is not totally different from 
demonstration elsewhere ; proof is only one kind of demon 
stration. Logicians however seem generally not to be aware 
of this fact. When the mathematician " demonstrates " a 
conclusion the logician feels uneasy, though he can not deny 
that the conclusion is proved. But uneasiness becomes protest 
and open renunciation when he attends at the " demonstra 
tions " of the anatomist. He shudders internally at the blas 
phemous assertion that " this which I hold in my hand " is 
" demonstrated." But his trials are not over ; the illiterate 
lecturer on cookery overwhelms him by publicly announcing 
the " demonstration " of an omelette to the eyes of females. 

But I think the logician has no real cause of quarrel even 
with the cook. For demonstration is merely pointing out or 
showing ; 3 and if the conclusion of an inference is seen and 
thus may be shown, so also may a nerve or again an omelette. 

*As we remarked before, the statements in this Book are subject 
to correction by the Book that follows. 

256 



CHAP. Ill A GENERAL IDEA OF INFERENCE 257 

It is useless to deny this, and the task of the logician is to 
distinguish inference from other kinds of demonstration. 

3. When in ordinary fact some result can be seen and is 
pointed out, perhaps no one would wish to call this " demon 
stration." It is mere perceiving or observation. It is called 
demonstration when, to see the result, it is necessary for us 
first to manipulate the facts; when you show within and by 
virtue of a preparation you are said to demonstrate. But if 
the preparation experiments outwardly, if it alters and ar 
ranges the external facts, then the demonstration is not an 
inference. It is inference where the preparation is ideal, 
where the rearrangement which displays the unknown fact is 
an operation in our heads. To see and, if it pleases us, also to 
show a new relation of elements in a logical construction, 4 is 
demonstration in the sense of reasoning. 

4. In what does this mental preparation consist ? We 
have seen in our account of the synthetic judgment its general 
character. It demands in the first place certain data; 5 it 
must have two or more connections of elements, as A B 
B C C D ; and these are the premises. It is necessary 
again that these premises should be judgments actual or sug 
gested, 6 and what they assert or suppose must consist in logical 
connections of content. For if the data consisted of unrefined 
sensuous material, or were mere imaginations, the result would 
be sensuous or merely imaginary; it would be a psychological 
effect and not a logical consequence. The premises are thus 
so far two or more judgments, and the operation on these 
data will consist in joining them into a whole. We must 
fasten them together, so that they cease to be several and are 
one construction, one individual whole. Thus instead of 
A B B C we must have A B C. 

Now if this were done arbitrarily it would not be done 
logically, and we should have no reason to think the result 
true. If we took A B and C D and joined them together 
as A B C D, our procedure would be as futile as if in 
anatomy we showed connections by manufacturing them, or 
as if in order to clear a preparation, we employed some agent 
which radically changed it. In relation to fact our results in 
this case would be invalid.* 

*A11 this is subject to correction by Book III. 7 



258 THE PRINCIPLES OF LOGIC BOOK II. Pi. I 

We can not logically join our premises into a whole unless 
they offer us points of connection. But if the terms between 
which the relations subsist are all of them different, 8 we are 
perfectly helpless, for we can not make an arch without a 
key-stone. Hence, if we are to construct, we must have an 
identity of the terminal points. Thus, in A B B C, B is 
the same and we connect A B C; in A B C and 
C D, C is the same and we connect A B C D. The 
operation consists in the extension and enlargement of one 
datum by others, by means of the identity of common links. 
And because these links of union were given us, therefore we 
assume that our construction is true; although we have made 
it, yet it answers to facts. 

Having thus turned our premises into one whole, we pro 
ceed to our conclusion by mere inspection.* If A B 
C D is true of reality, then in that we can see A C or 
A D, or again B D, relations which previously we did 
not know. Then, leaving out of view those parts of our 
construction in which we are not interested, we extract the 
conclusion we desire to assert. We first do a certain work 
on our data; and this work is the construction. We then 
by inspection discover and select a new relation, and this 
intuition is the conclusion. 10 

5. I will illustrate the above by several examples. Take 
three pictures on a wall A, B, and C; if I see them all at 
once as A B C there seems so far no inference, 11 for my 
mere analytic judgment will give me A C (Book I. Chap. 
II.). But suppose I see first A B, and then afterwards 
B C, no mere analysis will give me A C. I must first 
put them together as A B C, and this is the construction 
of a synthetic judgment. I then perceive A C, and this is 
the conclusion, which is inferred not because it is seen in fact, 
but seen in my head. 

Let us take an instance from geographical position. A is 
ten miles north of B, B is ten miles east of C, D is ten miles 
north of C; what is the relation of A to D? If I draw the 
figure on a piece of paper that relation is not inferred ; 12 but 
if I draw the lines in my head, in that case I reason. In 

* I omit to consider here the selective action. That is not of the 
essence of all inference. 9 Vid. Book III. Part I. Chap. I. 



CHAP. Ill A GENERAL IDEA OF INFERENCE 259 

either case we employ " demonstration," but only in the latter 
do we demonstrate logically. 

" A = B and B C therefore A = C." In this argument 
there is no demonstration to sense, for the showing is ideal. 
The terms are put together through the sameness of B, and 
are combined into a whole united by the relation of quan 
titative identity. The whole is a series united by that charac 
ter, and here is the construction. We then inspecting the 
series find a new relation A C, and here is the conclusion. 

Take an example we have given in Chapter I. ; if three 
strings A, B, and C are struck together and we hear that they 
all produce the same note, we hardly infer 13 that they are in 
tune with one another. But first strike A and B, and then 
strike B and C ; on this, if A and B have no difference in note, 
and B and C have no difference in note, I proceed to construct 
the ideal group of ABC united throughout by sameness of 
note. This is a mental synthesis ; and a mere analytical percep 
tion then adds that A and C are in tune with one another. 

We may see this again in an ordinary syllogism. We 
must not state it so as to beg the question, or to have no com 
mon term, but may state it thus, " Man is mortal and Caesar 
is man and therefore Caesar is mortal." There is first a 
construction as Csesar-man-mortal, and then by inspection we 
get Caesar-mortal. 

6. It is useless to attempt to lay down rules for either 
part of this process. It is the man who perceives the points 
of union within his premises who can put (as the saying is) 
two and two together who is able to reason. And so long 
as he secures the unity of his construction he has reasoned 
rightly. In the next Chapter we shall see that no models for 
construction can possibly be invented. And for the process 
of inspection one wants a good eye; for there are no rules 
which can tell you what to perceive. 

We must free ourselves from these superstitions, if we can, 
and there are others beside which have oppressed us too long. 
It is ridiculous for instance to think about the order of our 
premises. The construction when made need have no order 
in time, and the order of its making may be left entirely to 
private convenience or else to chance. 

And there is another superstition we may here dispose 



26O THE PRINCIPLES OF LOGIC BOOK II. PT. I 

of. 14 The number of terms is not limited to three. In the 

geographical example of the previous section we certainly 

A A Dl /A D A 



do not argue thus 



C- 



B* 



, and 



D 



C 



but we first complete our construction 



C 



A 



, and then 



go to D A. It is true no doubt that in making a con 
struction we are forced to establish one link at a time; but 
it is wholly false that we are compelled to conclude before 
we take in another premise. Logic sets no limit to the number 
of premises which may precede the conclusion, and it is 
the weakness of our heads which narrows our constructions 
and narrows them sometimes to the prejudice of our inference. 
There is no branch of science where constructive power is 
wholly uncalled for, and certainly some where it is of the 
first importance. And perhaps we may say without exaggera 
tion that a man, who can not use more than three terms in 
reasoning, is unlikely to do much in any subject. But, how 
ever that may be, the limit is psychological and is not logicaL 

ADDITIONAL NOTES 

^This chapter must be taken as no more than a provisional 
clearing of the ground. Not only is the warning in the footnote to 
i to be borne in mind, but, in addition, the chapter contains 
serious errors the correction of which can only be indicated in 
passing. 

2 " Into a whole" should be "into a connected whole," and (in the 
next line) " not related " should be " not so related." 

3 " Demonstration is merely pointing out." This is a grave mis 
take, and the term is, I think, nowhere so used in practice. It every 
where and always means showing the necessary and ideal connection 
and sequence. Whether and how far you have before you external 
fact and its alteration, or deal merely with what is "in your head," 
is utterly irrelevant. The " demonstration " in every case has to 
bring out not the fact but the ideal bond and process. Cf. on Bk. 
III. I. II. 5, and T. E. I. 

4 " In a logical construction " should be " in and as the result 
of &c." 

5 On " data " and " premisses " see Index, s. v. Premisses, and cf . 
Bosanquet, Logic, II, pp. 12 and 203. 



CHAP. Ill A GENERAL IDEA OF INFERENCE 26l 

6 The words " actual or suggested " should be omitted. See the 
first Note on Book II. And (at the end of this paragraph) it would 
be better to insert " new " before " individual," in the words " one 
individual whole." 

7 " All this " should have been " Much of this." 

8 " Different " should have been " merely different." 

9 The " selective action " is really quite essential. See the Index 
s. v. Selection. What I meant here was merely that "elimination" is 
not always necessary. You do not always in the conclusion omit part 
of the construction. See Bk. III. I. I. 2. 

10 " This intuition is the conclusion." Certainly not so, unless the 
new relation appears in it as " following." The " conclusion " means 
seeing as part of the whole and because of the whole. See Note 4. 

11 " So far no inference" except so far as the analytic judgment 
itself involves inference. See Index, s. v. Analysis. 

12 " If I draw the figure &c." This and what follows is seriously 
wrong. See Note 3. 

13 "We hardly infer, etc." Yes, but how far the "we hear" is 
already itself inferential, still remains a question. See Note II. 

14 "And there is another &c." On this see Bosanquet, K & R, 
p. 307, and Logic, II, pp. 12 foil. My statement here was wrong in 
forgetting that the necessary establishment by synthetic construction 
of each link, one at a time, itself is inference. On the other side I 
was right in insisting that in the final conclusion there is an inference 
from the whole construction without regard to the number of terms 
contained in that. Cf. Bk. Ill, I. II. 5. 



2321.1 



CHAPTER IV 

THE PRINCIPLES OF REASONING 1 

I. We have seen in outline the main character of infer 
ence and we naturally recur to a former question, Is there 
any axiom or principle of reasoning? The result of our 
enquiry in the Second Chapter was that we could find nothing 
quite satisfactory. The syllogistic maxims were all too nar 
row, and the axiom that " Things which are related to the 
same are related to each other," we found on the other hand 
was much too wide. It may serve us however as a point of 
departure. When properly restricted it will express the truth, 
so far as is required by the present Book. 2 

I will repeat the result we arrived at before. The principle 
that elements which stand in relation to a common point are 
themselves related, is not the actual principle that operates in 
any given special inference. 3 In its abstract form it is useless 
for the purpose of getting a conclusion. It assures us, before 
any construction is made, that anything which we have as an 
element of knowledge stands in some relation with every other 
element. But it will not enable us to go beyond this, and 
by combining our premises to get a definite relation. If A 
is prior to B in time, and B is west of C in space, then on 
the strength of B we can put these together, but we can not 
by means of our combination get a definite relation of A to 
C. We knew long ago that A and C po-existed as members 
within the universe of knowledge, and we desire to learn now 
not that general connection, but some special attitude of A to 
C. But in order to get this, and to be able so to speak to 
draw a new line from A to C, it is necessary first to connect 
A and C in a special manner. They must be interrelated not 
generally and in the universe at large, but in some special 
world. If one is merely in time and the other merely in space, 
they have so far not got any binding centre. To be specially 
related they must be related to the same, and under conditions 
which secure an unity of construction. 

262 



CHAP. IV THE PRINCIPLES OF REASONING 263 

If what operates in inference is the principle of the indi 
viduality of synthesis, the axiom of that operation must not 
be taken too widely, and at the cost of clumsiness we must 
state it in two pieces. " Where elements A and C are related 
homogeneously to a common B, A and C are related within 
the same genus. Or where one relation only (either A B 
or B C) is within the category of subject and attribute, 
there is a valid conclusion within the category of either A B 
or B C." To express the same otherwise, " There is no 
conclusion where the relations are heterogeneous unless one 
of the two joins an attribute to a subject. In the latter case 
an inference is possible even outside the category of subject 
and attribute." 

2. We found first in our examination of the syllogism 
that there were inferences which fell outside its single cate 
gory of subject and attribute. We found again that if we 
kept outside all special categories, mere interrelation was 
much too vague to form a bond. The conclusion, which in 
the next place naturally offers itself, is that inference must 
take place within several special categories (such as time, 
space, subject and attribute, &c.), but must always be confined 
in each case to one category. To get a relation of time in 
the conclusion you would have to keep in your premises to 
time-relations, and the same thing again with other kinds of 
relation. And, if this were true, the axiom would run, " Things 
related to the same within one kind will be interrelated within 
that kind." 

But there are inferences which will not submit to this 
principle. " Gold is heavier than lead and lead is a metal," 
" A runs faster than B and B is twice as tall," " A is stronger 
than B and B is full grown," " A is equal to B in weight and 
B is moved with such or such velocity " are premises which 
certainly will yield conclusions, and yet their relations are 
heterogeneous. And this shows that we may cross from cate 
gory to category. On the other hand we are unable to do 
this unless there exists a special condition ; one relation must 
be that of attribute to subject. From " A is equal to B and 
B has such velocity " we have seen you can not get to the 
conclusion " A has such velocity." You can not do so till 
you predicate of A that point in B which brought it into 



264 THE PRINCIPLES OF LOGIC BOOK II. PT. I 

relation with the other element (C). And from "A is equal 
to B and B is in my pocket " you can not infer that A is in 
my pocket, since the spatial relation which is affirmed of B 
is not true of B as equal to A. You can not argue to a relation 
of A to my pocket, but your conclusion must be " A is equal 
to something which is in my pocket." We have still the old 
relation of A to B, but qualified by the addition of an ad 
jective of B. And it is true, I think, in all possible cases that 
the relation between a subject and attribute is the only one 
which, if used with another category, is able to give us a new 
relation.* 

The remarks we let fall in a previous chapter (II. 7) 
may have prepared the reader for our result. The categories 
do not stand on one and the same footing. 5 It is possible 
after all to express unconditionally the principle of inference, 
and it is possible to do this within the one category of subject 
and attribute (p. 296). But we are not yet arrived at the 
stage where this is possible, and must content ourselves here 
with the formula that ended the foregoing section, " Related 
to the same within the same kind are interrelated within that 
kind," with a further axiom of possible inference where one 
relation is that of subject to attribute. 

3. Our main principle, it is obvious, will have as many 
forms as there happen to be categories or kinds of relation. 
It is not the business of this work to elaborate any theory as 
to how these kinds are connected or are subordinated. It is 
again not our purpose to draw out and defend a complete 
enumeration or scheme of such classes. But in order to make 
clear the general result, I will state and illustrate four or five 
main principles which operate in inference. We may call 
them the principles (i) of the synthesis of subject and attri 
bute, (ii) of identity, (iii) of degree, (iv) of space, and (v) 
of time. 

I. Principle of synthesis of subject and attribute. 

* Other examples are "A has a voice (B), that voice overpowers 
Z s voice (C), therefore A overpowers C." "A has a voice (B) which 
is in tune with C, therefore A has something in tune with C." In the 
first of these the relation of the conclusion is hardly between a subject 
and attribute. 4 A by virtue of its attribute, which attribute acquired 
a momentary independence, has got a new relation to another subject. 



CHAP. IV THE PRINCIPLES OF REASONING 265 

(a) The attributes of one subject are interrelated. 

(/3) Where two subjects have the same or a different attri 
bute they are alike or different. 

(y) (i) Where the attribute is not taken as distinct from 
every subject, what is asserted of the attribute is asserted of 
its subject, (ii) Where the subject is not taken as distinct 
from every attribute, what is affirmed of the subject is affirmed 
of any attribute considered as its attribute. 

Examples, (a) This man is a logician, this man is a fool, 
therefore a logician may be * (under some conditions is) a 
fool. 

(13) This dog is white, this horse is white (or brown), this 
dog and this horse are alike (or different) . 

(y) (i) This figure is a triangle, a triangle has the angles 
equal to two right angles, this figure has the angles equal to 
two right angles, (ii) Gold is heavier than lead; lead is a 
metal. Therefore lead-metal (or some metal) is lighter than 
gold, or metal may be lighter than gold. 

I may remark on (y) that, if we were to say " What is 
true of the attribute is true of the subject, and what is true of 
the subject is true of the attribute," we should fall into an 
error. The subject qua subject and the attribute qua attribute 
have each predicates which can not be applied to the other. 
Thus " Iron is heavy, heavy is a quality " is no ground for the 
assertion " Iron is a quality," nor from " Iron is heavy, iron 
is a substance," can you go to the conclusion " Heavy may be 
a substance" (cf. Book I. Chap. III. 10). If on the other 
hand we laid down as a condition of the inference that this 
attribute and this subject must be taken together, we should 
then have become circular. 6 

II. Synthesis of Identity. 

Where one term has one and the same point in common 
with two or more terms, there these others have the same 
point in common. 

Examples. " Coin A has the same inscription as coin B, 
and coin B as coin C, therefore A as C; " " Instrument A is 
in tune with my tuning-fork (B), and so too are instruments 
C and D, therefore they are all in tune with one another;" 

*May be because, the subject being undefined, the conditions are 
partly unknown. Vid. Book I. Chap. VII. 26. 



266 THE PRINCIPLES OF LOGIC BOOK II. Px. I 

" If A is the brother of B, and B of C, and C is the sister of 
D, then A is the brother of D." 

III. Synthesis of Degree. 

When one term does, by virtue of one and the same point 
in it, stand in a relation of degree with two or more other 
terms, then these others also are related in degree. 

Examples. " A is hotter than B and B than C, therefore A 
than C ; " " Colour A is brighter than B and B than C, there 
fore A than C ; " " Sound A is lower in tone than B and B 
than C, therefore A than C." I will not enquire here whether 
" A = B and B = C, therefore A = C," falls under this head 
or under the previous head of the synthesis of identity. 

IV. and V. Synthesis of Time and Space. 7 

Where one and the same term stands to two or more other 
terms in any relation of time or space, there we must have a 
relation of time or space between these others. 

Examples. " A is north of B and B west of C, therefore C 
south-east of A ; " "A is a day before B, B contemporary 
with C, therefore C a day after A." 

This list, as we have said, does not pretend to be complete, 
and it would not be possible for us here to discuss the ques 
tions which any such pretence would at once give rise to. 
Take for instance the synthesis of cause and effect. Does 
this fall entirely under the head of time? Does it fall under 
the head of subject and attribute? Does it fall under both 
or again under neither ? The answers to these questions would 
be hard to get, and, if we got them, they would be of no use 
to us here. They would not much serve to confirm the result 
we already have reached ; they would possibly supply one more 
illustration, where I hope enough have already been given. 

4. But there is another question which can not be 
passed by. We have called these syntheses Principles of 
inference, and have ejected the syllogism to enthrone them in 
its stead. But how are we to understand the title they lay 
claim to? We know what the syllogism tried to accomplish, 
for it professed to control from a central office every possible 
event in all parts of its kingdom. It issued some two dozen 
forms of reasoning, to which all inference was expected to 
conform. Thus you had always some model with relations 
ready drawn between all the terms both in premises and con- 



CHAP. IV THE PRINCIPLES OF REASONING 267 

elusion, and no liberty was left you save to fill up the blanks 
with terms of your own. The moods and figures were a bed 
of Procrustes into which all arguments had somehow to be 
forced, and they were therefore not merely principles of rea 
soning, but actual canons and tests of inference. Within 
this pale you were secure of salvation, and on the outside it 
was heresy to doubt you were lost. Such was the claim 
which the syllogism put forth, and enforced as long as it had 
any strength. 

Like some other chimseras that have had their day, the 
syllogism is effete and its realm is masterless ; and the question 
for us who aspire to the inheritance is to know in what charac 
ter we mean to succeed. Do we wish to substitute one des 
potism for another? Are our principles of inference to be 
tests and canons? Most assuredly not; for if the thing were 
desirable, and I am much too staunch a Protestant to desire 
it, it is at all events thoroughly impossible. 

5. Our principles give us under each head of inference 
the general and abstract form of the operation. They do not 
profess in all cases to give us the individual operation itself 
which is necessary. It is not merely that the terms are left 
blank, for the special relations of the premises and conclusion 
are also left blank. The kind of construction is indicated 
generally, and the kind of conclusion you will find within it; 
but the actual construction, and the actual new relation to 
which that will give rise, are left entirely to private judgment. 8 

From such premises as " A to the right of B and B to the 
right of C," there is and there can be no form of reasoning 
which will give you the conclusion. It is true that the axiom 
goes so far as to assure you that A and C must be related in 
space, for 9 you do not know that unless you know that the 
two space-relations belong to one world. And you do not 
know this unless you are sure that they have a common 
meeting-point in space (Book I. Chap. II. 21). But the 
axiom will not tell you anything beyond. It will neither give 
you the definite relation, nor even assure you that you will be 
able to attain to any such relation. A is greater than B, and 
C is greater than B, therefore (if the point in B is the same) 
A and C must certainly be related in degree ; but you do not 
know how. B is south of both A and C, therefore A and C are 



268 THE PRINCIPLES OF LOGIC BOOK II. PT. I 

related in space ; but you have no means of getting to know 
their particular relation. For the individual construction can 
not here be drawn, and it is that alone which can supply the 
conclusion. 

Where the inference is valid, the special operation by which 
it is performed falls outside the axiom, and it is impossible 
therefore that the axiom can supply any test of validity. 
Where the inference is invalid, what makes it invalid may 
fall without the axiom, and the axiom is therefore no test of 
invalidity. If I like to argue that, because A and C are both 
greater than B, they are equal to one another, the principle 
has nothing to say against it. If I choose to go from " B is 
south of both A and C " to, " therefore A and C lie east and 
west," again the principle is perfectly satisfied. It can no more 
tell me that here I am wrong than that I am right if I say, 
" A is due north-west of C, because B is five miles south of 
A and again the same distance west of C." The general form 
is valid in either case, but the actual operation, whether 
erroneous or correct, is in either case beyond the scope of the 
principle. It is not a matter for superior direction; it is a 
matter for private inspiration and insight. 

6. It is impossible that there should be fixed models for 
reasoning; you can not draw out exhaustive schemata of valid 
inference. There are principles which are tests of the general 
possibility of making a construction: but of the actual con 
struction there can be no canons. The attempt to manufacture 
them would lead to the search for a completed infinity; for 
the number of special relations has no end, and the possible 
connections in time, space, and degree are indefinite and inex 
haustible. To find the canons of valid inference you must 
first make a list of valid inferences. You will manufacture a 
major premise for each, and that major premise derived from 
each operation will appear as its canon. Your success, if you 
succeeded, would be the capture of a phantasm, but in the 
endlessness of the field you would be for ever eluded, No 
canon will fix for us the pale of orthodoxy, until that day 
comes when the nature of things will change itself to gratify 
our stubborn illusions. 

7. The popular belief in logic endows it with ability to 
test all reasonings offered it. In a given case of given premises 



CHAP. IV THE PRINCIPLES OF REASONING 269 

the logician is thought to be a spiritual Director who, if he 
can not supply, at least tests right and wrong. Thus, if logic 
is no art which provides us with arguments, yet, once give 
it the premises, and it is both the art of extracting conclusions 
and of assaying all those which amateurs have extracted with 
out its authority. But, understood in this sense, logic has no 
existence, for there is and there can be no art of reasoning. 
Logic has to lay down a general theory of reasoning, which is 
true in general and in the abstract. But when it goes beyond 
that, it ceases to be a science, it ceases to be logic, and it 
becomes, what too much of it has already become, an effete 
chimsera which cries out for burial. 

8. It should not lie alone. There is another false science 
more unlovely in life and more unpleasant in decay, from 
which I myself should be loath to divide it. 10 Just as Logic 
has been perverted into the art of reasoning, so Ethics has been 
perverted into the art of morality. They are twin delusions 
we shall consign, if we are wise, to a common grave. 

But I would not grudge Casuistry a Christian burial. I 
should be glad to see it dead and done with on any terms ; and 
then, if all the truth must be spoken, in its later years it has 
suffered much wrong. That it became odious beyond parallel 
and in parts most filthy, is not to be denied ; but it ill becomes 
the parents of a monster, who have begotten it and nourished 
it, to cry out when it follows the laws of its nature. And, if I 
am to say what I think, I must express my conviction that it 
is not only the Catholic priest, but it also is our Utilitarian 
moralist, who embraces the delusion which has borne such a 
progeny. If you believe, as our Utilitarian believes, that the 
philosopher should know the reason why each action is to be 
judged moral or immoral; if you believe that he at least 
should guide his action reflectively by an ethical code, which 
provides an universal rule and canon for every possible case, 
and should enlighten his more uninitiated fellows, then it seems 
to me you have wedded the mistake from which this offensive 
offspring has issued. It may be true that the office of pro 
fessional confessor has made necessary a completer codifi 
cation of offences, and has joined doctrinal vagaries to ethica 
blunders. We may allow that it was the lust for spiritual 
tyranny which choked the last whisper of the unsanctified 



27O THE PRINCIPLES OF LOGIC BOOK II. PT. I 

conscience. It may be true that, in his effort theoretically to 
exhaust the possibilities of human depravity, the celibate priest 
dwelt with curious refinement on the morbid subject of sexual 
transgression. But unless his principle is wholly unsound I 
confess that I can hardly find fault with his practice; for if 
there is to be an art and a code of morality, I do not see how 
we can narrow its scope beforehand. The field is not limited 
by our dislikes, and whoever works at the disgusting parts, is 
surely deserving not of blame but of gratitude. Hence if the 
Utilitarian has declined to follow the priest, he has also de 
clined to follow his own principles; he has stopped short not 
from logical reasons but from psychological causes. 

9. It is natural to think that logic has to tell us how we 
are to reason from special premises ; and it is natural to think 
that ethics must inform us how we are to act in particular 
cases. Our uncritical logic and our uncritical ethics naturally 
assume these doctrines as self-evident. But the mistake, if 
natural, is in both cases palpable. Unless you artificially limit 
the facts, then models of reasoning can not be procured, since 
you would need in the end an infinitude of schemes to parallel 
the infinitude of possible relations. And a code of morality 
is no less impossible. To anticipate the conclusion in each 
special case you would have to anticipate all possible cases; 
for the particular condition which makes this conduct right 
here and wrong elsewhere, will fall outside the abstractions of 
the code. You are thus committed to a dilemma : at a certain 
point you must cease to profess to go right by rule, or else, 
anticipating all possible combinations of circumstances, you 
must succeed in manufacturing countless major premises. 
The second alternative is in the first place illusory, since the 
principle is really got from the intuition, and in the next place 
it is impossible, since the number of principles will be limitless 
and endless. But if you accept the first alternative, and admit 
that only in certain cases it is possible to deduce the conclusion 
from a principle, you have given up the hope of your " prac 
tical reason," and denied the axiom from which you set out. 

The syllogistic logic possesses one merit. If its basis is 
mistaken and its conclusion false, at least it has not stopped 
short of its goal. In Barbara Celarent its code is perfected, 
and it has carried out the purpose with which it began. We 



CHAP. IV THE PRINCIPLES OF REASONING 271 

can not say so much of the Casuistry of Hedonism. The con 
fident dogmatism of its setting-out has been lost in vagueness 
and in hesitation. It flies to ambiguities it does not venture 
to analyze, and sighs faintly to a Deity which it dares not 
invoke. But if the principle of our most fashionable Ethics 
is true, then an art of Casuistry and a Science of Sin are the 
goal of that Ethics, and the non-recognition of this evident 
result, if creditable to the heart, does no honour to the head. 
If the popular moralist will not declare for a thorough-going 
Casuistry, if he retires in confusion from the breath of its 
impurity, he should at least take courage to put away the prin 
ciples which have given it life. We may apply to him as he 
stands a saying of Strauss, " He partly does not know what 
he wants, and partly does not want what he knows." * 

10. If we return to the subject of the syllogistic logic, we 
may see on the one hand that its moods and figures will not 
take in any one of our syntheses except the synthesis of subject 
and attribute. The fifth, the fourth, the third, and the second, 
refuse to enter the traditional limits. On the other hand the 
first of our syntheses covers every argument of the syllogistic 
logic. An inspection of the figures would at once assure us 
that with positive reasoning this assertion holds good, and we 
must now proceed to test our conclusion by applying it to the 
subject of negative inference. 

* Compare on the subject of Casuistry my pamphlet, Mr. Sidgwick s 
Hedonism, 8, and Ethical Studies, pp. 142, 174, foil (Ed. II. pp. IS7, 
193, foil.)- 



ADDITIONAL NOTES 

i There is a main point in this Chapter where, if not correction, 
at least some explanation seems necessary. All inference depends on 
the unbroken individuality of a single subject; and in this sense all 
inference may be said to fall under the category of subject and 
attribute (Bk. II. I. VI. 13). But, so understood, this category must 
not be taken as merely one among others. It is pre-supposed through 
out as the condition of the rest, which, as against it, will be subordinate 
and special. On the other hand there are inferences which are made 
simply under and by the use of the above category in an individual 
case. This will be true, for instance, of the entire syllogistic logic. 
Hence to say that on my view logic is confined to the sphere of sub 
ject and attribute, or substantive and adjective, would be true or false 



272 THE PRINCIPLES OF LOGIC BOOK II. PT. I 

according to the sense given to such a statement. Everything, I 
agree, must with me fall under this main principle, and I know of 
no other main principle which to myself is intelligible. But to add 
that on my view the other special categories are not necessary, and 
that the conclusions got under these categories could, so far as 
correct, be got without them, would, I submit, be untrue. And I am 
bound to claim whatever merit is due to me for having insisted 
on the opposite. But this double sense in which, in this Chapter and 
elsewhere, the category of subject and attribute may be said at once 
to preside and yet to be co-ordinate, is, I admit, misleading. And 
this double sense, if borne in mind throughout these pages, tends, 
I think, to make part of the detail superfluous. 

The reader should further keep in view the following distinctions. 
We have, first, the knowledge that everything falls within and qualifies 
one individual Universe. We next, in any particular case, have to 
do also with some subordinate individual whole. Now, so far as 
this whole is not taken as known immediately, all the elements 
within it must be somehow interrelated. They all are at least related 
among themselves as common adjectives. Further, having distin 
guished the adjectives within the whole, you can go on to qualify 
this whole by what beyond it is true of any of these adjectives so 
long, that is, as you do not, by a further abstraction, set free and 
substantiate this adjective. And so again, subject to the same con 
dition, you can infer similarity (3). 

But the knowledge you so far possess does not enable you to 
draw conclusions under the more special categories such as Space 
or Time or Degree. These have powers and rights of their own, 
though, while acting by and under these, you can, at the same time 
and concurrently, make use in addition of your power under the 
more general category of subject and attribute. But, so long as we 
remain clear in principle, the effort to distinguish in detail the pre 
cise limits as to where, in this or that case, the above concurrent 
use comes in, seems really superfluous. 

2 " So far as is required &c." Cf. Bk. II. I. II. 9. 

3 " Is not the actual &c." " Is not by itself the actual &c.," would 
have been better. And (lower down) "anything which we shall 
have" is better, I think, than "anything which we have." Again 
lower down, for "get a definite relation" substitute (in the first 
sentence) "a more definite relation," and (in the second sentence) 
substitute "a new direct relation." And (still lower down) after 
"not that general connection" add "nor even anything that follows 
from the mere co-inlierence of A, B, and C in a new apprehended 
whole." 

4 The statement "in the first of these &c.," seems clearly wrong. 
And, otherwise, the conclusion would become illegitimate. 

5 " The categories . . . footing." See i. And cf. the Index. 

