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Full text of "An introduction to logic, by H.W.B. Joseph .."

J 




THE LIBRARY 

OF 

THE UNIVERSITY 

OF CALIFORNIA 

LOS ANGELES 



Oxford University Press, Ely House, London W. I 

GLASGOW NEW YORK TORONTO MELBOURNE WELLINGTON 

CAPE TOWN SALISBURY IBADAN NAIROBI LUSAKA ADDIS ABABA 

BOMBAY CALCUTTA MADRAS KARACHI LAHORE DACCA 

KUALA LUMPUR HONG KONG TOKYO 



AN INTRODUCTION 



TO 



LOGIC 



Br 
H. W. B. JOSEPH 

FELLOW AND TUTOR OF NEW COLLEGE 



SECOND EDITION, REVISED 



OXFORD 
AT THE CLARENDON PRESS 



FIRST EDITION I906 

SECOND EDITION I916 

REPRINTED I925, 1931, I946, 1950, 1957, 

1961, I966, I967 

PRINTED IN GREAT BRITAIN 



College 
library 

377 



TO 

J. E. J. 



1G1 i 



PREFACE TO THE SECOND EDITION 

The present edition, the preparation of which has been some- 
what delayed by reason of the war, has been carefully revised 
throughout, and is enlarged to the extent of some 40 pages. 
Though it does not differ in its main teaching from the first edition, 
there are very few pages without some slight alteration, if only 
for the sake of greater clearness, or of more consistency in phrase- 
ology. I hope the alterations are improvements ; I must confess 
to some dissatisfaction at finding how many I desired to make. 
The following list of some of the principal alterations and additions 
may be of use to any reader who is interested in a comparison. 

c. i. On p. 5, n. 1 (upon the distinction between the form and 
matter of thought), I have endeavoured to show that the 
matter of thought, in this antithesis, is not the same as its 
4 subject-matter ' ; and I have altered the language of 
many passages accordingly. The latter part of p. 10, n. 1, 
and the last page and a half of the chapter, are new. 

c. ii. Much of this chapter has been rewritten. In particular, 
the general discussion of the nature of a term on pp. 14-28, 
and that of the distinction between abstract and concrete 
terms, on pp. 32-35, are largely new. The former includes 
some discussion of concepts ; and both have involved small 
consequential alterations at many subsequent points. 

c. iii. The note on p. 52, on the position of ' first substances ' 
in Aristotle's doctrine of categories, dissents from p. 39, n. 1, of 
the first edition. 

c. v. In this chapter I have laid more stress on the makeshift 
character of most classification, and have done more justice 
to the use of negative differentiae. 

c. vi. This chapter has been largely rearranged and rewritten. 
I now prefer, in order to express the truth in the contention 



PREFACE TO THE SECOND EDITION 

of those who have denied connotation to proper names, to 
distinguish between intension and connotation, allowing 
them the former, but not the latter. 

c. viii. This chapter also has been largely rewritten, parti- 
cularly in the discussion of the modality of judgements, and 
of the distinction between analytic and synthetic judge- 
ments. The close print on pp. 192-195, 201-205, 214-215, 
is new matter. In this and subsequent chapters I think 
that much which in the first edition was said about judge- 
ments should properly have been said about propositions, 
and correction has been made accordingly. I have made use 
in certain places of expressions borrowed from Prof. Cook 
Wilson. 

c. ix. On p. 228, and also on p. 120, n. 1, 1 have inserted a few 
remarks on Symbolic Logic, which will in some measure 
explain why the book does not deal more fully with that 
subject. 

c. x. The discussion of the inferential character of so-called 
Immediate Inference (pp. 240-247) has been enlarged and 
recast ; pp. 241-242 are new matter. 

c. xii. The discussion of the Fourth Figure of Syllogism, 
pp. 280-284, has been largely rewritten. 

c. xiii. In the note beginning on p. 296, the discussion of the 
passage Cat. iii. l b 10-15 (pp. 298-299) has been emended. 

c. xiv. In pp. 310-311 I have emphasized the subsumptive 
and therefore inferior character of syllogistic thinking. The 
close-print discussion on pp. 331-334 is new. 

c. xviii. The attempt in the last three pages, 397-399, to 
characterize the difference between inductive and deductive 
reasoning is new. 

c. xix. The new matter in this chapter, which has also been 
considerably rewritten, is chiefly in pp. 403-404, 410-413, 
418-419, 421, n.l. 

c. xx. I have corrected language which spoke of an event 
causally connected with another as its cause, both here and 
subsequently ; the point is discussed on pp. 426-428. 



PREFACE TO THE SECOND EDITION 

c. xxi. In pp. 475-476 I have dwelt on one or two further 
matters belonging to the pursuit of the inductive sciences 
which are no part of their reasoning. 

c. xxii. A rather obscure passage in the previous edition 
(pp. 459-460) is replaced by pp. 495-496. 

c. xxiii. I have tried to improve the statement of what explana- 
tion is on pp. 502, 521-522 ; and p. 523, n. 1, is new. The 
close print on pp. 524-527 is an answer to a criticism which 
Dr. Bosanquet has made upon the view of induction taken 
in this book. 

c. xxv. I have on pp. 546-549 rewritten and to some extent 
altered the tenour of what was said before (on pp. 506-509 
of the first edition) concerning the foundation of our power 
to generalize in mathematics. 

c. xxvii. Some additional matter is contained in the first 
notes on pp. 572, 580, 582, 589, 595. 

I have taken account of such criticisms as I have seen in print, 
though I have not thought all equally well founded ; for these, 
and also for various criticisms privately communicated, I desire to 
express my thanks. I should like here to name again Prof. J. A. 
Smith, Mr. H. H. Joachim, and Mr. H. A. Prichard, who 
were all good enough to send me comments on divers points, 
Besides these, Prof. W. G. de Burgh, of University College, 
Reading, very kindly helped me with a list of criticisms and 
suggestions based on his use of the book with students ; and 
Miss Augusta Klein sent me a series of most careful notes upon 
the first eight chapters. These were particularly helpful upon 
points of science referred to by way of illustration, and upon the 
theory of classification, with the logical doctrines on which it 
rests ; and the principal changes which I have introduced on 
those topics are due to her criticism, though not involving a 
full acceptance of it. 

But chiefly here I desire to put on record the debt which I owe, 
in common with so many other of his older or younger pupils, 
to Prof. J. Cook Wilson, whose death occurred while these sheets 
were passing through the press. Various footnotes will show 



PREFACE TO THE SECOND EDITION 

the use that I have made of his unpublished teaching ; but his 
illness prevented me from submitting to him what I have written, 
and his authority must be made responsible for no errors that 
I may have made. His few and scattered publications can do 
little to convey to strangers the power and stimulus of his personal 
teaching. And there are subjects on which, by his combina- 
tion of scholarly and mathematical with philosophic insight, 
he was qualified as few have been to produce new work of real 
value. The hope has vanished that he might put in permanent 
form the full results of his thinking. But those who knew him 
well will not misjudge this failure. For they will remember him 
as not more patient and eager in philosophic reflection than in his 
devotion during many years to a suffering wife and in his endur- 
ance afterwards of his own wasting and fatal illness. 

H. W. B. J. 

Advantage has been taken of reprinting to correct a number of 
small errors, mostly typographical, to which my attention has been 
called by the kindness of readers. 

H. W. B. J. 

January, 1925. 



PREFACE TO THE FIRST EDITION 

If an apology that precedes it could mitigate an offence, 1 
should be inclined to convert my preface into an apology for 
publishing this book. Progress, and the hope of progress, in 
logical investigations, have lain perhaps during the last three 
generations chiefly in two directions, either of analysing more 
closely the processes of thought exhibited in the sciences, or of 
determining what knowledge is, and the relation of the knowing 
mind to what it knows. Though I have been compelled to deal 
in some degree with the first of these questions, I am well aware 
that it demands a scientific knowledge which I do not possess ; the 
second I have not attempted systematically to discuss. The aim 
of the following book is more modest. There is a body of what 
might be called traditional doctrine in Logic, which is not only 
in fact used by itself as an instrument of intellectual discipline, 
but ought also to be in some degree mastered by those who would 
proceed to the higher and abstruser problems. It is of this 
traditional doctrine that Benjamin Jowett is recorded to have 
said, that Logic is neither a science, nor an art, but a dodge. 
I could perhaps best describe the motive with which this work 
was begun, as the desire to expound the traditional Logic in a way 
that did not deserve this accusation. The accusation was doubtless 
provoked by the attempt to force into a limited number of forms 
processes of thought, many of which can only with pretence and 
violence be made to fit them : an attempt, it may be added, at 
least as characteristic of ' Inductive Logic ' as of any other. 

In the course of centuries, the tradition has become divergent, 
and often corrupt. In this difficulty, I have ventured, like one or 
two other modern writers, to go back largely to its source in 
Aristotle. Problems of thought cannot in any case be studied 
without careful regard to their terminology, and their terminology 



PREFACE TO THE FIRST EDITION 

cannot be understood without reference to its history. The 
terminology of Logic owes more to Aristotle than to any one else ; 
but there is this further reason for attention to what he said, that 
much prevalent falsehood or confusion in the tradition is a corrup- 
tion of truths expressed by him. At the same time, I have not 
pretended to believe in the verbal inspiration of his writings. 

I have in particular been anxious to teach nothing to beginners 
which they should afterwards have merely to unlearn. They may 
of course come to dissent from the positions here taken up ; but 
only, I hope, because they think I have the worst of the argument 
on a proper issue, and not because, as meat for babes, I have been 
dogmatically expounding acknowledged fictions. 

While dealing largely with the more technical parts of logical 
tradition and terminology, I have done my best to avoid a super- 
fluity of technical terms ; and the subjects discussed have been for 
the most part discussed in detail, and the principles involved in 
them debated. The dryness with which the more formal branches 
of Logic are often charged springs, I think, in part from their 
being presented in too cut-and-dried a manner ; those who go 
beyond the jejune outline, and get into an argument, often find 
the subject then first begin to grow interesting. At any rate 
I have tried to secure this result by greater fullness, and attention 
to controversial issues. In every study there must be something 
to learn by heart ; but Logic should appeal as far as possible to 
the reason, and not to the memory. Thus such a question as the 
' reduction ' of syllogisms has been dealt with at length, not from 
any wish to overrate the importance of syllogistic reasoning, or 
burden the student with needless antiquarianism, but because the 
only thing of any real value in the subject of reduction is just that 
investigation of the nature of our processes of thinking which ia 
involved in asking whether there is any justification for reducing 
all syllogisms to the first figure. 

Topics whose main interest is obviously historical or antiquarian 
have been either relegated to footnotes or placed in closer type and 
between brackets ; and as I have followed the advice to translate 
what Greek I quote, I do not think that there is anything in these 



PREFACE TO THE FIRST EDITION 

discussions which a reader need be altogether precluded from 
following by ignorance of that language. I have also put between 
brackets in closer type other passages which, for one reason or 
another, might be omitted without spoiling the argument ; among 
the matters so treated is the fourth figure of syllogism ; for I have 
reverted to the Aristotelian doctrine of three figures, with the 
moods of the fourth as indirect moods of the first. 

I hope that I have sufficiently acknowledged all detailed obliga- 
tions to previous writers in the places where they occur. But I owe 
here a more comprehensive acknowledgement both to the published 
work of Sigwart, Lotze, Mr. F. H. Bradley, and Professor Bosan- 
quet, and to the instruction received in private discussion with 
various friends. Among these I should like to mention in particular 
Mr. J. Cook Wilson, Fellow of New College, Wykeham Professor 
of Logic in the University of Oxford, whose reluctance to write 
is a source to many of serious disappointment and concern ; 
Mr. J. A. Smith, Fellow of Balliol College ; Mr. C. C. J. Webb, 
Fellow of Magdalen College ; Mr. H. H. Joachim, Fellow of 
Merton College ; and Mr. H. A. Prichard, Fellow of Trinity 
College, Oxford. To the last three of these, and also to Mr. C. 
Cannan, Secretary to the Delegates of the University Press, I am 
further indebted for the great kindness with which they read large 
portions of the work in MS. or in proof ; without their suggestions 
and corrections it would be even more imperfect than it is. 
Lastly, I have to thank my sister, Miss J. M. Joseph, for the 
help she gave me in reading the whole of the proof-sheets and in 
undertaking the laborious and ungrateful task of checking the 
index. 



CONTENTS 

CHAPTER PAGE 

I. Of the General Character of the Enquiry . 1 

II. Of Terms, and their Principal Distinctions . 14 

III. Of the Categories ...... 48 

IV. Of the Predicables ..... 66 
V. Of the Rules of Definition and Division : 

Classification and Dichotomy . .111 

VI. Of the Intension and Extension of Terms and 

OF THEIR DENOTATION AND CONNOTATION . 136 

VII. Of the Proposition or Judgement . . . 159 
VIII. Of the Various Forms of the Judgement . 171 
IX. Of the Distribution of Terms in the Judge- 
ment : AND OF THE OPPOSITION OF JUDGE- 
MENTS ....... 216 

X. Of Immediate Inferences .... 232 

XL Of Syllogism in General .... 249 

XII. Of the Moods and Figures of Syllogism . . 254 

XIII. Of the Reduction of the Imperfect Syllo- 

gistic Figures ...... 287 

XIV. Of the Principles of Syllogistic Inference . 294 
XV. Of Hypothetical and Disjunctive Reasoning . 335 

XVI. Of Enthymeme, Sorites, and Dilemma . . 350 

XVII. Of the Form and Matter of Inference . . 366 

XVIII. Of Induction 378 

XIX. Of the Presuppositions of Inductive Reason- 
ing : the Law of Causation . . . 400 
XX. Of the Rules by which to judge of Causes and 

Effects ...•••• ^26 
XXI. Of Operations preliminary to the Application 

of the Foregoing Rules ...» 458 



CONTENTS 

CHAPTEB PAGB 

XXII. Op Non-eeciprocating Causal Relations . . 478 

XXIII. Of Explanation 502 

XXIV. Op Induction by Simple Enumeration and the 

Argument from Analogy . . . 528 

XXV. Of Mathematical Reasoning .... 543 

XXVI. Of the Methodology of the Sciences . . 554 

XXVII. Appendix on Fallacies ..... 566 

INDEX 600 



CHAPTER I 

OF THE GENERAL CHARACTER OF THE ENQUIRY 

It is a common practice to begin a treatise on any science with 
a discussion of its definition. By this means the reader's attention 
is directed to the proper objects, and to those features of them, with 
which the science is concerned ; a real advantage, when, as with 
Logic, those objects are not apprehended through the senses, and 
for this reason ordinarily attract little notice. But the same reason 
which makes a definition of Logic at the outset useful, makes con- 
troversy about its definition comparatively useless at such an early 
stage. The reader is too unfamiliar with the subject-matter of his 
science to be able to judge what definition best indicates its nature ; 
he cannot expect thoroughly to understand the definition that is 
given, until he has become familiar with that which is defined. The 
definition will at first guide more than enlighten him ; but if, as he 
proceeds, he finds that it helps to shew unity in the different en- 
quiries upon which he successively enters, it will so far be justified. 