6 To " We should then have become circular " add " or should 
have failed altogether." So far, that is, as you take this attribute and 



CHAP. IV THE PRINCIPLES OF REASONING 273 

this subject as immediately one, you remain within one individual 
whole of immediate qualification. 

7 Here Nos. IV and V must be corrected by the insertion of 
" within one world of time or space " after " Where one and the 
same term." We can not assume the spatial or temporal unity of 
all spaces or times. (See Appearance, the Index.) Whether a similar 
correction should be made in No. Ill will depend on the sense which 
there is given to " by virtue of one and the same point." 

The real question everywhere is whether the consequence is the 
self -development of that which we take as the subject, or whether, 
by the intrusion of something foreign, the identity of the subject 
is broken. When we are asked by a writer in Mind (I regret to 
have lost the reference), whether in "A cheats B, B cheats C, and 
therefore A cheats C," we have a valid inference the answer is easy. 
We have here a good inference if we take the action of A on B as 
itself developing itself, without loss of identity, through B into action 
on C. On the other hand the inference is vitiated, so far as we 
suppose a foreign condition to be necessary, such as to destroy the 
process when viewed as the self-development of A s action. 

In connection with the Synthesis of Degree I may remark that, 
though I failed in this volume to notice what is called the argument 
a fortiori, I should at once have placed it under the above head. 
The argument obviously depends on the comparative amount of 
ground. 

s "Private judgment" should be "individual judgment"; and a 
similar correction should be made in the last words of this section. 

9 " For you do not know, etc." The " for " seems here to involve 
some confusion. When (see Note 7) the axiom has been corrected, 
it would be better to substitute for " the two space-relations belong to 
one world " the words " the premises fall under the axiom." 

10 It would, I think, have been better if this attack upon Casuistry 
and Hedonism had been shortened, if not omitted. 



CHAPTER V 

NEGATIVE REASONING 1 

i. The general nature of negative reasoning does not 
vitally differ from that of positive. We have, given us in the 
premises, two or more relations presenting us with certain 
identical points, and on the basis of these points we combine 
the relations into an individual whole. We then by inspection 
find a new relation within that whole. The conclusion rnay 
connect two terms directly, as in A B C . * . A C, or it 
may connect them indirectly, as A B C . . A (B)C, or 
A(B) C. 2 The new line that is drawn may fall clear of the 
middle-point of the construction, or may pass through it on the 
line of the old relations. Negative reasoning and positive have 
all these qualities in common. It is true that in a negative 
inference the line that connects the terms of one relation is a 
line of denial; one part of the figure, which ideally we con 
struct, consists of a repulsion; and the fresh connection we 
draw from that construction is a connection by exclusion. But 
these differences are varieties within the same main principle. 

2. It might seem as if nothing remained for us to do but 
to state and illustrate those negative formulae which corre 
spond to the axioms of affirmative reasoning. And to this we 
shall at once proceed to address ourselves; but it is right to 
premise that there are further difficulties which lie in wait for 
us at the end of this section. 

In negative reasoning we may so state the principle, 3 " If 
B is related within one genus positively to A and negatively to 
C, then A and C are negatively related within that genus. And 
if the affirmative and negative relations (A B, B C) are 
heterogeneous, yet, if one is in the category of subject and 
attribute, there is a negative inference within one or both of 
the two categories which have appeared in the premises." 
Unless A B B C are within the same genus, or unless one 
is a relation of subject and attribute, there is no connection 
at all. 

274 



CHAP. V NEGATIVE REASONING 275 

I. Synthesis of subject and attribute. 

(a) Where the attribute is not taken as distinct from every 
subject, what is denied of the attribute is denied of the subject, 
and where the attribute is denied the subject is denied. 

(b) Where the subject is not taken as distinct from every 
attribute, what is denied of the subject is denied of its attri 
butes, and where the subject is denied then, in that sense, the 
attribute is denied. 

(c) Where two subjects have the same or a different attri 
bute, they are so far not different or not the same. 

Examples: (a) "A triangle has not got two right angles; 
this is a triangle, and has therefore not two right angles." " A 
rectangular triangle is not equilateral ; this figure is equilateral, 
and therefore can not be a rectangular triangle." (b) " Man 
is not a quadruped, man is a mammal, therefore a mammal 
may be (the human mammal is) not a quadruped; and a 
quadruped is not a mammal in every sense of that adjective." 
(c) " My horse is vertebrate, this animal is a worm, and there 
fore is not the same as my horse." 

II. The Synthesis of Identity must become a Synthesis of 
Identity and Difference, "Where two terms have the same 
point in common, and one of them by virtue of this point is 
different from a third, there the other and the third differ in 
this same point." 

Example: "A piano (A) is in tune with B, which is not 
in tune with C, and therefore A and C are not in tune with 
each other." 

In the Synthesis of Degree, of Space, and of Time, we have 
no occasion to alter the formulae. We may give as examples, 

III. A is as heavy as B, B is not lighter than C, therefore 
A is not lighter than C. 

IV. A is not before B in time, B is contemporary with C, 
therefore A is not before C. 

V. A is due east of B, C is not north of B, therefore C is 
not north of A. 

3. We seem to have performed our task successfully, but 
must deal with a further complication. We may be taken to 
have sinned against two prominent rules of the traditional 
logic, since on the principles we have given you may get a 
conclusion from two negative premises, and that conclusion 



276 THE PRINCIPLES OF LOGIC BOOK II. Pi. I 

may at least in part be affirmative. Yet I can not reject these 
traditional rules as errors, and if they have committed over 
sights is a question which turns on their interpretation. With 
out doubt if you interpret negative premises strictly, that is, 
take them in the shape of bare denials, then the rule which 
forbids an inference is valid. And the second rule, which 
confines the conclusion to a mere denial, is without doubt valid 
unless you break through another syllogistic precept. If you 
insist on eliding the middle term, then not only must the result 
be partly negative, but it really is limited to a judgment which 
denies. And thus, if in their statement the rules turn out to 
have gone too far, they at all events have been based on a 
solid foundation. 

It is not hard to understand this; from two bare denials 
there can come no conclusion, because there can not be any 
construction. Why no construction? Because there is either 
no common point, or, if there is a common point, because you 
do not know the position of the other terms. Let us take the 
last first; in negative reasoning we may represent the denials 
by lines of exclusion ; but, if we interpret the premises strictly, 
we find ourselves unable to give these lines any definite posi 
tion. A is not C nor B, but the exclusion of C and the ex 
clusion of B, though we represent them truly by lines of rejec 
tion, fall we know not where. The excluded has got no 
determinate position, and therefore no known relation to other 
elements. 

And this is not all, for if we wish to see the real state of 
the case, we must go back to our doctrine of the negative 
judgment (Bk. I. Chap. III.). A mere denial does not in any 
way give existence or position to the thing it denies. 4 Thus 
in " A is not B " we assert the simple rejection of B by an 
unstated quality belonging to A, and in respect of B we know 
nothing at all but its banishment from our universe. But it is 
obvious that, when a term is so banished, we know about it 
nothing definite save its rejection by A. No matter then how 
many negative premises we may have, since by adding to the 
number of our banished terms we do not get any nearer a 
conclusion. The exiles do not move in any real world at all, 
and to unite them by a line of connection is impossible. 

Thus even if two denials have a common subject, we can 



CHAP. V NEGATIVE REASONING 277 

not go from those denials to a further relation.* And we 
are stopped elsewhere by another obstacle, for we have not 
got the common centre required for a construction. In " A is 
not B and B is not C," we have in the one case the exclusion 
of B, and in the other case the exclusion by B ; we have first 
absence and then presence. And again, if we give our premises 
another form and say " B is not A and B is not C," we can 
not go to a relation between A and C, since (apart from 
other reasons) the quality of B may be quite different in each 
denial. Perhaps from " C is not A and B is not A " we might 
be tempted to argue to a positive relation of partial identity 
between C and B. But here again our centre would be 
wanting, for we do not know if the quality which ensures the 
rejection is not wholly different in each of these cases. And 
thus our premises may furnish a ground for suspicion, but they 
no more give us proof than would such positive premises as 
" A is like B and C," or " A is like B, and B is like C." In 
short given two denials there is either no common point, or 
else the two relations which start from that centre terminate 
in nothing which can be related. 

The rule which forbids all the premises to deny is thus 
shown to have a solid foundation; and we may say the same 
of the rule which prohibits a positive conclusion. For since 
the predicate denied is completely expelled from the world of 
the subject, we are left with no relation beside the repulsion. 
It is clear then that you can not have a positive connection 
either between the predicate and that which exists in friend 
ship with the subject, or between the subject and what shares 
the fortunes of the predicate. In "A B B C," if one 
relation is negative, we can not in any way draw a line A C 
which falls outside B. For A and C will be separated in 
two different worlds, and if one is in any way to come in 
contact with the other, the line of connection must pass 
through B. But on one side of B is a mere rejection, and it is 
therefore evident that a positive line can not be drawn beyond 
the centre, and that the new relation must add to the rejection 
which already exists in B. It is indeed not true that this 

* In "A is not B and not C, therefore B and C are so far alike " 
the premises are positive. B and C are both discrepant in quality with 
A, or have the psychical fact of rejection in common. 

2321.1 x 



278 THE PRINCIPLES OF LOGIC BOOK II. PT. I 

extension is a mere denial, and again it is not true that the 
conclusion must be wholly negative ; but for all that the second 
traditional rule has, like the first, a rational foundation. 

4. But though both the precepts stand on a solid basis, 
the meaning of the first calls for some restriction, and the 
second is not true without an exception. Two denials should 
not give a conclusion at all, and yet you can not say that of 
two premises which deny. In his Principles of Science, p. 63, 
Prof. Jevons has called attention to the subject; 

"Whatever is not metallic is not capable of powerful magnetic 
influence, (i) 

Carbon is not metallic, (2) 

Therefore, carbon is not capable of powerful magnetic influ 
ence (3)." 

This argument no doubt has quaternio terminorum and is 
vicious technically, but the fact remains that from two denials 
you somehow have proved a further denial. " A is not B, 
what is not B is not C, therefore A is not C." The premises 
are surely negative to start with, and it appears pedantic either 
to urge on one side that " A is not-B " is simply positive, or 
on the other that B and not-B afford no junction. If from 
negative premises I can get my conclusion, it seems idle to 
object that I have first transformed one premise; for that 
objection does not show that the premises are not negative, 
and it does not show that I have failed to get my conclusion. 
And if we leave the limits of the syllogistic logic examples 
come to us from every side ; " A degree A can not be less 
than B, B is not less than C, therefore C can not be greater 
than A, or A must be equal to or greater than C ; " " Event 
A is not before B, C is not after B, therefore A is not before 
C, or C is simultaneous with A or before it ; " " C is not 
north of B, B is not north of A, therefore A is not south of C, 
or A is due east, or west, or on the north side of C." It is 
bootless here to fall doggedly back on the technical rules of 
mood and figure, since, if we keep to these, we can not even 
prove the positive conclusions from the positive premises. If 
" A to right of B " is a positive relation of A to B which can 
not be reduced to predicate and copula, why should we not 
have in " A not to right of B " a negative relation which is 



CHAP. V NEGATIVE REASONING 27Q 

also irreducible? The traditional logic may object to the 
latter, but it has put itself out of court by first objecting to 
the former; and, if it is quite wrong in one case, it may be 
quite wrong in another. 

5. In this case it is not wrong, for it happens to be right. 
The restricted portion of the field it occupies happens here to 
be the limit of the subject. For denial as such can not fall 
outside the single category in which the syllogism is shut up. 

A denial as such, we have seen long ago, is merely the 
exclusion of an ideal suggestion, and hence no negative rela 
tion between positive existences can ever be expressed by a 
mere denial. But then on the other hand a bare denial can 
never be found, for, when A excludes some relation to B 
which is offered in idea, there must always be a ground for 
that rejection. The base of the rejection must be a positive 
quality, unspecified but necessary; and hence, wherever we 
have negative judgment, we have in addition some positive 
assertion, which may not be explicit but which must be there. 
And this, as we saw, is such a fount of ambiguity that in 
denials we seldom know all we are saying (p. 125). 

We may verify this in the examples we have used. In the 
first we assume that A has degree, and upon that basis of 
positive assertion we proceed, by exclusion of the alternatives 
denied, to a positive result. In the second the argument 
really starts from " A is an event with a position in the series 
after or simultaneous with B." In the third we assume that A 
falls in space and in a relation to B marked out by exclusion. 
In all these if we kept to mere denial we could not prove 
anything, since we may deny " less than B," or " prior to B," 
or " north of B," of what has no degree and no time and no 
position. Such a course might be unusual but is legitimate 
and recognized, because the denial as such covers all pos 
sibilities. 

6. If we take as our rule that from negative premises you 
can not argue, then, stated so, that rule is incorrect^; and it is 
false even to say that denials give no inference, since every 
denial has a positive side. That positive side is latent and 
may escape us ; in " 7 is not less than 5 + i, 5 + i not less 
than 4, and therefore 7 is not less than 4," we do not say that 
7 is a number at all and must stand in some numerical 



280 THE PRINCIPLES OF LOGIC BOOK II. Px. I 

relation with 5 + i. And thus in assuming it we have passed 
beyond the denial, though not beyond what the denial im 
plies. It is necessary therefore in expressing our rule to 
make a distinction. You can not argue, we must say, from 
two denials, so long as you keep to bare denial. If you 
treat the assertion which those denials imply, then you are 
not keeping to the side of denial. And, if we formulate it 
so, the rule will hold good. 

Denial implies removal or exclusion, and from exclusions 
or removals you can get a conclusion. " Removal of A is 
removal of B, removal of B is removal of C," gives " Removal 
of A is removal of C ; " and " Absence of A is absence of B, 
absence of B is absence of C," proves that absence of A is 
absence of C. But here our real premises are " What re 
moves A removes B," and " That which is without A is also 
without B." You can hardly say that these premises are 
quite positive, but they contain much more than a bare denial. 
Thus negation must always remain ambiguous (Book I. 
Chap. III.), for "No A is B," may merely banish B, while 
again it may assert " The absence of A is the presence of B." 
" If A is there then B will not be there," and " Since A is not 
there B must be there " are both expressed by this doubtful 
formula. But if we confine negation to mere denial it is the 
exclusion of an idea by an unspecified quality, and if we con 
fine the denial to its negative side it is the mere exclusion of 
a suggested idea. It is upon this last understanding that the 
traditional rule is actually valid. 

It would not be valid if negation were assertion. If in " A 
is not B " the exclusion of B were a condition necessary to 
the existence of A, then B must be banished if A is to be 
there, and if B is not there B can not be banished. And from 
negative premises, if so interpreted, it no doubt might be 
possible to get some conclusion. But this interpretation we 
long ago saw was erroneous. The denial excludes an ideal 
suggestion, and the fact which lies at the base of the exclusion 
need be no relation of A to B, but on the other hand a quality 
of A or again of some more ultimate reality. But this quality 
is latent and wholly unspecified. 

7. We have seen that, upon a strict interpretation of 
negative premises, the first of the rules we mentioned is valid. 



CHAP. V NEGATIVE REASONING 28l 

What then is to become of our principles of synthesis, since 
they collide with the rule and can not be true ? But I think it 
is better to leave them standing, for they are valid if the 
sense of negative premises is not confined to what they deny. 

Otherwise of course they must be corrected. It is im 
possible to have any negative inference which will fall wholly 
within the categories of identity, or time, or space, or again 
degree. One premise at least must confine itself to the rela 
tion of subject and attribute. 

This is very obvious. One premise must deny, and no 
denial as such can be referred to any category beyond the 
relation of attribute to subject. The denial is the exclusion 
of an ideal suggestion, and a relation of time, or space, or 
degree falls within this suggestion which the subject repels. 
It is clear then that the denial of a connection, say of space, 
is not a connection in the category of space. The subject 
excludes, it is true, by a quality, but you do not know what 
that quality is. And since you do not know what quality 
repels, the repulsion and the quality which forms its basis can 
not pass beyond the sphere of simple attribution. Thus " A 
is not north of B," if restricted to denial, means " A repels the 
suggestion A to north of B ; " and we can not possibly take 
this as anything more than an adjective of A. 

If we refer to the examples we gave in illustration (2), 
we must so interpret the negative premises. "B is not in 
tune with C " means " B excludes the attribute of being in 
tune with C," and " B is not lighter than C " means " B ex 
cludes a certain relation of degree to C." But of course B 
might repel these relations with C although it possessed no 
note at all, and although it had no degree of any kind; and in 
the same way the denial that B is in such a position may be 
true though B has no place whatever. If one of the premises 
be confined to denial that premise is shut up within the 
category of subject and attribute. m f 

But having so restricted the character of our premises it is 
natural to expect a restricted result. Our rule will now be, 
" In all negative inferences the conclusion is confined within 
the relation of subject and attribute, unless that conclusio 
can in any way be affirmative." m 

8. But can the conclusion be anything but negative! 



282 THE PRINCIPLES OF LOGIC BOOK II. Pi. I 

This is the question we have next to discuss. The rule for 
bade an arhrmative result, and we saw that this rule was 
based upon truth. For since in A B B C one relation is 
negative, A C can not be joined by a line of connection 
which passes anywhere except through B. And, since part 
of this line must consist of an exclusion, we saw that A C 
must have a negative character (3). 

The result is unshaken, but it omits a possibility. The 
conclusion need not take the form of A C, since the result 
which we get from the union of our premises, may be found in 
the whole ideal construction. The syllogistic practice is to 
elide the middle; but if we do not choose to perform this 
elision, who on the one hand can order us to do so ? And on 
the other hand who can deny that the result which we obtain 
is a real inference? " A takes precedence of (is lighter than, 
sits on the right of) B, B is not younger than C, therefore A 
takes precedence of (is lighter than, sits on the right of) a 
person (B) not younger than C." There is here no direct 
conclusion A C, and there is again no inference within one 
category, and at the same time one premise seems to be used 
as mere denial. On the other hand I see no reasonable ground 
on which we can deny that we have got a conclusion. Yet 
this conclusion is neither a mere denial, nor does it fall within 
the category of subject and attribute. 

We may go beyond this. In the syllogism itself, if we 
decline to elide the middle term B, we may have an inference 
the conclusion of which is more than a denial. Take an 
instance in Celarent, "A lung-breathing animal (B) is not a 
fish (C). All Cetacea (A) breathe by means of lungs (B)." 
From this the regular conclusion is " A is not C." But " All 
Cetacea have a quality, viz., breathing through lungs, which 
excludes the assertion that any are fish," will surely come with 
out flaw from the premises. It certainly is more than a bare 
denial, and it is no mere repetition of the premises. And to 
say, If A does not exclude C after the middle has been elided, 
there shall be no inference and there can be no conclusion, 
seems purely arbitrary. Nor indeed do I see how this in 
sistence on elision, if we pressed it to its consequences, would 
prove compatible with the general validity of the third figure. 

9. The result we are left with may thus be stated. From 



CHAP. V NEGATIVE REASONING 283 

two denials there is no conclusion. If one premise denies and 
keeps to denial, then one premise at least is limited to the 
genus of subject and attribute. If the middle term B falls out 
of the conclusion, if A and C are connected through B, but 
not by means of an intermediate B, then the conclusion denies 
and falls also within the above-named genus. But if B is kept 
standing, the conclusion may at least in part be positive, and 
is not confined to a single category. 

The general formula for negative reasoning, if we confine 
ourselves to the side of bare denial, may be stated as follows : 5 
If B repels a content C, and is in relation with a third term 
A, then A and C will either be related directly by way of 
denial or else will be elements in a whole A B C, of which 
at least one member will be confined to the genus of subject 
and attribute. And I think with this we may take leave of a 
subject which has proved perhaps more troublesome than in 
teresting. 



ADDITIONAL NOTES 

1 The statement that all reasoning, negative as well as positive, 
depends on an ideal whole, and that this whole can be called a con 
struction, is so far correct. But otherwise this section, and much of 
what follows, is unsatisfactory. Every negation (see on Bk. I. Chap. 
III.) implies a disjunction. And only because, and so far as, negative 
reasoning is based on and further developes a disjunctive totality and 
system does it possess a real value. For an admirable exposition 
of this view the reader is referred to Bosanquet s Logic. 

If we keep to mere denial, what is denied will certainly fall some 
where else in the Universe, since no mere ideas are possible. But, 
because the variety of special worlds within the Universe is indefinite, 
and because the merely denied is not, so far, located, you can base 
no special connection on the fact of mere simple denial. If negation 
is to be fruitful, it must (to repeat this) stand upon and move within 
a scheme of specialized alternatives, related to each other at once 
as positive and negative. 

Hence it is scarcely worth while for me to attempt to correct 
chapter in detail. I will, however, touch on a certain number < 
points. 

2 The usual demand for the elision of the middle term seems n 
defensible, and any rule that the conclusion must merely deny shou 
therefore be modified. See 8. But the rule which condemns 



284 THE PRINCIPLES OF LOGIC BOOK II. PT. I 

two negative premisses, in the sense of two denials, must stand. For 
what is denied may fall in worlds not so connected as to make a 
construction possible. Hence, unless by going beyond mere denial one 
premiss becomes positive, no conclusion can be reached. In 4 after 
quaternio terminorum " we should add " or else one positive premiss." 

3l lf you keep to mere denial, as distinct from exclusion, repulsion 
or absence, all that is implied is an unspecified whole (x) containing 
two diversities (A and B). These must be positive, but, so far as 
you merely deny one of the other, you attend simply to their differ 
ence. Further, by identifying one of them (A) with C, you can 
deny the other (B) of C. But neither here nor elsewhere is there 
any inference through mere denial beyond the category of subject 
and attribute. As soon as you have assumed worlds containing 
arrangements and relations other than those of identity and difference, 
you have gone beyond mere negation in the sense of denial. 

Hence the "general formula" (9) can not stand, and should 
perhaps be read thus " If you deny of B a content C, C can also 
be denied of that which is identical with B, and can further be 
related indirectly by denial with that which is related positively to B." 
But, though in the latter case the " conclusion " need not be " con 
fined to a single category," the inference, and what actually is 
concluded, never goes beyond the category of subject and attribute. 
Statements to the contrary ( 2, 8, and 9) are erroneous. 

4 In the way of minor corrections I may here note that we should 
insert "definite" before "existence or position"; and (at the end of 
the paragraph) should read "move in any one real world at all." 
And, generally, I would remind the reader that such terms as "re 
moval," " exclusion," " repulsion," and even " absence," all are affirma 
tive in the sense of at least containing a positive aspect. And this 
aspect goes beyond what is contained in negation, if and so far as we 
take that as mere denial. 

6 For " the general formula " see Note 3. 



CHAPTER VI 

TWO CONDITIONS OF INFERENCE 

I. We may briefly recapitulate the result we have 
reached. An inference is always an ideal construction result 
ing in the perception of a new connection. So far as this 
perception of the conclusion is concerned, there is no possibility 
of laying down rules, and the syllogistic logic teaches a super 
stition. That logic again has failed to include all the prin 
ciples of synthesis which operate in construction, and it is 
falsely confined to a single category. It is wrong again as 
to the number of the premises ; and, in insisting on the neces 
sity of a major premise, it is clinging blindly to exploded meta 
physics in direct defiance of the most palpable facts. And it 
makes a further mistake as to the necessity of elision. 

It might seem that having thus rejected the syllogism we 
must throw in our lot with its hereditary enemies. But yet, 
if the friends of the syllogism will allow it, we would rather 
take a place on their side. Our differences are trivial com 
pared with our agreements, and as against the enemy our 
cause is the same, for we have in common these two beliefs : 
(i) It is impossible to reason except upon the basis of identity, 
(ii) It is impossible to reason unless at least one premise is 
universal. It will be time to say vlcerunt empirici when these 
positions have both been forced. 

2. (i) I will begin with the necessity of an identical 
point. We know that an inference is an ideal construction, 
and the reality of this construction depends on its unity; if 
the construction is not individual it is merely fictitious. But 
how can any construction have unity unless it is united by 
a common point? And how can any point be common, unless 
in both the premises it is one and the same? 

It is obvious that suppose the problem before us is to find 
the relation of S to P by means of their common relation to M, 
and if, by the hypothesis, S-M and M-P must be given 
separately, an advance is impossible, unless in both premises 

285 



286 THE PRINCIPLES OF LOGIC BOOK II. Px. I 

M is the same. Given S M 1 & M 2 P you can make no 
construction, for you have no bridge to carry you over from 
M 1 to M 2 . The back of your inference now is broken and the 
extremities no longer belong to any individual principle. Un 
less M in both cases is absolutely the same you can not inter 
relate S and P. 

If we are willing to give up the superstition of the copula 
and to admit a diversity of relations in judgment, we may say 
that in inference every pair of premises has one term the same, 
and that, if it is not the same, there can be no inference. 

3. It is obvious, if we dismiss our hardened prejudices 
and consider the question fairly by itself, that you can not 
argue on the strength of mere likeness. 1 Whatever else may 
be right this at all events must be wrong ; " A is similar to 
B, and B to C, and therefore A is like C," is a vicious infer 
ence, one that need not always be mistaken in fact, but that 
always must be a logical error. In practice I think we should 
all admit this. An inference based on nothing but likeness 
is utterly invalid; it is certainly ambiguous and probably 
false. 

Likeness and sameness should never be confused, for the 
former refers properly to a general impression. Similarity is 
a perceived relation between two terms which implies and 
rests upon a partial identity. If we say that A and B are 
alike, we must be taken to assert that they have something the 
same. But we do not specify this point of sameness, and the 
moment we do that we have gone beyond mere similarity. If 
A and B for instance both have lungs or gills they are so 
far the same, and, on the strength of and because of this 
partial identity, they may present themselves to us as 
generally similar. But now add to these the further statement 
" B and C are alike." If we reduce the likeness here to 
partial identity we may find that the common point is here 
once again the possession of lungs or gills, and on the strength 
of this we may go on to argue that A and C (the extremes) are 
alike. But what actually interrelates A and C is not general 
similarity at all. If all you knew was that B was like C, the 
point of identity would be quite unspecified, and the fact 
might be, not that both had lungs or gills, but that each had 
one eye or the freedom of the will. In this case though each 



CHAP. VI TWO CONDITIONS OF INFERENCE 287 

pair has its own internal likeness, you could not infer the 
similarity of A to C. 

And if in answer I am told that this is irrelevant, and that 
it does not apply where the likeness is exact, I can only reply 
that I am waiting, and have been waiting for years, to be told 
what is meant by an " exact likeness." " A and B are not the 
same, but they are exactly alike, and therefore whatever is 
true of B must be true of A." But what can this mean? In 
the case of some twins it might be right to punish one for the 
other, and we should no longer care to identify criminals. 
If a picture is " exactly like " a person, then if one is not dead 
the other will be alive. If a cast is " exactly like " an original 
I suppose the same thing will be in two places at once ; and it 
is no mere metaphor if in certain cases the father is said to 
survive in his children, though the children might then cease 
to survive the father. But it is idle to pursue these frivolous 
consequences; the meaning which "exactly like" carries to 
my mind is nothing whatever but "partially the same" or 
"identical in some point or points." Likeness is always a 
perceived relation based upon a partial identity. In mere 
general similarity the identity will be indefinite; where the 
likeness is more special it must at least be partly defined, 
and where the similarity is called "exact" I understand that 
there is a definite point or points, in respect of which the same 
ness is complete. And if likeness did not imply identity all 
inference based upon it would be vicious. In practice every 
one would allow it to be vicious, nor do I understand how in 
theory it is possible to take it as having any other character. 
I am most anxious to enter into (if I can), and to discuss 
the meaning our "advanced thinkers" may have attached 
" likeness " or " similarity." But I am forced to say again in 
this place what I had to say elsewhere some years aga 
While our "advanced thinkers" merely sing the old song 
which they have learnt and which their fathers have taught 
them, they can hardly expect to have its meaning discussed 
nor can they complain if they are treated as having no 



construction of given premises is not possible un- 
less each pair of premises has a common point. And 
* Ethical Studies, p. 151 ( Ed - IL P- 



288 THE PRINCIPLES OF LOGIC BOOK II. ?T. I 

common point must be an identical term. Thus in "A B 
B C therefore A B C" the B in each premise must not 
be merely alike, but must be absolutely the same. But here, 
after having avoided one error, we are threatened by another 
and opposite mistake. For if it is wrong to say that B is not 
the same, it is equally wrong to deny that it is different. 

This may look mysterious but is really quite simple. If 
B in both premises were so far the same that no difference of 
any kind belonged to it, then it is obvious at once that both 
premises must be identical, or else that their differences do 
not concern B. But in each of these cases the inference dis 
appears. If the premises are the same their repetition is 
meaningless, and if the differences they contain are indifferent 
to B it is clear that no construction can be made, since, if B 
is the centre, it carries no radii and has no circumference. An 
identity which is not a synthesis of differences is plainly inert 
and utterly useless. 

B is the same amid difference, and though different is the 
same, for it is an ideal content, the product of abstraction, 
appearing in and differenced by two several contexts. So far 
as it is the one content B, so far it is absolutely and entirely 
the same ; so far as it is a member of diverse connections, so 
far it carries with it a difference. And the process of inference 
depends entirely on this double aspect; for it is because B is 
different and yet the same, that its differences are able to be 
interrelated. If it were not different it would have nothing 
to connect, and if it were not the same there could be no 
connection. Inference rests upon the assumption that, if the 
ideal content is the same, then its differences will be the radii 
of one centre. In other words if B is the same, what is true 
of it in one context is true of it in another. 

5. We have returned to what we called the Principle of 
Identity (Book I. Chap. V.). We might call it again the 
Axiom of the Identity of Indiscernibles, and we can put the 
thing in more simple language if we say that inference rests 
on the principle that what seems the same is the same, 2 and 
can not be made different by any diversity, and that so long as 
an ideal content is identical no change of context can destroy 
its unity. The assumption in this principle may be decried as 
monstrous, and I do not deny that perhaps it is false. In a 



CHAP. VI TWO CONDITIONS OF INFERENCE 2Q 

metaphysical work this question would press on us, but in 
logic we are not obliged to discuss it (Book III. Part II. 
Chap. IV.). The axiom may be monstrous or again it may 
be true, but at least one thing is beyond all doubt, that it is 
the indispensable basis of reasoning. It may be false meta 
physically, but there is no single inference you possibly can 
make but assumes its validity at every step. 

6. It is easy to misunderstand it, and it is sure to be 
misunderstood. I shall be told that spaces and times are 
indiscernible and yet are not identical. But this objection 
rests on a complete mistake. As spaces or times of a certain 
character A and B surely are identical ; as different elements 
within the same series A and B are surely not indiscernible. 
It is one superstition to think you have relations whose 
terminal points are nothing beyond the relation.* It is 
another superstition to fancy relations as an arbitrary network 
stuck on from the outside by destiny or chance, and making 
no reasonable difference to anything. And the root of both 
superstitions is the same. It is the refusal to recognize that 

* I am prepared to go a good deal beyond this. 3 If occasion offered 
I should be ready to argue that you can not have a relation between 
points that are not different in quality. Not only, for instance, must 
spaces related be more than a mere relation in space, but they must 
also have a difference in quality. It is not possible to contemplate 
points in relation unless you distinguish them by a qualitative reference 
to the right or left or upper or lower sides of your body, and the 
different sensations which are at the root of these divisions, or again 
unless, by a qualitative mark such as A or B, you choose to make one 
different from the other. It may be objected that in certain cases the 
difference of quality is only one aspect of the whole relation. This 
view at least recognizes the existence of the difference, and I will not 
here discuss it. The ultimate connection of quality and relation is a 
most difficult problem. But it is clear that taken in their phenomenal 
appearance the one can not be reduced to the other. Is this double 
aspect true of the reality? Has that, as we are forced in the end to 
apprehend it, a single nature which combines two sides, and is so the 
root of the double appearance? Can we suppose that qualities are 
generated by the strife of some counterpart of what appears to us 
as relations? Or is it true that supersensible qualities are the reality 
which we perceive as phenomenal relations? Or is the question un 
answerable? If it is, we at least must not do violence to the given on 
the strength of a theory which we can not defend (cf. Book I. Chap. 
II. 65 foil.). 



2QO THE PRINCIPLES OF LOGIC BOOK II. PT. I 

the content of the given has always two sides, 4 sensible quali 
ties and relations, and that one side can never, except by an 
artifice, be separate from or merged in the other. I do not 
say that these two elements are metaphysically irreducible; 
I do say that, taking them each as it stands, you must treat 
them each as a character of the given. It is a dire illusion 
to take the content of the given as either qualities without 
relation or relations without qualities, or to treat the one 
side as external to the other. Both are given together and 
given within the content. It was shown above (Bk. I. Chap. 
II. 21) that space and time-relations are no principium in- 
dividuationis ; for they fall within the what, and do not make 
the this. 

And another result was brought out in that Chapter. Un 
less judgments of sense make a false assertion they affirm 
or deny connections of content, and they do not affirm any 
thing else whatever. It is absurd to object that if Caesar is 
the same, he is in Gaul and in Italy, two places at once, or 
that if he is thirty he is also twenty-nine. The " at once " 
and the "also " conceal the old error. Of course it is not true 
that the identical Caesar under the same conditions 5 can be 
differently related to Italy in space or to his own birth in 
time; but then surely the conditions vary indefinitely. The 
mere lumping together unspecified conditions under the head 
" is now " does not show that the conditions are indiscernible, 
and that striking the differences out of the account we are 
forced to predicate contradictions of Caesar. What is true of 
Caesar in a certain context is true of the same Caesar in any 
other context. But this does not mean that one context is 
the other or is to be confused with the other. It means that 
Caesar has two different contexts, and that the truth of one 
can be no reason whatever for the falsehood of the other. If 
we fancy this is so we have given to one or to both assertions 
a meaning which is false, and we must be sent back once 
more to study the discussions of Book I. Chapter II. 

7. And there is another misunderstanding against which 
we must guard. That what is true of B here is true of B 
everywhere, means that, wherever B happens to be, you can 
say of it always what you have said of it once. This B you 
assert of is the self-same B that appears in the differences, but 



CHAP. VI TWO CONDITIONS OF INFERENCE 2QI 

it is not the B just as it appears in those differences. In 
A B, B C, the B is identical, and A and C are connected 
by that identity. But A and C are not themselves identical, 
and you can not predicate B C of A B. The B, of which 
what has once been said holds good for ever, is not the B 
which is one thing with A or one thing with C. It is the ab 
straction, 6 the idealized content B, which is different from its 
contexts and yet connected with them, and on the strength of 
its oneness connects them together. The identity is always a 
synthesis of differences which themselves are not identical the 
one with the other, and apart from these differences the 
identity disappears into blank indiscriminateness. 

I will try to illustrate the whole question briefly. We 
have a shed in the corner of a field, and, that shed being burnt, 
another is set up not distinguishable in itself from the first. 
Let the first be B A and the second B C ; in what sense 
is it true that what holds of B once will hold of it always? 
The objection is obvious, In the shed B A an event D hap 
pened, but can we say that the event took place in B C? 
And if we can not say that, and if B is not distinguishable, how 
are we going to defend our axiom? 

We are in no kind of perplexity. The content B is ob 
viously not the individual shed. The two sheds are made 
individual by their places in the series, and those places fall 
outside the abstraction B. What is true of B is universal 
propositions and is nothing besides. The event D can not 
be asserted truly until it becomes a hypothetical statement 
(Book I. Chap. II.). 

But the objection will be pressed, " The sheds and their 
environment are a certain content, and that content is the 
same. If, on the strength of this content, we said of the shed 
B A D happened here yesterday/ why can we not also 
upon this ground now say of the shed B C D happened here 
last year ? The content is what we go from, and we have 
that in both cases." I reply, By all means: the content is 
the same. Let us try to carry out the process you recom 
mend. We can not of course connect D with B C unless 
we establish a chain of relations through the identity of their 
end-points (ibid.). You can not go direct from the content . 
to the temporal event D, for that, as we have seen, is not 



THE PRINCIPLES OF LOGIC BOOK II. PT. I 

predicated categorically (ibid.). 7 You must start from the 
content as given in one time. Well, starting from B A you 
got a chain of events which took you back to D. But, if 
you start from B C, you have a chain of events which takes 
you back first to the origin of B C, when B did not exist, 
and then again through the destruction of B A, to the time 
when B once more existed and was connected with D. Your 
process informs you that D the event will not fall within the 
identity of the ideal content B C. That content has been 
qualified by a limitation in time, and qualified again by a 
definition of its component elements, which excludes their 
identity with the elements of B A. If you deny that these 
qualifications are objects of knowledge, then I admit D is true 
of B C, and why in the world should we not think it true? 
But if you admit that these qualifications are distinctions, then 
the content of the sheds is not indiscernible, and therefore by 
your admission is not identical. 8 

This, I think, is a sufficient answer to the objection, but 
it omits to take notice of several difficulties. There are ques 
tions which no doubt might occasion us trouble, but they 
do not seem to concern us here. We have been forced to 
notice a metaphysical problem which, at least in this work, 
we can not deal with, and hence objections which we can not 
here attempt to answer may be directed against us. But at 
least on one side I think we are safe ; we need fear no col 
lision with the Philosophy of Experience, for that philosophy 
does not know the ground it stands on. Since Hume s bold 
speculations on the subject of identity were suppressed by 
himself, the English school has repeated a lesson by rote and 
flaunted a blind ancestral prejudice. 

8. The importance of the subject may excuse a repe 
tition. That what is the same ideally is really the same is 
without any doubt an enormous assumption, and I do not say 
that this assumption is true. What I do say is (a) that all 
inference presupposes it, and (b) that the objection to it rests 
on nothing but metaphysics. 

(a) If we only will look at the palpable facts, we must 
admit that logic stands or falls with this axiom. Wherever 
we join one premise with another we must do so by means of 
an identical point, which, given as it is in diverse presenta- 



CHAP. VI TWO CONDITIONS OF INFERENCE 2Q3 

tions, is held to be the same because it has the same content, 
and which, so far as it is not ideally discernible, is taken as one. 
Failing this identity the construction falls apart. I confess I 
do not know how to make this any clearer. I can only say 
to any one who doubts it, Show me an inference where this 
does not hold good, and I will show you a vicious inference, 
and you yourself shall admit that it is vicious. 

(b) It sounds terrible to say that Identity is an ideal syn 
thesis of differences, and that this identity is real fact. The 
words are strange to the common mind, but it has always 
tacitly accepted their meaning. We believe that a body has 
changed its place, but at the end of the movement the change 
that is past is no fact of sense. We abstract the body from 
its present position and, treating this abstraction as a con 
tinuous identity, we predicate of it the changing differences. 
But do we doubt that motion is a real fact? And if we are 
told, It is the material atoms which are the same throughout; 
then why I would ask do we take them for the same, despite 
their differences of time and space, except because their ideal 
content is the same? The identity of indiscernibles may be 
true or false, but not only is it impossible to reason without it, 
but it is the abstract formula for our common-sense belief. 

The authority of common sense is no authority for me, 
but the result we have reached may bring out one fact.^ The 
objection, raised by the Philosophy of Experience against a 
real identity, does not rest on any difficulty felt by common 
sense, and it is not an objection it would ever think of raising. 
It is a metaphysical objection, and it rests entirely on a 
metaphysical doctrine. It is because the Philosophy of Ex 
perience is sure that there is no reality except exclusive par 
ticulars, that it is horror-struck at the thought of a real 
universal. And because its belief is not proved nor thought 
to need proof, nor in any way discussed, because it is a mere 
inherited preconception which has got to think itself a real 
fact, it is scarcely so much to be called a doctrine as an 
orthodox dogma and traditional superstition. 

And, as it must happen with all orthodox dogmas, its 
votaries do not take their professions in earnest. If an uni 
versal content may ever be real, on what ground can they 
deny the identity of thoughts because one is yesterday and 

2321. I U 



294 THE PRINCIPLES OF LOGIC BOOK II. Px. I 

the other to-day? But if such ideal sameness is not real, 
then how can any process or change or continuity be any 
thing but illusion? If a thing is not now the same that it 
was, if it is only alike, then it can not have changed. And if 
it is the same, on what ground do we make that assertion 
except on the ground of identity of content? It is frivolous 9 
to say that identity may be real, where existence is continuous 
and is not broken in the series of time, but is not real any 
where else. For if you allow that any lapse or change is a 
fact, you have admitted the reality of an element not confined 
to this or that particular, and you have admitted it on the 
ground of the identity of indiscernibles. You have already 
thrown your principle overboard, and if it is false in one 
place it may be false in another. Or to put the same thing 
in another form, if you are afraid to break with common sense 
in one point, what makes you so very bold in another? If I 
am to answer the question for you, I am forced to say that 
you have partly no head and partly no heart. You do not 
see the consequences deducible from your doctrine, and when 
a consequence begins to look like a reductio ad absurdum, you 
refuse to follow it. And this is what we call or used to call 
" advanced thinking." 10 

9. It is against such opponents that the syllogism is right. 
The doctrine of copula and terms which it cherishes is in 
defensible, but it is right in demanding an identity in reason 
ing. The middle is an identity which connects the differences, 
and, being such an identity, the middle is an universal. In 
this point again the syllogism is right. For though the major 
premise is a superstition, one premise at least must be uni 
versal or else there can be no inference at all. We have here 
again a condition necessary to reasoning. 

10. (ii) We saw in the second chapter of Book I., and 
later on again in Chapter VI. 39, that in the end no judg 
ment is really particular. 11 They are all universal. And we 
might content ourselves here with recalling the result we there 
have reached, but, perhaps at the risk of superfluity, we may 
add some further remarks on the subject. If one of the 
premises were not universal, how could they both have a com 
mon identity? The term B must be shared by both the 
premises. It is a single content in two different contexts. But, 



CHAP. VI TWO CONDITIONS OF INFERENCE 295 

since thus it is universal, at least one premise must have the 
same character. 

This simple consideration is, I think, sufficient for any 
one who has put himself at the right point of view. But not 
withstanding all our previous discussions, there no doubt will 
be readers still unwilling or unable to follow us in this argu 
ment. " In A precedes B and B precedes C can B," we shall 
hear, "be really universal? Nay even in the syllogism, if we 
take the third figure, is the middle term really an universal? 
It is so technically because it is distributed, or understood in 
its full extension, but these technical distinctions have long 
ago been thrown overboard, and with them has gone the uni 
versality of singulars." I will briefly reply to the above objec 
tion. 

II. An universal judgment is one that holds of any 
subject which is a synthesis of differences. It is a proposition 
the truth of which is not confined to any single this. The 
subject extends beyond the judgment, and, where the subject 
goes, the judgment is true. In this sense we have seen that 
all judgments are universal. But we are limited here to a 
simpler issue, for we have to show, given a valid inference, 
that at least one premise is universal. It is quite enough, as 
we have just remarked, to consider the identity of the middle 
term: but a more detailed exposition may perhaps be wel 
come. 

There are certain cases which call for no discussion. 
Where the middle term is an abstract attribute, and this forms 
the subject of one of the premises, there one premise must 
be allowed to be universal.* 

The difficulty which is felt arises from those cases where 
the middle term is a singular, or where it is not the ostensible 
subject of either premise. Take for instance " A is to right of 
B, and B of C, and therefore A of C," or " A and C have 
the note B in common, and therefore C is in tune with A, 
and both related by the identity of B." How in such infer 
ences as these can we show that one premise must be universal? 

* In order to bring arguments into this form we may freely convert 
any negative judgments. Thus in the second figure we may convert 
as required, negative premises or conclusions. The case 
presents no difficulty. 12 



296 THE PRINCIPLES OF LOGIC BOOK II. Pi. I 

12. Unless our previous discussions have led us quite 
wrong, such a question as this can be readily answered. " B 
is to right of C " is an universal judgment because B is an 
identity which has the differences of its spatial relations to A 
and C. ia It transcends the context B C and is therefore 
universal. Or, from another point of view, the relation B C 
is true of a subject which extends itself beyond those limits, 
and is the identical subject of which the relation A B is 
also true. If you take the relations as qualifying B, then B is 
the universal which exhibits these differences. Or again if you 
go somewhat further back, then the unity of the common 
space is the genuine subject of which these relations are 
diverse attributes. We can always find an identical subject 
although that subject need not be apparent. In " Caesar is 
angry and Caesar is silent, and therefore silence may accom 
pany anger," it is the grammatical subject which supplies the 
universal within whose identity the synthesis holds good. But 
where from " A has a certain note B and C has also the self 
same note," we infer a relation between A and C, it is doubt 
ful where the actual subject lies. If we are willing to accept 
the grammatical subject, then in " C has the note B," C is our 
universal. For C is disturbed from its original context and 
expanded ideally so as to form a whole with A. And, if it 
were not universal, it could not be treated as a subject waiting 
to receive a predicate beyond its original given existence.* 
This would be the right interpretation if A and C are to be 
considered as subjects. But it is better here, I think, to take 
the middle as the actual subject of both the premises. B is 
the universal of which we predicate the difference B A and 
the difference B C, and it is the bond of identity which 
interrelates the whole. 

13. We shall see hereafter that every inference may be 
taken as holding within the identity of one subject (Book III. 
Part I. Chap. VI. 34), and if we take this view it is obvious 
that the subject of both premises is universal. For the present 
it may prove sufficient to remember that, inference being an 
ideal construction and involving therefore an ideal centre, one 
premise must be taken as true beyond the limits of a par- 

* Of course if you suppose the relation A C to be a perception 
got simply from the given, then there is no inference and cadit qu&stio. 



CHAP. VI TWO CONDITIONS OF INFERENCE 

ticular subject. If we keep hold of this reflection we shall 
not be shaken by any puzzles which are laid before us. In 
the previous Book I have endeavoured to anticipate and 
to cut the root of those difficulties which are the most likely 
to be raised, and it is to the discussion of that Book that I 
must refer back the reader who is still inclined to hesitate. 

In the ensuing Part of the present Book we shall criticize 
some inadequate views of inference, and shall begin with that 
belief which is most opposed to the doctrines set forth in the 
present Chapter. 



ADDITIONAL NOTES 

1 On Similarity, Likeness, and Identity, see the Indexes, to this 
volume and to Appearance and Essays. 

2 " What seems the same is the same." It should be " is so far 
the same." Error as to the exact point of sameness remains possible. 
And after " diversity " should perhaps have come " further " or 
"added". What must be rejected everywhere is the idea of a simi 
larity which does not imply sameness. The " Axiom " so far as it is 
an axiom holds obviously also in Metaphysics. On the ultimate dif 
ficulty as to Identity, see Essays, Index. 

3 These points have been taken up by me in later works. There 
is here a partial failure to realize the true conclusion that, just as 
terms and relations are neither present at the beginning of knowledge, 
so both alike are subordinated and transformed in the ultimate end. 
Terms and relations are (as is seen in this volume) alike abstractions, 
and (we must add) are, each alike, unreal as such. 

* " The content of the given has always two sides." We must re 
member here that, if so, Immediate Experience or Feeling must not 
be called "given." See Bk. III. I. Chap. VII, and Appearance and 
Essays. 

With regard (three lines below) to "metaphysically irreducible," 
we can not possibly (I should say) "reduce" these "elements." 
But we can know that in the ultimate whole they lose their characters, 
as such, and so far as irreducible. 

5 "Under the same conditions." What is true of B once is true 
of B always under the same conditions. And, if you object that the 
different conditions must both be true of B, that must be admitted. 
It points to the conclusion that, while mere B A and mere B ( 
are in the end abstractions and neither in the end true, both are. still 
true relatively. We have to assume a concrete whole containing still 
further conditions such as to modify these terms and to unite them 
in something higher. But in this whole, we ^ must remember, con 
ditions and terms cease in the end, as such, to exist. 



298 THE PRINCIPLES OF LOGIC BOOK II. Px. I 

6 " It is the abstraction." It would be better to say " the universal," 
because the identity may perhaps be that of an organic individual 
whole, and, so far, not "abstract." 

7 " Is not predicated categorically." " Unconditionally " would be 
better. 

8 " Is not identical." And even in the case of a single shed, where 
it remains throughout one and the same, it still is qualified by its 
temporal diversity, so as to be also so far different, and, so far again, 
not indiscernible. 

9 " It is frivolous to say, etc." " Frivolous " may perhaps in some 
cases go too far, but " irrational " would, I think, hold everywhere. 
If you keep to change as perceived, then within that perception you 
have identity in diversity, and you have ideality, though so far you 
do not abstract it. Either that, or your perception is not the percep 
tion of change. 

On the relation of Continuity to Identity, see further Appearance, 
the Index and the Note on p. 616. 

10 " Advanced thinking." The above tirade, if unnecessary, was 
in 1883, I still think, wholly justifiable. 

11 " No judgment is really particular." We may put it thus, that 
all judgments are of content, and that no content sticks in the mere 
"this." See Appearance, Index. And further, on Designation, see 
Essays, Index. The lesser conclusion as to one premiss is, however, 
sufficient here. Cf. Bosanquet, Logic, II, pp. 203-4. 

12 This footnote might without loss have been omitted. 

13 " Because B is an identity, etc." " Because, in making the infer 
ence, B is used as an identity, etc.," would have been better. And 
so below, in " For C is disturbed, etc.," we should perhaps insert 
after C the words "in the inference." 



BOOK II. PART II 
CHAPTER I 

THE THEORY OF ASSOCIATION OF IDEAS x 

I. The end we had before us in the first part of this Book 
was to give a general account of inference. The account was 
m a certain sense provisional, since the examples it dealt with 
did not pretend to illustrate every kind of inference. But 
within those limits the result we arrived at seemed irref ragably 
The end we have before us in this Second Part, is the 
criticism and refutation of certain theories which are out of 
harmony with the conclusion we have reached. 

The title of this chapter calls for explanation. "The 
Association of Ideas," it may be objected, "is not so much a 
theory as a fact; a fact which on the one hand is quite 
indisputable, and which on the other hand can be discrepant 
with no theory except a theory which runs counter to fact." 
But the objection would rest on an entire misunderstanding. 
The psychological fact of "Association" is of course un 
questionable. The account of that fact which is given by the 
orthodox English philosophy, is in my judgment not only 
questionable but false. And, beside being false, it is incom 
patible with any tolerably accurate theory of reasoning. For 
the universality and identity, which we saw were necessary for 
every inference, do not exist in the theory of " Experience." 
We are offered in their stead a fictitious substitute, which does 
not exist and therefore can not work, and which would not 
work even if it existed. 

2. "Inseparable Association," and the "Chemistry of 
Ideas," are phrases which are only too familiar to most of us. 
They recall a controversy which has served in some measure 
to obscure the questions it professed to elucidate. But the 
more refined developements of the Association doctrine do 

299 



3OO THE PRINCIPLES OF LOGIC BOOK II. PT. II 

not immediately concern us here.* For they have no direct 
bearing on the theory of inference; and it is solely as it 
touches the subject of reasoning that we have here to do with 
Association. We may confine our attention to the common 
doctrine, as exemplified in the ordinary working of the Laws 
of Resemblance and Contiguity. 

3. The " association of ideas " is a phrase which may be 
taken to express a well-known psychological fact. And if 
taken so, it is nothing but a title. The fact, which it stands 
for, is a familiar experience, and the meaning of the title is 
not proposed as an accurate theory of that fact. It is a name 
which must not be pressed into a doctrine. 

But, as understood by the Philosophy of Experience, the 
" association of ideas " has long ceased to be a way of marking 
a thing which we all admit has real existence. It has become 
the battle-cry of a school, and a metaphysical doctrine and 
theory of things. It contains a belief as to the nature of the 
mind, or at least as to the mode in which the mind works, 
which is irreconcileable with the views we have already 
adopted. Hence if " association " is to stand for a mere 
psychological fact, then of course, like every one else, I believe 
in it ; and I propose to give here the explanation of that fact. 
But, if " association " means that view of the fact which has 
been embraced by a certain school, then I do not believe in it ; 
and I propose to show that in this latter sense " association " 
has no real existence. It has not only been extended to take 
in phenomena which can not properly come within its limits, 
but within any limits, however narrow, it is a false view of 
things. 

4. The word Association, I suppose, implies properly 
some kind of voluntary union. That signification of course 
disappears, but it leaves a shade of meaning behind. For 
things are not associated by their own necessity, and by virtue 
of some internal connection. Such a group as the family, and 
even the state, can hardly be called associations in any strict 
sense. Association implies chance, that is, it depends on 
circumstances external to that which is conjoined. And so, 
when we use the term, we must be taken to suggest that, if 
A and B had not been associated, they would nevertheless 
* We shall append some remarks at the end of this chapter, 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 30! 

have been A and B. For the conditions, which happened to 
bring them together, do not follow in fact, nor are deducible 
in idea, from the existence or character of mere A and B. 
We may perhaps explain by a reference to the hypothetical 
judgment. In such a judgment, if the condition is known, 2 
you assert not a conjunction but always a connection. But 
in a categorical judgment of perception, and that means in a 
hypothetical judgment where the condition is unknown, you 
assert a conjunction and not a connection. The former word 
corresponds to Association. The conjunction with B is pre 
dicated of A on the strength of a condition, that does not 
come into the subject, but is imported by the force of such 
circumstances as, in their relation to A, are chance. 

Association thus comes to mean chance-conjunction, and 
in our mental history we find of course very often that ideas 
are conjoined by the merest accident. If you take these 
ideas and consider them by themselves, you can find no con 
nection and no reason for their union. Mere circumstances, 
which, so far as the ideas are concerned, might never have 
existed, did bring them together. And a union caused by 
such chance-conjunction is the common meaning of Mental 
Association. In this sense of the term it answers to that 
which, I suppose, we all admit to be fact; but it conveys no 
theory of any kind whatever. It makes no assertion as to the 
nature of ideas, and it makes no assertion as to the laws of 
their reproduction. It calls attention to one fact among others. 
It does not profess to reduce well-nigh everything in the mind 
but sensations, impressions, or feelings, to this single fact. 

5. The school of Experience, in its more consistent de 
velopment, has turned the metaphorical expression of one 
fact into a theory which may be said to cover all. It has a 
doctrine as to the ultimate constituents of mind. They are 
particular feelings and particular ideas, in either case repellent 
units. And they have absolutely no internal bond of con 
nection. There is no ground common to the different units, 
which could serve as a real basis for their union. Univer 
sality and identity are derided as fictions. In the procession 
of these units we may separate two trains, the train of sen 
sations and the train of ideas; but these all are separate 
individual realities. " All our distinct perceptions are distinct 



3O2 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

existences, and the mind never perceives any real connection 
among distinct existences" (Hume). The philosophy of 
Experience is psychological Atomism. 

There is nothing which the atoms possess in common, and 
there could be no " real connection " between them. They 
are conjoined by the agency of chance or fate. That im 
pressions should come to us in a certain arrangement, and 
should in some cases precede feebler counterparts of them 
selves this springs from the unknown necessity of a nature, 
which we can not say is the nature of the units. And the 
secondary conjunction of impressions with ideas and of ideas 
with one another, what is this but the accident of Association, 
whose laws are nothing but general expressions for certain 
recurring kinds of irrational combination ? Destiny and chance 
are two names of one lord that sways the procession of fleet 
ing units. In their short-lived occupation of that void which 
is the soul, they are combined by the accident of presentation 
or by the fate of association. And the " final inexplicability " 
of J. S. Mill may recall an echo of the " free will " of 
Epikurus. 

6. Having thus anticipated by a sweeping theory the 
nature of everything that is to be experienced, the school for 
the future, so long as it keeps true to the metaphysical doc 
trine on which it stands, may call itself the Philosophy of 
Experience. And it is also analytical 3 ; for does it not assume 
that every complex phenomenon of the mind is resolvable into 
the units which its theory has established? Its first principles 
no doubt are never analyzed; but analysis, it is obvious, must 
be broken off somewhere. If the " analytical school " is con 
tent to stop, then the limit of human thinking has been reached. 
If the Philosophy of Experience is content with the result, 
then surely the product of analysis must be fact. Analysis 
in the future will consist in the attempt to reconstruct syn 
thetically the phenomena of the mind from elements gained 
in accordance with first principles, and according to the Laws 
which first principles have established (cf. Book III. Part I. 
Chap. VI. 10). It is hardly necessary that in every case 
the existence of each element should be verified a posteriori. 
If, for the explanation of visual extension, it were first neces 
sary to verify in actual observation the fact of colour-sensa- 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 303 

tions devoid of all extension, it is possible that the analysis 
could not be performed. And, since that analysis has been 
firmly established, it is clear that its basis can not be unreal. 
If we confine ourselves to the limits and the method of the 
school of Experience, we may be sure of one thing; if we 
are true to Experience we must be true to fact. 

7. We can appreciate now the nature of the claim which 
is laid to the titles of " experience " and " analysis." But we 
must hasten to examine the character of those Laws which 
rule the void and which move ideas. They answer, in the 
psychical empty space, to what is called " cohesion " or " at 
traction " in the external void (Hume, Treatise, I. I. 4). The 
two main principles are the law of Contiguity, and the law 
of Similarity or Agreement. 

I. " Actions, Sensations, and States of Feeling, occurring 
together or in close succession, tend to grow together, or 
cohere, in such a way that, when any one of them is after 
wards presented to the mind, the others are apt to be brought 
up in idea." Bain, Senses, p. 327. 

II. "Present Actions, Sensations, Thoughts, or Emotions 
tend to revive their LIKE among previous Impressions, or 

States." Ibid.p.4$7- 

Or, to put the same thing in the opposite order, 
laws the first is, that similar ideas tend to excite one another. 
The second is, that when two impressions have been frequently 
experienced (or even thought of) either simultaneously or in 
immediate succession, then whenever one of these impressions, 
or the idea of it, recurs, it tends to excite the idea of the 
other." J. S. Mill, Logic, II. p. 44, Ed. IX. 

A briefer, and on the whole more accurate expression, 
would perhaps be this; Mental units which have co-existed 
cohere, and mental units which are like recall one ano 

least in image. 

88 In saying that I entirely and utterly reject each one 
of these statements, I may be taken to deny the existence of 
fact. But (to repeat once more a distinction I have drawn) 
what I find it impossible to make myself believe is not 
fact which these formula may be taken as loosely Beating- 
It is on the contrary their theory of that fact which I can n 
swallow And I have no insurmountable objection to the use 



304 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

of such statements ; but I can not for one moment allow that 
they are true. 

I shall give hereafter in greater detail those reasons which 
lead me to believe that these laws are nothing but fictions. 
But the main ground of objection may be stated at once. 
The ideas which are recalled according to these laws are 
particular existences. Individual atoms are the units of asso 
ciation. And I should maintain, on the contrary, that in 
all reproduction what operates everywhere is a common 
identity. No particular ideas are ever associated or ever 
could be. What is associated is and must be always 
universal. 

It will be found, I think, the most convenient course, if 
I first give some account of the way in which I conceive 
association is effected, and then attempt to show that the 
method, commonly accepted as fact, is wholly fictitious. 

9. In the previous Book (p. 34, foil.) I have to some ex 
tent anticipated this discussion, and, trusting that the result 
to which we there came may be recalled by the reader, I may 
perhaps be here allowed to be brief. I have no hope of 
persuading the orthodox believer, and others may be willing 
to help in working out the sketch of a doctrine. 

The main Law of Reproduction may be laid down thus; 
Any part of a single state of mind tends, if reproduced, to 
re-instate the remainder; or Any element tends to reproduce 
those elements with which it has formed one state of mind. 
This may be called the law of Redintegration. For we may 
take this name from Sir W. Hamilton (Reid, p. 897), having 
found nothing else that we could well take. 

There are several points in the formula which call for 
explanation. We might ask, in the first place, What is a single 
state of mind? Does it exclude succession? It certainly does 
not do so. It may be further defined as any psychical com 
plex which is present together, presence signifying presenta 
tion, a certain direct relation to the mind which does not imply 
succession in time. As I have endeavoured (p. 53) to throw 
some light on the meaning of this term, I must be excused 
from a further discussion of it here. 

In the second place the " parts " of this present state need 
not be either perceptions or ideas. For the formula includes 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 305 

every possible kind of mental element; and this is the reason 
why we can not accept the principle as we find it laid down 
by Wolff and others. I will not here ask, if in the end it 
is not possible that association is confined to intellectual or 
perceptive elements (vid. Book III. I. Chap. III. 20-22). 
It is better for ordinary purposes to suppose that it also ap 
plies to desires and feelings. But subject to this correction 
we may adopt, if we please, Wolff s statement of the law. 

" Si quse simul percepimus et unius perceptio denuo pro- 
ducatur, sive sensuum sive imaginationis vi ; imaginatio pro- 
ducit et perceptionem alterius seu quod perinde est per 
ceptio praeterita integra recurrit, cujus prsesens continet 
partem" (Psych. Emp. 104). 

Maas, following Wolff, has thus formulated the principle. 
" Given an idea or perception, then all those ideas, which be 
long with it to one total perceptive state, may immediately 
associate themselves with it, and no other ideas can do so." 
Or " Every idea, or perception, recalls to the mind its total 
perceptive context" (Versuch, Verb. Ausg. 1797, 13). 

This law of Redintegration, we must bear in mind, does 
not exclude any succession of events which comes as a whole 
before the mind; and it is not to be confined to perceptions 
and ideas. 

10. The law of redintegration is a very different thing 
from the law of contiguity, as that is understood by the school 
of Experience. Superficially alike, they are separated by the 
chasm that divides irreconcilable views of the world. For 
contiguity is cohesion between psychical units, and its elements 
are particular existing phenomena. What it couples is the 
actual individual impression or image, as such. It is not asso 
ciation between universals. But Redintegration is not any 
thing else. For it never re-instates the particular fact, 
can not deal with anything that could be a phenomenon, or 
could ever exist. It does not couple psychical units, but is 
entirely confined to what is universal. 

We should find it hard to overstate the enormous diver 
gence of these two interpretations of the fact of association. 
Contiguity asserts a conjunction between existences, 
integration asserts a connection between universals, which as 
such do not exist. What operates in the first is an external 



306 THE PRINCIPLES OF LOGIC BOOK II. Px. II 

relation between individuals. What works in the second is an 
ideal identity within the individuals. The first deals with the 
that, and the second with the what. The first unites facts, and 
the second mere content. 

According to the view which to me seems the truth, to 
talk of an association between psychical particulars is to utter 
mere nonsense. These particulars in the first place have got 
no permanence ; their life endures for a fleeting moment. In 
the second place they can never have more than one life; 
when they are dead they are done with. 4 There is no Hades 
where they wait in disconsolate exile, till Association an 
nounces resurrection and recall. When the fact is bodily 
buried in the past, no miracle opens the mouth of the grave 
and calls up to the light a perished reality, unchanged by the 
processes that rule in nature. These touching beliefs of a 
pious legend may babble in the tradition of a senile psychology, 
or contort themselves in the metaphysics of some frantic 
dogma, but philosophy must register them and sigh and 
pass on. 

There is nothing we know which can warrant the belief 
that a particular fact can survive its moment, or that, when it 
is past, it can ever live again. We know it is true in our actual 
experience that reproduction presents us with particular 
images; but to assert that these are the perished originals is 
to demand a miracle to support our false beliefs. We have 
absolutely no kind of warrant in experience for our assurance, 
that what comes into the mind by Association is the particular 
as we had it. For the particular fact is made particular by 
an elaborate context and a detailed content. And this is not 
the context or content which comes back. What is recalled 
has not only got different relations ; itself is different. It has 
lost some features, and some clothing of its qualities, and it 
has acquired some new ones. If then there is a resurrection 
assuredly what rises must be the ghost and not the individual. 
And if the ghost is not content with its spiritual body, it must 
come with some members which are not its own. In the hurry 
of the moment, we have reason to suspect, that the bodies of 
the dead may be used as common stock. 