Logic is a science, in the sense that it seeks to know the principles 
of some subject which it studies. The different sciences differ in 
the subjects which they so study ; astronomy studies the nature, 
movements, and history of the heavenly bodies, botany the structure, 
growth, history, and habits of plants, geometry the properties and 
relations of lines, surfaces, and figures in space ; but each attempts 
to discover the principles underlying the subjects with which it has 
to deal, and to explain their great variety by the help of one set 
of principles. These principles are often spoken of as laws ; and in 
the physical sciences that deal with change, as ' laws of nature '. 
The phrase may suggest that ' nature ' is not the sum of things and 
of events in the physical universe, but a sort of power prescribing 
to these the rules which they are to follow in their behaviour ; as 
the King in Parliament prescribes rules of conduct to his people. 
That, however, is not what we have to understand in science by 
a ' law ' ; a law in science is not, like human laws, a rule enjoined but 
sometimes disregarded ; it is a principle illustrated — and existing 

1770 B 



2 AN INTRODUCTION TO LOGIC [chap. 

only in the necessity of its being illustrated — in the department of 
fact to which it belongs. There are therefore no breaches of scien- 
tific law, or of a law of nature x ; if events are observed which do 
not conform to what we have hitherto called a law, we conclude not 
that the law is broken, but that we were ignorant of the true law ; 
if water, for example, were observed to boil on the top of Mont Blanc 
at a lower temperature than 212° Fahr., we should infer not that the 
law that water boils at 212° Fahr. was broken but that it is not a 
law of nature that water boils at 212° Fahr., — that there are other 
conditions which have to be fulfilled, if water is to boil at that tem- 
perature ; and the ' law ' is that it should boil only when those 
conditions are fulfilled. Such laws, the general principles to which 
things in their properties and their behaviour do actually conform, 
are what the physical sciences seek to discover, each in its own 
department, and if Logic is a science, it must have a subject of its 
own, in which it seeks for principles and laws. 

That subject is thought, but thought is always thought about 
something ; and thinking cannot be studied in abstraction from 
anything thought about. But yet in the same way that we may 
study the laws of motion, as they are exemplified in the movement 
of all bodies, without studying all the bodies that ever move, so we 
may study the laws of thought, as they are exemplified in thinking 
about all subjects, without studying all the subjects that are ever 
thought of. This comparison may be pushed further. Just as we 
must have experience of moving bodies, before we can investigate 
the laws of their motion, so we must have experience of thinking 
about things, before we can investigate the principles of thinking ; 
only this means, in the case of thinking, that we must ourselves 
think about things first, for no one can have experience of thinking 
except in his own mind. Again, although, in studying the laws 
of motion, we do not study every body that moves, yet we must 
always have before our minds some body, which we take as repre- 
senting all possible bodies like it ; and in the same way, when we 
investigate the principles that regulate our thinking, though we do 
not need to study all things ever thought of, we must have before 
our minds something thought of, in order to realize in it how we 
think about it and all possible things like it. For example, it is a 
general principle of our thought, that we do not conceive of qualities 

1 The question of the possibility of a ' miraculous ' breach of natural law 
need not be considered here; something is said of it inc. xix, infra, pp. 417-421, 



I] GENERAL CHARACTER OF THE ENQUIRY 3 

except as existing in some substance ; and that nevertheless the 
same quality is thought to exist in many substances ; green is 
a quality, which exists not by itself, but in grass and leaves of trees 
and so forth ; at the same time, green may exist in many different 
leaves or blades of grass. The general principle which is thus 
illustrated in the quality green is readily understood to be true of 
all possible qualities ; but unless we were able to think of some 
particular quality to illustrate it, we could not understand the 
general principle at all. 

What has been now said will serve to remove an objection which 
Locke brought against the study of Logic. 'God', says Locke 1 , 
' has not been so sparing to men, to make them barely two-legged 
creatures, and left it to Aristotle to make them rational.' He is 
urging that men thought rationally, or logically, i. e. in accordance 
with the principles that Logic discovers to regulate all sound thought, 
long before those principles were recognized ; and that this is still 
so with each of us ; we do not therefore need Logic to teach us how 
to think. That is quite true, and would be a pertinent criticism 
against any one who pretended that no one could think rationally 
without studying Logic ; but it is not the business of Logic to make 
men rational, but rather to teach them in what their being rational 
consists. And this they could never learn, if they were not rational 
first ; just as a man could never study (say) the principles of volun- 
tary motion, if he was not first accustomed to move his limbs as 
he willed. Had God made men barely two-legged creatures, Aris- 
totle would in vain have taught them to be rational, for they would 
not have understood his teaching. 

Logic, then, is the science which studies the general principles in 
accordance with which we think about things, whatever things they 
may be ; and so it presupposes that we have thought about things. 
Now our thought about them is expressed partly in the daily con- 
versation of life or musings of our minds ; partly and most sys- 
tematically in the various sciences. Those sciences are the best 
examples of human thinking about things, the most careful, clear, 
and coherent, that exist. In them, therefore, the logician can best 
study the laws of men's thinking ; and it is in this sense that we 
may accept the old definition of Logic, scientia scientiarum. 2 What 
* the courses of the stars ' are to astronomy, what figures, lines, and 

1 Essay, Bk. IV. c. xvii. § 4. . 

* Joannes Philoponus cites it ad Ar. Anal. Post. a. is. 76 a 15. 

62 



4 AN INTRODUCTION TO LOGIC [chap. 

surfaces are to geometry, what plants are to botany, or the calendar 
of Newgate to the crimi aologist, that the other sciences are to the 
logician : they are the material which he has to investigate, the 
particular facts which are given him, in order that he may discover 
the principles displayed in them. He has to ask what knowledge 
is as knowledge, apart — so far as possible — from the question, what 
it is about ; and he must therefore examine divers ' knowledges ', 
and see in what they are alike ; and among the best pieces of know- 
ledge that exist, the best ' knowledges ', are the various sciences. 
But he is not concerned with the detail of any particular science ; 
only with those kinds (or forms) of thinking which are exemplified 
in all our thinkings — though not necessarily the same in all — but 
best exemplified in the sciences. 

It is important to understand what is meant by saying that 
Logic is concerned with forms of thinking ; for many logicians w T ho 
have laid stress on this, and pointed out that Logic is a formal 
science, have understood by that expression more than seems to be 
true. There is a sense in which Logic is undoubtedly formal. By 
form we mean what is the same in many individuals called materially 
different — the device, for example, on different coins struck from the 
same die, or the anatomical structure of different mammalian verte- 
brates, or the identical mode in which the law requires the different 
Colleges of the University of Oxford to publish their accounts. And 
all science is formal, in the sense that it deals with what is common 
to different instances. A scientific man has no interest in a specimen 
exactly similar to one which he has already examined ; he wants 
new types, or fresh details, but the mere multiplication of specimens 
all alike does not affect him. 1 So the logician studies the forms of 
thinking, such as that involved in referring a quality to a substance 
possessing it ; but when he has once grasped the nature of this act 
of thought, he is quite uninterested in the thousand different such 
acts which he performs during the day ; they differ only materially, 
as to what quality is referred to what substance ; formally, so far 
as the notion of a quality as existing in a substance is concerned, 
they are the same ; and the forms that run through all our thinking 
about different matters are what he studies. 

But those who have insisted most that Logic is a formal science, 
or the science of the formal laws of thought, have not merely 

1 Unless indeed he is collecting statistics as to the comparative frequency 
of different types. 



I] GENERAL CHARACTER OF THE ENQUIRY 5 

meant that Logic is in this like other sciences, which all deal with 
what is formal or universal in their subject-matter. 1 They have 
meant to exclude from Logic any consideration of forms or modes 
of thinking which are not alike exemplified in thinking about 
absolutely every subject. It is as if the botanist were to regard 
only those laws which are exemplified in every plant, or the geo- 
meter were to consider no properties of figures, except what are 
common to all figures. They have thought that one might abstract 
entirely from and disregard all question as to what he thinks about, 
and still find that there are certain principles in accordance with 
which, if he is to think about anything, he will think. But the 
truth is, that we think in different ways about subjects of different 
kinds, and therefore we must, if we wish to study the principles 
that pervade our thinking, consider to some extent the differences 
in our thought arising from differences in that about which we 
think. The distinction between form and matter may as it were 
be taken at different levels. This is plain in a science that 
deals with some order of sensible things, like zoology. We may 
say of all men and all horses that they have severally a common 
form, that as compared to a man a horse is formally different, but as 
compared to one another all horses are formally the same, though 
each horse in his body is materially different from every other. 
Or we may consider not the form of horse common to Black Bess 

1 It is important to realize that the subject-matter of Logic is our thinking 
about divers things, not the things which that thinking is about ; they are 
the subject-matter of that thinking. Just as the form and matter of a coin 
are both in the coin, so the form and matter of thought (if we are to keep 
the meaning of the antithesis) must be both in the thought ; we must not 
suppose that the formal identity is in the thought, the material differences 
in the things thought about. An analogy may help to make this point clearer, 
on which I confess that there was some confusion in the hist edition of this 
book. Hunger and thirst are formally the same as being both appetites, 
materially different as being the one for food, the other for drink ; but the 
material difference is not the difference between food and drink, nor the 
matter of the appetites food and drink respectively ; the matter is rather 
the special character which the appetites have through being for these objects. 
So the matter of a thought is the special character which it has through 
being about a certain subject, not the subject which it is about. It may 
be added, as a caution to the unwary, that the antithesis of form and 
matter is used in various ways by no means all of them analogous ; and its 
application to thought is not really the same as its application to coins or 
animals. What is different in particular thoughts is not related to their 
common form as the gold or silver of two coins to their common device, or 
the flesh and bones of two animals to their common structure, but rather as 
the specialty of their structures to the generic identity, or as particular in- 
stances to the common nature of which they are instances. Cf. infra, pp. 75-77. 



6 AN INTRODUCTION TO LOGIC [chap 

and Bucephalus and Rosinante, but the form of vertebrate common 
to man, horse, eagle, crocodile, &c. ; and now man and horse (as 
compared with oysters for example) are formally alike. Or we 
may take the four orders in Cuvier's now obsolete division of the 
animal kingdom, vertebrata, coelenterata, radiata, and annulosa, 
and regard them as only different examples of the common form of 
animal ; and from this point of view a horse and an oyster differ 
materially, but not formally. When however we have reached this 
stage, and achieved the conception of animal, as something exem- 
plified equally in kinds of animal so different, it is clear that we can 
only understand what animal structure is by seeing it as it exists 
in all the different orders of animals ; whereas we can understand 
fairly the structure of a mammalian vertebrate without seeing it 
as it exists in every genus of mammals ; still more can we under- 
stand the structure of a horse without familiarity with all horses. 
The higher the level therefore at which in Zoology the distinction 
between form and matter is taken, the less can we study the form in 
isolation from variety of matter ; no example taken from one order 
of animals, say the starfish, will enable us to realize what animality 
is. It is the same in studying the forms of thought. The most 
general forms of thought exist diversely modified in thinking about 
different subjects ; and they can no more be fully known without 
attending to the different matters in which they appear differently, 
than animal nature can be fully known without attending to the 
different orders of animal in which it appears differently. Thus we 
may take the Proposition, and point out that in every affirmative 
categorical proposition there is a subject about which something is 
said, and a predicate, or something which is said about it. This is 
true equally of the propositions, ' A horse is an animal,' ' First- 
class railway tickets are white,' and ' Londres is London * . We may 
if we like, because in all propositions there is formally the same dis- 
tinction of subject and predicate, take symbols which shall stand 
for subject and predicate, whatever they are, and say that all affir- 
mative categorical propositions are of the form ' S is P ' . But when 
we ask for the meaning of this form, and in what sense S is P, it is 
clear that the meaning varies in different propositions. 1 Londres 
is just the same as London ; but a horse is not just the same as an 
animal ; it may be said that ' animal ' is an attribute of horse, and 

1 Professor Cook Wilson has called attention in his lectures to the dangerous 
ambiguity of this symbolization. Cf. infra, pp. 22-24. 



I] GENERAL CHARACTER OF THE ENQUIRY 7 

' white ' of first-class railway tickets, but animal is an attribute 
belonging to horses in quite a different way from that in which white 
belongs to first-class railway tickets ; these might as well be of any 
other colour, and still entitle the holder to travel first-class by the 
railway ; a horse could not cease to be an animal and still continue 
to be a horse. 1 The meaning of the formula 'S is P ' cannot pos- 
sibly be fully known merely by understanding that 8 and P are some 
subject and predicate ; it is necessary to understand what kind of 
subject and predicate they are, what the relation is between them, and 
in what sense one is the other ; and if this sense is different in different 
cases, just as animal is something different in a dog and a starfish, 
then the thorough study of the form of thought involves the con- 
sideration of material differences in the thoughts also. But logicians 
who emphasize the purely formal character of Logic maintain that 
it can exhaust the form of thought in treating that as one and the 
same in every possible instance of thinking ; an impracticable task, 
because the form itself (as in the above example of a form of 
thought which we call a proposition) is modified according to the 
instance in which it appears. On the other hand, and even although 
the forms of our thought cannot be studied apart from the differences 
connected with the particular sort of subject about which we may 
think, yet Logic is not interested in these differences for their own 
sake, but only for the sake of the divers forms of thinking involved 
in them ; and so far as the same form is exemplified over and over 
again in different particular ' bits ' of thinking, the study of the 
common form alone belongs to Logic. 

[The truth that form cannot be studied apart from matter might 
be otherwise expressed by saying, that the general form can only 
be studied in one or other of the special forms in which it is mani- 
fested ; and these special forms can only be illustrated in examples 
that are materially different from one another. The proposition 
' Londres is London ' is a special form of proposition equally well 
exemplified in ' Koln is Cologne ' ; as Bucephalus is an animal of 
a special form equally well exemplified in Black Bess. What is 
important to realize is the need of following the common form out 
into the differences which it displays in different matter.] 

The foregoing discussion will probably become plainer if it be 
read again at a later stage, when the reader is more practised in 
reflecting on his thoughts. A distinction which is readily seen in 

1 In strictness, the generic nature of a subject should not be called an 
attribute of it. Cf. infra, pp. 82-83. 



8 AN INTRODUCTION TO LOGIC [chap. 

regard to material subjects, like animals or plants, is not so easily 
seen in immaterial subjects, like our thoughts. The natural man 
thinks much about things, and asks and answers questions 
about them ; but it is by an effort that he comes to see how 
these things are only known to him in his perceptions of them and 
his thoughts about them, and so comes to turn his attention inward 
upon the nature of the acts of perceiving or of thinking. Nor can 
these new objects of his study be preserved and dissected like a 
material thing ; a man cannot catch a thought and bottle it ; he 
must create it by thinking it, if he wishes to think about it ; and the 
task will be found difficult while it is strange, and not altogether easy 
when familiar. 

[Mediaeval logicians sometimes say that Logic deals with second 
intentions ; by this is meant what has been pointed out in the last 
paragraph. The mind intends or directs itself at first upon material 
things and their qualities or relations ; and these are its first inten- 
tions ; it may afterwards intend or direct itself upon its own modes 
of thinking as exhibited in its first intentions ; and what it then 
discovers are its second intentions. Thus we observe animals, and 
give them names according to their kind, calling them stag and ox, 
worm and lobster ; and again we observe how these kinds agree and 
differ, and call some vertebrate, and some invertebrate, but all 
animals ; and all these names, which are names we give to objects, 
are names of the first intention. But we may also observe how we 
have been thinking about these animals, as having some properties 
common to all, and some peculiar to the members of each kind ; 
and we may call the members of each kind, or their common nature, 
a species, and the members of the several kinds together, or the 
wider common nature, a genus ; and genus and species are names 
of the second intention. The unity on the strength of which we call 
them of one species or of one genus will indeed be something in the 
animals themselves ; and so our names of second intention will in 
this instance signify something real in things. The distinction 
therefore presents difficulties which call our attention to the fact, 
that we cannot altogether keep reflection upon thought apart from 
reflection upon the nature of things thought about.] 