But if we are willing to throw over our orthodox creed, we 
may escape with less demand on our faith. The doctrine of 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 307 

Redintegration does not ask us to subscribe to the belief that 
what is past exists over again. It offers a simpler explanation 
of the facts. Given any presentation X, which has a content 
such as . . .abode. . ., it asserts that the oneness 
of this presentation is in a certain sense a connection of its 
content. The fact of the presentation absolutely disappears. 
What is left behind is a mental result, 5 into the ultimate meta 
physical nature of which we do not here enquire. But this 
result is not a phenomenon, not a particular image or relation 
of such images. It is an alteration of the mind, which shows 
itself to us as a tendency to pass from content to content. 
It is a connection, not between this a and this &, or this c 
and this d, but between the universals a and &, or c and d. 
It is a quality of the mind which manifests itself in the fact 
that, if we have one part of the content which appeared in X, 
then although everything which particularized that content in 
X, and gave it existence, has disappeared this bare universal 
a b, c, or d, when given with a different set of particulars, may 
re-instate by its ideal identity any other of the universals, a, b, 
c, or d. It will recall it certainly in a particular clothing, but 
this clothing will be determined by present mental circum 
stances, and will not be the clothing of its past existence. And 
this particular clothing, again and in the second place, is not 
the bond which works in the reproduction. What works is the 
connection between the universals, and the basis of that work 
ing is the ideal identity of some element in what is present am 

in what is past. 

ii I have illustrated my meaning already by anticipa 
tion (p. 35), and shall illustrate it hereafter. At present 
must hasten to meet an objection. I maintain that all asso 
ciation is between universals, and that no other associate 
exists Every kind of reproduction, in my judgment, takes 
place by virtue of identity plus the connection of universals. 
"And do you really," there may here come a protest, 
you really believe this holds good with emotions? If castor- 
oil has made me sick once, so that I can not see it or even 
think of it without uneasiness, is this too a ^J^J5 
universals?" I reply without hesitation that beheve t 
so; and that I must believe this or else accept a ^miracle a 
miracle moreover which is not in harmony with the facts it 



308 THE PRINCIPLES OF LOGIC BOOK II. Pi. II 

is invoked to explain. You believe then, I feel inclined to 
reply, that the actual feelings, which accompanied your vomit 
ing, have risen from the dead in a paler form once more to 
trouble you. I could not credit that even if it answered to 
the facts. And it does not answer, since the new feeling is 
clearly different from the old one. The old feeling was the 
event it was, by its presence in a certain series of events. It 
had a number of accompaniments, conditions, and circum 
stances, which belonged to it as this feeling. The psycho 
logical environment was in great part different. Nay, if we 
could observe it, we should probably find that its actual in 
ternal content has varied. We should see degrees or shades 
of quality, which in the two cases would probably not be the 
same. Your miraculous supposition is therefore not even a 
fiction which will work. 

And if you say that, by the sameness of the feeling, you 
mean a feeling which is the same in kind, and for all practical 
purposes one with the other, this is exactly the thesis which 
I wish to establish, and which you have objected to. The 
feelings of sickness are the same in the main, that is, they 
have an identical content, which is the same although the 
contexts are different. But, if so, is it not, I would ask, 
admitted that what is reproduced is not the particular but is 
the universal? The first conjunction of castor-oil and sick 
ness has no longer the smallest existence as fact. But it gave 
rise to a connection of elements in the mind, which elements 
are an idealized part of the content of this perished fact. 
The new presentation of castor-oil is a fact which is certainly 
not the old fact ; yet it has a content which is partly the same. 
The presence of this identical universal supplies the antecedent 
to the hypothetical connection of elements in the mind, and 
this then passes from hypothesis into actual fact. In other 
words the ideal identity of this castor-oil with that castor-oil 
recovers ideally, and in an universal form, another element of 
the original context, And, so far as mere reproduction goes, 
nothing but the universal could ever be called up. It is the 
fresh presentation which adds detail to the reproduced ele 
ment. This new perception re-particularizes the universal, and 
does so in a way which will not be the old way, and in many 
cases will be strikingly different. But such re-particularization 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 309 

(if the term may be allowed) is not association, and is not 
reproduction. For though the new particular feeling of sick 
ness is no doubt the result of reproduction, yet it never was 
associated, and it can not have been reproduced, since it exists 
now for the first time. You may say that by a miracle the 
old feeling of sickness without detriment to its sameness has 
been changed en route; but this very change and this very 
difference is the denial of your doctrine, unless your doctrine 
too is from time to time changed by a parallel miracle. 

I do not say that we should be right to reduce all repro 
duction to logical redintegration. 6 That is a point on which I 
shall touch hereafter (Book III. I. Chap. III. 20). It does 
not concern us here. For it is not necessary to believe that 
the " idea " of a feeling is a logical idea, and that it is a con 
scious or even an unconscious symbol. What must however 
be believed is that it is an universal. And this need give 
rise to not the smallest psychological difficulty. Whatever 
differences may separate the various kinds of psychical phe 
nomena, they are all alike in one point. They all have con 
tent 7 as well as existence. They are not confined to the 
"that," but each has a "what," since there is a complex 
quality and relations of quality.* And, this being so, we 
have all that is required for the formation of universals. For 
an identity of content in different contexts is and must be an 
universal, whether we are dealing with perceptions or feelings 
or volitions. 

12. To suppose the presence and the operation of uni 
versals in all reproduction, introduces a unity into our view 
of the soul. It enables us to interpret all stages of mind 
as the growth of one principle. We can thus accept without 
abridgment the very highest phenomena, and we can show 
their root in the lowest and rudest beginnings of the soul. 
We may say that experience will begin when a present per 
ception has one part of its content identical with a past, 
and when this common universal re-instates another part of 
the original context. But that past element most certainly 
does not reappear in its particular form. It too is universal, 
and it is the connection of these universals which operates in 
the mind. Hence the content of the perception, which is now 
* Quality at this stage covers quantity. 

2321.1 X 



3IO THE PRINCIPLES OF LOGIC BOOK II. PT. II 

present, is extended by means of this ideal synthesis, and, 
itself individual, individualizes the result. This true account 
is in harmony with fact. But, on the other hand, to suppose 
that one or more particular feelings or images are magically 
recalled and adhere to the perception, is directly contrary to 
the plain facts of observation. For these separate particulars 
are palpably absent; and in order to explain their obvious 
absence it is necessary to invoke a Law of Obliviscence, by 
which their details may again be shorn off. But this Law of 
Obliviscence has no title to exist in the shape which is given 
to it, except that it is demanded by an erroneous theory (vid. 
inf. 25). A miracle is first invoked to explain the facts, 
and then a fiction introduced to square the facts to the miracle. 

But the unviolated facts support redintegration by identity. 
In a rudimentary soul a present sensation has its content in 
creased by internal extension. There are not several facts 
before the mind, but there is a single fact whose content, 
after enlargement, consists in part of an unconscious inference. 
The sensation is extended by an ideal supplement, and this 
supplement, through union with the individual sensation, be 
comes for the mind individual fact. On this view there is 
no psychical phenomenon which intervenes between the sensa 
tion and the resulting perception. We have not to postulate 
the irrelevant and conflicting detail of particular images, and 
have no need to rid ourselves of this palpable fiction by any 
arbitrary Law. Or again, if the result of the new sensation 
be desire or action, our theory still maintains its superiority. 
Let us however try to exhibit this in detail. 

What is the fact to be explained ? It is, I think, this. 
A sensation Ab has once led to an action Cd; and now a 
sensation E& (the same with A in respect of &) is presented. 
E& is then followed by an action ~Fd, which in respect of d is 
identical with Cd. Such is the fact, and we have two com 
peting explanations. On the first and incorrect interpretation 
E& calls up a particular image of Ab. The latter is associated 
with the particular idea of an action Cd, and Cd produces Fd. 
The transition is thus, E& Ab Cd d; and this transition 
is discrete from atom to atom. This is the first interpretation. 
On the other, Eb directly redintegrates d f and Ebd directly 
produces EbdF. The transition may be stated as Eb d F ; 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 3! I 

but, since b and d are universals and are not psychical phe 
nomena, the actual transition is unbroken from E to F. Now 
which of these explanations accords best with fact ? The fact 
is that the supposed intermediate units, A& and Cd, can not be 
verified in observation. Their presence is deduced a priori, 
and is not pointed out a posteriori. We are then asked to 
believe that their presence exists though we can not see it; 
for it is hidden by the Laws of Obliviscence. But this mys 
terious agency has itself been manufactured a priori. It again 
can not be verified in actual experience. Hence we have first 
a principle which produces something other than our fact, 
and then an arbitrary invention to patch up this mistake. 
Such is the first interpretation ; and let us look at the second. 
On that, I will not say that nothing is asserted either more 
or less than what can be observed, but I will say this. Not 
only is one principle used throughout, and that one sufficient 
to explain the facts, but there is no result, and not the fraction 
of a phenomenon, postulated by this principle, but what can be 
shown a posteriori. And, even apart from all question of truth 
and falsehood, a theory which demands two compensating 
hypotheses, must surely be rejected in favour of a theory, 
which works as well with one single hypothesis. 

13. But I shall be told, " This statement of the case is 
absurd. In the first place, and apart from truth and falsehood, 
the theory you advocate does not cover the facts. It fails 
to explain the suggestion of similars. Again and in the second 
place, the hypothesis you adopt is demonstrably false. And a 
single hypothesis is not admissible if it is insufficient, if it is 
not true, and if a true explanation is within our reach, 
answer, In the first place, as I shall soon point out, the 
reduction of suggestion to redintegration is an accomplished 
fact. And in the second place the falsity of redintegration 
can not be shown; but on the other hand what can be demon 
strated is, that your hypothesis is false. For (i) there is no 
such thing as Association by Contiguity; (ii) there is no such 
thing as Association by Similarity. I will try to make both o 
these last points quite plain, and will then return to de 
the true explanation. 

14 (i) Let us begin with Contiguity. What is the true 
view? The true doctrine is that, when elements have co- 



312 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

existed, they tend to be connected. What does this mean? 
It means that if (say) in a perception A the elements p and 
y are conjoined, the mind gets a tendency to join one to the 
other whenever either reappears. But what are P and y ? 
They are universals. They have been detached from their 
original environment, and to some extent stripped of their 
particular qualities. They are not individual images. Thus 
if I have seen a black man stabbed with a sword in a certain 
street at a certain time and under certain conditions, what is 
left in the mind is not a connection between these special 
sensations, or between special images which are their feebler 
counterparts. I might shudder when I saw a white cow 
threatened with a butcher s knife at another time and place 
and under different conditions. For what is associated is not 
the images, it is always universals or types, which as such 
have no real existence, even in the mind. This is the true 
view. We will pass to the consideration of the erroneous 
doctrine. 

There is not much doubt, I think, as to what that doc 
trine really is. But its adherents allow themselves a looseness 
of statement which is sometimes excessive; and we hardly 
know the point at which their mythology becomes conscious. 
We are at times led to think that past perceptions continue 
to exist, and on occasion rise to be seen of men. For observe 
the definition. 

" Actions, Sensations, and States of Feeling, occurring to 
gether or in close succession, tend to grow together, or co 
here, in such a way that, when any one of them is afterwards 
presented to the mind, the others are apt to be brought up in 
idea." " When two impressions have been frequently experi 
enced (or even thought of) either simultaneously or in im 
mediate succession, then whenever one of these impressions, or 
the idea of it, recurs, it tends to excite the idea of the other." 

A definition is not the place where one looks for fancy, but 
for actual belief. But consider these phrases, " when any one 
of them is afterwards presented" " whenever one of these im 
pressions recurs." Are they feasible unless the writer believes 
in the coarsest form of subterranean existence and of the 
Resurrection of the Body? But neither of the writers pro 
fesses to hold that belief. They both repudiate it. And yet 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 313 

that does not prevent both of them from speaking as if they 
accepted it in full, and at least one of them from reasoning on 
the assumption of its truth.* 

15. This point perhaps may be dismissed as a mere ques 
tion of statement ; for there is no doubt that our authors would 
stoutly deny that the past impression is recalled to life. 
" Whenever one of these impressions, or the idea of it, re 
curs " are words that must be used in a popular sense. Then 
what is the exact sense? Are we to amend the formula by 
writing simply, " whenever the idea of one of these impres 
sions recurs " ? 

Even so we are still in the land of mythology. The 
" ideas " that are meant are particular existences. The fleet 
ing impressions in their passage through the void throw off 
feebler counterparts, shed pale doubles of themselves. And 
the idea, like the impression, is a particular unit ; it is no uni 
versal but an actual phenomenon. It certainly is called " the 
idea of the impression," but this phrase does not mean that 
the two have any substantial identity. It means that one fol 
lows the other in time, and in fainter traces shows a similar 
detail. But if this is what is meant, it is not what is said. 

" Whenever," we are told, " the idea of it recurs." But the 
idea, like the impression, exists only for a moment. Then 
how can it " recur " unless it is the same ; and how can it be 
the same unless it has remained? We may figure to ourselves 
the faithful ghost, haunting the place where the body is not, 
and called up to the light by the spell of Association. But 
we surely must know that these pious legends are not literally 
true. For the image, like the sensation, endures but for a 
moment. And if the impression does not "recur/; then the 
idea does not "recur"; since in this respect there i 
ference between them. 

It is mere mythology to talk of the copy, which the im 
pression has sloughed off, persisting in the world and preser 
ing its identity through the flux of change. The word recurs 



*I refer to J. S. Mill. See his Hamilton, Chap. XI. and 



314 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

We must call them " different ideas of the impression." And 
here, I think, we are approaching danger. For we naturally 
consider that, in a case of association, there is some one con 
nection throughout all the instances. We can hardly help be 
lieving, and talking as if we believed, that when (as we should 
like to say) something " recurs," then something else " recurs " 
also. But we must strip off this illusion, or wear it only 
when we come before the public. There is nothing that recurs. 
The original impression is one mental unit, the first idea is 
another, the second idea is a third passing atom, and so on for 
ever. There is no real bond which unites them together. 
There is no common internal identity, which is the same in all 
and recurs amid change. If we call them " the ideas of one 
impression," even this is mere fable. We have a likeness no 
doubt, in all these cases. A hundred images, or more it may 
be, with all their differences and all their particularity, are yet 
each of them particular in such a way that they are all like 
each other, and all like the impression. This is startling, I 
admit, but even this does not warrant us in considering any 
one to be the same as the other, and united by holding the one 
substance of their prototype. If we desire a legend which 
perhaps may be harmless, we may call them all " ideas of the 
impression " in the sense that, like Abraham, the impression 
while it lived had them all in its loins. For no vehicle conveys 
the eternal verities half so well as does the labyrinth of a 
fantastic genealogy, with its one-sided begettings and ab 
normal parturition. 

16. " Whenever one of these impressions, or the idea of 
it, recurs, it tends to excite the idea of the other." This is 
what we started from. What are we left with ? " Impres 
sions " is gone : " recurs " is gone : " idea of it " is gone. It 
seems that we must thus amend our formula, " Whenever an 
idea like one of these impressions occurs, it tends to excite 
the idea of the other." This surely will stand: this at last 
must be true. Unfortunately not so; for it still says too 
much and must be further cut down; and yet already it has 
begun to say too little, and will now no longer cover the facts. 
But I will at present keep to the too much. The phrase " to 
excite the idea of the other " must at once be corrected. It 
should run "to excite an idea like the other." And we must 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 315 

further amend the beginning of our formula. For " when 
two impressions have been frequently experienced" is quite 
mythological. // two impressions were " frequently experi 
enced," they would be two no longer. The phrase is nonsen 
sical, unless several experiences are one experience: and that 
we know is not true. We must alter this also, and in our final 
correction the law must be stated. 

" When we have experienced (or even thought of) several 
pairs of impressions (simultaneous or successive), which pairs 
of impressions are like one another; then whenever an idea 
occurs which is like all the impressions on one side of these 
pairs, it tends to excite an idea which is like all the impressions 
on the other side." 

This I believe to be the meaning of Association by Con 
tiguity. And at this point perhaps it may occur to us to ask, 
what is it that is contiguous, and what is it that is associated? 
The impressions are not associated; I presume that is ob 
vious. They are conjoined in presentation, just like anything 
else we perceive together is conjoined. It is the ideas which 
are associated, since one, as we see, can bring up another. 
But then in what sense are the ideas contiguous? They are 
now successive, or simultaneous, because of the contiguity. 
Contiguity conjoins them, and it would be nonsense to ^say 
that they become conjoined because already they are contigu 
ous. For if they are contiguous, then both must be there, and 
how can one call in the other? And if they are not contigu 
ous, then it is not their contiguity which brings them together. 
This consideration seems to me quite palpable; but the result 
is fatal to the Law of Contiguity. 

The law operates by means of and through contiguity, and 
therefore presupposes it. But there is no contiguity save that 
of the impressions. It must be then the contiguity of 
impressions which works. Because they were together once, 
the ideas come together now. But, if so, what becomes of 
association? For the impressions are not associated, and 
association is, if anywhere, between a present and an absent 
idea What is associated was therefore not contiguous, and 
what was contiguous is now not associated. Association and 
contiguitv fall hopelessly asunder; and hence let our law b 
never so real, it can not be the Law of Association by Con- 



3l6 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

tiguity. In short, the whole thing comes to this. If impres 
sions have been contiguous, then ideas which are like them 
now tend to excite one another. And for myself, I can not 
see how in any intelligible sense this is the association of ideas. 

17. And now (to come to the other side of the failure) if 
we state the law in this corrected form, it will not cover the 
facts of the case. For commonly an impression is what is first 
given, and then this impression calls up an idea. Thus if one 
fire has already been felt to be hot, then, if another fire is seen, 
the idea heat comes. Thus an idea is excited by what is not 
an idea, and by what never has been contiguous to anything. 
We must once more and finally thus amend our formula, 
"If any mental units have been contiguous, then any others 
which resemble them may excite one another." There is not 
left here a vestige of association. And the union of the ele 
ments somehow takes place by virtue of the past contiguity of 
something else. 

1 8. Association by contiguity may be taken as exploded. 
But the philosophy of Experience is, to some extent at least, 
prepared for this result. It will admit so much, that mere 
contiguity will not work by itself. And it proposes to sup 
port it by another agent. There is no such thing, it is ready 
to allow, as association by bare contiguity. All reproduction 
in a certain sense depends on similarity. 

" There never could have been association by contiguity 
without a previous association by resemblance. Why does a 
sensation received this instant remind me of sensations which 
I formerly had (as we commonly say), along with it? I 
never had them along with this very sensation. I never had 
this sensation until now, and can never have it again. I had 
the former sensations in conjunction not with it, but with a 
sensation exactly like it. And my present sensation could 
not remind me of those former sensations unlike itself, unless 
by first reminding me of the sensation like itself, which really 
did co-exist with them. There is thus a law of association 
anterior to, and presupposed by, the law of contiguity : namely, 
that a sensation tends to recall what is called the idea of 
itself, that is, the remembrance of a sensation like itself, if 
such has previously been experienced." " There is, therefore, 
a suggestion by resemblance a calling up of the idea of a 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 317 

past sensation by a present sensation like it which not only 
does not depend on association by contiguity, but is itself the 
foundation which association by contiguity requires for its 
support." J. S. Mill, on James Mill, I. 112, 113. 

"There can be no contiguity without similarity, and no 
similarity without contiguity. When, looking at a river, we 
pronounce its name, we are properly said to exemplify con 
tiguity; the river and the name by frequent association are so 
united that each recalls the other. But mark the steps of the 
recall. What is strictly present to our view is the impression 
made by the river while we gaze on it. It is necessary that 
this impression should, by virtue of similarity or identity, 
re-instate the previous impression of the river, to which the 
previous impression of the name was contiguous. If one could 
suppose failure in the re-instatement of the former idea of the 
river, under the new presentation, there would be no oppor 
tunity given to the contiguous bond to come into operation." 
Bain, ibid. p. 121. 

Let us try to understand this amended doctrine. In the 
first place we must remember that, when identity is spoken of, 
it is not really mecmt. What is meant is more or less of 
similarity. And this point must not be lost sight of. 

In the second place I must be allowed to complain of a 
serious inaccuracy in the extract I have quoted from Professor 
Bain. It surely is nonsense to talk of " re-instating the 
previous impression," and I must add that in this context the 
nonsense seems inexcusable. And again in the first of the ex 
tracts there is ambiguity. The " remembrance of a sensation," 
we must clearly understand, does not revive the sensation itself, 
and does not establish any actual relation with that mental 
unit which no longer exists. If this is not so, and if a psy 
chical phenomenon can maintain or recover its existence and 
identity through the flux of events, then the whole theory 
from which the school of Association starts has been tacitly 
thrown over. 

But, if an impression when past is done with, if it is really 
non-existent, then not only can it not be re-instated bodily, 
but itself can not even be re-instated in idea. The fact which 
is covered by the delusive phrase " idea of it," is merely the 
fact that a sensation came first, and then subsequently there 



318 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

came a paler counterpart. And, when we once discern this 
fact through the mist of ambiguous and misleading formulae, 
there is an end to the theory which hides or obscures it. 

What was contiguous is now non-existent, and what is 
" re-instated " has never been contiguous. Let us look at the 
facts. A sensation A excites by similarity an image b, and, 
on this, contiguity has to do all the rest. But has b ever been 
contiguous to anything? In the case before us there are two 
possibilities. The fact from which we start is this we have 
had an impression B along with an impression C, and we have 
an impression A. Now what are the two possibilities ? In the 
first place it is possible that we never have had a feeble image 
resembling B. And this is more than possible, for in an early 
mind it is also probable. But in this case, when A excites an 
image b, there is absolutely no contiguity of anything with 
anything. Not one of the supposed elements in our reproduc 
tion has ever been contiguous with any other; and, this being 
so, reproduction will not take place. This first possibility ap 
pears to me to have been overlooked. Let us now pass to the 
second. We here have had the contiguous impressions B C. 
These we suppose to have been followed by one or more pale 
pairs of images & 1 c 1 , b 2 c 2 , & 3 c z . These are all like 
each other, but they all are realities each of which is not the 
same as any other. We now experience a sensation A. This 
also is like the previous sensation we have called B, and is 
like the images & 1 , b 2 , b\ But every one of these, I must beg 
the reader to remember, is by this time absolutely non-existent. 
What then is to happen when A is presented? It calls up by 
similarity an image b 4 . But this is not what we want. For 
we want an image b* c 4 ; and contiguity is invoked to pre 
sent us with c 4 . But is invoked in vain. For as yet c* has 
never existed, and ex hypothesi it is to be made to exist by 
means of contiguity. On the other hand b* has never been 
contiguous to anything at all. We have reached once again 
the old result. There is no association by contiguity. What 
is called up by association has never been contiguous; and 
what has been contiguous can not be called up. The contiguity 
which now operates is a past contiguity, which is not recalled 
and can not be recalled, but which, according to the pious 
legend, is somehow passed on like original sin. 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 319 

But if this is so, then Association by Contiguity is exploded 
finally. No exciting of similars will save it from annihilation. 
For the similars excited have not been contiguous, and what 
was really contiguous can not be excited. If present sensations 
are qualified by images in the way described, still on that 
(false) hypothesis there is no reproduction by association. 
There can be no association where the elements are not co 
existing associates. But if they do already co-exist and thus 
are associated, then how in the name of all that is miraculous 
can one bring about the co-existence of the other, and by 
means of their co-existence? 

19. If the school of Experience is in earnest with its 
principles there can be no such thing as Association. But is 
it in earnest? Notwithstanding all its public protestations 
may it not secretly look for the Resurrection of the Body? 
Does not the charm of Similarity shake the realm of Hades, 
and conjure from its grave the reluctant past? Is anything too 
hard for Association? Its spell has prevailed over the mind 
of its votaries, and, though their lips may deny, yet Associa 
tion itself has helped their unbelief by its own divine power. 
They do believe in the miracle of resurrection. But they be 
lieve blindly and unconsciously, compelled by the strength of 
a tacit conjunction of meaning with phrase. 

We saw that, by the admission of its advanced disciples, 
association depends upon similarity. If there is no reproduc 
tion by Similarity, it is admitted that there is no Association at 
all. I shall now press this consequence. If you do not believe 
in this kind of Association, you believe in none. But if you 
do believe in it you believe in a miracle which upsets all law. 
And furthermore there is no evidence a posteriori to confirm 
this miracle. In plain words Association by Similarity is a 
downright fiction. It is not called for by the facts; and it 
involves besides metaphysical assumptions which I confess 
stagger me, and which I think may somewhat surprise others. 
I shall show the reader how the school of Experience has 
swallowed the most outrageous metaphysical doctrines, and 
that he must follow their example or leave their company. 

20. (ii) Association by similarity, if it is anything at all, 
is a means of exciting ideas that are not present. If it will 
not give us what at present, and apart from its agency, we are 



32O THE PRINCIPLES OF LOGIC BOOK II. PT. II 

without, then it surely is a self -condemned fiasco, that is not 
worth discussing. We may perhaps agree that an agency 
which recalls and yet recalls not anything but what is already 
on the spot, is something like a piece of nonsense. And I 
propose to show that Association by Similarity is this piece 
of nonsense. 

Similarity is a relation. But it is a relation which, strictly 
speaking, does not exist unless both terms are before the 
mind. Things may perhaps be the same in certain points 
although no one sees them ; but they can not properly resemble 
one another, unless they convey the impression of resemblance ; 
and they can not convey it unless they are both before the 
mind. This is not merely an assertion I have chosen to make. 8 
Let us see what is told us by J. S. Mill. 

" Any objects, whether physical or mental, are related, or 
are in a relation, to one another, in virtue of any complex 
state of consciousness into which they both enter" (on James 
Mill, II. 10). 

" Likeness and unlikeness are themselves only a matter of 
feeling: and that when we have two feelings, the feeling of 
their likeness or unlikeness is inextricably interwoven with 
the fact of having the feelings. One of the conditions, under 
which we have feelings, is that they are like and unlike: and 
in the case of simple feelings, we can not separate the like 
ness or unlikeness from the feelings themselves. It is by no 
means certain, however, that when we have two feelings in 
immediate succession, the feeling .of their likeness is not a 
third feeling which follows instead of being involved in the 
two" (ibid. p. 18). 

" I have two sensations ; we will suppose them to be simple 
ones; two sensations of white, or one sensation of white 
and another of black. I call the first two sensations like; 
the last two unlike. What is the fact or phenomenon con 
stituting the fundamentum of this relation? The two sensa 
tions first, and then what we call a feeling of resemblance, 
or of want of resemblance. Let us confine ourselves to the 
former case. Resemblance is evidently a feeling; a state of 
the consciousness of the observer" (Logic, I. 75). 

Is not this quite plain? Does it leave any doubt? Is it 
not clear that two mental elements are not like, unless I have 



CHAP. I THE THEORY Of ASSOCIATION OF IDEAS 32 1 

them before me at once or in immediate succession? But, if 
so, what meaning can we attach to the calling up of an idea 
by similarity? If the relation does not exist until the idea is 
called up, how can the idea be called up by the relation? Is 
it not, the moment we look below the surface, mere verbiage 
and nonsense? 

21. In the first place what is called up is absolutely 
non-existent. We are told, not once but again and again, 
that a feeling gone is gone for ever. And the same thing 
holds of particular images. If these exist, then the past 
exists, and the procession in the mind is not real but illusory. 
Are we to believe this, and believe it in the teeth of our as 
severations? But if we can not believe it, and if the past 
does not exist, then we must believe in a relation between the 
existent and the non-existent; and believe that the whole 
(relation and relateds) is one state of our minds. If, on 
the other hand, the past can exist, this miracle will not save 
us from annihilation. In the relation of similarity both terms 
must be present, and the fact that one calls up the other by 
this relation, postulates that one of the terms must be absent. 
It is therefore both present and absent at once. On either 
hypothesis we are landed in contradictions; and I have re 
deemed the promise I gave to the reader. An idea is absent 
and at the same time present. It is not there and so is 
brought in by a relation, which relation is nothing if the idea 
is not there. And a union, which is impossible out of the 
mind, persists between the existent and what is wholly non 
existent. Could anything be more insane than this wild meta- 
physic ? 

22. But I shall be told " You are deceiving us ; it is 
incredible, it is impossible that our sober countrymen can 
have been so imposed upon." I answer, That question is 
easily settled. It is admitted that by " association " they must 
mean something, and what else do they mean? 

The Experience Philosophy has to meet two objections. 
It has to explain how the non-existent can be related to the 
existent. And when it has done that, it must explain how 
the absent can be recalled by the present, when similarity 
implies common presence and reproduction excludes it. Sup 
pose that the former difficulty has been slurred over by some 



322 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

metaphysical formula of " the potential and the actual," or 
some distinction between my mind and other minds, yet the 
second remains. Suppose that your past series somehow 
exists, yet how, I ask, are you going to get at it? Mere 
partial identity of the present and the past would not be what 
you want, since this would not be an actual relation in your 
mind. 

This is what Maas meant by the following objection. 
" The mere similarity of two ideas (or sensations) can not 
possibly be a cause of their association. For similarity is an 
objective relation of the ideas themselves; while association 
is a subjective connection in the imagination. But the latter 
does not follow from the former, nor tend to follow from it " 
(Versuch, p. 55). By " similarity " Maas of course here meant 
"partial identity," and his argument is quite simple. The 
question is, Why does my mind go from one element to 
another? If you say, it goes because the elements seem like 
to it that supposes both to be there. But if you say, it goes 
because they are like apart from it then it goes by a miracle, 
for it is influenced by something which to it is nothing. Sir 
W. Hamilton (Reid, p. 914) has replied to this argument 
by a criticism which shows that he did not understand it. 

The Experience Philosophy may have a reply to these 
objections, but I confess I can not anticipate its answer. Per 
haps it may fall back on a simpler view. It may say, after 
Wundt (Phys. Psych. 788), "every perception or idea tends 
to call into consciousness another like itself." As to the truth 
of this expression I shall have something to say afterwards. 
But at present I say this. Whatever else it is, it is giving 
up Association and throwing it overboard. For it is the mere 
statement of a phenomenon; and it is not an explanation. 
The entirest belief in the truth of this formula is compatible 
with the entirest disbelief in the doctrine of Association. We 
might explain the alleged fact that, given any one element, 
another like it may come up, by a theory of the spontaneous 
fission or gemmation of ideas ; and this in my opinion would 
be a theory which, by the side of Association, is sober and 
rational. We might explain it again by a physiological dis 
position to a certain cerebral function, which (given the 
stimulus of a new perception or idea) passes into fact. And 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 323 

against this explanation I will not say one word. I will in 
sist only on this, that it is not a psychological explanation at 
all, and that in the hands of those who know their own busi 
ness it is not offered as such. If this is the only possible ex 
planation, then a psychological explanation is relinquished as 
impossible, and the Laws of Association as commonly given 
will not explain anything. Thus the Philosophy of Experi 
ence must take its choice. It must either rehabilitate its bar 
barous mythology, or admit that, though the fact of reproduc 
tion is known, it has no psychological explanation to offer, and 
is confessedly bankrupt. It has rested its all on reproduction 
by similarity, and we have shown that this is an impossibility. 

23. But our proof no doubt will not cause much disquiet. 
I shall be told " You can not demonstrate away the facts." 
And I will therefore proceed to my second contention. The 
explanation offered is not only impossible, but it is also un 
called for. There is no evidence for it a posteriori. The facts 
of reproduction are much better explained on another theory. 
We have seen this already in our first Book, but I will exhibit 
it once more. 

Let us take a fairly simple instance of reproduction. A 
young child, or one of the lower animals, is given on Monday 
a round piece of sugar, eats it and finds it sweet. On Tuesday 
it sees a square piece of sugar, and proceeds to eat it. In 
this we have of course volitional phenomena as well as intel 
lectual, but perhaps we may simplify the case so as to make it 
serve. 

Now on the Association theory how is the fact inter 
preted? I suppose in some way like this. The presentation 
to the eye of Tuesday s piece calls up by similarity the 
idea of Monday s piece. That is a feeble counterpart of the 
original sensation, and it calls up by contiguity feeble 
counterparts of Monday s felt movements and Monday s 
following sweet taste. The fact which ensues is hence the 
mental presence of Tuesday s perceived square piece, felt to 
be like another paler imagined round piece, with which latter 
a whole set of other images come in. Now the conclusion, at 
which we have to arrive, is the qualification of Tuesday s 
piece by these images which are attendant on the idea of 
Monday s piece; and at first sight there seems no way to this 



324 THE PRINCIPLES OF LOGIC BOOK II. Pi. II 

result. For the conclusion is not merely a vicious inference, 
but it does not even look like a probable mistake. Tuesday s 
sensation and Monday s image are not only separate facts 
which, because alike, are therefore not the same; but they 
differ perceptibly both in quality and environment. What is 
to lead the mind to take one for the other ? 

Sudden at this crisis, and in pity at distress, there leaves 
the heaven with rapid wing a goddess Primitive Credulity. 9 
Breathing in the ear of the bewildered infant she whispers, 
The thing which has happened once will happen once more. 
Sugar was sweet, and sugar will be sweet. And Primitive 
Credulity is accepted forthwith as the mistress of our life. 
She leads our steps on the path of experience, until her fal 
lacies, which can not always be pleasant, at length become 
suspect. We wake up indignant at the kindly fraud by which 
the goddess so long has deceived us. So she shakes her 
wings, and flying to the stars, where there are no philoso 
phers, leaves us here to the guidance of I can not think 
what. 

The school has not yet accepted this legend, and I narrate 
it partly because I am not sure that it is not relevant, but 
mainly because it has always seemed to me perhaps the most 
striking of all those creations which we owe to the imagina 
tion of Professor Bain (Emots. p. 511 and foil.). 

24. The less poetical but not less fabulous view would 
appear to be this. Given a perception A together with an 
image b, which resembles it and has a train of attendant 
images c, d, and e the problem is how to transfer to A the 
content of e. And what accomplishes the feat is the Law of 
Obliviscence. This powerful agent obscures everything in the 
train between A and e; and it also obscures any part of e 
which is not suitable to A. The residue of e then adheres to 
A; that is, I think, the two run into one. And so we get 
the conclusion "This piece of sugar is sweet," by a process 
which logically may seem rather vicious, but which appears 
none the less to be the essence of reasoning.* 

* In the lowest stages of mind this theoretical conclusion of course 
would not appear. There would be action or attempt without anything 
like a judgment. The principle however would be exactly the same; 
and when the theoretical conclusion comes, it must come in this way. 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 325 

I can not say if this statement of the Association doctrine 
is fair, but I hope it may be so. Let us see what objection 
we can find to its process. 

The main objection is that there is a great deal too much 
of it. It is much too elaborate for simple phenomena. It 
first introduces a complication which does not exist; and 
then, having invented this complication, it removes it by a 
process which is not real. 

It is obviously no fact which we can discover by observa 
tion, that when Tuesday s sugar is presented to sense, a similar 
piece or similar pieces come up, in their particularity and with 
all their differences, before the mind. No one gets such a 
fact from observation. It is in short a theoretical fiction. I 
do admit that afterwards, when memory is developing, there 
is something which can give ground for a mistake of this 
kind. But then of course reproduction must come before 
memory, and in the present case we are not concerned with 
the latter (cf. p. 36). The fact before the mind is that this 
sugar suggests both sweetness and eating without any images 
of any other pieces of sugar at all. In the first Book I 
enlarged on this point by anticipation, and, I confess, it seems 
to me quite plain. 

25. But I shall be told, that although we can not be aware 
of them, these images exist, and they are removed or adapted 
by the Laws of Obliviscence. But this process strikes me as 
another fiction, piled up to support the first fiction against the 
pressure of experience. I will quote a passage from J. S. 
Mill. 

" The reader ... is now . . . familiar with the . . . 
fact, . . . that when, through the frequent repetition of a 
series of sensations, the corresponding train of ideas rushes 
through the mind with extreme rapidity, some of the links are 
apt to disappear from consciousness as completely as if they 
had never formed part of the series. It has been a subject of 
dispute among philosophers which of three things takes place 
in this case. Do the lost ideas pass through the mind without 
consciousness? Do they pass consciously through the mind 
and are they then instantly forgotten ? Or do they never come 
into the mind at all, being, as it were, overleaped and pressed 

2321. I Y 



326 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

out by the rush of the subsequent ideas?" (on James Mill, 
I. 106). 

The question opened in the above quotation may be stated 
thus : Given an indirect connection of ideas in the mind, to 
find the way in which it becomes direct. I do not wish here 
to enter into this general question. But I must point out that 
Mr. Mill has raised it in a form which precludes any satis 
factory solution. For the ideas connected are not really a 
mere series of particular images, and the fact has thus been 
perverted beforehand. And if we suppose that, in some ex 
ceptional case, we have got a mere train of individual images, 
then not one of the " three things " could possibly be opera 
tive. For so long as the ideas remained these mere images, 
no connection at all would be established between them. We 
may be sure that, whatever in the end may be the detail of 
the psychological process, one side of it would consist in turn 
ing these images into universals. And for this reason the 
Laws of Obliviscence, as we have them stated by Mr. Mill, 
are fictitious processes. Even if you start with a complica 
tion and a train of ideas, yet they can not deal with it. 

But the point on which I desire to insist, is that in an 
elementary case of reproduction, such as we are now con 
sidering, the complication presupposed by these Laws has no 
existence at all. The data from which they start are pure 
inventions, and it is hence an impossibility that any one of the 
suggested " three things " should happen. The fact which 
Obliviscence postulates is this: A is the sugar calling up by 
similarity an image of sugar b; and b calls up by contiguity 
an image of movement c; and c calls up an image d of a 
particular sweet taste. But this fact does not exist, and the 
alleged process stands therefore on unreality. 

There is in the first place no reason to suppose that this 
train of ideas, which is presumed to rush through the mind, is 
a counterpart of the original perception and action. What 
ground can we have for an assumption that the particular 
images, b, c, and d f are like in all their detail to any train of 
impressions we ever have had? Admit the train, what reason 
have you to affirm that there is anything more than a general 
likeness? What ground have you for the assertion that, if 
you could look into the past, you would see a train of impres- 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 327 

sions B, C, and D, of which these present images are copies? 
Why must d be an " exact likeness " of the particular pleasant 
eating D? These dogmas seem to me to be nothing but 
postulates. The fact, so far as I observe it, shows me that, 
without respect for the past, such images vary freely within 
a certain limit, and that this limit is fixed by the universal 
connection which appears in all of them. But, if so, then 
what is associated is not particular images. The universal 
which has been deposited is the active principle, and the par 
ticular images as such are quite inert. 

And in the second place the alleged process imports an 
other gross fiction into the data. It tells us that similarity calls 
up an image b, which is a copy of Monday s piece of sugar. 
We have just seen that, if present, the image need be no copy: 
and now we go further. For in our elementary case the 
image b has no existence. I repeat once more that it is a 
pure invention, necessary for the theory but absent from the 
fact. When Tuesday s piece of sugar is present, the attributes 
of whiteness and crystalline appearance reproduce the ideas of 
movement and sweet taste, without any such link as another 
and different piece of sugar. It is not merely that we can 
not find such an image now. We never could have found it. 
It never has been there. And we need not ask at length if 
the Laws of Obliviscence could serve to obscure it, unless 
some evidence is produced to show that it is more than a mere 
chimaera. 

And, as we have seen, it is a chimsera that will not work. 
For when you have got your image of Monday s sugar, you 
are left precisely where you were before. You have got an 
element which has just been born, and which therefore can 
never have been contiguous to anything in its life. And if 
you say " But it resembles what was contiguous ; " then this 
is not only to desert your principles, but it also tends to 
expose you to ridicule. If you want what is the former piece 
of sugar, you can not get it. But if you want what is like the 
former piece, then you have it already in the present per 
ception. 

Your fictions do not help you, and why should you cherish 
them? Why invent the existence of similar images which 
lure the unwary to vicious inferences? Why suppose that 



328 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

" trains of ideas," of which the mind knows nothing, float 
across it in procession, and then go on to manufacture a Law 
of Obliviscence which ties a bandage over its eyes? Because, 
if you do not, you are forced to admit that the mind does not 
go always from particulars to particulars, that indeed it never 
can go from particulars direct to particulars, that in short the 
Experience psychology is exploded. 

26. Let us give once more the natural interpretation of 
the simple fact. The natural view is that Monday s experience 
remains in the mind, not in the shape of particular images, 
but as a connection between elements of content. This is a 
result which in its metaphysical nature we can not here char 
acterize, 10 but, in its appearance to us, it is easy to describe. 
It is a tendency to pass from one universal to another, when 
ever the first of these is presented in an actual perception or 
image. In the instance we are examining, the shape, the size, 
the person giving, the where, the when, and the how have all 
gone. Nothing is left but a tendency to pass from element to 
element, from whiteness and crystalline appearance and hard 
ness to eating and sweetness. 

Monday s experience, let us say, has established the con 
nection " white-eaten-sweet." On Tuesday " white " is given, 
and so we have " this-white." We advance by means of an 
elementary synthesis to " this-white-eaten-sweet," and, ignor 
ing that part which does not interest us, we get " this-eaten- 
sweet," or, elliptically, " this-sweet." I grant you the " sweet " 
is now fully particular, but its particularity has had nothing 
to do with its recall. On the contrary its detail depends upon 
the context which has recalled it. And there is no particular 
image of " white " at all ; for the universal " white " is what 
has worked, and that of course was given in the present 
perception. 

Where is Similarity here? It does not exist. Similarity 
implies the feeling of diversity, and here the difference of 
particulars never comes before the mind; it is in no sense 
present. 

Let us give up Similarity - Contiguity -(- Obliviscence or 
Primitive Credulity. Let us postulate Identity + Contiguity, 
and then all is easy. But there are two things we must re 
member. The contiguity is a connection of universals, and is 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 329 

therefore not the contiguity of the Association school. And 
the identity is not present to the mind. The mind, if you 
keep to simple cases, knows nothing of any difference. It 
goes straight from what is given to an additional fact. 

27. Let us state our view as a working hypothesis, 
something that need not be true or even possible. Let it be 
granted there is a mind X with certain functions; let it be 
granted that X may be stimulated to perform again any 
function which it ever has performed ; let it be granted that in 
every function there is a connection of elements, as a-b; let it 
be granted that presence of a tends to excite X to per 
form again the function which contains a-b; then let a be 
given in a fresh context, as Ca. On this X is stimulated to go 
on to b thus, Car-b; and the product Cab now comes before 
the mind which is the fact to be explained. If this ex 
planation is false, admit at least that it is simple. 

We are asked to believe it is more in accordance with 
" experience " to say, Similarity is a tertium quid ensuing only 
on the presence of a pair of elements, and, when but one is 
present, Similarity brings the other. It is " science " when we 
asseverate that mental phenomena are realities which can exist 
only while they are perceived, and then speak of " recalling " 
them, as if they were ambassadors on foreign employment, or 
" calling them up " as though they were servants in the kitchen, 
and as if " relations " were wires that rang the bell, or were 
fishing-lines baited with similarity to draw up from non- 
existence the ghosts of the past. It is " positive knowledge " 
to make that come before the mind which does not come be 
fore the mind, and then to remove it by a fictitious expedient. 
Yes, sooner than run the risk of believing in metaphysics, there 
is no superstition so gross, no mythology so preposterous that 
we ought not to believe in it, and believe anything sooner than 
cease to believe in it. 

28. But what is it that forces us to these desperate 
shifts? Not the facts themselves, for we violate them. It is 
simply the shrinking, as we think, from metaphysics. And 
this, after all, is nothing but metaphysics. It is our unreason- 
ing fidelity to a metaphysical dogma which has driven us to 
adopt these embarrassing results. For why is it we are so 
sure that identity is impossible, and that a synthesis of urn- 



33O THE PRINCIPLES OF LOGIC BOOK II. PT. II 

versals is a " survival " of superstitions, which in the nine 
teenth century are out of date? It is because we are sure 
that there can be no reality but particular existences, and no 
mental connection but a relation of these units; and that 
hence identity is not possible. But this is of course a meta 
physical view, and, what is more, it is nothing but a dogma. 
The Philosophers of Experience have, so far as I know, never 
offered any proof of it ; they have heard it from their fathers, 
and their fathers had heard it. It is held true because of 
the continuity of tradition in a Church, which must have truth, 
since it has never failed to preserve its continuity. Has the 
school ever tried to support it by any mere rational con 
siderations ? 

So far as I know, it has been assumed that, if you are not 
able to swallow down this dogma, you are forced to accept 
an intolerable alternative. You are given a choice between 
naked universals, existing as such, and bare particulars. You 
can not stomach the first, and so you take the last. But why 
should you take either? Why not adopt the view that the 
real is the concrete individual, and that the bare particular 
and abstract universal are distinctions within it, which, apart 
from it, are only two forms of one fiction? You say, This is 
unintelligible. But perhaps you never heard of it, or heard 
of it too late, when you were already compromised, and had 
no inclination to begin life again. Let it then be unintel 
ligible ; but permit me to add that the view you have adopted 
calls for something stronger, to back it against facts, than an 
a priori deduction from a metaphysical alternative. 

29. We have shown so far that, in the extension of our 
experience, there is a synthetic construction by virtue of 
identity, and that association by similarity has no part in it. 
We have shown that the test which we bring to inferences, in 
order to examine their validity, is also the principle which 
operates in all extension of experience. On our view the 
origin of the fact is explained, and its existence is at the 
same time justified. But, on the fashionable theory of Asso 
ciation, early inferences are made by what afterwards we find 
to be the essence of bad reasoning. And, to explain the origin 
of this unjustifiable fact, open fictions have had to be invented. 

But not only is Association by Similarity a fictitious ac- 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 33! 

count of the reasoning process. It is a fiction altogether; 
there is no evidence for it at all. And it is to the final proof 
of this point that we must now address ourselves. 

Our previous objections have raised at least a presumption 
against the alleged phenomenon. Let us now ask, Is there 
any evidence of any kind which tends to confirm it ? I know 
of none whatever. 

We are told (J. S. Mill, Hamilton, p. 315, note) that the 
elementary case of the suggestion of similars will not come 
under the head of redintegration. But the answer to this is 
very simple. Reproduction by mere similarity is a fact which, 
if real, would certainly stand by itself. Who doubts it? But 
then the existence of this fact is just what we deny. The 
general fact that ideas and perceptions give rise to others 
which are like them, is of course admitted. But this not only 
can be reduced to redintegration, but long ago it has been so 
reduced. I will exhibit this in a concrete instance. 

30. I am walking on the shore in England and see a 
promontory A, and then suddenly I have the idea of another 
promontory B which is in Wales, and I say How like is A to 
B. This is the fact which is to be explained. The false theory 
tells us to explain the fact by postulating a direct connection 
between A and the idea of B, for it says The suggestion is 
perfectly simple. But in the first place the postulate de 
mands an absurdity, and in the second place the suggestion 
is certainly not simple. If instead of asserting we are 
willing to analyze, we soon find the true explanation c 

fact 

The content of A, like the content of every other percep 
tion, is complex, and has several elements. Let us say that 
it has an element of form which is p. Now let us look at B, 
the idea which is to come up. That also possesses a complex 
content, and we find in it the same element p, in connection 
with others, q, r, s, t. These are the conditions, and let us ; 

what follows. , . , 

In the first place A is presented, and so presents p, which 
by redintegration stimulates the mind X to produce qr. Wl 

happens then? 1 i-rr.^u 

Several things may happen, and it is exceedingly difficult 

to work out the minute psychological conditions which settle 



332 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

the result. But this is a question with which we are not here 
concerned. One result would be the identification of qr with 
Ap. A would then be qualified as Apqr, and this would be 
an unconscious inference. In the present case we are to sup 
pose that this can not happen; for we suppose that q, r (say a 
certain colour and a certain size) are discrepant with A. 
What then may we expect? We might expect that qr would 
be simply dropped. It might not catch the attention, and the 
mind might be arrested by a new sensation. We might expect 
again that, if qr is not dropped, it might be used as a means 
for a wandering course through a train of ideas, foreign to 
both A and B, and which might take us anywhere. But we 
are to assume that none of these possibilities become real; 
and that instead the idea B rises in the mind. How do we 
explain this? 

Very simply. B (we remember) had a content pqrst, and 
now we have A which has brought in p, and so introduced 
qr. But qr will not coalesce with A. Let them then instead 
go on to complete the synthesis pqrst, a synthesis which by its 
discrepancy with A is freed from union with it. But an inde 
pendent pqrst is B, and may be recognized as B. And now, 
B being there along with A, the perception of its resemblance 
calls for no special explanation. This account of the matter 
appears to me simple and natural and true. 

31. It may be objected, in the first place, that, if the 
sensation is simple, this theory will not work. I admit it, and 
I should be sorry if in such a case it did work. I would 
rather that any theory, which I adopt, did not explain im 
possibilities. And that any actual presentation should be 
simple is quite impossible. Even if it had no internal charac 
ters, yet it must be qualified by the relations of its environment. 
And this complexity would be quite enough for the purpose. 
For the identity of the simple internal character, over against 
the difference of two sets of external relations, would give 
rise to redintegration and to the perception of the resemblance. 
I think a sober antagonist will hardly deny this. And if it 
should be denied, then I am inclined to reply with a reductlo 
ad absurdum. If the suggestion is quite simple, perhaps there 
is no difference between the similars, or perhaps they are 
quite different. But on either alternative they can not be 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 333 

similar; and again, if neither alternative is true, then the sug 
gestion is now admitted not to be simple, because the elements 
have a complex content. 

I can think of another case where mistake is possible, and 
where suggestion might seem to dispense with redintegration. 
If an idea before the mind is unsteady and wavering, it tends 
to pass into something different. This difference may be 
recognized, and may appear as an idea, which is not the first 
idea, and yet is seen to resemble it. But the unsteadiness 
will in no case be reproduction by similarity. If the new 
idea, which is similar to the other, is produced by a change 
in the actual impressions, then this of course is not reproduc 
tion at all. But if the alteration takes place apart from the 
stimulus of a fresh sensation, it will still be a case of redinte 
gration. For that will be the principle which determines the 
direction of the idea s unsteadiness. 

We must pass next to an objection which I feel bound to 
notice, though I confess I am not able to understand it. We 
are told that the form, say of a triangle, is not one single 
feature among others, which therefore could call up the other 
features ; and that yet a triangle may call up another which 
is similar in nothing but form (J. S. Mill, on James Mill, I. 
113). But why the form of a figure is not to be a " feature " 
of it we are not told, and I at least can not imagine. I was 
glad to find when, after forgetting this passage, I came on it 
again, that accidentally (30) I had chosen to work out an 
instance where the form is the base of the redintegration. 
And I will say no more. 

And there is another misunderstanding which we may 
remove in conclusion. After pointing out that " in the very 
heart of Similarity is an indispensable bond of Contiguity; 
showing that it is not possible for either process to be ac 
complished in separation from the other," Professor Bam, i: 
L understand him rightly, goes on to argue that, notwithstand 
ing this, at least a partial reproduction by pure Similarity 
does actually take place. 

" It might, therefore, be supposed that Similarity is, after 
all, but a mode of Contiguity, namely, the contiguity or asso 
ciation of the different features or parts of a complex whole^ 
The inference is too hasty. Because contiguity is a part 



334 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

the fact of the restoration of similars, it is not the entire fact. 
There is a distinct and characteristic step preceding the play 
of this mutual coherence of the parts of the thing to be 
recovered. The striking into the former track of the agreeing 
part of the new and the old, is a mental movement by itself, 
which the other follows, but does not do away with. The 
effect above described, as the consciousness of agreement or 
identity, the flash of a felt similarity, is real and distinct. We 
are conscious of it by itself ; there are occasions where we 
have it without the other, that is to say, without the full 
re-instatement of the former object in its entireness. We are 
often aware of an identity without being able to say what is 
the thing identified ; as when a portrait gives us the impression 
that we have seen the original, without enabling us to say who 
the original is. We have been affected by the stroke of 
identity or similarity ; but the restoration fails from the feeble 
ness of the contiguous adherence of the parts of the object 
identified. There is thus a genuine effect of the nature of 
pure similarity, or resemblance, and a mode of consciousness 
accompanying that effect; but there is not the full energy of 
reproduction without a concurring bond of pure contiguity. 
A portrait may fail to give us the consciousness of having 
ever seen the original. On the supposition that we have seen 
the original, this would be a failure of pure similarity " (Bain 
on James Mill, I. 122-3). 

Before I criticize this passage, let me show how easily the 
fact which it mentions comes under our theory. When the 
promontory A by means of p calls up q, r, these are not 
referred to A. And, unless the synthesis p, q, r, s, t is com 
pleted, they can not re-instate B. The uneasiness of partial 
but incomplete recognition is caused by the presence of con 
nected elements, such as p, q, r, s, which, by actual incom 
pleteness and by vague suggestion of completeness, give us 
the feeling that at every moment another object is coming. 
But, although the whole pqrs keeps calling in other elements 
such as u, x, y, w, yet none of these makes up a totality we 
are able to subsume under any head which we know. Should, 
however, t be called in, then B comes at once. In this case 
we have the feeling of discovery, while in the former case we 
have the feeling of search. And all is consistent. 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 335 

In Professor Bain s account we have no consistency. 11 
His view, as I understand it, is that though, for the full 
reproduction of B, contiguity is required, yet partial repro 
duction takes place without it. In other words, the stroke of 
similarity affects us enough for us to strike into a former 
track, but the adhesion of the contiguous bond is too feeble to 
drag on the mutual play of the parts. The hammer of simi 
larity comes down, but the flash of agreement is a flash in the 
pan, which fails to explode the barrel of contiguity. But in 
this place again, I think truth has been sacrificed to imagina 
tion. 

If anything is brought up which suggests agreement, then 
this must involve what is called contiguity. For apart from 
such contiguity there would be nothing to recognize. This is 
readily shown. In the first place let the similarity " amount 
to identity": let the differences, which went along with and 
qualified B, be none of them called up. Then what is there? 
Why nothing but one part of the content of A, say p. And 
p agrees with nothing; for what can it agree with? There is 
nothing save itself. But in the second place, if the differences 
which qualified B and made it B, are called up, then obviously 
we have contiguity at once ; for p by contiguity has re-instated 
pqrst. " Oh but," I may hear, " we do not go on to t, and 
so we never do get so far as B. We go only as far as fqrs, 
so that we are not able to recognize the result. It would be 
contiguity if we went from p to t : but if we stop at s, it is not 
contiguity at all. 

But this would surely be no less feeble than arbitrary. ^ 
the whole of the differences between a portrait and the idea 
of the original can not be given by contiguity, why then should 
any of them? Why not all be given by similarity? And if 
any are given by contiguity, why should not all be given, fo 
all of them are demonstrably " contiguous "? In oth 
words, if similarity will not bring up all the differences why 
should it bring up any? Why should not all be 
contiguity ? 

Because as before we do not start from the fact, but start 
from a vicious theory of that fact. In the perception A/> the 
* is not really a particular image; and if you said q,r,s, t 
were associated with this mere adjective p, you would have 



THE PRINCIPLES OF LOGIC BOOK II. PT. II 

deserted your vicious theory. You try to save it by inventing 
a fictitious substantival image p, which then can be brought 
in by similarity. But the result is a system of compromise 
and oscillation. You will not boldly say that A brings up all 
of B by similarity, and your theory forbids you to say it does 
so by contiguity. To satisfy both the fact and your theory 
you say, One arbitrary part is done by one agency, and the 
rest by the other. And you satisfy neither your theory nor 
the fact. For what is actually contiguous is not like, and what 
is supposed like could never have been contiguous. The par 
ticular image, which on your theory is called up, has never 
been contiguous to anything whatever. And the actual ele 
ment, which does re-instate qrst by contiguity, is not anything 
we can call like A at all. It is an universal which is part of 
A s content. Into this confusion we are led by forcing on the 
facts our bad metaphysics; and the confusion at once gives 
place to order when we recognize that Association by Simi 
larity has no existence. 

32. We have seen that reproduction of a similar idea 
comes under the general head of Redintegration. And if the 
English votary of Association, instead of declaiming against 
the blindness of Germans, had been willing to learn from them, 
he might long ago have amended his theory. 

" Si quod nunc percipitur specie vel genere idem est cum eo, 
quod alias una cum aliis perceptum fuerat, imaginatio etiam 
horum perceptionem producere debet. Quae enim specie vel 
genere eadem sunt, ea sibi mutuo similia sunt, quatenus ad 
eandem speciem, vel ad idem genus referuntur (233, 234, 
OntoL), consequenter qusedam in iisdem eadem sunt ( 195, 
Onto!.). Quare si nunc percipimus A specie vel genere idem 
cum B, quod alias cum C perceperamus ; qusedam omnino 
percipimus, quae antea simul cum aliis in B percepimus. 
Quamobrem cum perceptio ceterorum, quae ipsi B inerant et 
in A minime deprehenduntur, vi imaginationis una produci 
debeant ( 104) ; imaginatio quoque producit perceptionem 
ipsius B. . . . 

" Idem confirmatur a posteriori. Ponamus enim nos in 
convivio simul vidisse hospites et vitra vino plena. Quodsi 
domi die sequente oculos in vitra convertis, quibus vinum 
infundi solet; extemplo tibi occurrit phantasma hospitum ac 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 337 

vitrorum vino plenorum rerumque ceterarum in convivio 
prsesentium. Vitra, quae domi conspicis, specie saltern eadem 
sunt cum vitris, quae videras in convivio." * 

Let us hear now what Maas has to say. I translate from 
the second edition of his Versuch iiber die Einbildungskraft, 

1797- 

" The first of these rules we have mentioned is the so- 
called Law of Similarity: All ideas which are like are asso- 
ciated.f I am aware that many psychologists give this law a 
place co-ordinate with the law of partial perception " [redinte 
gration] " and consider it independent. But on this view the 
former stands too high, and the latter too low. Similar ideas 
can not be associated unless, and so far as, either they or their 
marks form part of one total perceptive state. But this holds 
good without exception. Two ideas, a and b, are like one 
another in so far as they have a common mark /3. Suppose 
now that it is a fact that b has associated itself with a." [The 
explanation of this fact is that] " b contains the marks ft tf, 
f,and a the marks /?, or, y." [On the presentation of b] " the 
marks , y associate themselves with the 0," [which appears 
in &, and Pay is then recognized as a.] : The association 
which takes place is thus between connected ideas, which are 
parts of one perceptive state." s. 55.$ 

I admit that the passage is so brief and cramped that ] 
have been obliged to interpolate a commentary. But there 

* These quotations are from 105 of Wolff s Psych. Emp. Ed. Nova, 
1738. First published in 1732. 

t" Ideas" here includes perceptions. 

$"Die erste von den eben erwahnten Regeln ist das sogenannte 
Gesetz der Aenlichkeit : alle ahnlichen Vorstellungen associiren sich. 
Es ist mir nicht unbekannt, dass diese Regel von vielen Psychology 
dem Gesetze der Partialvorstellungen koordinirt, und fur em, von 
diesem unabhangiges Gesetz gehalten wird. Allein das heisst dem 
erstern einen zu hohen, dem andern einen zu niedrigen Rang anweisen. 
Aehnliche Vorstellungen konnen sich nur in sofern associiren als sie, 
Oder ihre Merkmale, zu einer Totalvorstellung gehoren, welches aber 
bei ihnen ohne Ausnahme der Fall ist. Zwei Vorstellungen a und 
sind einander ahnlich, sofern beide das gemeinschaftliche Merkmal 
haben. Wenn also b, der die Merkmale fi,*, zukommen, sich mit 
worin die Merkmale ft a, y angetroffen werden vergesellscha tel : so 
associiren sich a, 7 mit ft sind also zusammengehonge Partialvorste 
lungen." 



338 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

are other passages, which I need not quote, which would settle 
the meaning even if it were doubtful. 

From these extracts it will be plain that the school oi 
Association have had something to learn which they never 
have learnt.* 

33. There is a possible objection we may here anticipate. 
" Admitted," it may be said, " that your theory explains the 
suggestion of similars, yet it does so indirectly. We explain 
it directly and by a simple law. And the simpler explanation 
is surely the better one." Anything more unscientific than 
such an objection I can hardly conceive. It proposes to give 
a simple explanation of a complex case; in other words, to 
decline analysis, and to reassert the fact as a principle. And 
it proposes in consequence (as we have shown at length) to 
treat the simple as a complication of the complex. But the 
price you pay for turning a derivative law into an ultimate 
principle is somewhat ruinous. You have to import into the 
simplest processes a mass of detail which is demonstrably not 
there. And this is surely a procedure which science will not 
justify. 

And if I am told, " At all events the process of suggestion, 
as you describe it, is much too complex for a primitive mind," 
that objection once more only serves to strengthen me. For 
the process does not exist in a primitive mind. Similarity is a 
somewhat late perception, and hence can not appear at an 
early stage. For a rude understanding, if things are not the 
same, they are simply different. To see, or to feel, that two 
things are not the same and yet are alike, are diverse and yet 
in part identical, is a feat impossible for a low intelligence. 
It demands an advance in reflection and distinction which no 
sane psychology can place at the beginning of mental evolu 
tion. No doubt you may say that from the very first mental 

* Sir W. Hamilton not only refers to the true account of Associa 
tion by Similarity, but even criticizes it. Unfortunately he had not 
the least idea of its meaning. He tells us first that we are to discount 
" Wolff who cannot properly be adduced." I have no notion what 
"properly" stands for here, and perhaps Sir W. Hamilton did not 
really know what Wolff says. He then proposes an emendation in 
the passage from Maas, which reduces it to nonsense, and his criticism 
shows that he had no idea of the real meaning of either Wolff or his 
followers (vid. Reid, 913-14). 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 339 

elements are alike, although the mind does not perceive it. 
But in saying this you open a question not welcome I should 
judge to the disciples of Experience. For if states of mind 
can be alike, and yet not like to the mind, what is such simi 
larity but the identity of elements within these states? The 
distinction on the one hand between what is or was in the 
mind, and, on the other hand, that which is felt by the mind 
or is now before it, is, if admitted, quite fatal to the orthodox 
English creed. We should have an attempt to purchase con 
sistency by suicide. 

If the school of Association desired to be consistent, it 
might find perhaps in the " mechanism of ideas," apart from 
consciousness, a way of propping its tottering beliefs. But 
that mechanism implies metaphysical doctrines as to the unity 
of the soul and the permanence of ideas, which in themselves 
would be somewhat difficult to maintain, and which would 
give the lie to our most cherished prejudices. 

But if consistency can be reached by no way but suicide, 
something after all may be said for the admission of the 
doctrine we have adopted that all association is between uni- 
versals, and that all consists in redintegration by identity. 

34. The answer no doubt will be the old " Non possumus. 
No two states of mind can have anything in common ; for, if 
so, they would be the same, and that is impossible." On this 
rock of obstinate metaphysical prejudice our explanations are 
broken. It would be useless to point out, as we have already 
pointed out, to the disciple of Experience that his own theory 
has been wrecked on this same iron dogma. He would say, 
I suppose, "Let the facts go unexplained, let miracles be 
invoked and fictions multiplied, let analysis be neglected and 
experience contemned only do not ask me to be false to my 
principles, do not ask me to defile the grave of my fathers. 
An advanced thinker once, an advanced thinker always." And 
I could not answer or reproach. I respect a fidelity which I 
can not imitate. 