If now we ask for a definition of Logic, to keep before our minds 
in the following chapters, perhaps it is simplest and least objection- 
able to call it the Science, or the Study, of Thought ; for to say of 
the Formal Principles of Thought might imply both that there were 
sciences which did not seek for principles, and that the form of 
thought can be studied without reference to differences in the matter 
of it ; neither of which things is true. 



I] GENERAL CHARACTER OF THE ENQUIRY 9 

It is sometimes held that Logic is rather an art than a science, or 
at any rate that it is an art as well. In considering this question, 
we must remember that there are two senses of the word art. We 
may say that a man understands the art of navigation when he is 
skilful in handling a ship, though he may be unable to explain the 
principles which he follows ; or we may say that he understands it, 
when he is familiar with the principles of navigation, as a piece of 
book-work, though he may never have navigated a ship. Thus an 
art may either mean practical skill in doing a thing, or theoretical 
knowledge of the way in which it is best done. In the latter sense, 
art presupposes science ; the rules of navigation are based upon 
a knowledge of astronomical, mechanical, meteorological and 
physical laws, and presuppose much knowledge of mathematical 
and other sciences. It is in this sense that Logic is called an art ; 
and hence it is clear that if there is an art of Logic, there must first 
be a science, for the study of the nature of sound thinking must 
precede the giving of instructions for thinking soundly. And even 
granting the existence of such an art, it remains distinct from the 
science ; so that the name Logic would be used of the two in dif- 
ferent senses, and we ought rather to say that Logic means the 
science or the art of thought, than that it is the science and the art 
thereof. That there is an art of Logic, based on the science of Logic, 
might be urged on the ground that Logic reveals to us what know- 
ledge about any subject really is, and certain canons of reasoning 
which no argument can violate and be sound. But more than this 
would be required in order to constitute an art. There should be 
rules prescribing measures by which to bring our thought into the 
forms indicated. An artist, as Aristotle says 1 , initiates change 
in something other than himself : a sculptor e.g. in the clay which 
he models, a physician in the body of his patient ; and if in his own 
body, he treats himself as he would another. The execution of 
such changes is indeed different from the rules to be observed in 
executing them. But the logician's business is not to give rules 
by following which others or he himself may alter their thought 
about things, their geometry or chemistry or biology ; he offers 
no prescription for coming to know about all subjects ; it is against 
such pretensions that a protest like Locke's, quoted above, may 
well be made. His business is to become conscious of the nature of 

1 Met. A. iii. 1070 a 7 ij fuv olv r^vr, i PX tj iv 5XX», f, fie <f>v<ris aoxn f" «y™ 
( : Art initiates— sc. change— in another thing, the nature <of a thin g) in itself ). 



10 AN INTRODUCTION TO LOGIC [chap. 

the thinking carried on in those sciences. Logic, as we have said, 
6tudies the way in which we already think about things. 

Nevertheless, it is not without effect upon our ordinary thinking. 
A good deal of our so-called thinking is incoherent, and breaks down 
when we criticize it. That we can indeed discover for ourselves 
without learning Logic ; an economist can correct his own or his 
predecessors' errors in political economy, a mathematician in mathe- 
matics ; they could no more wait for the logician to correct than to 
construct these sciences. 1 Yet the study of the thinking, good and 
bad, which has gone to their construction may give us a more lively 
consciousness of the difference between what its character should be 
and what it sometimes is, or as the Greeks would have said, between 
knowledge and opinion. Herein Logic may be compared with 
Ethics. Ethics investigates human conduct ; it discusses the 
judgements of right and wrong, of good and evil, that we pass upon 
men's acts and them ; it tries to determine what we really mean in 
calling an act wrong, and what we really require of a man in saying 
he should do what is right. All this would be impossible unless men 
already acted wrongly and rightly, and made moral judgements ; 
Ethics does not teach men to do that. But it does bring into clearer 
consciousness the nature of the ideals which we already have, the 
grounds of the judgements which we already make, the frequent 
discrepancy between what is done and what we recognize should 
be done. To this extent Ethics tells us what to do, though it does 
not enable us to do it. Similarly Logic helps us to realize what 
knowledge of a subject is : but it does not enable us to bring our 
opinions on every subject into the form that knowledge requires. 
Both Logic and Ethics are thus in some degree practical ; but we 
do not call Ethics an art, and it is not desirable any the more to call 
Logic so. 2 

1 The word logic is sometimes used not for the study of thought which 
has been described in this chapter, but for the thinking which it studies : 
as when we say that some one is a man of powerful logic, or of great logical 
acumen. It is important to recognize that this is a different sense of the 
word. 

2 It must not however be supposed either that Ethics can determine what 
ought to be done in every difficult case of conscience, or that Logic determines 
exhaustively the forms of reasoning which the sciences must employ. Cf. 
F. H. Bradley, Principles of Logic, pp. 247-249. The phrase normative science, 
which some writers have of late applied to Logic, Ethics and Aesthetics, has 
perhaps been suggested by the character in them to which this paragraph 
refers. But it is liable to create misunderstanding, as if it were the business 
of these enquiries to prescribe rather than to ascertain the principles which 
our rational thinking, or action, or appreciation of beauty exhibits. The 



I] GENERAL CHARACTER OF THE ENQUIRY 11 

It is perhaps from a desire to show the practical value of the 
study of Logic that men have insisted on viewing it as an art. But 
it would be a mistake to suppose that it can have no practical value 
unless it can furnish rules for ' the conduct of the understanding '. 
The direct help that it can give in this way is not very great. Its 
practical value in general education is firstly this : that it demands 
very careful and exact thinking about its own subject-matter, and 
thus tends to produce a habit of similar carefulness in the study of 
any other subject. In this it only does for the mind what a thorough 
training in any exact science might do. Secondly, it makes us 
realize better what the general forms of speech that we habitually 
use really mean, and familiarizes us with the task of examining our 
reasonings and looking to see whether they are conclusive. In this 
it has an effect which the study of some special science like botany 
is not equally calculated to produce. Thirdly, it brings more clearly 
into consciousness, as aforesaid, what knowing is, and so far furnishes 
us with a sort of standard by which to judge what we commonly call 
our knowledge of things ; it makes us more alive to shortcomings in 
our ordinary opinions. But it does not need for its justification 
that we should point to effects which it produces upon our thoughts 
about other subjects ; the nature of thought and knowledge is 
itself a subject worthy of investigation. 1 And, if we are to look 
also beyond this, its chief value lies in its bearing upon those ultimate 
problems, concerning the nature of reality, and man's place and 
destiny in the world, from which at first sight it might seem far 

peculiar character of Logic, Ethics, or Aesthetics seems to be this, that we 
who, in them, reflect upon thought, conduct, or art, ourselves also in other 
moments of our activity create these objects of our reflection ; and because in 
our reflection we recognize the failure of many of our attempts to think 
soundly, act rightly, or work beautifully, it is supposed to be the business 
of reflection, logical, ethical, or aesthetical, to rectify these failures. Such 
a supposition is in the main erroneous. It is by becoming better men of 
science that we shall correct our scientific blunders, by becoming better men 
that we shall correct our moral judgements and choices, by becoming better 
artists that we shall correct our aesthetical ; nor does the recognition of 
a should-be surpassing what is require that we pursue those reflective dis- 
ciplines. But the exercise of intelligence which they require presupposes the 
capacity and provokes the activity of that displayed in science, morality, or 
art themselves ; and so there is a connection between them and the improve- 
ment of our scientific or moral or aesthetic thinking, such as does not exist 
between biology and the improvement of species or between dynamics and 
the improvement of locomotives. 

1 Cf. Bosanquet, Logic 2 , i. p. 1 : ' I am wholly of Hegel's mind when he says 
that the species of syllogism are at least as well worth discovering as those 
of parrots or veronicas '. 



12 AN INTRODUCTION TO LOGIC [chap. 

remote. ' Logic,' says J. S. Mill, in the Introduction to his famous 
work \ ' is common ground on which the partisans of Hartley and 
of Reid, of Locke and of Kant may meet and join hands.' Conserere 
manus — it is only in this sense that rival schools join hands on the 
field of Logic. The dream of a Logic that shall be ' neutralized ' 
like the physical sciences will not be fulfilled. These may move 
securely within the limits of certain well-defined assumptions, which 
all workers, though they may fight over minor points, agree to 
respect. Logic, which studies the principles of our thought about 
all things, cannot be content to leave unquestioned the assumptions 
within the limits of which thought proceeds : for it is those very 
assumptions that it investigates. The history of Mill's own work 
disproves his saying, for it is on its metaphysical side that it has been 
most vehemently attacked. Into metaphysical controversies, how- 
ever, it is not the aim of this book to enter more than is absolutely 
necessary. But he would essay a vain task, who should attempt 
to expound the rudiments of Logic with no presuppositions about 
the nature of things. We may distinguish thought from the things 
thought about, but we cannot study it without any reference to 
what they are. All thought is thinking ' this about that ' ; and 
the general nature of the ' this ' and the ' that ' must be considered, 
if we are to consider what thought is ; otherwise, our subject 
becomes a blank. The operations of the mind are unintelligible, 
if we disregard altogether the nature of their objects. To know 
what desire is, we must know what can be desired ; there are some 
who hold that desire, by its very nature, is for pleasure ; if so, could 
we understand it without considering what pleasure is ? So we 
cannot understand thought without considering in general what 
thought is of. And consequently Logic, just because it studies our 
thought about things, is concerned with questions about the 
general nature of things. 2 Some would dissent from what in 
the following chapters is said on such questions. The controversies 
involved are not there pursued as they deserve, for this is not 
primarily a work on Metaphysics ; but they have at any rate been 
indicated where they arise. 

1 System of Logic, In trod. § 7. 

2 Thus recent Symbolic Logic is full of discussions about classes and the 
relations between classes, because it holds thinking to be fundamentally 
thinking about the relations of classes. It seems to me that classing and 
class -relations are a very secondary subject of thought, and that for thia 
reason Symbolic Logic gives a very distorted theory of thinking. 



i] GENERAL CHARACTER OF THE ENQUIRY 13 

[The connection between questions about our thinking, and what 
we must think things to be, is excellently shown in the so-called 
Laws of Thought. These are certain very general principles exem- 
plified in all thinking, and some have supposed the task of Logic 
to consist merely in developing their implications. They are known 
as the Law of Identity, the Law of Contradiction, and the Law of 
Excluded Middle. The Law of Identity may be formulated by saying 
that ' whatever is, is ' : or symbolically, that ' A is A ' ; the Law 
of Contradiction, that ' a thing cannot both be and not be so and so ', 
that ' contradictory propositions cannot both be true ', or that ' A 
cannot be B and not be B ' ; the Law of Excluded Middle, that ' a 
thing either is or is not so and so ', that ' contradictory proposi- 
tions cannot both be false ', or that ' A either is or is not B '. In 
other words, if we think about anything, then (1) we must think 
that it is what it is ; (2) we cannot think that it at once has a char- 
acter and has it not ; (3) we must think that it either has it or has 
it not. Now though these are called laws of thought, and in fact 
we cannot think except in accordance with them, yet they are really 
statements which we cannot but hold true about things. We cannot 
think contradictory propositions, because we see that a thing cannot 
have at once and not have the same character ; and the so-called 
necessity of thought is really the apprehension of a necessity in the 
being of things. This we may see if we ask what would follow, were 
it a necessity of thought only ; for then, while e.g. I could not think 
at once that this page is and is not white, the page itself might at 
once be white and not be white. But to admit this is to admit that 
I can think the page to have and not have the same character, in 
the very act of saying that I cannot think it ; and this is self -con- 
tradictory. The Law of Contradiction then is metaphysical or 
ontological. So also is the Law of Identity. It is because what is 
must be determinately what it is, that I must so think. That is why 
we find a difficulty in admitting the reality of absolute change, 
change when nothing remains the same ; for then we cannot say 
what it is which changes ; ' only the permanent ', said Kant, ' can 
change '. The Law of Excluded Middle 1 is so far different as 
a disjunctive proposition expresses doubt, and doubt belongs to the 
mind, not to things But to deny that this page need either be or 
not be white is to deny that it need be anything definite ; determin- 
ateness involves the mutual exclusiveness of determinate characters, 
which is the ground of negation ; and that is a statement about 
things. In other words, unless the primary Laws of Thought were 
Laws of Things, our thought would be doomed by its very nature to 
misapprehend the nature of things.] 

1 On this cf. further infra, p. 41, n. 1. 



CHAPTER II 
OF TERMS, AND THEIR PRINCIPAL DISTINCTIONS 

Logic, we have seen, studies our thought about things ; and that 
cannot be studied without some consideration of the nature of things ; 
but further, it cannot be carried on, nor yet studied, without the 
use of signs — generally written or spoken words, which make what 
we call language. The relations of thought to things on the one 
hand and words on the other are difficult and intricate ; but we 
cannot without some regard to them profitably attack the subject 
of this chapter. 

The true unit of thought, the simplest complete act of thought, 
or piece of thinking, is the Judgement, or Proposition : between 
which where a distinction is intended, it is that the proposition 
is the expression in words of a judgement. The close connection 
of language with thought appears already here ; for the utterance of 
the words, unless we were at the same time meaning with them, or 
judging, would not really be making a proposition ; else the man 
who repeated the words of an unknown tongue would be ' propound- 
ing '. We may indeed understand a proposition without judging 
it, but only by imaginatively putting ourselves in the situation of 
a man who is actually expressing his judgement by it. 

We may perceive without judging, though our present perception 
may be possible only through past judgements ; and here as else- 
where the history of how the individual mind has come to be able 
to do what it now does is elusive ; but that belongs rather to 
Psychology. I may pass a man in the street, and only afterwards 
eay to myself ' That must have been so-and-so ' ; I may be walking 
along a railway line in the dark, and hear a sound, and then hear 
it again, and for the first time think ' That is the noise of a train 
approaching '. I perceived the man, or heard the sound, the first 
time ; I judged about them after ; and when I judged (we shall 
return to this) I distinguished in the ' subject ' I judged about 
a character which I ' predicated ' of it. 

In judging then I always distinguish a particular element, the 



TERMS, AND THEIR PRINCIPAL DISTINCTIONS 15 

predicate, in the being of a subject which I could not think of unless 
I recognized in it some other than the predicated character. 1 I must 
think, severally yet together, of both ; and if I want to call attention 
to them separately, I must indicate them by different signs ; but 
in order to make the judgement, though I need a sign, I do not need 
to indicate them by different signs. The child that learns to say 
1 Pussy ' when it sees the cat means by the single word what we 
should express by the proposition ' There is the cat ' or ' I love the 
cat ', or whatever it may be ; and Mr. Alfred Jingle expressed his 
judgements with less than the full complement of words. 

Whether any thinking can be carried on without some sort of 
sensible signs 2 is disputed ; certainly it cannot be carried far. The 
signs need not be written or spoken words ; they may be gestures, or 
sensations of touch, by means of which Helen Keller was taught to 
think. In algebra, though they can be written, they are not words ; 
in geometry the figure serves to a great extent, and one may think 
out a demonstration by help of drawing the lines of the construction 
with less use mentally of words than would be necessary to com- 
municate it. Perhaps, with the figure before one, attending suc- 
cessively to its parts, one may dispense for a time with other signs 
altogether — other signs, because the figure itself is, as Plato noticed, 
a sort of sign : our demonstration is not true of it, since it is im- 
perfectly drawn, but it helps us to think of the figure whereof it is 
true. 3 And perhaps when we are perceiving a thing we can make 
judgements to ourselves about it, without help of any sign, because 
it is itself sensible ; and when we are not perceiving it, some ' mental 
image ' may serve instead of language. For the imagery which ac- 
companies thinking is not the object of thinking ; I may as a 
psychologist make it the object of my thinking, and say that it is 

1 Hence a definition is not properly a judgement, as Aristotle saw (v. Met. 
0. x. 1051 b 17 sq.). For when I define anything— e.g. a triangle, and say 
that it is a three-sided rectilinear figure — I have not before me a subject 
already distinguished by some other character than what I predicate. Even 
here however I distinguish elements in an unity which they constitute ; and 
hence the definition can be expressed in a proposition. For I give a name 
to this unity as an unity, and also to the elements distinguished in it. There 
are some objects of thought which have names, and by the help of instances 
we come to know them, but because they are simple, or because they are 
unique in nature, what they are cannot be expressed in a proposition— e.g. 
difference— though judgements may be so expressed which tell us various 
things about them : e.g. 'difference is a relation ' or ' attracts attention '. 

2 I do not imply that some signs are not sensible, but merely wish to call 
attention to the fact that all are so. 

* Rep. vi. 510 d, E. 



16 AN INTRODUCTION TO LOGIC [chap. 

vivid, or evanescent, or what not ; but that is not the thinking in 
connection with which it first arises. Its service to thought seems 
to be comparable with that of words, so that it has been called the 
1 inner speech-form ' ; though it is not articulated as language is. 
These considerations seem to point to the conclusion that language 
is necessary to thought because so much that we think of in things 
is not itself sensible, and we cannot fix our attention on what is not 
sensible, without the help of something that is ; but there need be 
no correspondence in detail between the sensible sign, and the 
structure of our thought and of its object. This has not always 
been realized ; and because a child first learns separate words, 
and then learns to combine them in sentences, and then to combine 
sentences in continuous discourse, it has sometimes been supposed 
that thought begins with isolated apprehensions of what it after- 
wards makes subjects and predicates in judgement, and then builds 
up judgements into reasoning. Such a view is an illusion produced 
by language, particularly through the consciousness of the separate- 
ness of words which modern writing and reading produces. It is 
indeed supposed by many that in early language words had not a 
separate existence, but only existed as it were confluently with one 
another in sentences. 1 Anyhow, there are no ' ideas ' 2 which we put 
together in thinking as we do words in speech and writing. 

Though the signs by help of which we think are thus various, 
words are incomparably the most important ; and they are almost 
always 3 the only ones by help of which we express logical doctrine. 
Words are signs sometimes of things thought of, sometimes of opera- 
tions of thinking, sometimes of both together. The subject-word 
in a proposition is a sign of something thought of, for which it is 
said to stand, and the proposition is not about it but about what it 

1 I have seen a letter written by an Alpine guide in admirable French, 
but wildly at fault in its division of words. 

2 No word in philosophy has been responsible for more confusion than the 
word idea. In Plato it meant what is called in Logic an universal, the common 
nature which thought recognizes in different particular things. Nowadays, 
it sometimes means an opinion (as when I say that my ideas on a subject 
have changed), sometimes ' mental images ', sometimes it is merely an element 
in a periphrasis : to ' have an idea of ' is simply to conceive or think of ; 
then we are apt to suppose that we think of things by means of ideas of 
them, which is no more an explanation of thinking than if I say that I think 
of things by means of thinking of them. 

3 Most writers make some use of symbols which are not words to represent 
objects of thought (e.g. Arabic numerals) ; and in Symbolic Logic they are 
extensively used to represent both objects and operations of thought. 



ii] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 17 

stands for : except when we say something about the word itself ; 
an instance of the former is ' Barkis is willin' ', of the latter ' Barkis 
is a proper name \ Words like if, because, therefore are signs of the 
acts of supposition or inference, and is is the sign of the act of 
judgement, though also implying that something exists. 2 Other 
verbs, and also adjectives, are signs at once of some object of thought 
predicated, and of the act of predication ; and the same verb may 
be a sign of the subject of predication as well. Thus in the pro- 
position ' Dogs bark ', ' dogs ' stands for the things about which the 
statement is made, ' bark ' both is the sign of (or expresses) what is 
predicated about them, and also of its being predicated ; if I wish 
to disentangle, as it were, the sign of what is predicated from the 
sign of predication, I must say ' Dogs are barking animals ', or some- 
thing of that sort. The word Perii expresses both the subject 
about which the statement is made, viz. the speaker (though it 
does not stand for it), what is predicated of it, and the act of 
predication ; and if subject and predicate are to be disentangled, 
one must say ' I am undone '. Even here the disentanglement is not 
complete, because ' undone ' does not so stand for what is predicated 
of me that I could make it the subject in another proposition about 
that ; for this purpose I should have to say ' I am a man undone ' ; I 
could then go on and say ' A man undone has no energy ', or what- 
ever it may be. 3 Words are often made signs of these divers things 
at once by means of inflection* To substitute for a proposition 
expressing subject or predicate or both by the same word or words 
that express also the act of predication another in which distinct 
words express each of the three is called putting it into logical form. 
Where (as often in Logic) we wish to make subject and predicate 
separately subjects of logical discussion, this transformation is 
necessary, though it often does violence to the idiom of language. 

Now the subject and predicate (Gk. v iroKeCfxevov and naTrj-yopovpevov), 
but not the act of predication, are called the terms in a judgement; 

1 Cf. infra, p. 19. 2 Cf. infra, pp. 163-166. 

8 Neither the words ' a man undone ' nor (in the previous example) ' barking 
animals ' stand for the character attributed ; that is ' being undone ' or ' the 
habit of barking ' ; and if we use words that stand for it, and not for the 
things characterized by it, it cannot be attributed by the verb to be, but by some 
verbiikehave — e.g. 'Dogs have the habit of barking'. Cf. infra, pp. 37-38, 157. 

4 Even in a comparatively uninflectional language like English, in a suitable 
context, a single word may be a proposition : for example, in a telegram, the 
word ' coming '. 

5 There is no reason why Logic should ' put into logical form ' the examples 
in which it studies thinking, where this is not wished. 

1779 O 



18 AN INTRODUCTION TO LOGIC [chap 

and thus every judgement contains two terms, and they may be called 
elements in the judgement or the proposition, and it may be said 
to be resolved into them. 1 This again illustrates how language and 
thought are bound up together. A proposition is a sentence, but 
not merely a sentence : it is a sentence expressing or meaning a 
judgement. Otherwise we could not speak of resolving it into its 
terms ; for the subject and predicate words, at which we thus 
arrive, need not have been in the unresolved proposition ; and 
a mere sentence could not be resolved into words that were 
not in it. 

It is easy then to see that a term is not the same as a word. In 
a judgement there are always two terms, but a single word may 
express both ; Caesar's famous message of three words ' Veni, vidi, 
vici ' contains as many distinct propositions, each of which may be 
resolved into the same subject-term ' I ' and a predicate-term 
which is different. Contrariwise many words may make one term ; 
and this is the commonest case. Subject and predicate may each 
be expressed by a single word, e.g. 'Tastes differ', 'Regret is 
foolish ' ; but in ' Dead men tell no tales ', ' The kingdom of heaven 
is within you ', each term consists of several words. Again some 
words cannot normally be the terms of a proposition at all. They 
do not indicate by themselves any object of thought, but are either 
used, like an article, in conjunction with some descriptive word, to 
designate an object, or, like an adverb, to qualify what another word 
expresses, or, like a preposition or conjunction, to mark some 
relation between different parts of a complex object of thought, or 

1 "Opov <a\S> els ov SiaXverai 17 Tvporams (' I call that a term into which the 
proposition is resolved'), Ar. Anal. Pri. a. i. 24 b 16. 'Term' is terminus, 
a translation of the Greek opos. It is not quite easy to see why the parts 
into which the judgement can be broken up were called opoi. The statement 
that ' a term is so called because it forms one end of a proposition ' (Jevons) 
is clearly wrong ; for that is an accident of language ; even in English ' hungry 
I was, and ye fed me ' would not be impossible, instead of ' I was hungry'. 
It may be that Aristotle, like the manuscripts of the Organon, symbolized 
the proposition in the form ' A — B ' (where we should write ' B is A '), and 
that the use of the word comes from the position of the symbols. Bonitz 
(Index Arist., s.v. opos, 530 a 21) thinks it a metaphor from mathematics, 
where if the ratio of two quantities was considered, these were called opm, 
being represented by lines, which are the boundaries of a plane ; in the 
judgement, there is a relation of subject and predicate, which might therefore 
be called opm too. The word is, however, also used like opm p6s, to mean 
definition ; and it may be that subject and predicate were called opoi as the 
determinate objects of our thought in a particular judgement, or as together 
comprising what is propounded, and limiting the judgement in which they 
occur to its own field. 



ii] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 19 

(as we have seen) to express an operation of thought. 1 Such 
words are called syncategorematic (o-vyKarriyoprifiaTiKa) because only 
capable of being used along with others in predication ; while 
words which signify what can by itself be a subject or predicate in 
thought are called categorematic. These, indeed, while capable of 
being used by themselves as terms, may also enter into a term among 
the words of which it is composed ; thus man is a term in the 
proposition ' Man hath found out many inventions ', but not in the 
proposition ' The heart of man is deceitful ' : the sea in the proposi- 
tion ' The sea shall give up his dead ', but not in the line ' She left 
lonely for ever the kings of the sea '. In this line the words italicized 
are syncategorematic ; but sea is not syncategorematic, because it 
can stand for a term, though here it does not do so. Terms com- 
posed of words of both kinds have been called ' mixed terms \ It is 
true that syncategorematic words, though standing for nothing 
whereof anything can be asserted, or which can be asserted of any- 
thing, can yet as words be made the subject of linguistic or gram- 
matical discussion, as when we say 'Of is a preposition ', or ' is the 
sign of the genitive case in English \ When words which stand for 
no complete object of thought are made objects of our thought 
themselves as words, it is said to be by a suppositio materialis. 

1 With the articles may be coupled words like some and any ; not, and no 
in 'no man ', are also syncategorematic ; so is the copula iff, as the sign of 
predication, though not when it means ' exists ' and is itself the predicate. 

2 The doctrine of suppositio, as of divers other ' properties of terms ', has 
happily fallen into oblivion ; but for the benefit of any one who wishes to 
understand the phrase suppositio materialis it may be worth while to add 
a note on it. All parts of speech were said to have signification ; then, as 
sounds having signification, they acquired properties which did not belong 
to them as mere sounds. These properties were not the same for every part 
of speech. Suppositio belonged to substantives denoting substances, copulatio 
to verbs and adjectives. Substantiality and adjectivality were characters of 
the things signified ; the adjective coupled some adjectival with some sub- 
stantival thing, the substantive ' put ' the latter ' under ' the former (v. Prantl, 
Geschichte der Logik im Abendlande, vol. II. Abschn. xv. Anna, 67 ; vol. III. 
xvii. 59). So far, the sense of suppositio seems to be active ; it is defined 
as acceptio termini substantivi pro aliquo ; suppositio puts the substantive, 
instead of what it stands for, under what is adjectival ; it takes the sub- 
stantive term for or as representative of something, and predicates about it. 
But since we do thus supponere the substantival term, suppositio was said to 
belong to it, in the sense that not the act of ' supposition ' belongs to it, but 
being the subject of that act ; and then it was itself said supponere pro aliquo, 
i.e. to stand for, or be put for (not to put for), something (cf. Prantl, vol. III. 
xvii. 61, 201 : Sanderson's Compendium Logicae Artis, Lib. II. c. 2). The 
same term had different kinds of 'supposition ' according to what it 'stood 
for'; e.g. in 'Homo est animal', homo stands for all men, and this is the 
tuppositio naturalis of a common term; in 'Homo currit', it stands for 

02 



20 AN INTRODUCTION TO LOGIC [chap. 

Some logicians have preferred to speak of names, rather than 
terms, or have been ready to apply to a term Hobbes's well-known 
definition of a name. 'A name ', he says, ' is a word taken at 
pleasure to serve for a mark, which may raise in our minds a thought 
like to some thought we had before, and which, being pronounced 
to others, may be a sign to them of what thought the speaker had, 
or had not, before in his mind . This definition, if we omit the 
words ' or had not ', expresses fairly well the function of a name ; 
but it is not equally appropriate to define a term ; for not all words 
or phrases which can be predicated of anything would be called 
names of it, and yet they may all serve as terms. That word is the 
name of anything which we might give in answer to the question 
' What is it called ? ' — either, if the thing is a concrete individual, 
a word used to direct our thought just to that individual, irre 
spectively of what it is, or, if our attention is to be directed by a 
name that signifies what that is which we are to think of, a word 
signifying not some attribute or detail in its being, but its essential 
or (if one may so say) most constitutive being. 2 Of the first sort 

some individual, and this is suppositio personalis. Now as a sound having 
signification, the term was distinguished into the sound as matter, and the 
signification as form ; and when a predication was true of a term as a sound 
or in respect of its matter, as in 'Homo est disyllabum ', it was said to be 
by suppositio materialis : when in respect of what it signified, by suppositio 
formalis. There can be suppositio materialis of any part of speech, but 
formalis only of substantives ; for only a substantive, or substantival phrase 
(haec enim significat rem ut subsistentem et ordinabilem sub alio, v. Prantl, 
vol. III. xvii. 60) can have suppositio formalis. Cf. p. 157, infra. 

1 Computation, or Logic, c. ii. § 4. By the words ' at pleasure ' Hobbea 
does not mean that everything about the formation of names is arbitrary, 
but that there is nothing in a particular sound making it of itself more suited 
than another to suggest what it stands for ; of course this does not apply 
to names derived from others already significant, but to the formation 
of underived names it does apply, unless they are ' onomatopoeic '. So 
Aristotle says that a name is (pa>vfj ar]iu.avTLKq Kara <tvv8i]kt]v, 'an articulate 
sound having signification by convention ' (de Interp. ii. 16 a 19). The words 
' or had not ' should go out : a name cannot be a sign of what I am not 
thinking of, and even a negative judgement does not express the thought 
I have not in my mind, but the thought which I have, that ' this is not that '. 
What does Hobbes mean by a thought ? — thinking, or the thing thought of ? 
a name makes one think of a thing, or 'raises in my mind the thought ' of 
a thing. My using it is a sign to others that I am thinking of that thing ; 
but it itself is rather a sign of the thing ; and when I use names only in my 
private thinking, they are not signs of my thinking at all, but rather instru- 
ments. A name also may consist of more words than one, e. g. Stoke Poges. 