But to those whose honour is not yet pledged I may per 
haps in conclusion be permitted to address myself. Do you 
wish I should like to ask in the first place, to speculate on 
first principles, or are you content to engage yourself on 
special subject matter? In the first case I would beg you 



34O THE PRINCIPLES OF LOGIC BOOK II. PT. II 

seriously to examine the question for yourself, and not to 
take any assertion on trust. I can not venture to anticipate 
the result you will then reach (if indeed you reach any), but I 
feel sure that any conclusion you do come to, will not be quite 
the same with the orthodox doctrine as handed down in 
England. And to those who are not prepared for metaphysical 
enquiry, who feel no call towards thankless hours of fruitless 
labour, who do not care to risk a waste of their lives on what 
the world for the most part regards as lunacy, and they them 
selves but half believe in to all such I would offer a humble 
suggestion. Is it not possible to study the facts of psychology, 
without encumbering oneself with beliefs or disbeliefs as to 
the ultimate nature of the mind and its contents ? You can not 
have metaphysical disbeliefs without corresponding beliefs; 
and, if you shrink from becoming a professional metaphysi 
cian, these beliefs must be dogmas. Would it not be better 
to study the facts, and to let metaphysics altogether alone ? 

If this can be done in the other sciences, it surely can be 
done in psychology too. In the other sciences we know how 
it is done. The so-called principles which explain the facts are 
working hypotheses, which are true because they work, and 
so far as they work, but which need not be considered as a 
categorical account of the nature of things. The physicist, 
for example, is not obliged to believe that atoms or ether do 
really exist in a shape which exactly corresponds to his ideas. 
If these ideas give a rational unity to the knowledge which 
exists, and lead to fresh discoveries, the most exacting demand 
upon the most exact of sciences is fully satisfied. The ideas 
are verified, and the ideas are true, for they hold good of the 
facts to which they are applied. And to suppose that the 
metaphysician should come in, and offer to interfere with the 
proceedings of the physicist or to criticize his conclusions, is 
in my judgment to take a most wrong view of metaphysics. 
It is the same with psychology. There is no reason why in 
this science we should not use doctrines which, if you take 
them as actual statements of fact, are quite preposterous. For 
the psychologist, as such, is not interested in knowing if his 
principles are true when taken categorically. If they are 
useful ways of explaining phenomena, if they bring unity into 
the subject and enable us to deal with the fresh facts which 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 34! 

arise, that is really all that, as psychologists, we can be con 
cerned with. Our principles are nothing but working hy 
potheses : we do not know and we do not care if they turn out 
to be fictions, when examined critically. 

That is the way in which psychology surely might be 
studied. And if we studied it in this way we should escape 
some controversies. I, for instance, should lose all right and 
all desire to criticize the " Laws of Association " on the ground 
of their untruth, if they only ceased to proclaim themselves 
as statements as to the real movement of the mind. Within 
the same field of empirical psychology I should offer what I 
think is a more convenient hypothesis, and any objection to 
that which rested on metaphysics would be at once ruled out 
of court. We might perhaps thus advance the study of the 
subject in a way which now seems quite impossible. And if 
we did not make much advance in knowledge, we should save 
ourselves at least a good deal of bitterness. 

35. The suggestion is offered in great humility, since the 
obstacles it must meet with are overpowering. The first 
obstacle is the prejudice of a bad tradition. It is supposed 
that the psychologist must be a philosopher. He is used to 
think himself so, and he is not likely to accept a lower place. 
And this objection is in fact, I fear, unanswerable. I would 
give him the name of philosopher for his asking, but I could 
not admit him as a student of first principles. And the second 
obstacle is like the first. We get into what, I suppose, deserves 
the name of an antinomy. The psychologist is to confine him 
self within certain limits; he is not to cross over into meta 
physics. But unfortunately if he is not a metaphysician he 
will not know what those limits are. And it is the same to 
some extent with all the sciences. The physicist, for instance, 
is constantly tempted to think that his ruling ideas are ultimate 
facts. And this temptation is fatal to the mere specialist. 
It is only, on the one hand, a general culture and largeness of 
mind, or else some education in metaphysics, which saves him 
from this error. And it is much worse in psychology. 12 The 
subject brings with it a special temptation; and, if all the truth 
must be told, the same great minds that devote themselves to 
physics, to chemistry, or to biology, do not take up psychology. 
And then again the psychologist is probably a dabbler in meta- 

2321.1 Z 



342 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

physics. A little metaphysics is not enough to show that his 
so-called principles are fictions. And our leading English 
psychologists perhaps only know a very little metaphysics. 
And, having a limited acquaintance with the subject, they 
persuade themselves, and (what is worse) one persuades the 
other, that they have completely mastered it. It is to be feared 
that this evil must to some extent continue. 

And there is a final obstacle. The student of metaphysics 
may form an opinion as to the real nature of psychical phe 
nomena. And knowing, as he thinks, the truth about these 
facts, he will be led to insist on a psychological interpretation 
which is strictly true. He will interfere with the empirical 
psychologist, and will himself contribute, by what he thinks 
good metaphysics, to the begetting of bad metaphysics in 
opposition. This is certainly an error, but it is an error, I 
fear, which will never quite vanish. When a man has once 
seen that every single science except metaphysics makes use 
of fictions, he is apt to conclude that the next step is for him 
to remove these fictions and to substitute the truth. But, if he 
looked closer, he would see that human beings can not get on 
without mythology. 13 In science, in politics, in art, and re 
ligion it will always be found, and can never be driven out. 
And, if we confine our attention to science, we must say that 
there is only one science which can have no hypotheses, and 
which is forbidden to employ any fiction or mythology, and 
that this science with some reason is suspected of non- 
existence. 

36. We have approached a large subject which we can 
not deal with, and which might well occasion misgiving and 
doubt. We need give way to neither in our rejection of the 
principles of the school of Association. We reject them in 
the name alike of metaphysics, of psychology, and of logic. 
In behalf of metaphysics we protest against the basis of dog 
matic Atomism, and we protest against the superstructure of 
a barbarous mythology. It is not true that mental phenomena 
are mere particulars. It is not true that ghosts of impressions 
leave their graves. It is ridiculous to couple the existent and 
non-existent, or the present and the absent, by a relation which 
implies the presence of both. In defence of psychology we 
protest against an hypothesis which has to postulate phe- 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 343 

nomena which are clearly absent, and then to postulate their 
removal by a process which is not present. When a single 
hypothesis explains the facts, it is surely unscientific to employ 
a complication which works no better. And, in behalf of logic, 
we must protest once more. The essence of inference can 
hardly be a principle which later we recognize as a principle 
of error; and which, if the theory of Association were true, 
we should hardly get to perceive was false. It is an ill omen 
for Logic if it fails to show that what in the highest stage is 
accepted as a canon, was active from the first development of 
the soul as the guide of its conduct and ruler of its life. 



NOTE TO CHAPTER I 

I. Though I have no space, and perhaps no strict right, to deal 
with the subject here, I must yield to the temptation of making some 
very brief remarks on the doctrines noticed in 2 of this chapter. 
These go by the names of Indissoluble Association and the Chemistry 
of Ideas. 

The first of these doctrines is supposed to have a very great 
metaphysical importance. Mere chance conjunction, if often repeated, 
will beget, we are told, an union of ideas which is irresistible. This 
shows that what seems to be a necessary connection may be no more 
than an accidental adherence. From this we conclude that a necessary 
connection is no canon of truth. And this proves that our trust must 
be placed elsewhere. The Logic of Experience tells us, of course, what 
it is we are to trust to. 

For myself, in the first place, I never could get any information 
from that Logic which seemed intelligible, and so I will confine myself 
to the former part of the preceding statement. 

2. The first fault I have to find is that it does not go far enough. 
We need not have a repeated conjunction. One single instance is 
enough to give rise to a necessary connection. For, as we should say, 
what is once true is true always. 

3. I have to complain, in the second place, that all kinds oi 
combination are called association. But association surely implies that 
the elements which are joined might not have been joined. And 
should be proved, or at all events made probable, before co-existei 
is assumed to be mere association. 

84 It may be replied, "Even if the things are connected, yet, as 
we perceive them, their union for us must be chance conjunction, and 
therefore association." But this again should in no case be asserted 
without some ground. It is not always self-evident that the mind co^ 
have had one element without the other. And where you fail 
show that this is the case, you cannot talk of association. 



344 THE PRINCIPLES OF LOGIC BOOK II. Px. II 

5. I shall be answered, " What we prove is that in certain cases 
mere chance association has produced necessary connection; and we 
argue from this that it may be fairly suspected of doing so in all. 
The possibility is proved and the possibility is enough." I can not 
enter here into the merits of this argument which I shall hereafter 
show is logically vicious (vid. Bk. III. II. Chap. III. 22) 14 ; but sup 
pose that for the present we admit it. What conclusion follows? 
That we are fallible men? We knew that before. That we are to 
trust to anything else? Then what else? Admit for argument s sake 
the possibility that all our beliefs are baseless, what then? Why 
nothing. If we mean to go on living and thinking, we dismiss this 
possibility as idle. Suppose we all are victimized by chance con 
junction, are we not right to be so victimized? 

6. Association implies other conditions. It implies contingent 
circumstances. When a chance conjunction is taken by an error 
for a necessary connection, the mistake really consists in defective 
analysis. The remedy is found in the progress of analysis, assisted 
probably by fresh fact. Where this remedy is impracticable, no remedy 
can be applied. For no other is possible. 

7. Apart from mental chemistry, which we shall consider pre 
sently, a connection of ideas could not continue to be necessary when 
it demonstrably has arisen from association. And this is quite ob 
vious. For the connection of ideas supposes a content which is 
ideally inseparable, and the knowledge of the association involves 
this ideal separation. The experience which shows the fact of the 
association, is at the same time the analysis which loosens its bond. 

8. This however is a minor point. To the objection that 
possibly all truth may be nothing but chance association, we reply (as 
above) that, supposing this for argument s sake to be true, we can 
not trouble ourselves with idle possibilities. But if you wish to go 
beyond this idle possibility, you must show cases where unreasoning 
chance conjunction has produced false belief -without confusion. You 
must show, that is, that the belief in the connection was wholly false; 
that it was not a true belief in a real fact made false simply by a 
confusion between the relevant and irrelevant elements in the connec 
tion. But this, I think, has never been shown. 

9. If association rests on conjunction in perception, then that 
is a valid ground for belief. It is deceptive merely so far as it is 
unanalyzed, and confuses the irrelevant with the relevant. Otherwise 
it is a proof of necessary connection. But then this latter is not mere 
association. For it is not every conjunction in presentation which 
can be called an association, but only those conjunctions which 
result from chance. And chance disappears before analysis. 

10. I will now turn to the doctrine of mental chemistry. Ele 
ments by virtue of repeated chance conjunction are said to cohere 
in such a way that they form a third product which has the qualities 
of neither. But this in the first place would not be association, since 
that term implies that the individuals continue. In a chemical union l5 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 345 

the molecules of the substances cease to be molecules of either sub 
stance. It is therefore nonsense to say that they are associated. 

11. This of course may be said to be a question of words. 
But the fact of such union in the case of ideas has, at least in my 
knowledge, never yet been shown. It can not be called impossible, 
nor should I at least have said that it was even improbable, but I 
have never seen any certain instance of it. 

12. In the case of emotions this " chemical union " does seem to 
take place. But even here there might be doubt if the emotion 
should properly be considered as an " union." It might rather be a 
new reaction on a fresh compound material. 16 But, however that be, 
it is true that the emotional product often can not be analyzed. 17 It 
can only be reconstructed perhaps in part hypothetically. And again 
if we take intellectual functions, there is no doubt that in the process 
of mental development " faculties " are produced which are different 
in kind from what went before. 18 But then again these functions are 
hardly unions of ideas. When you strictly keep to mental objects, I 
think you must say that no instance of what looks like chemical 
combination has yet been found. 

13. It is of course mere waste of time to bring forward as evi 
dence cases where the fact of the association is not admitted. It is 
for example a mere circle to instance the idea of visual extension, 
since visual sensations without extension are the merest hypothesis. 
Not only can this alleged fact not be observed, but there are very 
strong reasons for rejecting it wholly.* It is not less idle to bring 
forward a product, such as the sensation of white, and then roundly 
assert that it is the fusion of different sensations. Perhaps it is, but 
you would have to show the existence of these sensations in the 
particular case, and give some reason for your belief that they were 
transformed. It is finally ridiculous to adduce, as a chemical product, 
an idea which can be separated at once and with ease into its 
component parts. J. S. Mill when hard pressed seems to play as his 
trump card the idea of infinity (Hamilton, Note to Chapter XV.). 
But infinity, as he understands it, hardly calls for analysis. < 
it falls apart into its elements, for it is a mere mechanical union. 

The conclusion must be that the chemistry of ideas is no more 
than a hypothesis. I do not think in any case it would be the right 
way to state the fact. But the fact itself has not been clearly shown 
to exist. 19 In the second place, were we convinced that mere chance 
conjunction was able to lead to it, then nothing would follow except 
what we know, viz. that there is some general antecedent probability 
that any conviction is false. This result makes no difference either 
to theory or to practice. 

*Vid. Stumpf, Raumvorstellung. 



346 THE PRINCIPLES OF LOGIC BOOK II. PT. II 



ADDITIONAL NOTES 

1 The length of this Chapter was, I think, justified by the general 
state of psychology in England in 1883. The reader is asked to bear 
in mind that perhaps the greater part of it was written at a particular 
time, and for a special purpose, and hence should now be superfluous. 
This remark does not, however, apply to the doctrine that Association 
holds only between universals. This doctrine, as I have long ago 
mentioned (in Mind N. S., No. 20, p. 472, and, I think, elsewhere) 
I owe to Hegel (Encyk. 452 foil.). For my indebtedness to him 
in psychology otherwise see on Bk. III. I. VII. I may add here that, so 
far as I remember, in 1883 I had not yet made the acquaintance of 
Herbart, with Drobisch and Volkmann, or even of Waitz or of 
Lotze s Medicinische Psychologic. I had, however, read most of 
Steinthal s Sprachwissenschaft, I. 

2 "If the condition is known." It would be better to say "is taken 
to fall within the subject," and for "where the condition is unknown" 
to write " where you can not specify the condition." 

3 " Analytical." Cf . Bk. III. I. VI. 10. 

4 " When they are dead, etc." I should certainly have used other 
language here with reference to "survival," if I had been better ac 
quainted with the excellent work done in psychology by Herbartian 
writers. The doctrine that every mental state still survives and is 
active below the conscious level, was, and is, as a working hypothesis, 
not to be treated with contempt. 

5 "What is left behind is a mental result." Cf. 26. We have 
here the problem of Dispositions. This, I should say, is in the end 
insoluble, if you ask for anything beyond an empirical Law or Laws. 
Cf. Mind (O. S.), No. 47, p. 363, No. 13 (N. S.), p. 25, and No. 33, p. 9. 

6 " Logical." Cf. Bk. III. I. III. 20 and 23. Association becomes 
logical by its use for, and subordination to, a logical end ; where, that 
is, it is controlled, for the purpose of truth, by the identity and indi 
viduality of an object. Cf. Mind (O. S.), No. 47, pp. 381-2, and 
Essays, pp. 362 foil. 

7 " They all have content." Cf. 30 and 31. The point here is 
that you do not anywhere have a psychical fact which is purely simple 
and in this sense unique. Everything given, we must remember, is 
always in some sense itself qualified by its context. See T. E. V. 

8 "This is not merely an assertion I have chosen to make." Prof 
Sully on the other hand, in The Human Mind, I, 331 (1892), says (I 
understand) that it is so. While directing the reader to this criticism 
I may add that I neither saw nor see any need to reply to it. The 
reader who can not deal with it for himself will, I think, have read 
this Chapter in vain. 

9 " Primitive Credulity." Cf . Bk. III. I. VI. 32, and Essays, p. 377. 

10 " This is a result." See Note 5. 



CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 347 

11 " In Professor Bain s account, etc." Though the temptation 
was irresistible, I am sorry that I treated Bain, here and elsewhere, 
with so little respect. Let me say now that, so far as I know, he was 
the only writer of his time and school who made an original con 
tribution to psychology. Though one may find him at times to be 
absurd, one seldom finds that he has not at least made an instructive 
effort to see the facts for himself. 

12 " And it is much worse in psychology." The reader here must 
not forget that I was pointing to psychology as it was in England, 
still at least in the main, in 1883. To use such language now would be 
absurd and even monstrous. 

13 " Mythology." Cf. my Appearance and Essays, and, in particular 
on psychology, see Mind, Vol. IX, N. S., No. 33. It is hardly neces 
sary, I hope, for me to inform the reader that this view of truth, as 
being more or less mythological everywhere outside metaphysics, came 
to me from Plato and again still more from Hegel. 

14 Cf. here Appearance, p. 620. 

15 " Chemical union." I am of course here not endorsing but 
merely adopting the view offered me as to the real nature of chemical 
union. 

This, I presume, might be the place to discuss the doctrine of 
Fusion whether of one sensation with another or with ideas and 
Dispositions or again of these two last, each with themselves or 
with one another. But I can not venture upon such a difficult subject 

here. 

is "It might rather . . . material." This seems certainly 1 
better view. No psychical state, as a unity, can be wholly resolved 
into the mere compounding of units even " chemically." 

" " Often can not be analyzed." The meaning here is that there 
are some emotions, to ."analyze" which, except quite inadequately, 
you must have recourse to what you believe is their origin. 

is " Functions " and " faculties." This statement of course will apply 
to much of what are called "instincts." 

19 "But the fact itself . . . exist." By "the fact itself I mean 
the appearance of a complex psychical state, in which the elements, 
as such, have become indistinguishable, and which can nevertheless 
be taken as the mere product of their union. There are but few 
psychologists, I should think, who would now accept such a fact 
However that may be, we can and must, I should say, maintain that 
new products have been developed, but certainly not by chemical 
union of ideas. Every new mental product is rather a fresh reaction 
from the individual totality; and, to explain, we .must seek .to find the 
Laws by which Dispositions are formed, and by which the result 
former experience meets and more or less transforms the incoming 
stimulus. 



CHAPTER II 

THE ARGUMENT FROM PARTICULARS TO PARTICULARS 1 

i. At the point which we have reached a discussion of 
this subject may seem inexcusable. If we have shown that 
no association is possible except between universals, and that 
in the very lowest stages of mind universals are used, we may 
fairly be reproached by the reader who is anxious to learn 
something new, if we linger over errors the root of which has 
long since been torn up. For supposing that the results we 
have attained to are sound, the question is settled. To 
reason directly from particulars to particulars is wholly im 
possible. It must be at most a desire of the mind which 
this world can not gratify, a postulate a priori given by an 
intuition, that disappears before analysis and is rejected by 
experience. 

2. But since it is possible that the reader of this Chapter 
has not accepted the conclusions we obtained, since it is not 
unlikely that he has passed them over, let us try once again 
if we can not do something to turn the light into this refuge 
of darkness. We must not expect to persuade the disciple of 
the Experience Philosophy. It is not for anything we are 
likely to offer, that he will desert the fashionable and easy 
creed in which he has been reared. But at least we shall 
have tried not to leave him an excuse. He must not say 
that we have been afraid to look his idol in the face. 

There is however one thing we will not do for his sake. 
We decline to supply a direct examination of the well-known 
chapter in J. S. Mill s Logic. It would require much more 
space to set out the ambiguities inherent in that chapter, 2 than 
we can give to the discussion of the question itself; a dis 
cussion to which, I may remind the reader, I consider that at 
this stage he has no right. 

3. Why should we not reason from mere particulars? 
Do our reasonings never rest upon fact ? And what are facts 
if they are not particulars? Either then we never, starting 

348 



CHAP. II THE ARGUMENT FROM PARTICULARS 349 

from fact, conclude to fact, or else we infer particulars from 
particulars. This result may so be deduced from first prin 
ciples. And common experience supports the result. From 
cases we have known we go to fresh cases without an appeal 
to any general principle. We have seen something happen 
and, given a new instance, we argue at once that it will hap 
pen again. But we have no reason other than this fact to 
give for our conclusion. We thus in the second place have 
proved our thesis a posteriori, as before we proved it a priori. 
And now we add an indirect proof. If for reasoning were 
wanted major premises, then the lower animals could not 
reason. But they do reason, and therefore the thesis is proved. 
4. How shall we escape from this array of proofs ? Are 
they not unanswerable? To me they seem unanswerable, and 
I have not the smallest wish to escape them. I admit them 
and embrace them ; but I ask a question, What is it that they 
prove ? 

They prove first that, when we go from experience of 
facts, this experience is the foundation of our inference. They 
prove again that we do not always go from an explicit major 
premise, and that therefore another way of reasoning is pos 
sible. And in defence of these results I am as zealous as 
any of my readers can be. If he likes to say beside that a 
syllogism in extension is a petitio principii and no argument at 
all, he will urge what long ago I have endorsed. But let us 
come to the conclusion. If you mean to argue to no more 
than this, that experience of particulars is a basis of inference, 
and that no explicit major is required, I am ready to support 
you. But if you mean to conclude, Therefore we reason from 
particulars as such direct to particulars, I object at once. The 
conclusion does not follow from the premises, and it also is 
wholly contrary to experience. 

5. We have in fact to do here with a common-place 
logical blunder. The thesis to be proved is that an inference 
is made direct from particulars, as such, to other particulars. 
The conclusion which is proved is that from experience of 
particulars we somehow get a particular conclusion. Not to 
see the enormous difference of these assertions is to fall into 
a gross ignoratio elenchi. To prove the thesis in dispute it is 
necessary to assume that either we go direct from particulars 



35O THE PRINCIPLES OF LOGIC BOOK II. PT. II 

to particulars, or else advance through an explicit syllogism 
(perhaps even an explicit syllogism in extension). No sort of 
evidence is offered to show that this alternative exhausts the 
possibilities ; and it disappears the moment we confront it with 
facts. 

6. In reply to the assertion that we are able to argue 
from particulars to particulars, I would ask in the first place 
what particulars are meant. Am I to understand that the 
past experiences in their particularity are the premises used 
in this supposed inference? If I am told this is so, of course 
I reply that we have here a mere psychological fiction. Par 
ticular images of past occurrences, which retain the special 
marks of the originals, are not available. The doctrine that 
each perished perception leaves an unblurred unabridged 
counterpart of itself, is a preposterous invention (cf . pp. 35-7, 
and Book II. II. Chap. I.). 

7. It is again a mere error which sees in the lowest form 
of inference the presence of one or more images of the past, 
together with a fact which they are used to qualify. When a 
present perception is modified by the suggestions of past ex 
perience, these suggestions do not come from particular images 
of perished events. This theory is a second pure invention 
(cf. ibid.). 

8. In the third place when, at a higher stage of develop 
ment, the past event is as such called to mind, and when we 
do argue from a particular image, yet even then we do not 
argue from its particularity, from its psychological environ 
ment and temporary colouring. We argue from the content, 
the idea which can exist in different times and under diverse 
psychological conditions. And once more, and in the fourth 
place, this idea itself need not be used as a whole, but we 
may argue from one part of it. 

9. A child has come to know that, when the dog is 
pleased, he wags his tail. On this he argues that, when the 
cat wags its tail, it must be pleased. What is it he proceeds 
from? The error we are considering actually supposes that 
one or more images of foregone occasions, presenting the dog 
pleased and with his tail in motion, come before the mind, and 
that, on this, the perception of the cat now moving its tail 
directly gives rise to the conclusion, The cat is pleased. But the 



CHAP. II THE ARGUMENT FROM PARTICULARS 351 

question arises, How is it that one attribute is taken from the 
dog-images and given to the cat, without the rest going with 
it? Does not this use of one part of the dog-images, and the 
neglect of the rest, show that something happens to the images 
in question, and that, however it has come about, the inference 
is not drawn from the whole of any one of them? Suppose 
again that they differ among themselves, do we argue direct 
from the whole of all of them? But if not, from what else? 

10. The facts, I should have thought, would have left 
little doubt that the result of experience is a connection of 
attributes, where the differences of their particular subjects are 
blurred a confused universal, which may appear to the mind 
in a particular imagery, but is used without any regard to 
that. I confess I should have thought that it was very clear 
that, in the special cases where we argue from recollection, we 
use the past event as a type or instance. And since both this 
past event and the present perception come to us as instances, 
we neglect some of the differences that exist between them. 
We do not know the principle, but we feel " it is the same 
thing " in both cases. But, if so, the premise from which the 
conclusion directly comes, is not the particular. It is an 
universal extract, what we call a " general impression." 

ii. Reasoning from a particular to a particular is obvi 
ously an argument from analogy. In this we all know that 
we do not use the whole of that particular from which we 
argue. It was an inference by analogy which deceived the 
child (9). He took from the dog a relation of qualities and 
transferred it to the cat. What he argued from was this 
general relation, and it was a false analogy, just because it was 
a bad generalization. Again, why do we object to false 
analogies? Is it not because in them we treat some fact as 
another instance of a rule, when there is no common rule and 
the facts are not instances? And is not this a hint that in 
true analogy we use a principle though we can not state it ? 

12. This leads us to put another question. Suppose that 
per impossible we did have before our minds a number of 
particular images, and did argue from them directly; would 
not this inference be a very bad one? If I say " A, B, and C 
are a, and there is no difference between D and A, B, and^C, 
therefore D is a" is not this a circle a frivolous prtitiof 



352 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

Again if I say " A, B, and C are a, and D is different from 
A, B, and C, therefore D is a" is not this a bad argument, 
so glaringly bad that no child and no beast could be got to 
use it? 

But if we amend this semblance of reasoning, and bring it 
to the form of a real inference if we say " A, B, and C are a,, 
and therefore D, which resembles them, is a" we are no longer 
arguing from mere particulars. We are arguing from the 
resemblance, from a point or points which D has in common 
with A, B, and C. It is not because A, B, and C are a, but it is 
because in them some element $ is a, and because again we 
find /? in D, that we argue " therefore D is a." For whenever 
we reason from resemblance we reason from identity, from 
that which is the same in several particulars and is itself not a 
particular. And is it not obvious that, in arguing from par 
ticular cases, we leave out some of the differences, and that 
we could not argue if we did not leave them out? Is it not 
then palpable that, when the differences are disregarded, the 
residue is an universal? Is it not once more clear that, in 
vicious inferences by analogy, the fault can be found in a 
wrong generalization? 

13. I will conclude with an appeal to common experience. 
We all know very well that in our daily life we reason habitu 
ally from the results of past experience, although we may 
be wholly unable to give one single particular fact in support 
of our conclusion. We know again that there are persons, 
whose memory is so good that they recall past details in a 
way which to us is quite impossible, and who yet can not 
draw the conclusions which we draw, since they have never 
gone beyond the reproduction of these details. It is not the 
collection of particular facts, it is the general impression one 
gets from these facts which is really the sine qua non of 
reasoning ; and it is that from which we really go to our result. 

If you begin the discussion of a question, such as this, with 
a vicious disjunction, you can not go right. As a preliminary 
to discussion you have excluded the truth. From the alterna 
tive either an explicit syllogism or an inference from particu 
lars to particulars you can hardly fail to get a false result. 
You may infer The syllogism in extension is no argument, 
and therefore we go from particulars to particulars. You may 



CHAP. II THE ARGUMENT FROM PARTICULARS 353 

infer It is not possible to argue from particulars, and there 
fore we reason always in syllogisms, explicit and (if you like) 
also extensional. But to me it is nothing which conclusion 
you adopt. For both are errors, and both at bottom are one 
and the same error. They are twin branches from one root 
of inveterate prejudice and false assumption. 

14. The present chapter has been so short that I take this 
opportunity to deliver my mind from a weight that oppresses 
it. I intend to be guilty of what some readers may think an 
unpardonable omission. It is true that I do not undertake to 
criticize every theory from which I dissent; but there is one 
of those theories which I propose to pass over, that may seem 
to call for recognition and enquiry. Mr. Spencer, in his 
Psychology, has developed a view of the nature of inference, 
which, despite its ingenuity, despite its perception of some of 
those truths which the syllogism has forgotten, I am obliged to 
consider fundamentally mistaken. It has always seemed to 
me so arbitrary and so forced, so far away in the end from the 
real facts, that I can not believe a discussion of it here would 
tend to throw any light on the problems of logic. 3 

More than once, I admit, Mr. Spencer s position in English 
philosophy induced me to think that I had no right to omit 
all notice of his peculiar views. The sacrifice of space, the 
chance that I had failed to follow the process which had 
brought him his results, did not weigh against the danger that 
I might have seemed to avoid confronting my own doctrines 
with those of an established master in the subject. But there 
came to my mind another consideration, which decided the 
result and fixed my purpose to omit the examination, 
late Mr Mill and Professor Bain have both written systematic 
treatises on logic. They have entertained a view of Mr. Spen 
cer s powers and philosophical performances which is not 
mine. Mr. Mill especially has expressed his conviction in 
such terms, that beside it those praises, I should otherwise have 
felt were due to Mr. Spencer, would sound like detrac too* 
Both must have been aware that Mr. Spencer has ^more than 
once published what appears to be a novel theory of reasomng 
And yet neither (so far as I know) has examined the 1 
peculiar and salient assertions of that theory. 



354 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

And I thought that I might venture on a humble imitation 
of their common silence. Did they fail to follow Mr. Spencer s 
demonstrations, did they even think them an unprofitable sub 
ject, in either case I claim the protection of their authority. 
But, if neither is the truth and they considered Mr. Spencer 
to be of one mind with themselves, and to say the same thing 
in a different form, then once again they unite in excusing me. 
I surely am not wrong if I too omit all criticism, or at least 
delay it till I have seen some cause to think that it is wanted. 



ADDITIONAL NOTES 

1 On the argument from particulars, beside the references given, 
cf . also Bk. III. I. VII. 8 and III. II. I. 5. 

2 " The ambiguities inherent in that chapter." These are such that 
apparently (given sufficient good will) the chapter can mean that we 
never do or can argue directly from particulars (see Appearance, 
p. 596, note). With regard to J. S. Mill the questions to be answered, 
if any one thinks them worth answering, are these, (i) Had J. S. 
Mill any new view to offer? (ii) If so, what was it? (iii) What is 
the view logically required by his general position? But I must be 
forgiven if I go on to add " Let the dead bury their dead." 

3 With regard to Mr. Spencer s view I would suggest, as a possi 
bility, that it never was taken from the facts, but was a development 
of or from something about Comparison which he found in Hamilton. 
Reading so few books, Mr. Spencer was naturally more at the mercy 
of those that he did read. 






CHAPTER III 

THE INDUCTIVE METHODS OF PROOF 

I. We have seen that in reality there is no such thing 
as an inference from the particular to a fresh particular In 
this chapter we approach a cognate superstition. In England 
at least if we go with the fashion, 1 we all have to believe in 
an Inductive Logic, which, starting from particular given facts 
goes on to prove universal truths. Its processes, exact as the 
strictest syllogism, surrender themselves to the direction of 
Canons, reputed no less severe than Barbara and believed with 
reason to be far more fertile. I am afraid I may lose the 
reader s sympathy when I advise him to doubt the union of 
these qualities. 

2. To question the existence or deny the efficacy of those 
methods of reasoning (whatever they may be), by which 
modern science has made its conquests, would of course be 
absurd. To succeed on a great scale is to prove one s title. 
And it is not within the scope of this work to investigate either 
the nature of the processes which science employs, or the 
amount of evidence which it accepts as proof. What I wish to 
assert is that, starting from particular perceptions of sense, 
there is no way of going to universal truths by a process of 
demonstration perfectly exact, and in all its steps theoretically 
accurate. The induction of logicians, so far as it professes 
to make that attempt, I shall try to show will not stand 
criticism. 