2 The usage of the word ' name ' is somewhat uncertain, and the distinction 
not sharp, because it is often difficult to say whether what a word signifies 
about that of which it is predicated is its essential being. We should probably 
agree that we give a screw-wrench its name when we call it a screw-wrench, 



ii] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 21 

are proper names, like Caesar, the Thames, Europe ; of the second, 
the general names of substances, like man, river, lead, and the names 
of the kinds, attributes, and relations of things, like humanity 
( = human nature), jealousy, distance. But words used of a subject 
to signify its possession of some attribute or relation, or used of these 
to signify their presence in a certain subject, or something ' about ' 
them, are not names ; ' the Great Commoner ' is not a name of Pitt, 
' the sin of Adam ' not the name of disobedience, ' the needful ' not 
the name of money, nor ' the continuous ' of quantity. 1 Amber- 
gris is a valuable substance found in the body of some sperm- 
whales ; ' ambergris ' is the name of that substance, ' found in the 
body of some sperm-whales ' is not ; but both are terms in that 
proposition. And there is another reason for distinguishing name 
and term. There is always a contrast in our minds between a name 
and what it stands for ; but a term is so bound up with its meaning, 
that we often mean by ' terms ' the objects of thought which are 
subject and predicate, not the words signifying them. Only so could 
we speak of resolving into its terms a proposition which does not 
contain the words which we get by our resolution of it. We say too 
that the subject-term in a proposition is that about which we predi- 
cate ; but we seldom predicate about the words ; when the messenger 
announced to Macbeth ' The Queen, my lord, is dead ', it was not 
of the words that he spoke. To avoid confusion, it is sometimes 
necessary to indicate whether by the terms of a proposition we mean 
what is thought of, or the words signifying that ; and we might 
call the former the terms of thought, the latter, the terms verbal. 
We shall have to give different definitions of a term accordingly. 
We may define a term of thought as ' whatever can be thought of as 
the subject or predicate of a proposition ' : 2 a term verbal as ' a 

but not a carpenter, when we call him a carpenter ; because in the being of 
a carpenter to be a man is fundamental, to be a carpenter incidental, but 
in the being of a screw-wrench to be a screw-wrench is fundamental ; carpentry 
however is the name of the carpenter's trade. Aristotle has a formula which 
can be adapted here. If you can say of a thing called A that it is not some- 
thing else in order to be A, ovk a\\o n 6v tcrnv A, then A is its name. (What 
he says is that a predicate belongs to A essentially as A, if it is not something 
else than A in order to have the predicate : v. Anal. Post. a. iv. 73 b 5-8.) 

1 On the function of a name cf. Lotze, Mikrokosmos*, Bk. V. c. iii. § 5, 
E. T. vol. I. pp. 627-628. 

2 Or ' of a judgement '. It will be noticed that subject and predicate are 
equally ambiguous with term ; in the one definition they mean what is thought 
of, in the other the signifying words. Nothing is a term except when it i3 
thought of as subject or predicate, or used to signify these ; but when we 
consider terms in isolation, though there is no given judgement, we consider 



22 AN INTRODUCTION TO LOGIC [chap. 

word or combination of words capable of standing as the subject or 
predicate of a proposition'. 

To avoid ambiguity between terms as words and what they stand 
for or signify, logicians sometimes give to the latter, when they are 
not individuals, the name concepts. The word ' concept ' always 
signifies something thought of, never the name of it. Conception is 
sometimes used equivalently ; indeed in ordinary speech that is the 
word that would be used, and if a man spoke of the Greek conception 
of the heavens, he would mean what the Greeks conceived the 
heavens to be. But ' conception ' also means the act of conceiving, 
as when I say that the conception of an immaterial substance is 
known to us first in Plato. The ambiguity is common in English 
with words of this formation ; ' narration ' may signify either the 
act of narration or the story narrated, ' composition ' either the act 
of composing or what is composed ; we may say that a man is 
engaged in composition, or that he has sent his composition to the 
press. The Greek language distinguished the two meanings by 
different verbal terminations, the act by nouns in -cls (like aicrdva-Ls 
and v6i](ris, sensatio and intellectio), the object by adjectival words 
in -tov (like alo-dnrov and vot]t6v, sensatum and intellectum). As it 
is important not to confuse the two, it is best to use the word 
'conception ' to signify conceiving, and ' concept ', though it sounds 
less familiar, to signify what is conceived. 

A concept is not the same as a term of thought, because concrete 
individuals, like the Thames, may be terms of thought, as when I 
say ' The Thames flows through London ' or ' That ship is the 
Victory ' ; but they are not concepts, for we may perceive or 
think of, but not conceive them. Nevertheless many terms of 
thought are concepts, and it is important to recognize the part they 
play. The three following paragraphs may throw some light on 
this, though they belong in other respects more properly to the 
discussion of the nature of judgement. 

It is an old objection to judgement, that since its subject and 
predicate are different, it cannot be true ; for according to the Law 
of Identity, A is A, and not B. 1 But there can be no thinking unless 
we allow that the unity of a thing with itself does not preclude 
variety in what it is. Still the problem of the One and the Many is 

their capacity to be terms. Hence I have said ' can be thought \ or ' is 
capable of standing ', not ' is thought ', or ' stands '. 

1 Cf. supra, p. 13. This puzzle was started by Antisthenes the Cynic in 
the fourth century b. o. Cf . Lotze, Logic 2 , Bk. I. c. ii. B. §§ 56-60. 



ii] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 23 

among the chief problems of Logic and Metaphysics ; and if thinking 
expresses itself in the form ' A is B ', we must ask what this form 
means. Now consider the following examples: (1) 'Barkis is willin", 
(2) ' the Emperor is captured ', (3) ' a bacillus is a vegetable', (4) ' to 
obey is better than sacrifice ', (5) ' to doubt is to think ' . In the first, 
' Barkis is willin' ', the predicate is only one detail in the being of the 
subject, but the subject is indicated by a name, which does not 
single out anything else in its being : in the second, ' the Emperor is 
captured ', the predicate again is only one detail in the being of the 
subject, but the subject is indicated by a word which singles out 
another detail in its being ; in both there is a predicate-concept, in 
both the subject is a concrete individual, but in the second there is 
besides the concrete subject a subject-concept; this subject-concept 
however is but a detail in the being of the concrete subject. In the 
third, the subject is again a concrete thing, and there is a subject- 
concept ; but this is not a detail in the thing's being, but is its 
essential or constitutive being, neither is the predicate a detail in its 
being, but the general being of the subject-concept. Hence while the 
first ascribes a character to Barkis, viz. willingness, but does not 
mean that being Barkis is willingness, nor the second that being an 
Emperor is being taken captive, the third does mean that being a 
bacillus is being a vegetable. In the fourth, the subject is not a 
concrete thing, but a concept, i. e. something we conceive ; and the 
predicate is so too ; but it is not the general being of the subject- 
concept, and the proposition does not mean that obeying is supe- 
riority to sacrifice. Lastly, in the fifth, as in the fourth, the subject 
is a concept, but the predicate-concept is its general being, and the 
proposition does mean that doubting is thinking. 

Now the points to which these examples should chiefly direct our 
attention are these : — (i) concepts are characters (not necessarily 
sensible) which we find displayed in individuals ; (ii) they may be 
characters which as it were cover the whole being of these individuals 
— the phrase is Professor Cook Wilson's — or only details in their 
being ; (iii) one character may cover the whole being, or be the 
general being, of another ; (iv) where the predicate-character covers 
the whole being of the subject, or subject-character, the latter is 
the former essentially, and not only may the things denominated 
from the subject-character be denominated from the predicate- 
character (' a bacillus is a vegetable ', ' a doubter is a thinker '), but 
the subject-character itself is the predicate-character (being a bacillus 



24 AN INTRODUCTION TO LOGIC [chap 

is being a vegetable, doubting is thinking) ; (v) where the predicate- 
character is only a detail in the being of the subject, whether indi- 
vidual subject or subject-character, the latter is not thus essentially 
the former : the predicate-character is incidental to the subject, or 
coincidental * with the subject-character in the same individual 
subject ; and though the subject, or things denominated from 
the subject-character, may be denominated from the predicate- 
character, the subject, or the subject-character, is not the pre- 
dicate-character (Barkis is not willingness, being an Emperor is not 
being taken captive, obeying is not being better than sacrifice). 

Thus judgement involves concepts 2 among its terms of thought, 
but individuals may be terms of thought also ; but these terms of 
thought, whether individuals or concepts, are not in every judge- 
ment judged to be related to each other in the same way, though 
the forms of language do not always bring out these differences in 
the relation between subject and predicate. 

It was said that a concept is a character of something, not an 
individual thing ; neither is an individual sensible quality con- 
ceived — e. g. the black colour of this ink ; but its general or uni- 
versal character, that of which it is a particular instance, is conceived. 
It is only by an act of thought that I can apprehend that colour 
which is the same in black and red and blue. It is also only by an 
act of thought that I can apprehend blackness as something the 
same in the black of that ink and of this. Concepts therefore are 
not sensible. But it would be wrong, because they are not sensible, 
to suppose that they are not real independently of the conceiving 
mind : that they are products of the activity of conceiving. Unless 
what I conceive a thing to be and predicate of it is what the thing is, 
my thinking is vain, and doomed eternally to defeat itself. Suppose 
that a study of the literary or other evidence leads a man to judge 
that Gibraltar belongs to the British Crown. His j udgement concerns 
a rock at the entrance of the Mediterranean and a fact in its present 
history. The rock exists independently of his thinking about it ; but 
not less does belonging to the British Crown, 3 or his judgement could 
not be true. Yet belonging to the British Crown is not sensible. 4 

1 Cf. infra, p. 76. 

2 Except where both terms are proper names — e.g. 'Eboracum is York', 
' Verulamium is not Colchester '. 

3 The word exist is sometimes confined to the concrete individual and its 
particular sensible qualities, and anything else real is said not to exist but to be. 

4 Idealists of the school of Bishop Berkeley would say that Gibraltar does 
not exist independently of being perceived or imagined. Most idealists would 



n] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 25 

[The view that concepts are products of the conceiving mind is 
as old as Plato, who rejects it in the Parmenides 132 b, c ; it is ex- 
pressed by calling them not vo^rd, things conceived, but vorHxara, 
products of conceiving (as a poem or 7rotrj/xa is a product of the poet's 
making or ttoit/o-is). Aristotle often countenances it, though perhaps 
also holding these mental facts, our concepts, to be in a manner 
the same as the intelligible nature of things, the vor]\ia the same as 
the vot]t6v. Others, and among English philosophers notably Locke, 
have held that the object of conception is altogether mental ; that 
concepts are created by the mind in order through their instrumen- 
tality to acquire knowledge about real things, but are not real them- 
selves. This doctrine is known as Conceptualism. The objection 
to it is simple. It holds that concepts render possible a knowledge 
of real things when they are so formed as to correspond with the 
nature of the things ; but it cannot show how we could be aware of 
this correspondence without knowing the nature of the things directly, 
as well as the concepts. If we only know the nature of the things 
through the concepts, we can no more tell that they correspond, 
than we could tell that the existing portraits of a man were like him, 
if we only knew his features through the portraits. And indeed it 
would be nearer the truth to say that only what is real can be con- 
ceived, than that what is conceived is not real. We cannot conceive 
a square circle, though we can conceive a square and a circle, just 
because, though circle and square are real, their combination in the 
same individual figure is unreal and impossible. But there are 
difficulties also in the way of saying that all that is conceived is 
real. We may ascribe to the same individual subject a number of 
attributes, each of which is conceived, and their combination also 
conceived, and which yet are not really combined in this subject ; 
for example, I might think Gibraltar to be a fortress acquired by 
treachery ; to be a fortress is a real attribute of some subjects, to 
have been acquired by treachery of others, and their mode of com- 
bination is a real mode of combination, exemplified, if not in them, 
yet in other attributes : nevertheless such a belief would be erro- 
neous. The difficulty here is the difficulty of error. It may be 
said that other fortresses have been acquired by treachery, and 
therefore what I think Gibraltar to be is what they were ; and so 
I am conceiving something real, though ascribing it to the 
wrong subject. But— not to mention other difficulties which this 
answer does not remove — the elements thought to be combined, or 
(as it would be expressed) combined in our concept, may be such as 

hold that its existence is at least not dependent on the consciousness of this 
or that finite individual, whatever be the relation of things to mind in the 
universe as a whole. Without entering upon this question, I am concerned 
here to urge that what is apprehended in things by thinking, but is not 
sensible, is not les3 really in them nor more dependent on the mind than what 
is apprehended by sense-perception. 



26 AN INTRODUCTION TO LOGIC [chap. 

[have never been combined in any real subject. Our fathers thought 
Methuselah to be a man who lived for more than nine hundred 
years ; there are things that have done it, such as some of the big 
redwoods at Mariposa ; there are things that are men ; but none 
that both are men and have done it. Perhaps we ought still to say 
that what is conceived is something real, but that in these cases 
(where we are dealing with questions of historical fact) the elements 
of a complex predicate are conceived, but do not form a real unity, 
and are not one concept, because we do not see the necessity of their 
combination. Where we suppose ourselves to see a connection 
between conceived elements, which nevertheless does not exist — as 
Descartes thought that ' Vis Viva ' in a body was as the product 
of the mass into the velocity, not into the square of the velocity — 
there, when we escape from our error, we realize that we never saw the 
connection, because it never existed. We may be inclined to say that 
we conceived what was unreal ; but we ought rather to say that we 
thought we conceived what we did not conceive. 

There remains however a further difficulty about the existence, 
or reality, of objects of conception. We predicate what we con- 
ceive of individuals ; it was agreed above that a concept must be 
other than a mere product of our conceiving because we conceive 
the nature of what exists. Yet we can still conceive it when the 
individual whose nature we judge it to have been exists no longer. 
The whole question of the relation of the ultimate reality to its 
appearance in time is involved here.] 

[It has been said that concepts x are universal : that what we 
conceive is the common nature whereof we find instances in in- 
dividual things. But though we do not conceive the particular 
instance, our knowledge of it involves conceiving. To hear a sound 
is not an act of conception ; but if thought is at work, and I know it 
for a sound, I must be aware of what ' this heard ' is. I may be 
determined to action by hearing a sound, without thinking : and 
hearing words determines me to think of what they signify, without 
thinking about the words ; in this case too I hear sounds but do not 
think that they are sounds (though of course I do not think that 
they are not sounds) and so there is no conception of sound. But 
when I think about what I perceive, and apprehend what it is, 
the elements of its individual being are known as an instance of 
that whereof there may be other instances, and that is universal. 
Conception therefore is involved with my perception. This common 
nature or universal is not itself perceived, though known in the 
perception of its instances. But it is to be noted, that in some cases 
the instances can no more be perceived than can their universal 
nature. Relations illustrate this. The likeness between my two 
hands is not the likeness between your two hands, but each is an 

1 On the nature of concepts cf. further, pp. 68-71 infra, especially p. 69, n. 1. 



ill TERMS, AND THEIR PRINCIPAL DISTINCTIONS 27 

[instance of likeness ; nevertheless though we can see our hands, 
we cannot see the likenesses. By and bye it will appear how im- 
portant this fact is to the theory of induction. The inductive 
sciences seek to discover causal relations. Now causal relations 
are displayed in things ; the impact of these stones causes Achan's 
death, of those Stephen's. Yet the particular instances of causality 
cannot be perceived ; otherwise it would be as easy to perceive 
the cause of a flower's drooping as to see it droop. 

The existence of universals is often denied ; men are apt to 
imagine that if they exist one should be able to find them as one 
finds instances of them. Hence the remark of Antisthenes — Xititov 
fxev 6p&, linroTrjTa 8e ovx 6p<3, ' I see a horse, but not horseness ' : 
to which Plato replied, that it was because, though he had eyes, he 
had no intelligence. 1 The universal is not one of its own instances, 
and cannot be found like them. Nevertheless to deny that there 
are universals is to deny all identity between different individuals, 
and to do this is to say that we can never, by what we learn of the 
connection of characters in one individual, infer one from the 
presence of another in a second individual. We may allow that the 
relation of an universal to its instances is puzzling ; but the puzzle 
comes partly from trying to describe it in terms of some other 
relation. The universal is sometimes called a whole, or (for 
distinction) a logical whole, and its instances particulars, and we 
ask how they partake of or divide the whole among them ; is 
there in each a part, or is the whole present in each ? the first is 
inconsistent with its unity, the second makes it to be in many places 
at once. 2 But the question here assumes that the ' logical whole ' 
is like a physical whole or thing in space : that horses share horseness 
as they do a pottle of hay. If we wish to know the relation of its 
parts to a physical whole we must consider examples of the quanti- 
tative—England and its counties, a day and its hours ; so, if we 
wish to know the relation of its parts to a logical whole, we must 
consider examples of that in which this relation is exhibited — things 
of a kind, different instances of the same quality. We find in re- 
flecting on our thoughts about things, that we do think them to be 
things of a kind, instances of the same. That is why the present 
discussion is logical ; though it is one of the logical problems that 
concerns also the being of things. 

It has been maintained 3 that there are no instances of relations : 
that the likeness between my hands and the likeness between yours 
are not two likenesses but the same likeness — not instances of 

1 Cf. Ritter and Preller, Historia Philosophiae Graecae 9 , § 287. In the story 
which gives the answer, it is Diogenes who speaks, and a cup and a table 
take the place of the horse. 2 Cf. Plato, Parmenides, 131. 

3 Cf. B. Russell,TAe Problems of Philosophy, c. ix. (Home University Library), 
Principles of Mathematics, § 55. 



28 AN INTRODUCTION TO LOGIC [chap 

[likeness, but numerically one likeness. Without accepting this, 
it may be granted in regard both to relations and attributes that we 
are very apt to confuse the instances and the common nature. And 
we often denote them by the same name ; ' colour ' means particular 
colours when I speak of the colours in last night's sunset ; it also 
means colouredness ; every distance is a particular distance, but 
their common nature is called distance also. We do not make this 
confusion in regard to substances ; men and horses are instances of 
their kinds ; and individual men or horses are so much more obvi- 
ously different from one another than individual likenesses or dis- 
tances or ultramarines that we cannot overlook in them the distinction 
between the manifold individuals and the one common nature. 1 
But perhaps this distinction is more readily seen in substances 
because individual substances are something more than instances of 
their kind. The true instances of human nature are the human 
natures of individual men ; but the human nature of Caesar is what 
Caesar is ; and sensible individual substances at any rate we do not 
seem to discriminate altogether by what they are. 2 ] 

The foregoing consideration of what a term is in general, and of 
its relation on the one hand to a word and on the other to an object 
of thought, will have helped to familiarize us with some of the facts 
determining the main kinds of terms that Logic has to recognize. 
The ordinary classifications of terms are classifications of them as 
words which signify objects of thought ; but the distinctions are 
based on differences in what we think of, or what in general we 
think things to be. 

In respect of the objects of thought signified, terms are commonly 
divided first of all into abstract and concrete : but if we regard 
also their character as words, or terms verbal, 3 they must be divided 
into abstract, concrete, and attributive. A concrete term (verbal) 
is the name of a person or thing, an abstract term the name of 
a quality or attribute, or relation ; so that the distinction between 
the thing and its qualities, between substance and attribute or rela- 

1 Yet biologists do not seem always to have asked themselves which they 
mean when they write about evolution. Do individual men evolve, or is it 
the human nature which is displayed in them all ? and if the latter, and 
men are descended from animals whose nature was not human nature, but 
has evolved into human nature, what is the relation of the two, or are human 
nature and pithecanthropous nature the same common nature ? and if so, 
are there many species or only one ? 

2 Cf. infra, pp. 54-57. If there are individual substances that are not 
sensible but purely intelligible, they must be discriminated by the under- 
standing only. 

3 i. e. terms as = the word or words signifying an object of thought. 



ii] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 29 

tion, is the basis of the distinction between concrete and abstract 
terms. Attributive terms will be explained later. 1 

Our notion of a thing, as has been already indicated, involves 
two elements, which furnish the basis for a further division of both 
concrete and abstract terms into those which are singular and 
those which are common or general. 2 A thing is, first, an indi- 
vidual, having an existence distinct from that of other individuals *. 
the page, for example, on which these lines are printed is a different 
page from every other in this book. But secondly, a thing has 
a character, which may be the same in other things ; just as other 
pages in this book, though individually different, are equally pages. 
This character, which belongs alike to many individuals, is some- 
times called, as we saw, an universal ; and they, as so many different 
cases or examples of it, are called particulars : particulars, as we 
often say also, of a kind. 3 

Now the various particulars of a kind, so far as they have the 
same character, may be called by the same name : so far as they are 
distinct particulars, they will require different names to distinguish 
them. Their names as things of a kind are common or general 
names : for the name is common to all particulars of the kind, or 
applies generally to any ; acorn, squirrel, file, metal, are general 
names. Their names as individuals, if they have any, are singular ; 
like London, Zoroaster, the Matterhorn ; such names as these we 
call proper names. A general term is thus one that is predicable of 
any number of individuals in the same sense : a singular term one 
that is predicable of one individual only in the same sense : and a 
singular term is a proper name if it does not indicate what individual 
it stands for by reference to any special element in its being. Smith 
for example, as meaning one who works in metal, is a general term, 
because I mean the same by calling Dick or Thomas a smith ; if 
I use it as a proper name, numerous as are the persons who bear it, 
I do not mean the same in each use of it. I may refer to the de- 
fender of Acre, or to the witty canon of St. Paul's, or to any of 
a hundred and one others, and in each case my meaning is different ; 

1 v. infra, p. 36. 

2 That this distinction is applicable also to abstract terms is apt to be 
overlooked, and I wrongly denied it in the first edition, through not dis- 
tinguishing abstract terms and names of universals. I owe the correction 
to Mr. H. A. Prichard. 

3 Strictly, if what was said on the previous page is right, it is the constitu- 
tive nature of each concrete individual that is the instance of the kind. 



30 AN INTRODUCTION TO LOGIC [chap. 

nor is it through referring to anything in particular of what he was 
that I know, when I hear the name, that Sir Sydney Smith is meant, 
as it would be if my thought were directed to the same man by calling 
him ' the defender of Acre '. 

We are seldom at a loss for some general term by which a par- 
ticular thing may be denoted ; but comparatively few particulars 
have singular terms appropriated to them. Many particulars of 
a kind — for example, new pennies — are not distinguishable at all 
to our senses, except by each occupying (when we see them together) 
a different place ; these will not have each a different name, for we 
should never succeed in calling each individual always by its own 
proper name. In other cases, though the particulars of a kind 
might be tolerably distinguishable — for example, lumps of chalk of 
varying shapes and sizes — we have no occasion to refer to them 
individually, nor to burden our memory with so many names. We 
are content to employ a common or general name, and to specify 
the particular object (from among all those that bear the name) to 
which we wish to refer, by pointing, or the use of a demonstrative or 
possessive pronoun, or some periphrasis. Thus we say ' the picture 
there ', and point : or ' this year ', or ' my great-coat ', or ' the bust 
of Julius Caesar in the British Museum of which Froude used an 
engraving for the frontispiece of his life of Caesar '. Such expres- 
sions are indeed in a manner singular terms, for they serve to 
designate particular objects ; they are not however proper names ; 
they commonly include general terms and are partially descriptive, 
and they have been conveniently called designations. 

But where particulars of a kind are distinguishable, and we are 
interested in them singly and wish to be able to refer individually 
to them, we give them ' proper names '. Thus every individual 
man has a name of his own, and every field in the country is named, 
because the farmer needs to tell his men which particular field to 
work in ; and a railway company for a similar reason names or 
numbers its various engines and carriages. Though, however, many 
particular things have no proper names, all which have proper names 
have general names also ; the ' four- acre ' is a field, the ' Cornish- 
man ' is a train, William the Silent is a man ; and on the other hand 
any particular thing might, if it were worth while, be distinguished 
by a proper name. The proper name and the common name thus 
recognize respectively the two elements in our notion of a thing 
noted above : the proper name recognizes its distinct existence, the 



ii] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 3 J 

common name its character that it shares with other things : nor 
could our thought about things express itself fully without concrete 
terms of these two kinds. 

[This has not indeed been always admitted. Thus James Mill in his 
Analysis of the Phenomena of the Human Mind (vol. i. ch. viii. p. 260, 
London, 1869) writes that it is ' obvious, and certain, that men were 
led to class solely for the purpose of economizing in the use of names. 
Could the purposes of naming and discourse have been as con- 
veniently managed by a name for every individual, the names 
of classes, and the idea of classification, would never have existed. 
But as the limits of the human memory did not enable men to 
retain beyond a very limited number of names ; and even if it had, 
as it would have required a most inconvenient portion of time, 
to run over in discourse as many names of individuals, and of 
individual qualities, as there is occasion to refer to in discourse, it 
was necessary to have contrivances of abridgement ; that is, to 
employ names which marked equally a number of individuals, with 
all their separate properties ; and enabled us to speak of multitudes 
at once '. The position here taken up by Mill is known technically 
as that of nominalism, the doctrine that things called by the same 
name have only the name in common ; a doctrine frequently pro- 
fessed, but not often stated with such uncompromising clearness as 
in this passage. We do not however really call different individuals 
by a common name, except because they have or are believed to 
have a common nature ; nor is it conceivable that we could name 
an individual by a proper name, without at the same time recog- 
nizing in it, however vaguely, some character that, as capable of 
existing equally in other individuals, might be the ground of a 
general or common name. General names then are no mere means of 
abbreviating discourse, but their existence is grounded in what we 
must think the nature of objects of thought to be. Aristotle's dis- 
tinction x between 6/xw^y^a, or things called by the same name 
having only the name in common, and <rvv<avviJ.a, or things called by 
the same name having also what is meant by the name in common, 
may be mentioned here : the distinction is nowadays embodied 
from the side of names instead of things in that between equivocal 
and univocal terms (v. infra, p. 46). Opposed to nominalism is 
the doctrine known as realism, which maintains the reality of 
* universals ' or characters the same in more individuals than one — 
of squareness as well as squares, justice as well as just men and 
actions, man-ness as well as men. If the common nature be held 

1 Most clearly stated Cat. i. l a 1-12. The Aristotelian authorship of the 
Categories is disputed ; but that the doctrine in it is in the main Aristotelian 
can be shewn from treatises admittedly his. Cf. for this distinction Top. 
C. x. 148 a 24 sq. 



32 AN INTRODUCTION TO LOGIC [chap. 

[only to exist in the various instances, so that there would be no 
squareness unless there were squares, nor man-ness unless there 
were men, the doctrine is that of universalia in re ; if it be held to 
be eternal, so that with the first existence of squares or men began, 
and with their disappearance will end, only the manifestation and 
not the being of squareness or man-ness, it is that of universalia ante 
rem. Conceptualism (v. supra, p. 25) is an attempt to compromise 
between the Nominalists and the Realists by saying that different 
individuals cannot indeed share a common nature, because no com- 
mon natures but only individuals exist, but that nevertheless we 
form concepts which somehow correspond with each of a number of 
individuals, and by their means we are able to have general know- 
ledge, i. e. (on this view) knowledge about an unlimited number of 
individuals at once. Conceptualism is the doctrine of universalia 
post rem.] 

There are thus two kinds of concrete terms, viz. singular terms, 
or names of individuals, and common or general terms ; singular 
terms can be further distinguished into proper names, i. e. names 
permanently assigned to one individual, and designations, i. e. 
phrases which by a pronoun or what not serve to indicate an indi- 
vidual otherwise than by a name of its own. Now it has not been 
stated in the last sentence, what general terms are the names of. 
Are they also the names of individuals, or are they names of the 
character common to many individuals ? The former view seems 
incomplete, for it does not take account of their difference from 
singular terms. The latter view is plainly wrong, for man is clearly 
predicated of individual men, not of the nature common to them ; 
and when I say that man is mortal, I mean that men die, not that 
human nature dies ; that is displayed in a succession of individuals 
who are born and perish, but is not born and does not perish itself. 
We must then accept the former view. General concrete names 
are names of individuals, but names of them in respect of their 
common nature. Hence they imply the existence of universals, 
though they are not the names of these. 

Now such universals sometimes have names. It is true their 
names are not often used in ordinary talk, for our practical interests 
are in individuals, and only in philosophical reflection are we led 
to consider the existence of the universal realities whereof they are 
instances. Still, the nature of man is so interesting to us that we 

1 But what would happen with the death of the last man ? Cf. p. 26 
supra, on the existence of concepts. 



n] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 33 

have the name humanity x ; and we can form names, like ' horse- 
ness ' or ' goldness ', when we wish to distinguish the common 
nature of horses or parcels of gold from their instances, or we can 
use a periphrasis, like ' the nature of gold '. Are we to call such a 
name concrete or abstract ? It would commonly be called abstract, 
being the name of the common nature of many individuals, con- 
sidered apart or in abstraction from them or from what distinguishes 
them from one another ; though the substantial nature of a thing 
cannot properly be regarded as a mere attribute of it. 

The distinction of individual and universal is not confined to 
what is concrete. We have seen that attributes and relations also 
have their instances. The red of one rose is not numerically the 
same as the red of another, however much their being two depends 
on their being in different roses, and otherwise they would be in- 
distinguishable. 2 The distance from London to York, even if equal, 
is not the distance from London to Bideford. But as we can only 
distinguish the instances of the same attribute or relation by refer- 
ence to the substances to which they attach, only the latter 
and not the former have proper names. Hence we are apt to over- 
look that there are instances of what is abstract. Yet it is clear 
that the death of Caesar is one of many instances of death, just as 
Caesar is one of many instances of man ; and when it is said that 
there are so many births and deaths a year in London, birth and 
death are as clearly general terms as house and street in a total of 
streets and houses. And that means that they are used in the same 
sense of each birth or death, and that ' the birth of X ' or ' the death 
of Y ' is a singular term. 

So far the case is the same with abstract and with concrete terms. 
But men are interested chiefly in the individual instances of what 
is concrete, and in the general nature of their attributes or relations ; 
and so not only are there no proper names for these, but the general 
name, besides being used of them, is used also of their general 
nature, or universal. Death, when I speak of Caesar's death or 

1 Humanity has of course other meanings, viz. mankind collectively, and 
also kindliness ; in the text it means the human nature common to all men. 
Cf. also deity. 

2 Cf . supra, p. 27 ad fin. 

8 Hence it is a mistake to say that the plurals of abstract terms are con- 
crete. Deaths, colours, distances are not substances because there are many 
of them ; and a concrete term is the name of a substance. But the plurals 
of abstract terms often designate not individuals but kinds of attribute or 
relation. 