3. We need not discuss at any great length the Method 
which is called Complete Induction. 2 To examine a number 
of individuals and to say of all what you say of each, is in the 
first place no inference to an universal truth. A collective 
term, if taken collectively, is no more universal than if taken 
distributively (p. 82) ; and the inference, if admitted, does not 
reach the conclusion which we have in view. But in the 
second place, the inference itself is inadmissible. In other 
words, if you start from each and end with each, there is no 

355 



356 THE PRINCIPLES OF LOGIC BOOK II. Px. II 

process ; but if you predicate of the collection what is true of 
each member, there is palpable error. The Induction by way 
of Complete Enumeration must be rejected as either tautolo- 
gous or false (cf. Book II. I. Chap. II. 5). 

Or again if we take the Induction in another sense, it 
changes its character. If first by counting you arrive at all, 
and then from all pass on to any, that is not a process which 
need be false or need merely repeat the fact it began with; 
but then it is not based simply upon the particular data. If 
a flock of sheep have all had medicine, I know that, within the 
given enclosure, any sheep has been dosed, and I connect the 
attributes without thinking of the individuals. The conclusion 
is valid and is really universal ; but it implies a process which 
goes beyond counting. " This sheep and that sheep and the 
others are dosed ; " that is the first premise ; but a second is 
wanted. We may write it " This sheep and that sheep and 
the others are every sheep that is within this fold," or again 
" The fold does not contain any sheep but these which we 
have counted." It is on the strength of this premise that we 
go on to conclude, "If any sheep is now within the fold he 
must have been dosed." We seem to argue from " all " to 
" any," but the " all " has ceased to be the mere collection. 

We have first the assurance that the whole field has been 
surveyed, and that we have not neglected any relevant matter. 
Counting is the way in which we attempt to obtain this assur 
ance. But the enumeration, if it is to be complete, must be 
qualified by the privative judgment, Nothing in this fold can 
have been uncounted. The collection is thus identified with 
every possible sheep that comes under the condition of being 
in the fold. This is one side of our process. The other side 
consists in an act of abstraction, and in the selective perception 
of one connection of attributes throughout our whole subject 
matter. Then, given an individual possessing the condition of 
belonging to our fold, we pass at once to the other connected 
attribute. 

Now the procedure by which we get this general connection 
is in a sense " inductive " ; and assuredly once more it has 
employed counting. But then the counting by itself is not the 
induction, and is not by itself a generalization. The discrimi 
native analysis, that goes with the counting, is the real agent 



CHAP. Ill THE INDUCTIVE METHODS OF PROOF 357 

which procures the universal, and which contains the " induc 
tion " (cf. Book III.). It is this which generalizes from the 
facts. But it does not go beyond one single case, 3 since its 
validity depends on the privative judgment by which any folded 
sheep must be one case with the sheep observed. 

To repeat, if you confine yourself to mere counting, you 
get no general result. If you attempt to advance from the 
basis of mere counting your ground is unsafe. If you proceed 
from a complete Enumeration, then the warrant of complete 
ness falls outside the counting. What generalizes is the selec 
tive perception which isolates and secures the connection of 
adjectives. But the conclusion depen ds on the guarantee of 
completeness. It is valid because the connection is found in 
a whole, which is warranted to anticipate every possible case 
of a certain kind. 

4. But induction by way of Enumeration is not the 
method we are asked to believe in.* In the treatise which, 
partly from merits of its own and partly also from other 
causes, has threatened to fasten itself on us as a text book, 
we find the so-called Canons of Induction, collected and de 
veloped from other writers, and formulated with a show of 
rigorous accuracy. It is the illusory nature of these self- 
styled proofs that I wish to point out in the present chapter. 
We must not be afraid of the shadow of authority. The 
balance of authority among modern logicians is, I think, against 
the claim of the inductive proofs, and is not on their side. 
And perhaps already, from experience we have had, we may 
be prepared to find that Mr. Mill may at times be mistaken. 
5. We must remember above all things throughout this 
discussion that the question is not, Can discoveries be made by 
the use of the Methods ? They may be as efficacious in actual 
practice as is asserted by some, or as practically inadequate 
and unsuited for work as is affirmed by others. That is not 
the issue which we have before us. The question we have to 
answer here is, Are they valid ways of proof, by which we can 
go from facts to universals? 

For that is the claim which the Canons set up. " The 

* The reader of Mill s Logic will remember, on the other hand, that 
with him the whole inductive process is taken to stand or fall with a 
proof by way of incomplete Enumeration. 

2321.1 A a 



THE PRINCIPLES OF LOGIC BOOK II. PT. II 

business of Inductive Logic is to provide rules and models 
(such as the Syllogism and its rules are for ratiocination) to 
which if inductive arguments conform, those arguments are 
conclusive, and not otherwise. This is what the Four Methods 
profess to be " (J. S. Mill, Logic, Bk. III. ix. 6). " In saying 
that no discoveries were ever made by the Four Methods, he 
affirms that none were ever made by observation and experi 
ment; for assuredly if any were, it was by processes reducible 
to one or other of those methods" (ibid.). "But induction 
is not a mere mode of investigation." " Induction is proof ; 
it is inferring something unobserved from something observed ; 
it requires, therefore, an appropriate test of proof; and to 
provide that test is the special purpose of inductive logic " 
(Logic, III. ii. 5). We can have now no doubt about the 
nature of this claim; and this claim it is that we are going 
to discuss. 

6. I shall endeavour to show three things : first that the 
Four Inductive Methods can not be used if we start with mere 
facts, that the Canons presuppose universal truths as the 
material upon which the work is to be done ; and that therefore, 
if valid, the Methods are not inductive at all, in the sense of 
generalizing from particulars. In the next place I shall briefly 
exhibit the real nature of the reasoning used in the above Four 
Methods, and shall point out that its essence is not thus in 
ductive. And finally I shall show that not one of the Canons is 
a test of proof, and that by every one you can bring out what 
is false. None of these three positions depends on the others. 
If the Canons are invalid, if their essence is not inductive, or 
if they can not be applied to individual facts if, in short, any 
one of these contentions is established, the inductive logic is 
certainly refuted. And I hope to establish firmly all three. 
7. (I.) In the first place there is no doubt at all that 
the basis, from which we are to start in induction, consists 
primarily of particular given facts. I need cite no passages to 
establish this point. We naturally expect then to see on the 
one side the material as yet untouched by the Methods, and on 
the other the operation of these agents on the crude subject 
matter with which they must begin. This natural expectation 
is doomed to disappointment. 

(a) A suspicion of the shock which we are destined to 



CHAP. Ill THE INDUCTIVE METHODS OF PROOF 359 

receive may have come from the effrontery of the Method 
called " Residues." This estimable exemplar of " our great 
mental operation " comes up to us placarded as one of " the 
means which mankind possess for exploring the laws of nature 
by specific observation and experience," and then openly avows 
that it depends entirely on " previous inductions." Unless 
supplied beforehand, that is, with one or more ready-made 
universal propositions, it candidly declines to work at all. We 
enquire of " Residues " where we are then to begin, and it 
says, " I do not know ; you had better ask Difference/ " We 
anxiously turn to consider " Difference," and are staggered 
at once by the distressing extent of the family likeness. A 
chilling idea now steals into the mind; but we have gone too 
far to retreat at once, so, resolutely turning our back upon 
" Residues," we begin our examination. 

(b) We look at the samples of the work produced, and 
we find the same thing turning up everywhere. The material 
supplied to be dealt with by the Methods is never facts but 
is always universals. Sometimes an open and professed 
generalization is used as a starting point. But, where this is 
not done, the material is never a particular fact. It has always 
been subjected to such previous operation that it is able at 
once to be taken and used as a " case " or " instance." But 
this means that already it is an abstract statement, ideal and 
not real, capable of repetition with other environment, and 
without doubt universal. Take the very first instance : " Let 
the antecedent A be the contact of an alkaline substance and 
an oil. This combination being tried under several varieties 
of circumstances, resembling each other in nothing else, the 
results agree in the production of a greasy and detersive or 
saponaceous substance " (Logic, III. viii. i). And this is the 
raw material which is supplied. Before I begin my induction 
I am to know already that, under certain sets of definite con 
ditions exactly known, certain results have followed. But, i1 
I know this, I also know that these results will always follow 
given the conditions. Every one of the instances is already 
an universal proposition; and it is not a particular fad 
phenomenon at all.* . . 

8. It seems at first a strange obliquity of instinct 
* Cf . Whewell, Philosophy of Discovery, p. 263. 



360 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

choose illustrations which can not illustrate.* But on turning 
to examine the Canons themselves, our surprise gives place to 
another feeling. The illustrations have been selected, not 
according to choice, but from hard necessity. For the Canons 
are such that ex hypothesi they can not possibly work upon 
any material but universal propositions. 

FIRST CANON. 

// two or more instances of the phenomenon under investi 
gation have only one circumstance in common, the circum 
stance in which alone all the instances agree, is the cause (or 
effect) of the given phenomenon. 

SECOND CANON. 

// an instance in which the phenomenon under investiga 
tion occurs, and an instance in which it does not occur, have 
every circumstance in common save one, that one occurring 
only in the former; the circumstance in which alone the two 
instances differ, is the effect, or the cause, or an indispensable 
part of the cause, of the phenomenon. 

THIRD CANON. 

// two or more instances in which the phenomenon occurs 
have only one circumstance in common, while two or more 
instances in which it does not occur have nothing in common 
save the absence of that circumstance; the circumstance in 
which alone the two sets of instances differ, is the effect, or 
the cause, or an indispensable part of the cause, of the phe 
nomenon. 

FOURTH CANON. 

Subduct from any phenomenon such part as is known by 
previous inductions to be the effect of certain antecedents, and 
the residue of the phenomenon is the effect of the remaining 
antecedents. 

FIFTH CANON. 

Whatever phenomenon varies in any manner whenever 
another phenomenon varies in some particular manner, is 
either a cause or an effect of that phenomenon, or is connected 
* There is an exception which I will deal with in 9 



CHAP. Ill THE INDUCTIVE METHODS OF PROOF 361 

with it through some fact of causation. (Mill, Logic III 
viii.) 

Consider the phrases "only one circumstance in common" 
every circumstance in common but one," "nothing in com 
mon save the absence of that circumstance." Only think for a 
moment and realize what they mean, and then take on the 
other hand a given fact of perception. The fact is made a 
particular fact by the presence of that, the absence of which is 
postulated beforehand by these formulas. A universal judg 
ment is made universal by just those attributes which are 
pronounced indispensable in the material for these Methods. 
The moment you have reduced your particular fact to a per 
fectly definite set of elements, existing in relations which are 
accurately known, there you have left the fact behind you. 
You have already a judgment universal in the same sense in 
which the result of your " induction " is universal. Let us 
take once again the very first instance. The universal which 
you come to is " that the combination of an oil and an alkali 
causes the production of soap." The universals which you 
start with are that an oil and an alkali, if combined under con 
ditions be and de, in each case produce soap. But how can you 
deny that these latter are universals? No doubt they are 
impure ; but the result of the " induction " is surely not quite 
pure. And is an impure universal no universal at all? If 
you assert this, you deny the efficacy of your " induction." 
If you will not assert it, then you admit that your "induc 
tions " are not inductive, since the base they start from is 
not individual facts. If we regard the formulas for a little 
steadily, we must surely see that an " instance " which is 
capable of being so formulated, has had already done upon it 
that work which we heard the Methods, and the Methods 
alone, were capable of performing. And, if so, these Methods 
must retire from the field or withdraw their claims. Some 
thing like a farce has been played before us, whether we 
consider the airs and pretences of the Canons, or remember 
the promises and the boasts of their patron. 

9. But I may be reminded of and in fairness I must quote 
an instance, selected by the author himself, to show that his 
Methods can deal with common material. And the instance 



362 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

has the greater relevancy here, since he devised it expressly to 
meet the objection that the conditions of his formulas could 
not be found in facts. 

"If it had been my object to justify the processes them 
selves as means of investigation, there would have been no 
need to look far off, or make use of recondite or complicated 
instances. As a specimen of a truth ascertained by the Method 
of Agreement, I might have chosen the proposition Dogs 
bark/ This dog, and that dog, and the other dog, answer to 
ABC, ADE, AFG. The circumstance of being a dog, answers 
to A. Barking answers to a. As a truth made known by 
the Method of Difference, Fire burns might have sufficed. 
Before I touch the fire I am not burnt ; this is BC ; I touch it, 
and am burnt; this is ABC, aBC." (Logic, III. ix. 6.) 

The Canons we think are not hard to content if this will 
satisfy them. But surely their author had forgotten them for 
the moment. By seeing three barking dogs I perceive that 
they " have only one circumstance in common." By standing 
in front of a burning fireplace, and then touching the fire and 
being burnt, I am to know that the two facts " have every 
circumstance in common but one" Is not this preposterous? 
Surely it is clear in the first case that Mr. Mill s way of 
arguing might prove just as well that all dogs have the mange, 
and in the second that every fireplace blisters. And these con 
clusions hardly seem to be sound.* 

If we have succeeded so far in establishing this point, 
then the Methods of induction are placed in this dilemma. 
Because they presuppose universal truths, therefore they are 
not the only way of proving them. But if they are the only 
way of proving them, then every universal truth is unproved. 

10. (II.) The second assertion I have now to make good, 
is that the process of the Methods is not inductive. I do not 
mean merely that, as we have seen, they can not be applied 
except to universals. I mean in addition that it is not at all 

* As a test of the writer s accuracy in small points, we may notice 
that in the second example there is a mistake in the working of the 
Method. The right conclusion is " Touching burns " ; for the fire is 
not the differential condition. It was there before I touched it, and 
if it was not there, then we have two differences and another kind 
of mistake. 



CHAP. Ill THE INDUCTIVE METHODS OF PROOF 363 

of the essence of their process to bring out a conclusion more 
general than the premises. The process is one of elimination 
(cf. Book III. p. 412). By removing one part of an ideal con 
struction you establish the remainder. And hence the result 
will be more abstract than the whole original datum, but it 
need not be more abstract than some of the premises ; on the 
contrary it may be less so. 4 If five plums, two apples, and ten 
nuts balance the scales against three pears, two peaches, and 
six grapes, when I know that the nuts weigh the same as the 
grapes, and the apples as the peaches, I infer that the plums 
and the pears are equal by an ideal process of removing the 
rest. But if this is " induction," then " x r -f- 5 3 = a + 4 
2, and therefore x = a" and again " A is either b or c, A 
is not c, and therefore it is b" will also be inductions. And 
if everything is induction which is not syllogism, then cer 
tainly these inferences are all inductive. But such an assump 
tion would surely be quite erroneous. It finds its parallel in 
the counterpart mistake, that, because the Inductive Methods 
are not really " inductive," therefore they are syllogistic. 

The Methods are all of them Methods of Residues or 
Methods of Difference, and they all go to their conclusion in 
the self-same way. They fix a relation between certain wholes, 
and then, by the removal of parts of each, establish this 
relation between the remaining elements. In the Methods of 
Agreement and Concomitant Variations the principle is the 
same as it is in the rest. In the former the data are ABC- 
def, AGH dij, AKLdmn. It is then assumed that the d 
in def, dij, and dmn, can not be produced by a different cause ; 
and hence, since BC, GH, KL are different, they do not 
produce d. A is the residue or difference, and therefore A is 
the cause. The process we shall see is vicious, but, such as it 
is, it is elimination. In Concomitant Variations we seem to 
have A X BC d 1 ef; and then, when A 1 becomes A 2 , we have 
A 2 BC d 2 ef. From this whole take away X BC - - *ef, 2 BC 
*ef and the conclusion is A d. The principle involved is the 
same throughout, and the apparent failure to see this, and the 
setting down of two or three co-ordinate axioms for the 
different Methods, is another sign that the writer had never got 
really inside his subject. The different Methods are different 
applications of one single process, and since the premises 



364 THE PRINCIPLES OF LOGIC BOOK II. Px. II 

eliminated may be just as abstract as the conclusion left be 
hind, this process can hardly be called " inductive." 

ii. Having seen first of all that the Canons will not 
work unless applied to universals ; having seen, in the second 
place, that within these limits their procedure is not essentially 
one of generalization, we come now to the third of our objec 
tions. The Methods are vicious and the Canons are false. 

(III.) I do not mean to say that, for all the purposes of 
discovery, the flaws in the Methods amount to serious mis 
takes. Such a contention would lie beyond the scope of my 
volume. It is certain, however, that independent logicians, 
such as Dr. Whewell and Professor Jevons in our own coun 
try, and Professors Lotze and Sigwart in Germany, have taken 
a view of the process of scientific discovery which is not 
favourable to the claims of the Four Methods. But whatever 
may be the usefulness of these Methods, the point here at 
issue is their validity as proofs. 

What I wish to show is that they will not prove anything 
beyond this or that individual case. They pass to their more 
general conclusion by illegitimate assumptions. 

12. I think the reader will agree that, if a method will 
prove a false conclusion from premises which are true, then 
that method must be logically vicious, and its Canon, which 
serves as a test, must be false. Now it is stated by Mr. Mill 
himself that the Method of Agreement will prove false con 
clusions (Logic, Chap. X.). The Method is "uncertain" 
and has an " imperfection." But it still continues to figure as 
a proof, and the Canon is left standing in its naked falsity. 
We also have " axioms " implied in this Method, which can 
hardly be true if the Method is false, and which yet are left 
exposed to the daylight. We are told (Chap. X. i) that in 
chapters preceding false assumptions have been made, and 
yet the chapters with all their contents are recommended to 
us still as a sort of Gospel. And here I must frankly confess 
myself at a loss. Can the writer really have known that all his 
Canons were false statements? Whether he did or did not, I 
will not here enquire, for the discussion would not be likely to 
profit us. It will be perhaps convenient for the sake of argu 
ment to assume that he did not know the full vice of all his 
Methods. 



CHAP. Ill THE INDUCTIVE METHODS OF PROOF 365 

The Method of Agreement starts from the premises ABC 
def* AGH dijt AKL dmn: and its conclusion is that 
A is the cause of d. The principle it goes on is (as we saw 
before) that whatever is different in the different cases can be 
eliminated. And this principle is false, since a consequence, 
such as d, need not always follow from the same antecedent. 5 
The generalization is therefore vicious, and the Canon which 
regulates it is false. The axioms also, given in 2 of the 
same eighth chapter, are no less false. To make them true 
you must qualify them by adding " in this one case." But 
that means you must destroy their generalizing power. 

13. The Method of Difference is no less vicious. f From 
the premises ABC def, BC ef, it goes to the conclusion 
that A is the cause or an indispensable part of the cause of d. 
But this conclusion is fatally unsound. A may be here a single 
factor in the production of d, the presence of which is quite 
accidental. The rule may be for d to be produced entirely 
without A, and for A to be present without producing d. 
The foundation of the Method $ " that whatever can not be 
eliminated, is connected with the phenomenon by a law " is 
quite false, unless we add to it " in this one case" and thereby 
make it ineffectual for the purpose of generalizing. 

The Method of Joint Agreement and Difference is essen 
tially the same, and presents the same flaw. Its premises con 
sist of ABC def, AGtt dij, AKL dmn, BC ef, GH 
ij, KL mn. It infers from these the conclusion A d. 
The mistake is the same as that which vitiated Difference. 
The right conclusion is that, in these three cases, A has gone to 

produce d. . 

In the Method of Residues the process is the same, and is 
bad for the same reason. From ABC --def, B f, C e, 
the Method goes on at once to A d. But it could do so 
legitimately, only if it excluded the possibility of B or C, o 

*I have of course altered Mill s lettering. If his letters mean any 
thing, they involve a flagrant petitio; and if they do not, their sug 
gestion must tend to confuse us. 

t For further explanation see Bk. III. II. Chap. III. 11 foil. 
^ t There is no material difference between this and what is wrongly 
given, in the same 3, as different, and as the ground of the Method 
of Agreement; for you have postulated a connection your premises. 
I have given above the real ground of the Method of Agreement. 



366 THE PRINCIPLES OF LOGIC BOOK II. Pi. II 

both, having influenced, and been influenced by, A. Other 
wise the conclusion like all the rest is vicious, and its Canon 
is false, unless qualified by the words " in this one case" 

We come in the end to Concomitant Variations, and the 
principle of this has, I think, not been formulated with the 
desirable exactness. In the first place the words whenever 
in the Canon itself and invariably in the Axiom assigned to it 
are both ambiguous. If they mean that the groups of elements 
are causally connected, then this must rest upon a previous 
Method, and not upon mere facts. And in the second place, 
if we consider the process as a conclusion from these idealized 
premises, still it is impossible even then to demonstrate a 
result which will hold beyond this or that case (or cases). 
The premises appear to be A^C fref, A 2 BC d 2 ef, A 3 BC 
d z ef, and the conclusion arrived at seems to be A d. We 
have apparently to eliminate everything but A d, which is 
hence left as proved. But since once again the factors are not 
isolated, we have the old mistake of Difference once more. 
The real conclusion is "In this one case (or set of 
cases) without A no d." Because the modification of A has 
altered the result, therefore A is relevant to d in this alteration, 
or series of alterations. I may add that no amount of instances 
and of " approximation " will suffice to demonstrate logically. 

Should however finally the premises not have been so 
idealized as to be reducible to the formula we have given if 
we really have nothing whatever to start with but a certain 
number of observed concomitances then there literally is no 
conclusion at all, for the co-existence always may be mere 
chance coincidence. And, according as we understand the 
Canon and the Axiom, we must pronounce them to be either 
insufficient or false. 

14. I have shown that, if used in order to generalize 
beyond this or that individual instance as prepared for 
treatment, the Methods are vicious, and their Canons false. 
Their eliminative process will only show that the whole 
antecedent has been concerned in producing the whole con 
sequent (cf. Book III.). The attempt to go further and, 
by isolating the factors, to transcend the limits of the premises 
supplied, we have seen has broken down at all points. 6 

In the premises ABC def, BC ef, you are supposed to 






CHAP. Ill THE INDUCTIVE METHODS OF PROOF 367 

know that def is connected with ABC, and ef with BC: what 
you do not yet know is if, in ABC, A is really a factor. For it 
might be irrelevant, and BC without it might produce def. 
But now, having BC ef, and resting on the assumption 
which we call the Principle of Identity (Book I. Chap. V.), you 
are sure that, if BC ef is once true, it will be true for ever. 
And you proceed from this to argue that BC def must be 
false. For to produce def B must have been altered: and 
since in ABC def the result is produced with no possible 
alteration except mere A, A there must be relevant to the 
presence of def. Hence A in this case (of ABC def) must 
be, directly or indirectly, relevant to d. But you must not go 
further, and try in any way to specify the connection. For 
you can not do that without closing possibilities, and assum 
ing something not given in your premises.* 

And we must not forget that even this conclusion depends 
on our having assumed in the premises that, in ABC def f d 
is not irrelevant. Unless we are perfectly sure beforehand 
that the whole def has been produced by ABC, we can not 
advance one single step. This shows once more how absurd 
it is to imagine that the Methods can be applied to particular 
facts. They depend entirely on such an artificial preparation 
of the material supplied, as has already reduced it to the 
form of an universal. It would be waste of time to dwell 
further on the detail of the Four (or Five) Methods, since the 
process in all is the same at bottom.f 

15. We have seen that the Methods are not " inductive," 
since they will not generalize beyond the given instance. They 
fail again of being " inductive," since they can not be applied 
to simple facts. They will not work unless they are supplied 
with universals. They presuppose in short as their own con 
dition the result they profess alone to produce. Once more, 
the essence of their procedure is as much deductive as it is 
" inductive." The conclusion in some cases has less generality 
than some of the premises. 

On any one of these grounds (and I hope on all of them) 

*I should like here, and on the whole subject, to refer to Lotze s 
Logik, II. VII. 

f I must refer to the following Book for an account of inference by 

way of Elimination. 



368 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

we may set down the Inductive Logic as a fiasco. And, if I 
am told that these flaws, or most of them, are already ad 
mitted by Inductive Logicians, I will not retract the word 
I have used. But to satisfy the objector I will give way so 
far as to write for fiasco, confessed fiasco. 

1 6. If it really is the case that the Methods are not 
sound; if it really is the case that the Canons are not true; 
if it really is the case that " induction " is not proof, and 
that he has all along known this, and been well aware of 
it in that case I would suggest to the Inductive Logician 
that he has provoked a possible harsh remark. And however 
mistaken that harsh judgment might be, yet I can not help 
thinking that it would be better if he were to tell the public, 
what they certainly do not know, and the opposite of which 
his too large professions have led them to believe. But if, as 
I suppose, the Inductive Logician himself makes the mistake 
which his public has accepted if, that is, while admitting 
that, like all things human, his Methods have " imperfections," 
he has no idea that, taken as proofs, they are radically vicious 
in that case I will end by expressing the hope of a final 
agreement. 7 By abridging claims that will not stand criticism, 
and by reforming the root and principle of his fabric, he will 
bring no ruin to the bulk of his edifice. Even if we confined 
ourselves to Mr. Mill s Logic, we should find that, when his 
so-called Four Inductive Methods were wholly removed, and 
his inference from mere particulars banished as a misunder 
standing, the more valuable and even the larger part of his 
discussions on Science would remain untouched. 



ADDITIONAL NOTES 

1 " If we go with the fashion." I have to remind the reader once 
more that this refers to the year 1883. 

2 This account of Complete Enumeration and the Collective Judg 
ment is very seriously wrong. Indeed what is said in this volume 
about the Collective Judgment (see Index) needs correction perhaps 
throughout. For a true account of the matter I must refer the reader 
to Bosanquet, K & R, pp. 76 foil., and Logic, I, 152 foil. The 
main point is this, that all counting presupposes and depends on a 
qualitative Whole, and that the Collective Judgment asserts a generic 



CHAP. Ill THE INDUCTIVE METHODS OF PROOF 369 

connection within its group. Hence no mere particulars can be counted. 
I regret the superficiality of my treatment in this work. 

3 " One single case." If this means " One single sheep," it is ob 
viously wrong; and it is still wrong even if it means "each single 
sheep." What is true is that the group is taken as a region within 
which a universal connection holds throughout. Hence, and hence 
alone, we can use such expressions as " any " and " one case with." 

A minor point is that for " any folded sheep " we should read 
"any sheep folded here." This difference points to the weakness 
of the Collective Judgment. But on the whole subject see Bosanquet, 
Logic, I, 152 foil. 

4 " On the contrary it may be less so." What I meant here is 
this, that the residue may be less abstract than something which has 
been removed, or which has at least been used in the removal. But 
the point (however defensible) might have been omitted as superfluous. 

5 " Need not always follow from the same antecedent." This state 
ment would, of course, be false if the sequence were pure and so 
" reciprocal." But here you can not assume that your premises are 
pure, since you are not taken to know what your " one circumstance " 
really is. On the Method of Difference cf. Bk. III. II. III. 13. 

6 " At all points," i.e. if induction is taken as proof. 

7 There is no positive doctrine as to " Induction " set out in this 
work, nor had I any independent view on the subject. In the main 
I should have accepted, and should still accept, the view advocated 
by Jevons, with its two main features of Hypothesis and Verification. 



CHAPTER IV 

JEVONS EQUATION AL LOGIC * 

i. It is pleasant, after leaving the delusions of one s 
youth, to find oneself in contact with something like fact. The 
Equational Logic has proved by its results that it has a hold 
on the world of reality. What works must at least be partially 
right. And this new theory of logic does work. One may 
see that its method remains inapplicable to part of its subject. 
One may question its convenience in certain cases, and even 
doubt its formula in all. But one must believe so much as 
this. At the lowest estimate the new system will prove what 
ever the syllogism is able to prove. In some points it certainly 
is a far more rigid test of true reasoning. It deals very easily 
with many of the problems which accommodate themselves 
to numerical reasoning. And it maintains, on the ground 
both of reason and experience, that, in comparison with the 
syllogism, it is both easier to learn and harder to forget. 

In writing this chapter on equational logic, as it appears 
in the theory of Professor Jevons, I wish I could do two 
things I can not do. I wish I could give an account of the 
doctrine intelligible to those who have no acquaintance with 
it. And I wish I could form something like an estimate of 
its educational value and practical powers. But both want of 
space and want of experience compel me to a narrower and 
less grateful task. The object of this chapter is to ask if that 
account of the reasoning process which has been offered us is 
strictly accurate, whether as a theory it is free from mistakes. 
An answer in the negative will be given to this question. 

2. We may divide the enquiry into three main parts. In 
the first (A) we shall ask if propositions are identities: in the 
second (B) if direct reasoning consists in substitution. In the 
third (C) we shall discuss the Indirect Method, and with it 
the claims of the Logical Machine. It may prove convenient 
to state beforehand the main results which we expect to reach. 
We shall show in the first place (A) that, though every propo- 

370 



CHAP. IV JEVONS EQUATIONAL LOGIC 371 

sition does and must assert identity, yet that is not the 
object of all propositions. Our second conclusion (B) will be 
that substitution is not the real essence of reasoning, and that 
certain inferences will not by fair means come under this head. 
We shall show again that, although most arguments can be 
exhibited in the form of equations, yet the formula of inference 
which our author has given is not correct. In the third place 
(C) we shall argue that the Indirect Method, though perfectly 
valid, does not proceed by substitution: and finally we shall 
give our reasons for contesting a part of the claims put forth 
by the Machine. The reader is supposed to have made some 
acquaintance with the early part of The Principles of Science. 
3. (A) In asking if propositions are equations, we must 
remember that the sign = does not mean equal (cf. p. 23). 
It denotes sameness or identity. So that the word " equa 
tion," which we have chosen to start with, may at once be 
dismissed. The question is, Do judgments consist in the 
assertion of identity ? This point has already come before us, 
and great part of what follows is repetition. 

1. If we dismiss all theories and look simply at the facts, 
then to ask that question is to answer it in the negative. How 
can it be said that in " Caesar is sick," or " This pond is 
frozen," or " Mammals are warm-blooded," we really mean to 
assert self-sameness? To say that, in making such statements 
as these, our real object is the denial of difference that we 
wish to say, Although Caesar is sick he still is Caesar is pal 
pably absurd. We do not wish, premising the difference, to 
insist on the identity. The difference itself is the information 
which we wish to convey. 

2. If all propositions asserted mere identity, then every 
proposition would have to be false. If A = B and B BC, 
and we go from this to the conclusion A C, then either B 
makes a difference to A or it makes no difference. In the one 
case the proposition becomes quite false, and in the other it 
disappears, since B = o. How can it be true that ABC is 
the same as A? Is BC nothing, then nothing is asserted. 
Is BC a difference, then how are they the same? 

Partial identities are thus all false; but simple identities 
will fare no better. If " = " is taken to stand for " is the 
same as," then " A = B " can not possibly be true. If there is 



372 THE PRINCIPLES OF LOGIC BOOK II. Pi. II 

no difference, then nothing is said; if anything is said, then 
sameness is denied. 

3. It is obvious, if we are to keep to identity, that sub 
ject and predicate must be wholly the same. AB = AB, 
ABC = ABC. But even here it is doubtful if we can stay. 
For even when we reach a tautologous statement we have still 
a difference in the position of the terms (cf. Book I. Chap. V.). 
If we wish to be consistent even that must go. We must 
take one side of our former reduplication; we must say, for 
instance, AB or ABC. In that, having given up our search 
for identity, we suddenly find the whole content of our asser 
tion. Assume AB, then A is B. Assume ABC, then A is C. 
In our seeking to get an equational truth, we got all the dif 
ferences together on each side. But the synthesis of these 
differents was just what we really wanted to assert. Strike 
out one side, and strike out the " =," and we have the content 
of the whole judgment.* 

Assertion is not confined to the affirmation of sameness, 
and identity and equality are but one kind of predicate. If 
we use the language of the traditional logic, then in " S = P " 
the " = " has nothing to do with the copula : it falls entirely 
within the predicate, and " A = AB " is " A = AB." If 
we wish to say that A is equal to or the same as B, the natural 
mode is, I think, to say that A and B are the same or equal. 
If we will not do that, and so openly admit the existence of 
difference, we must come in the end to " A = B," on the left 
hand side, is just the same as " A = B," on the right hand 
side. And since the sides are different even that is not true. 
4. The foregoing section merely asserts that a difference 
is affirmed by every proposition. Judgment can not be reduced 
to one-sided identification. In the attempt to reduce it we 
found that we got the whole matter of the judgment on each 
side of the copula. Thus in " sodium = sodium metal con 
ducting electricity " the judgment falls on the right hand side. 
The assertion consists in the synthesis with sodium of the 
being a metal and conducting electricity; and, when we know 
that, the " sodium " and the " =," of the subject and copula, 
are false or meaningless. You say that it makes no difference 

* We are not dealing here with " simple identities." For them 
see 6. 