1779 D 



34 AN INTRODUCTION TO LOGIC [chap. 

Alexander's, is a general abstract term, comparable with the general 
concrete term man ; when I say that death comes in many forms, 
it is the name of an universal, comparable not with man but with 
humanity. So colour is a general abstract term, if I speak of the 
colours of yesterday's sunset, but the name of an universal — viz. 
colouredness — when I say that colour has divers species. The fact 
that many words are used both as general abstract terms and as 
names of the universals of attributes or relations helps to make 
us regard the names of the universals of substances as abstract. 
* Colour ', as predicable not of a coloured thing but of its attribute, 
is an abstract term ; meaning colouredness it is a word of the same 
sort as ' goldness ' ; hence we think ' goldness ' an abstract term 
also. 1 

[It will be seen that there are really two antitheses confused 
together when the division of concrete and abstract is offered as 
an exhaustive division of all terms of thought, viz. (a) the antithesis 
of individual and universal ; (b) that of substance and attribute 
or relation. The second member is called abstract in each antithesis 
— though what belongs to the first member in (a) may belong to the 
second in (b) — because by abstraction two things are meant, viz. 
(a) considering the common or universal nature of divers subjects 
apart from the particular instances ; (b) considering some particular 
element in the nature or being of anything apart from the rest of 
its nature. The former is what Locke has most prominently in mind 
when he speaks of the formation of those abstract ideas, which exist, 
on his view, only in the mind, and do duty instead of any real identity 
in the various things called univocally by the same common name. 
The latter is what Aristotle meant when he said that the mathema- 
tician considers the subjects of his study h a^cupeVet, in abstraction, 
i.e. that he demonstrates the properties that belong to what is circular 
or triangular merely in virtue of being circular or triangular, neglect- 
ing — because they are irrelevant — all other characters of those things 
besides their figure. If we are to avoid confusing the two antitheses 
we must say that (A) our thought recognizes, and therefore we have 
names for (i) individuals, (ii) universals ; the names of individuals 
may be either (1) names of them considered as this or that deter- 
minate individual, i. e. proper names or designations ; these are the 
singular terms of the traditional doctrine ; or (2) names of them 
considered as of a certain sort : these are the general terms of the 
traditional doctrine. (B) Our thought also recognizes, and therefore 

1 Sometimes particular abstracts and their universal nature may be indi- 
cated by different words. Act is a general abstract name, action the name of 
the common nature of all acts. But ' action ' is also used as equivalent to 
' act ', and we speak of an action, and of actions in the plural. 



ii] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 35 

[we have names for (i) substances or things ; (ii) their attributes 
or relations ; and the distinction of singular and general applies 
to the names of both these, since both substances and their attributes 
and relations are found as instances of a sort ; but singular names 
of attributes or relations are all designations, formed by help of 
naming the individual substance involved, and not proper names. 
The distinction of singular and general does not apply to names of 
universals. Now the traditional doctrine ignores the distinction of 
individual and universal in regard to attributes and relations, and 
calls the names either of the instances or of their common nature 
abstract terms ; and when names are coined for the common nature 
of substances, which as a rule in common speech have not got names, 
it is inclined to count them as abstract also, not having in mind the 
distinction of individual and universal. 1 

These antitheses, though we certainly make them when we reflect 
on things, no doubt present difficulties to a closer examination. The 
nature of relations, and their difference from the terms related, have 
perplexed many, and have led some philosophers, like Mr. F. H. 
Bradley, to deny that relations can belong to Reality ; it appears 
to us as a system of things in relation, but transcends this in its 
own being. And even if we find no difficulty in the existence of 
relations, we may be perplexed by the distinction between the two 
kinds of related terms, substances and attributes. The individual 
substance, we think, exists, and its attributes are elements in its 
being existing only in it and not apart from it. But that of which 
they are attributes must be something of a determinate kind, not 
a mere point of reference for a multitude of attributes. A concrete 
name denotes such a determinate thing ; but on the other hand 
its concrete nature threatens to break up into a number of dis- 
tinguishable factors, each of which by itself would be called an 
attribute. Now they cannot be attributes of each other, nor yet 
of that which would be left — if anything would be left — if we 
abstracted them all, a ' something, we know not what, which we 
feign as a support of qualities ', in Locke's phrase. We might 
say that each is an attribute of the complete thing, of the individual 
in its whole being : that in fact the so-called attribute is rather an 
element in the being of that whereof it is called an attribute. But 
this still leaves it a question whether in the being of the individual 
substance we rightly distinguish its substantial nature, on the 
strength of which we call it by a general concrete name, and the 
attributes called by abstract names, or whether the substantial 
nature is really but a complex of elements or factors in the thing's 
being, which, if they were not so numerous, could be named sepa- 
rately, and would then be regarded as so many attributes. On this 
cf . infra, pp. 53-54.] 

1 I owe the outline of this paragraph to Mr. H. A. Prichard. 

D2 



36 AN INTRODUCTION TO LOGIC [chap 

Abstract terms then are the names of attributes or relations ; 
but we must understand this definition rather widely. It is not 
only sensible qualities, like flavours or odours, whose names are 
abstract terms ; each element in the being of the individual concrete 
thing, considered singly and in distinction from, although as quali- 
fying, the thing, 1 is abstract, and its name (where it has any) an 
abstract term. Moreover, the thing in question need not be a single 
thing (or person) such as a stone or an elephant ; it may be an 
assemblage of what we regard as distinct things (or persons), like 
a forest, or an army ; but if there are features belonging to this 
assemblage, though they are not qualities of any one thing in it (as 
a forest may be extensive and an army skilfully or unskilfully 
disposed), these features considered in themselves are abstract, and 
their names, ' extent ' or ' disposition ', abstract also. Hence dis- 
cipline, civilization, paternity, are all abstract terms, though it is 
only by a doubtful extension of language that we could call any of 
them a quality, like fragrance or sweetness. And we have seen 
that commonly, though confusedly, terms like ' animality ' and 
' triangularity ' are also called abstract, names, that is, not of the 
distinguishable individual elements in the being of the individual 
concrete thing, but of the universals whereof either individual 
concrete things, or the various distinguishable individual elements 
in their being, are instances. 

Besides abstract and concrete terms verbal, there is a kind of 
terms verbal which cannot well be classed with either — viz. adjectives 
and adjectival terms. These are called attributive terms, e.g. red, 
beaten, insolvent. They are not the names of qualities, like redness, 
defeat, insolvency ; on the other hand, it is those qualities which 
furnish their meaning, not the nature of the various kinds of object 
to which the qualities may belong. Thus cloth may be red and so 
may silk, but we should not explain what is meant by calling them 
red if we were to explain the nature either of silk or cloth ; and a 
man may be insolvent and so may a company, but to explain what 

1 It may be objected that whether a colour is abstract cannot depend on 
our considering it in a certain way ; if it is not abstract, we are wrong so 
to consider it ; if it is, it is so however we consider it. But if a substance 
is an unity into whose being various elements enter and combine not in the 
way in which material things combine into an aggregate, but in the way in 
which attributes combine into the being of a concrete thing, then to say 
that these elements considered singly are abstract merely means that they 
are several and can be distinguished, though only existing in the concrete 
unities which they form. 



ii] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 37 

is meant by calling them insolvent we must explain the nature not 
of man, nor of a company, but of insolvency. 1 

J. S. Mill held that adjectives are really concrete, on the ground 
that ' white ' is predicated, or is the name, of snow, milk, or linen, 
and not of their colour ; that it is an army and not a defeat that is 
beaten. 2 But it is clear that the subjects of which an adjective 
may be predicated can as well be abstract as concrete ; and if the 
adjective is concrete because it is predicated of a thing, it should 
equally be abstract because it is predicated of an attribute ; so that 
if we say that cabbages are common, common will be concrete ; while 
if we say that indolence is common, it will be abstract. The fact is 
that the distinction of attributive terms from abstract and concrete 
corresponds to no further distinction in terms of thought. There 
are substances, and there are attributes or relations, and the latter 
qualify the former ; but their qualifying them is not a third co- 
ordinate sort of reality. It is the nature of an attribute to be of 
a subject, as of a relation to be of its terms 3 ; and when we recognize 
this in instances, we are said to attribute them to their subjects. 
But that is an act of judgement, not a term ; there is an attributive 
act, but no third kind of object of thought which we can call attri- 
butive. In language however there are words which, though they 
can be used as predicates, and therefore satisfy the definition of 
a term verbal, are not properly names either of a substance or of 
an attribute. Adjectives are such words ; but so also are verbs. 
Verbs however were overlooked by those who placed adjectives 

1 The meaning of attributives may, however, be incapable of explanation 
without reference to that, in the nature of the subjects whereto the qualities 
belong, which makes them susceptible of these qualities. Thus neither silk 
nor cloth could be red unless they had a surface ; neither a man nor a company 
could be insolvent unless capable of having debts. Cf. p. 112,n. 1, infra. It 
may be added that terms like father or musician are adjectival in sense, and 
would by some be classed as attributive ; for though they are substantives, 
and are predicated of concrete things, they do not primarily signify the 
concrete things of which they are predicated ; a father must be somewhat 
else, to be a father. Cf. p. 20, n. 2, supra, and pp. 156-158, infra. Sometimes 
indeed an attributive term may signify more of the nature of the subject 
than the subject term does, e.g. if I say 'the obstacle was human ', meaning 
* a human being ' ; for to be a human being is more of the nature of the subject 
than to be an obstacle. 

2 System of Logic, I. ii. 4. 

3 Mr. F. H. Bradley however holds that a relation between two terms must 
be related to them by a second relation, and so ad infinitum, and the impossi 
bility of this infinite process is one reason why he holds that Reality cannot 
be, though it may appear as, a system of terms in relation. Cf. Appearance 
and Reality, Bk. I. c. ii. The view in the text has the support of Professor 
Cook Wilson. 



38 AN INTRODUCTION TO LOGIC [chap 

among terms. For the terms are the parts into which a proposition 
is resolved ; in them, taken singly, the act of predication is not seen ; 
they are as it were dead members, which could only have been 
taken apart because the life of judgement had fled and no longer 
bound them together. But in the verb this life lingers, even if 
a verb be taken without its subject. Hence logicians, anxious to 
express a judgement in a way to facilitate its resolution into its 
terms, have often preferred to sunder, even in language, the word 
which expresses the predicate from that which expresses its predi- 
cation : to take the term as it were out of the verb, and say of 
Lear not, with the doctor, 1 that he ' sleeps still ', but that he 
' is still sleeping '. Now in such a case the predicate is often 
adjectival in form ; although not always, for the proposition ' He 
plays cricket ' would become, if it were meant that he played 
habitually, not ' He is playing cricket ' but ' He is a cricketer '. 
Such an adjectival predicate is one of the parts into which the pro- 
position is resolved, 2 whereas the verb belongs rather to the un- 
resolved proposition. The whole question of the separate character 
of the adjective, or adjectival word, belongs indeed rather to 
grammar than to logic. But when ' term ' means name, or term 
verbal, as these are either substantival or adjectival, and the con- 
crete and abstract are both substantival, some place is wanted for 
the adjectival, and so they are classed separately as attributive 
terms. If their form were to be ignored, and they were to be 
referred either to concrete or to abstract, they should rather be 
considered abstract than (as J. S. Mill would have it) concrete ; 
for their invention implies the consideration of some quality or 
character in the thing in abstraction from the rest of the thing's 
nature. 

A special class of terms is constituted by those which are called 
collective. Like most other distinctions of terms recognized in 
Logic, this is based on a distinction in things. Individual things 
or persons may be considered singly : they may also, since there 
are many of them, be considered in groups ; and the names of such 
groups are collective terms. Thus a group or collection of books 
forms a library ; a group of human beings related in certain ways 

1 King Lear, Act iv. 7. 1. 13. Cf. p. 17, supra. 

2 Adjectives can indeed be used as subjects, e.g. Beati immaculati in via, 
where it is possible to take either term as predicate. In many languages 
an article is generally necessary in order to make an adjective do duty as 
a substantive. 



ii] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 39 

forms a family ; related in rather different ways, a tribe ; in other 
ways yet, an army or a club. Any term that denotes a collection 
of objects, with certain resemblances or relations among them, is col- 
lective. Collective terms may be either singular or general ; for we 
may wish to refer to a group composed of determinate individuals 
(as when we say ' the family of King Henry VIII ') or simply to 
a group of individuals, no matter who or what, that is composed in 
a certain way, such as a family or a regiment : but they are the 
names of the individuals taken together, and not of the mode of 
organization among them. 1 A general collective term is said to be 
used distributively of the different groups that it can severally 
denote, and collectively of the individuals in any one group ; thus if 
we speak of British regiments the term is used distributively of the 
Coldstream Guards, the 60th Rifles, the Argyll and Sutherland High- 
landers, &c, and collectively of the men in each several regiment. 2 

We may sum up what has been so far said of the kinds of terms 
as follows : — Terms as individual objects of thought are either con- 
crete or abstract ; as names or terms verbal, concrete abstract or 
attributive ; there are also names of universals, which are commonly 
classed as abstract : concrete terms (verbal) are either singular, and 
then either proper names or designations, or else general : abstract 
terms can only be made singular by help of a singular concrete term, 
and without this are general ; some concrete (and a few abstract) 
terms are collective, and some abstract terms denote attributes of 
a group or aggregate, not of its members. It may be added that 
attributive terms are obviously general. 

We pass now to a fresh division of terms, made from another point 
of view. As we may give a name to a group of things taken 
together, which would apply to none of them by itself, so we may 
give to a thing or quality, when we regard it in its relation to some 
other thing or quality, a name which would not apply to it con- 
sidered in itself. Such terms, attributing to one thing or quality 
some definite relation to another, are called relative terms : and 
in contrast with them, terms that indicate a thing or quality 

1 We may speak collectively of a group of abstracts, as when we say that 
thenaturalare more numerous than the theological virtues, or that the Triviuro 
and Quadrivium may be traced back to the fourth century b. c. My attention 
was called to this by Miss Augusta Klein. But there are no names for groups 
of instances of attributes or relations ; terms indicating them must do so by 
reference to the individual subjects in which they are displayed. 

2 The frequent division of terms into abstract, concrete, and collective, aa 
if the third were co-alternative with the other two, is therefore a mere blunder. 



40 AN INTRODUCTION TO LOGIC [chap. 

considered in itself are called absolute. It is clear that if one thing 
or quality stands in relation to another, the latter must also stand 
in relation to the first ; and the name applied to the latter to indicate 
this reverse relation is ' correlative ' ; or, since each is correlative to 
the other, the two together are called correlatives. Instances of 
relative terms are equal, greater, subject, parent : with their correla- 
tives equal, less, ruler, child ; apple, sound, man are absolute terms. 

Relative terms are necessarily general, 1 like attributive terms ; 
for the same relation may be exemplified in many particular in- 
stances, and therefore many subjects may stand in that relation 
which the relative term is used of them to indicate. They have this 
further resemblance to attributive terms, that though meaning 
a relation, they are applied to a subject standing in that relation : 
as attributive terms are to a subject possessing the attribute which 
constitutes their meaning. 2 The existence of attributive terms is 
grounded in the fact that the various objects of our thought do 
possess distinguishable attributes ; and that of relative terms in 
the fact that they do stand in distinguishable relations one to 
another. It has been contended that all terms are really relative, 
because every object of thought stands in relation to other 
objects ; at least only the totality of existence can be absolute, 
beyond which there is nothing for it to stand in relation to. But 
though it is true that everything stands in relation to other things, 
things are sometimes considered rather in themselves, and receive 
names accordingly ; and sometimes they are considered in definite 
relations to another thing, and receive names that indicate that 
particular relation. And this is sufficient ground for the distinction 
between absolute and relative terms, though there are cases in which 
it is hard to say whether a given term is one or the other. Man 
is clearly absolute, and father relative, though mountain might be 
disputed ; for a mountain is so only by its elevation above the plain, 
and yet in calling it a mountain we have in mind many features 
besides this relation. 

Terms have been further divided into positive, negative, and priva- 
tive. A positive term is said to imply the presence of a quality (or 
qualities), e. g. greed, greedy : a negative term to imply the absence 
of a quality, e. g. colourless, unfit, unfitness : a privative term to 

1 Except when a relative word is combined with others into a term whose 
whole meaning is singular: e. g. first is general, but the first Pharaohis singular. 
8 Cf. supra, p. 37, n. 1. 



ii] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 41 

imply the absence of a quality where it has been or might be expected 
to be present, e.g. deaf, deafness, desiccated. 