CHAP. IV JEVONS EQUATIONAL LOGIC 373 

to sodium that it is a metal and conducts electricity. That 
surely is a rather odd method of saying that there is no 
difference whatever to make, and a still more eccentric method 
of implying that this makes all the difference to sodium. 

5. No proposition asserts mere identity, but without the 
statement or implication of identity no judgment can be made. 
The solution of this puzzle, which the end of the foregoing 
section hints at, is that sameness and difference imply one 
another, and are different sides of the self-same fact. Mere 
identity or difference is therefore unmeaning. And hence, 
although it is false that in judging we always mean to identify 
the subject and predicate, yet in every judgment an identity 
can be found. For where sameness is asserted difference is 
presupposed. Where difference is asserted there is a basis of 
sameness which underlies it. And it follows as a consequence 
that, if you do not mind your implications being put on a level 
with your meanings, you can show every judgment in the form 
of difference united by identity. 

6. For in every judgment the differences joined may be 
taken as the qualities of a single subject 2 (cf. p. 27, and p. 
180). In " sodium = sodium metal" we assert that within 
the subject called sodium the attributes sodium and metal 
are conjoined; and if you please you may express this by 
saying, that, under the differences sodium and metal, there is 
yet no change from one subject to another. Again, in " Equi 
lateral triangle = equiangular triangle " what I mean to say 
is that, despite these differences, you still have one and the 
same triangle, or again that, if one of these qualities exists, you 
will have the other in the self -same subject. Take again " The 
Pole Star = the slowest-moving star : " this means either that 
one star possesses these two differences, or that, in spite of 
these differences, the star is the same. In every case we have 
identity and diversity, and, though we accentuate one or the 
other, yet in every case both must co-exist. 

I will illustrate the foregoing by other instances. Take 
" These fifteen statements are every one perjuries." The 
identical subject is here either each statement or the quality 
of perjury which appears in each. There are hence four 
meanings. In the first I assert that in every statement 
perjury must be added to its other qualities. In the second 



2321. I 



374 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

I deny that, though the statements are false, 3 we have any 
right to abolish the perjury by making thirty statements out 
of fifteen. In the third I complain that a single crime has 
occurred with fifteen different sets of details. In the fourth I 
refuse to admit the diversity of the fifteen qualifications as any 
proof that the crime is not the same. 

Or take the instance of equality or sameness itself. When 
I say that A and B are equal, I assert that in the differents A 
and B their quantity x is for all that the same. If I say " A 
and B are precisely the same," I must first take A and B as 
differenced by place or time or some other particular, and then 
against that assert their identity. The equality in one case 
and the sameness in the other may be treated as the subject 
in which A and B co-exist as attributes. 

If the doctrine already put forward is true, there can be no 
such things as " simple identities." " Equiangular triangle = 
equilateral triangle " is false if it denies the difference of 
quality, or is false if it ignores the distinction of subjects. The 
identity it asserts must exist under differences. Thus among 
triangles the subject of equilateral is one and the same with 
the subject of equiangular. The natural way to state the fact 
is to say, The different subjects are the same, or The diverse 
qualities imply one another. 

7. The result of our enquiry as to propositions is not of 
good augury for the doctrine of Substitution. True we find 
that all subjects assert an identity, but then they no less assert 
a difference. Our sign " = " has turned out quite inapplicable. 
If S and P are made quite identical, the judgment disappears 
or falls only on one side. If again S and P are allowed to be 
different, the sign of identity asserts a falsehood. This so far 
is ominous. It is ominous again that every identity can be 
shown as the connection of attributes within a subject. And 
there is another omen we have not yet noticed. All judg 
ments, we long ago have found, can be understood as assertions 
of identity. But the class of relations in time and space, it 
appears, are not amenable to the Method of Substitution, or 
at least in public decline to appear so (cf. Book I. p. 22). I 
can not but think that with such auspices against it any cause 
must be lost. 

8. (B) We come now to the second branch of our sub- 






CHAP. IV JEVONS EQUATION AL LOGIC 375 

ject. Does the process of reasoning consist in substitution? 
The foregoing has shown that this is not possible. 

(i) The terms which we substitute must be the same: but 
if the same then you can not substitute. If your process does 
not give you a difference, it is no process. If it gives you a 
difference you have broken the identity. Thus if reasoning 
consists in substitution, its essence lies in the substitution of 
differ ents. 

Let us take as an example, " A is equal to B, and B to C, 
and therefore A to C." It is impossible here by substitution 
of identicals to come to any conclusion whatever. For what 
is there identical ? A is not the same as B, nor B as C, nor is 
" equal to B " the same as A. The identity really lies in the 
quantity of A, B, and C. The quantity of A and B is the 
same, and so is that of C and B. The quantity therefore of 
A and C is the same. But you can not show this by substi 
tution. For in the quantity of each there is no difference. 
The terms are x A, x B, x C. Now if you substitute x A for 
x B, you substitute things which are not the same. But if you 
substitute mere x, you do nothing at all, for already you have 
the term x B. A is equal to B, but it is not the same. The 
quantity is the same, but it is one and not two. 

The real process of the reasoning consists in connecting 
the differences A and C on the basis of their common identity 
x. It may also be stated as a substitution. Take x with any 
one of the differences, and substitute x with any other differ 
ence. The differences then found co-existing in x will be the 
conclusion which we require. But this substitution is a re 
placement by differ -ents. 

9. (2) Substitution, so far as it works at all, is an 
indirect method of synthesizing differences. The rule is to 
substitute the " expression " for the term. But the " expres 
sion " is the judgment about the term. The rule then says 
" Substitute the judgment for the term." In other words, 
a term will not do ; you must have a premise, and that means 
a judgment. You must leave your identity and get to dif 
ferences. 

In "sodium is metal and conducts electricity" (4), 
sodium-metal takes the place of sodium, and metal gives way 
to metal-conductor, and we say this makes no difference to 



376 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

sodium, or sodium is the same with all this difference. But 
the real subject, which remains the same, is something which 
underlies these differences; and the real process is the addi 
tion of difference which developes the connection of attributes 
in this subject. It is entirely to mistake our object in view 
if, while we try to get the synthesis of diverse attributes, we 
talk as if all we wanted was to keep the identity of the subject. 
It is simply to stand the process on its head, if we make every 
step by uniting differences, and then speak as if throughout 
we had done nothing but remove them. 

" Substitute for the terms their expressions," that is in 
other words combine the premises. It is an artificial way of 
performing the old task. For reasons which I can not here 
enter into, the artifice in some cases is very useful. But it is 
simply the syllogism turned upside down, and it is confined 
to the same insufficient limits. 

10. (3) The method of Substitution has set itself free 
from some of the superstitions of the traditional logic. For 
certain purposes it is far more useful. Everything again that 
can be proved by syllogism can also be proved by its modern 
rival. But on the other hand Substitution will prove nothing 
that can not be shown by syllogism. The limit of both is 
precisely the same. They are confined to the relation of sub 
ject and attribute and the connection of attributes within a 
subject; and beyond that category neither will work (cf. Bk. 
II. Parti. Chap. II. 6). 

To prove syllogistically that, because A and C are both 
equal to B, they are equal to one another, is quite impos 
sible.* But it is just as impossible to prove the conclusion by 
substitution. The premises you have got are A = A equal to 
B, B = B equal to C; and the quaternio terminorum can only 
be avoided by taking the premises in a sense which is false. 

It is needless to repeat against the equational logic the 

* " Quantity of A is the same as quantity of B, quantity of B is the 
same as quantity of C, and therefore quantity of A is quantity of C " 
will not do at all. If the quantity is taken in abstraction then it 
certainly is the same, but you can not show from that that A, B, and C 
are related as equals or related in any way. But if you take the 
quantity in its relations to A and B and C, in that case you have 
quaternio terminorum, or otherwise the premises become false. The 
relation of equality never could be got out in the conclusion. 



CHAP. IV JEVONS EQUATIONAL LOGIC 377 

objections we have urged against the syllogism. If a logic 
will not deal with the syntheses of degree, of space, and of 
time; if even, as we shall see, its own Indirect Method falls 
outside its boundaries, then that logic does not give the true 
method of reasoning. It is not made too narrow because it 
requires an identity underlying the terms of its premises. It 
is made too narrow because in its conclusions it is confined to 
the category of subject and attribute. In a remarkable pas 
sage (Principles, Ed. II. p. 22) I understand Professor Jevons 
to admit these limitations. His logic, so far as it exists at 
present, appears to be confined to " simple relations." " A 
simple logical relation is that which exists between properties 
and circumstances of the same object or class." But, if that 
is so, then the theory of reasoning will cover only one portion 
of the facts. 

ii. (4) We have seen that, within the syllogistic limits, 
equational logic will work very well; and we also have seen 
the nature of its process. However right it is to insist that in 
reasoning identity is necessary, yet exactly the same must be 
said of difference. And I can not think that, in laying down 
his principle of inference and in reducing it to a formula, 
Professor Jevons has avoided serious mistakes. 

" So far as there exists sameness, identity or likeness, what 
is true of one thing will be true of the other." " In whatever 
relation a thing stands to a second thing, in the same relation 
it stands to the like or equivalent of that second thing " (pp. 

9> I?)- 

Now if the " likeness " in these formulas means absence of 
difference, we see at once that they are tautologous or false. 
For so far as mere identity exists, what is true of any one 
thing must for that very reason be false of another. If, in the 
case of A, B, and C, the judgment A C is true of A so far as 
A is simply the same as B, then it either is not true of A at 
all, or else the differences have all disappeared, and the judg 
ment becomes x = x. So again, if A is related to B, it is 
related to that which is the same as B. But " the same as B " 
will be simply B, and we have not advanced one single step. 

12. But if the formulas have another meaning, then what 
shall we say that their meaning is? They certainly can not 
mean that mere likeness will do. A need not be like C because 



THE PRINCIPLES OF LOGIC BOOK II. PT. II 

both are like B. And it is obvious that if B and C are 
" equivalent," A need not stand in one relation to both. Two 
coins are equivalent and one is in my pocket, but neither logic 
nor fact makes me master of the other. It is clear that this 
can not be our author s meaning. 

The equivalence or likeness, to be that which is meant, 
must exist to a sufficient extent or degree. But what is the 
degree which is sufficient ? " The general test of equality is 
substitution" (Principles, p. 19). But here again our ques 
tion is not answered. It would never do to say, you may sub 
stitute when you have a sufficient degree of likeness, and that 
degree again consists in your ability to make a substitution. 
And this is not what is meant. What I think is meant is that 
a certain amount of likeness will give conclusions, and that, 
when you can substitute, you may know it is there. But I 
do not think that Professor Jevons has anywhere told us in 
what that degree itself consists. 

13. Still I think he has given us the materials for an 
answer. The question we have before us is this: Given a 
term B in relation with C; or otherwise, Given C as what is 
true of B, then what amount of sameness between A and B 
will warrant us in writing A for B? The first answer to be 
given is that no amount is wanted. There is not the very 
smallest need for A and B to be like or equivalent. But the 
second answer to be given is this: the sameness required is 
the sameness of the one subject. If A and B are both qualities 
of X, or again if B is a quality of A, then A and C will be 
interrelated. The quality of the subject is the middle term, 
whose predicates in some way qualify the subject. Or the 
identity of the subject 4 is the middle term and, so far as this 
identity extends, the attributes must all be related and con 
joined. 

We have finished our examination of the theory of propo 
sitions, and also of reasoning by substitution. We come now 
to a third and most important point, the question of the Indi 
rect Method and the Logical Machine. I will anticipate briefly 
the result we shall reach, (a) The essence of the Indirect 
Method is a process which can not possibly be reduced to 
substitution, (b) In part of that process substitution may 
be used, but another form of reasoning is just as applicable, 



CHAP. IV JEVONS EQUATIONAL LOGIC 379 

(c) The Machine will not really give complete conclusions. 

(d) It is improperly limited to one kind of reasoning. 

14. (C) (a) The Indirect Method is a process of ex 
clusion. In using it you must first find all the possibilities, 
and then by removal of the rest you leave only one. In other 
words, you have a disjunction, and remove all alternatives 
except a single remainder. Because the subject, if taken as 
real, must be taken as fully determined and particularized, 
therefore the remaining possibility is real (cf. Book I. Chap. 
IV. ) . A is b, c, or d, it is not b or c, it therefore is d. This 
is the essence of the Indirect Method, and we already have 
to some extent made its acquaintance. 

15. We know that this process falls outside syllogism. 
And from that we might argue at this stage of our enquiry 
that it can not be reduced to substitution. But if it can not be 
reduced to substitution, Professor Jevons best work contra 
dicts his theory. Let us see how he tries to avoid this conse 
quence. 

" The general rule is that from the denial of any of the 
alternatives the affirmation of the remainder can be inferred. 
Now this result clearly follows from our process of substi 
tution; for if we have the proposition 



and we insert this expression for A on one side of the self- 
evident identity 

Ab = Kb, 
we obtain Ab = AB& -|- AbC -|- A&D ; 

and, as the first of the three alternatives is self-contradictory, 
we strike it out according to the law of contradiction; there 
remains 

Ab=AbC-\-AbD. 

Thus our system fully includes and explains that mood of 
the Disjunctive Syllogism technically called the modus tollendo 
ponens" (Principles, p. 77).* 

But this, I think, will not stand a moment s examination. 

*I may remind the reader that [ here means "or," and b means 
" Not-B." I do not use these signs in the text. 



380 THE PRINCIPLES OF LOGIC BOOK II. Pi. II 

In the first place the operation of striking out one part and 
asserting the rest is the essence of the method, and yet it is not 
even in appearance reduced to substitution. In the second 
place in this example the reasoning by substitution is perfectly 
useless. It does not bring you one step on your way towards 
the conclusion. 

I will take a perfectly simple instance. " A is b or c" and 
" A is not b" These are the premises, and from these I 
should say that you go directly to the conclusion " A is c" 
Professor Jevons, if I understand him rightly, contends that 
you go through a process of substitution. A = b or c, 
A = not-b. Insert the expression for A, "A is b or c" on one 
side of A not-b = A not-b. Then A not-b, = A not-b and b 
or A not-b and c. But A not-b and b = o, therefore A not-b 
= o or not-b and c. 

But surely, if words have any meaning, when I know that 
A is b or c, and that A is not b f I do know at once that b 
must be removed. And, on my removing b by an ideal 
experiment, c by itself is what I have left. If I please I may 
write this " c or o." But I really can not perceive what 
advantage I get by turning in a circle to come back to my 
starting-place. A is b or c, and it is not b. If possible how 
ever let A be b. But, if it is b, it will be b and not-&. That 
is impossible, and therefore follows what? Why simply that 
A is not b. I have used the premise to prove itself. And, 
if in answer I am told that this is not so, for I have enriched 
what was given me by the alternative " or o," then it seems 
to me that I may fairly reply, If you do not know, given 
only b and c, that when b is gone, c is what is left behind; 
then how on earth can you tell that, given " c or o," when o 
is gone, c is all that is left? I confess to me one is no clearer 
than the other. 

1 6. What I think has occasioned this complete mistake 
is an erroneous idea as to indirect reasoning. For that we 
must have a disjunction to start with, and by removing one 
member we prove the other. And we generally have to use 
direct reasoning downwards. We assume as one of our 
premises that alternative which we want in the end to get rid 
of, and on this assumption we bring out a conclusion which 
contradicts something contained in the premises. This is the 



CHAP. IV JEVONS EQUATIONAL LOGIC 381 

usual course, but it is not more than usual. Direct reasoning 
downwards is not always wanted. For when the premises 
themselves give the removal of one alternative, what more can 
we prove by such direct reasoning? We have in our hands 
not only the disjunction, but also the exclusion of one alter 
native. Where direct reasoning is required it is simply pre 
liminary to the final operation, and is wanted merely to prepare 
the subject; and when the premises give the subject ready 
prepared, what is there which we possibly can have to wait 
for? 

And I think this mistake is connected with another. I 
suspect that an error as to the Laws of Contradiction and 
Excluded Middle has helped to lead our author into this pitfall. 
But when we know that the Law of Excluded Middle 5 is one 
case of disjunction, and in no sense the basis of it (Book I. 
p. 151), we see at once that no mystical force arises from the 
proof of a self-contradiction. If we get to that by turning 
in a circle, the end will hardly justify the means. It has no 
power to absolve our consciences from the ordinary sin of 
logical fallacy.^ 

I must not be considered as wanting in respect, if I 
illustrate what I mean by another instance. Suppose that my 
premise is " A is b." Will any one deny that to prove from 
this that " A is b " is a frivolous circle ? But it is easily done. 
For, if possible, suppose that A is not b; then A will be both 
b and not-&: or insert, on one side of the self-evident identity 
A not-fc = A not-&, the expression for A. Then A not-& = A 
not-& and b. As one side of our equation is now self-contra 
dictory, we strike it out according to the law of contradiction, 
and then there remains A not-& = o, or A is b. I must be 
allowed to state my conviction that this circle is the same as 
what we had above. In both cases alike the premise has been 
used to bring out nothing whatever but that which it gave. 

The Indirect Method, we so far have seen, can not be 
reduced to a process of substitution. 

17. (b) If we consider that Method as employed by 
Professor Jevons, it does make use of the equational form, 
but there is no real necessity for its so doing. This process 
consists of the following four steps. 

"i. By the Law of Duality develope the utmost number of 



382 THE PRINCIPLES OF LOGIC BOOK II. Px. II 

alternatives which may exist in the description of the required 
class or term as regards the terms involved in the premises. 

2. For each term in these alternatives substitute its de 
scription as given in the premises. 

3. Strike out every alternative which is then found to 
break the Law of Contradiction. 

4. The remaining terms may be equated to the term in 
question as the desired description " (Principles, pp. 89-90) . 

The one part of this process which employs substitution, 
we see, is the second. But it is performed just as well by the 
ordinary method. All the possible combinations of the terms 
are given us, and our object is merely by means of the premises 
to remove those combinations which the premises contradict. 
In what shape then ought we to have our premises? Surely 
one would say in the shape of -combinations. It is just such 
combinations that the ordinary process would give us directly, 
and we get them by substitution in a roundabout way. For the 
" description " of the term is, as we saw, the judgment we 
make about the term. Hence this part of the method, as 
employed by Professor Jevons, is valid just so far as it can 
be stated syllogistically. For the premises are combinations 
of attributes. They are related, as Professor Jevons says, 
" just as the qualities of the same object " (ibid. p. 114) ; and 
if they were anything else, his method could not deal with 
them. We can combine them directly, if we please : and it is 
simply our choice, and perhaps sometimes our convenience, 
if we combine them from behind through their common 
subject. 

Thus we may use substitution to prepare for our conclu 
sion. But we can not use it to draw that conclusion. Its 
operation ends with the second step. 

18. We see, from examining the method itself, that it 
deals with syntheses or combinations, and does not deal at 
all with equations. And the method, as practically worked 
with the machine, confirms the truth of the view which we 
have taken. Professor Jevons himself with the greatest can 
dour has called attention to this consideration. 

" It is no doubt a remarkable fact that a simple identity 
can not be impressed upon the machine except in the form of 
two partial identities, and this may be thought by some logi- 



CHAP. IV JEVONS EQUATIONAL LOGIC 383 

cians to militate against the equational mode of representing 
propositions" (Principles, 112). 

It would be to me even more than remarkable if the ma 
chine could work with simple identities. But the fact, which 
Professor Jevons rightly finds remarkable, has I think a still 
more remarkable counterpart. The conclusions of the machine, 
if I understand them properly, contradict one another when 
read as equations in the sense of assertions of simple identity. 
A B C is consistent with Not-A B C ; 6 but how 
can we reconcile A = C with C = Not-A ? 

19. (c) We come now to the subject of the Logical 
Machine, and we have to enquire what work it performs. Of 
the mechanism employed I have no knowledge. I am so 
incompetent to say anything about it, that I can not have the 
pleasure of congratulating Professor Jevons on what I must 
believe is no small achievement. But what the machine does 
perform is this. All the possible combinations of the terms 
are worked out, and are lying ready drawn up in the machine. 
The operator puts in at one end his premises, each in the 
shape of a combination. The combinations of these premises 
remove, each one, all the possibilitites with which it is irrecon- 
cileable. And what comes out, so to speak, at the other end 
of the machine is all the residue of possible combinations 
which have not been so excluded by the premises. It is easy 
to exaggerate the powers of the machine. But I think it is 
impossible to deny that it executes such work, as must other 
wise be done by a process of thinking. For myself I do 
not hesitate to say that it performs mechanically an operation 
which, if performed ideally, would be an inference. And in 
this sense I think Professor Jevons is justified in his claim to 
have made a reasoning machine. 7 Apart from the practical 
utility of the instrument, which in certain cases may be con 
siderable, we must admit that, from a merely theoretical point 
of view, it is a most interesting and instructive phenomenon. 
If Professor Jevons had made no other contributions to logic, 
we might yet be sure that his name would go down with the 
history of the science. 

But to say on the other hand that the machine will execute 
the whole process our minds perform in the inference that 
the raw material goes in at one side, and the finished con 
clusion comes out at the other, would be travelling far beyond 



384 THE PRINCIPLES OF LOGIC BOOK II. Pi. II 

the fact. Before the premises can be worked on the instru 
ment, they have of course to be reduced and formulated, so as 
to take the shape of combinations of letters. But this is not 
the most important point. The result that comes out and is 
presented by the machine, is not really the conclusion. The 
process is not finished when the machinery stops; and the 
rest is left to be done by the mind. What is called " reading " 
the conclusion is to some extent making it. 

20. I will explain what I mean. In the machine is drawn 
up a complete disjunction of the possible arrangements of 
those terms which we employ. Before we begin to work 
the problem the machine thus supplies us with one of our 
premises. It states all possibilities, and this is its strength. 
But it states mere possibilities, and this is its weakness. We 
begin our operation, and insert the combinations which are 
given us by our data. These combinations are the rest of the 
premises. The machine, as it receives each combination, re 
moves from the list of all the possibilities those which are 
inconsistent with this datum. Then the remainder of the 
possible combinations are exposed. But they still remain bare 
possibilities, and are never stated as actual facts. 

The process may be taken as having five parts, i. The 
complete disjunctive statement of possible combinations. 
This is given ready-made by the machine. 2. The reduction 
of the premises to the shape of combinations. This is done 
entirely by the operator. 3. The discovery of those alterna 
tives which are inconsistent with the combinations of the 
premises. This step is performed entirely by the machine. 
4. The removal of those alternatives. This step again is 
performed by the machine, and it is the first part of that final 
inference which gives the conclusion. 5. The assertion that 
what is left is true, and that, if but one possibility remains, 
that is fact. This is absolutely necessary to complete the 
inference, and this is done entirely by the operator. 

The final step may seem to some persons a final super 
fluity. But on that view of the nature of reasoning by way 
of the exclusion of alternatives which has seemed to me 
true, it is integral and essential. Yet it can not be said to be 
performed by the instrument. 

21. I wish to stand on this statement of the case. But 



CHAP. IV JEVONS EQUATIONAL LOGIC 385 

it is possible to use also an argumcntum ad hominem. If the 
too undiscriminating friends of the machine assert that its 
result is a categorical statement, they can hardly fail to com 
promise it deeply. They will make it an instrument for the 
production of falsehoods. Let us take one result that is given 
by the machine (Principles, 109). 

A B C. NotA B C. 

A not B C. Not A not B not C. 



Now, there being here but one possibility, if A is assumed, 
we are practically safe in contending that the machine cate 
gorically asserts this one possibility. But, suppose we take 
the same line throughout, we plunge at once into a sea of non 
sense. Contradictory possibilities can co-exist as long as they 
remain mere possibilities, but the moment you affirm them 
as actual fact, they exclude one another. And, if so, either 
the machine brings out false conclusions, or all must be read 
as mere possibilities. You have no warrant from the machine 
for the assertion A is C. A may be C ; and because it may 
be, and because there is nothing else that it may be, and 
because you know that it must be something to C one way or 
the other, you therefore infer that A is C, a conclusion not 
given to you by the machine. 

22. (d) The machine performs more than we have a 
right to ask, and it is a pity to credit it with fictitious powers. 
We have seen that it does not bring out a conclusion. But it 
is limited beside in another respect. Although it does not work 
by substitution, yet its range is limited to that kind of inference 
which is possible in equational logic or in syllogism. It can 
not deal with any other combinations than those which repre 
sent the co-existence of qualities within a subject. And this 
is a very serious defect; for it means that the machine refuses 
to touch more than a part of the subject. 

This is not the fault of the Indirect Method itself. Apart 
from restrictions artificially imposed on it, that is applicable 
everywhere and to all kinds of matter. If my premises are 
" A is to the right of B, and B of C," I may go directly from 
these to my conclusion; but, if I choose, I may use the i 
direct method. The possibilities of A with respect to C are 



386 THE PRINCIPLES OF LOGIC BOOK II. PT. II 

either absence of any spatial relation, or A to the right of C, or 
to the left of C, or neither and above it, or below it, &c. But 
the premise " A to the right of B," will exclude (as we should 
see by an ideal construction) every alternative we can find 
other than A to the right of C. For, if we assumed any one of 
the others, we should bring out a result incompatible with our 
premise. The remaining possibility is therefore fact. This is 
perfectly familiar and common-place reasoning, and a system, 
in which it can find no place, must assuredly be called at least 
incomplete. 

23. The result of our perhaps too brief examination may 
be stated as follows: 

1. The Indirect Method has absolutely no vital connection 
with the Substitution of Similars. 

2. That Method itself is flawless and complete, but as used 
by Professor Jevons it is improperly limited. 

3. The machine which works within these limits will not 
actually give a categorical conclusion. 

4. These unfortunate limits are also those of equational 
reasoning. 

5. They coincide exactly with the boundary of the syllo 
gism, and a large part of reasoning falls entirely without them. 

6. The method of Substitution is syllogism upside down, 
and its principle has not been accurately formulated by Pro 
fessor Jevons. 

I must leave this subject with an expression of regret. I 
am sorry to have had no more space available ; and I am 
sorry to have dwelt almost wholly on those points in which I 
am unable to follow the author. It would have been more 
pleasant, if it had been possible, to have called attention to 
the various merits of his logical work. But still, even if my 
praises could do him any service, fortunately he does not 
stand in need of them. I may end this chapter by expressing 
my belief, that no living Englishman 8 has done one half the 
service to logic that Professor Jevons has done. No living 
writer, to the best of my knowledge, now Professor Lotze is 
dead, has done more. Personally to myself, and so far as my 
own studies are concerned, Professor Jevons book has been 
of very great use ; and I could not truly say that of any other 
English Logic. It is not inability to accept conclusions which 



CHAP. IV JEVONS EQUATIONAL LOGIC 387 

prevents one learning. And there can not be any one who has 
left unread the Principles of Science, who has not something 
to learn from it.* 

* Since this chapter was written Professor Jevons lamented death 
has taken place, and has deprived me of any opportunity I might other 
wise have had of learning from him in what points I have failed to 
understand his doctrines. I have thought it best to leave the chapter 
as it stood. 

But there is another point on which the reader may look for some 
explanation. He may ask why I have failed to examine one of those 
views of Equational Logic which treat the subject mathematically. 
And I am compelled to throw the burden of the answer on those who 
had charge of my education, and who failed to give me the requisite 
instruction. It would have been otherwise a pleasure to have seen 
how the defects of the Equational theory appeared in a mathematical 
form. For, at the risk of seeming no less prejudiced than ignorant, I 
am forced to state the matter so. If I knew perhaps what Mathe 
matics were, I should see how there is nothing special or limited about 
them, and how they are the soul of logic in general and (for all I 
know) of metaphysics too. Meanwhile I may suggest to the mathe 
matical logician that, so long as he fails to treat (for example) such 
simple arguments as " A before B, and B with C, therefore A before 
C," he has no strict right to demand a hearing. Logic is not logic 
at all if its theory is based on a previous mutilation of the facts of the 
subject. It may do something which perhaps is very much better, but 
it does not give any account (adequate or inadequate) of reasoning in 
general. And at the risk of exhibiting prejudice once more, I may 
say that this consideration seems to me to be vital. 3 



ADDITIONAL NOTES 

1 On the subject of this Chapter see the Notes on Book I, Chap. VI, 
and also T. E. III. 

2 "Single subject," "self-same subject." Cf. Bk. I. VI. n and 
T. E. III. 

3 " Though the statements are false." These words would, I think, 
have been better omitted. The " four meanings " are as follows, 
(i) Every statement contains a diversity, but (ii) its diversity does 
not make it two, so that by dividing it you can get rid of the connected 
unity which makes its character here of wilful falsity. And the 
essence of its character, while (iv) remaining throughout one and the 
same, is yet (iii) affected by, and made more intense by the number 
of its instances. 

4 " The identity of the subject." See Note 2. 



THE PRINCIPLES OF LOGIC BOOK II. PT. II 

s Excluded Middle." See Bk. I. V, Note 12. 

6 "A B C is consistent, etc." It would be better before "is" 
to insert "(as commonly understood)"; for, if A is taken as pure, 
i. e. as unconditional, the above statement would be incorrect. Cf . 21, 
and see the Note on Bk. II. II. III. 12. 

7 " A reasoning machine." Dr. Bosanquet (K & R, pp. 327 foil., 
and Logic, II, 150) has called attention to the point that all instruments 
of measurement and observation have a right to be called " reasoning 
machines." 

8 " No living Englishman." This was of course published in 1883, 
and I think that it was true. My eulogy may perhaps on the whole 
be exaggerated, and that question I leave to others to decide. What 
I wrote remains as the expression of the gratitude I felt towards one 
whose book had helped me greatly in my logical struggles. 

9 The second paragraph of this foot-note would have been better 
omitted. When writing it I did not know of the existence of a 
mathematical logic which was not equational. But even now I am 
in effect perhaps in no better case. 

Whether a student of logic, who is incapable of learning mathe 
matics and has therefore to leave out of his theory a recognized part 
of the facts, should never have written on logic at all, or should 
later at least suppress all that he once wrote I will not offer to 
discuss. And what should be his attitude towards a claim to base 
the principles of logic on mathematics, I once more hardly know. 
If a person like myself ventures to point out that something of 
what is thus offered seems to himself to be untenable and irrational 
he can be met with the reply that, if he understood mathematics, 
he would forthwith think otherwise. And what his answer to this 
should be, I confess I can not say. 

I am of course unable to accept a claim made on behalf of mathe 
matics to have rationally solved logical and metaphysical problems 
in a way unintelligible except to the mathematician. And there is 
one thing only which would incline me to accept such a claim. It 
would have to be made by a man, who can meet on their own ground 
the non-mathematical logicians and metaphysicians can show that he 
understands and enters into their views and their puzzles and can 
inspire the belief that he himself is somehow able better, even outside 
mathematics, to deal rationally with ultimate problems. But my whole 
acquaintance with this subject is unfortunately too limited even to 
justify perhaps what now I have ventured to set down. 



BC 71 .88 1922a v.l SMC 

Bradley, F. H. 

The principles of logic 

47092899