There is a certain difficulty in the notion of a negative term, and 
in the account of it just given ; for no term can be purely negative, 
and imply merely the absence of a quality. The Irishman's receipt 
for making a gun, to take a hole and pour iron round it, is not more 
difficult to execute, than it would be to frame a term whose mean- 
ing consisted simply in the fact that a particular quality was not 
meant. A term must have some positive meaning, in order to be 
a term at all. 

It is indeed sometimes said that a negative term includes in its 
meaning whatever is not meant by the corresponding positive term. 
According to this view, there is no positive term to which we may 
not frame a corresponding negative ; to man there corresponds not- 
man, to book not-book, to square not-square, to colour not-colour ; notr 
man is everything which is not man, and includes therefore not only 
the other animal species, but plants and minerals, books and insti- 
tutions, birth and immortality ; not-book includes all these but 
books, and man besides ; and so forth. The two ' contradictory ' 
terms (as they are called) comprise between them all that is ; 
nothing can be conceived, of which one or the other is not predi- 
cate ; and they divide the universe between them. What the 
positive term is, does not matter ; for whatever it be, the negative 
term covers everything else ; and therefore it may be expressed by 
a symbol ; let A represent any term, and not- A its contradictory ; 
we may then say that A and not-A between them make up all 
that is, or that there is nothing of which one or other may not be 
predicated. ' Everything is either A or not-A' 1 

1 This formula, ' Everything is either A or not-^4,' is sometimes given as 
the ' Law of Excluded Middle. '. The ' Law of Excluded Middle ' (cf. supra, 
p. 13) is that of two contradictory propositions one or other must be true ; 
they cannot both be false, and therefore any third or middle course between 
accepting one and accepting the other is excluded. It has been asked whether 
either of such contradictory propositions as Virtue is triangular and Virtue is 
not triangular need be accepted ; the former is clearly false, but the latter 
does not seem true. The answer is that if any one were to assert that virtue 
is triangular (as the Pythagoreans held justice to have the nature of a square) 
we should be right to contradict him ; but that no one who realizes virtue 
to be incapable of any spatial character at all would ever put to himself the 
alternatives, ' is virtue triangular or is it not ? ' and that to one who, not 
realizing this, asserted it to be triangular, the proper contradiction is that it 
has no figure. The case therefore furnishes no exception to the truth of the 
Law of Excluded Middle, provided the alternatives are not at the outset 
realized as nonsense ; but no one to whom they are nonsense would expect 



42 AN INTRODUCTION TO LOGIC [chap. 

Such negative terms as these do not really figure in our thought ; 
they are ' mere figments of logic ' x ; Aristotle long ago pointed 
out that ovK-avdpu>nos was not properly a name at all ; and he 
perhaps extended his countenance too much to it, when he said that, 
if we were to call it anything, we must call it a ' name indeter- 
minate ' (ovo/jia aoptcxTov) because, being the name of nothing posi- 
tive and in particular, it had a purely indeterminate signification; 
it was applicable equally to things existent and non-existent. 2 

The invention of such terms however is explained when we re- 
member the relation of a term to judgement. The latter, as we have 
seen, is the primitive and remains the complete act of thought, and 
terms are got by abstraction from it. Now the affirmative judge- 
ment ' All flesh is grass ' ma}'- be resolved into the terms flesh (the 
subject) and grass (the predicate affirmed of it) ; and the negative 
judgement ' Man is not a fly ' 3 into the terms man (the subject) 
and fly (the predicate denied of it). But since we do therein affirm 
that man is not a fly, it seems possible to say that the predicate, 
not a fly, is affirmed of man, as well as that the predicate fly is 
denied of him. This attempt to reduce negative and affirmative 
judgements to a common affirmative type, by throwing the negative 
into the predicate, is not really defensible, for the negative term 
not a fly does not signify the nature of anything, and so is not really 
a term ; it should, if it were a general term covering everything 
except the corresponding positive, be predicable of all subjects 
except flies in the same sense ; but there is no common character 
in all these which it is intended to signify. Hence, as we should not 
take the trouble to affirm of man nothing in particular, the only 
point of the judgement must lie in denying of him something in 
particular ; so that the meaning of the ' infinite ' judgement (as it 

to test by them the validity of the laws of thought ; for talking nonsense 
is not thinking. The objection to stating the Law of Excluded Middle in 
the form ' Everything is either A or not-^4 ' is this, that it seems to sanction 
the formation of nonsensical contradictories, such as we have examined, no 
less than of contradictories that are rational. Cf. also Bradley, Principles 
of Logic, I. v. §§ 23, 24. 

1 Stock, Deductive Logic, § 133. 

2 de Interpr. ii. 16 a 30-33 : the technical term in Latin is nomen infinitum, 
whence the English phrase ' infinite term ' is derived : but infinite means in 
this context indeterminate ; and for the sake of perspicuity, the latter word 
has been used in the text. 

8 Why hath not man a microscopic eye ? 

For this plain reason, man is not a fly. 

— Pope, Essay on Man, i. 193. 



ii] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 43 

is called) ' Man is not-a-fly ' lies in the negative judgement ' Man 
is-not a fly ', and it is clear that we have not resolved the negative 
into the affirmative form, when such affirmative can only be under- 
stood by restoration to the negative. 1 But it is out of such attempts 
that so-called purely negative terms like ' not-fly ' have arisen ; 
and it is only by understanding that the term A has been the pre- 
dicate of a negative judgement, that we can understand how the term 
not-A should ever have been formed. 

There are however certain negative terms which are not such 
mere figments of logic as the ' infinite terms ' considered above. 
Where the positive is not a general concrete term but is attributive, 
there the corresponding negative may be quite legitimate ; indeed 
the distinctions of positive, negative, and privative most properly 
apply not to all, but only to attributive terms, or to abstract terms 
founded upon these. 2 For all attributive terms imply a subject of 
which they may be predicated, and to which they refer that attribute 
which constitutes their meaning. Therefore even if the term be 
negative, it still suggests a subject which, lacking the attribute which 
the negative term excludes, is conceived as having some character 
instead. And here we have a basis of positive meaning to the nega- 
tive term ; for let A be a positive term ; then not-A will signify 
what a subject, which might be A, will be if it is not A. Thus intem- 
perate signifies what a man, who might be temperate, will be if he 
is not that ; uneven suggests what a line or surface, such as the sur- 
face of a road, will be if it is not even ; not-blue suggests what a 
thing which might be blue (that is, an object having some colour) 
will be if it has not that colour. The definiteness of the positive 
meaning which a negative term thus conveys will vary greatly, ac- 
cording to the range of alternative attributes which we conceive 
possible to a subject that might conceivably have possessed the 
attribute denied of it ; thus intemperate has a more definite meaning 
than not-blue, because when temperance is excluded, though there 
are many degrees of intemperance, yet they have more affinity with 
one another as opposed to temperance than have the remaining 
coiours as opposed to blue ; unruffled has a more definite meaning 

1 Cf. Arist. Metaph. A. vii. 1017 a 18 ovrat 8e Xeyerat Kai to fif] XevKov tlvai, on 
<5 o-vfx$e(iT]Ktv, eKflvo io-nv ('And in this sense the not-white is said to be, 
because that is which is not white') — i.e. to be not white cannot itself con- 
stitute the being of anything, but that may have a positive being of which 
we can deny that it is white. 

8 Cf. infra, p. 45. 



44 AN INTRODUCTION TO LOGIC [chap. 

still, for a surface which is not in any way ruffled can only be 
smooth. 1 

It has been alleged that ' not-blue ' does not necessarily imply 
' coloured in some other way than blue ', nor ' not-even ' a surface 
of another kind than even ; that it is as true to say of banter that it 
is not blue as of a buttercup, and that larceny is as much not-even as 
Lombard Street. But such a contention misinterprets our thought. 
Just as privative terms imply the absence of an attribute from 
a subject that possessed or should have possessed it, and therefore 
must convey a notion of what the subject consequently is without 
that attribute, so negative terms (at any rate when they are not 
mere figments of logic) imply the absence of an attribute from 
a subject that might conceivably have possessed it, and therefore 
convey a notion of what the subject is instead. The attribute 
which a negative term excludes belongs to a genus of attributes 
(as blue belongs to the genus colour, or prudence to the genus 
feature of human character, or square to the genus figure) ; and 
if a subject is unsusceptible of any attribute within that genus, we 
should not be at pains to deny of it some particular attribute 
therein ; since the soul for example has no figure, we should not 
say that it is not-square ; since furniture has no feature of human 
character, we should not call a towel-horse imprudent. The nega- 
tive term is only used of what must have some attribute within its 
genus ; and this genus furnishes a substratum of positive meaning 
to the negative term ; not-blue does mean ' coloured not with blue ' 
and not-even ' having a surface which is uneven ' . 2 

1 The old Greek proverb will illustrate the point here — e'a-dXoi pev yap 
dTrAcof, navTo8(ma>s 8e kcikoL (' Men are good in one way, but bad in many '). 

2 The genus within which any attribute falls, or the subjects susceptible 
of some attribute within that genus, may be called with de Morgan (Formal 
Logic, p. 41) a 'limited universe' ; thus blue is a predicate in the universe 
of colour, or of coloured objects : prudent in the universe of human character. 
A positive term and its corresponding negative (e.g. blue and not-blue) may 
then be said to divide between them not indeed the whole universe, but the 
limited universe or whole of things to which they belong ; the members of 
this limited universe have a positive common character, which gives the 
negative term a positive meaning; whereas if we consider the whole universe, 
there is no positive character common to all things included in it, except 
the character of being — which, as Aristotle pointed out, considered in itself 
and not as realized in some special mode of being, is not a significant term : 
cf. p. 50 infra, and de Interp. iii. 16 b 22. Such a ' limited universe ' is some- 
times called an ' universe of discourse ' ; but this only means the limited 
whole which is the subject of discourse, and its limits — e.g. those of the 
whole within which blue and non-blue fall — are determined by the nature 
of things, not by our discoursing of it. 



n] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 45 

Many negative terms indeed are not themselves attributives, but 
are abstracts which presuppose an attributive ; and what has been 
said of negative attributives is confirmed by the fact that these 
abstracts — such as injustice, inequality, non-intervention — are very 
positive in their meaning. ' Injustice ' does not mean whatever is 
not justice (such as ' accidence and adjectives and names of Jewish 
kings '), but the quality of being unjust ; ' inequality ' means the 
relation of being unequal ; ' non-intervention ' the conduct of the non- 
intervening. Abstract negative terms like not-equality or not-colour 
are as unreal as concrete negative terms like not-Socrates or not-book. 

It may be asked, if all negative terms (and the same is true of 
privative) have a positive meaning, what is the use of the distinction 
between them ? The answer is as follows. First, with regard to 
the distinction of positive and privative terms ; there are some states 
which can only be understood as the privation of a positive state : 
deafness would have no meaning, but for our knowing what it is to 
hear ; we cannot think of a body as desiccated, except we think 
of it as having first contained moisture. 1 

Secondly, with regard to the distinction between positive and 
negative terms : there is a real difference between a term which 
signifies one definite attribute, and a term which signifies any attri- 
bute within a genus except one; the latter is in most cases" compara- 
tively indeterminate and uninstructive ; e. g. vertebrate signifies a 

1 These two examples are not quite parallel. A notion of deafness can be 
had by any one who knows what hearing is. A notion of ' desiccated ' cannot 
be had by any one who knows what moisture is, but he must also know 
what dryness is. ' Desiccated ' is a privative term, because it means a dryness 
due to the withdrawal of moisture previously present ; but ' dry ' is just as 
positive a term as ' moist '. It sometimes happens, with two mutually 
exclusive alternatives like dry and moist, that men dispute whether or not 
both are positive. Some philosophers have maintained that pain is merely 
the privation of pleasure, and evil the privation of good; others, that pain 
and evil are just as positive as good and pleasure. In these cases, it will be 
also in dispute, whether or not pain and evil are privative terms. But the 
dispute arises from our uncertainty how to think about the things ; and so 
furnishes another illustration of what has been pointed out in the text, that 
logical distinctions of terms reflect and are based upon distinctions in the 
things thought about. 

2 Sometimes, as Miss Augusta Klein has pointed out to me, the positive 
term may be less determinate in meaning ; there are more ways of being 
coloured than colourless, of being fed than unfed. Here obviously the negative 
term has a positive meaning ; we know the look of a colourless fluid^ and 
an unfed animal is in a very positive state. If it be said that ' unfed ' has 
a meaning also for those who do not know what state an animal is in which 
has not been fed, we may reply that for them it means ' which has not been 
fed ', and so mere negation is shown to belong to judgement, as stated above. 



46 AN INTRODUCTION TO LOGIC [chap. 

definite anatomical structure ; invertebrate signifies an animal struc- 
ture which is not vertebrate, but fails to characterize it further. 
Positive terms are positive directly and precisely, negative terms 
indirectly and for the most part vaguely. This distinction is impor- 
tant, and we are therefore justified in calling attention to it ; 
it will be seen for example presently * to be one of the rules of 
definition to state what a thing is, not what it is not ; this is best 
expressed by the injunction to avoid, as far as possible, negative 
terms ; and there is no way in which the point of this instruction 
could be so well conveyed as by the help of the distinction of negative 
and positive terms. 

[The doctrine about negative terms impugned in the foregoing 
paragraphs furnishes a good example of the dangers that beset 
a purely formal logic. If we regard only the form of a proposition, 
' A is not B ' (in which the terms are A and B), we may ' permute ' it 
to the form ' A is not-Z? ' (in which the terms are A and not-B) ; and 
we may formally regard A, B and not-B all equally as terms. But 
whether not-B is a genuine predicate, and the proposition ' A is 
not-B ' really affirms anything, will depend upon the matter of the 
proposition — upon what kind of a term B stands for. In respect of 
form, B has a corresponding negative not-B ; but we cannot tell by 
considering the form alone whether any thought or notion of not-B 
is possible. It may be noted also that the Law of Contradiction 
should not be formulated symbolically as ' A cannot be both B and 
not-B ', or ' A cannot be not- A ', but rather as ' A cannot both be and 
not be B ', or ' A cannot not be A'. For if not-B is something positive 
other than B, or not- A than A, what is B or A may have such other 
positive character besides. If ' to be not-B ' is necessarily incon- 
sistent with being B, it is neither more nor less than ' not to be B '.] 

We have still to notice the distinction of univocal, equivocal, and 
analogous terms. Univocal terms are terms with only one meaning, 
so that they are used in the same sense of every subject of which 
they are used at all : equivocal (or ambiguous) terms are terms 
with more than one meaning, so that they may be used of different 
subjects in different senses — e.g. fair, as used of a complexion and 
of a bargain : analogous terms are terms which have more than 
one meaning, but the meanings have a certain degree of identity 
or correspondence — e. g. we speak of the foot of a man and the 
foot of a mountain, meaning different things, but in both cases 
that on which something stands. We ought in strictness to regard 

1 Cf. infra, p. 98. 



ii] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 41 

this distinction as one not in terms but in the use of terms ; for 
fair is used univocally of all fair complexions, and is only equivocal 
when we use it at once in different senses. All proper names be- 
longing to more than one individual are used equivocally of such 
different individuals. 

[The history of the words univocal, equivocal, and analogous 
will illustrate the tendency to treat Logic from the standpoint of 
an affair of names. The Aristotelian distinction already alluded 
to (p. 31) between avvutw^a and oixcawfjia was one of things. Uni- 
vocum and equivocum are merely translations of (twwvv^ov and 
6fxu)vv[xov, and they were defined in the same way (cf. Cracken- 
thorpe's Logic, Bk. II. c. i. ' Aequivoca ita describuntur : aequi- 
voca sunt quorum nomen solum est commune, ratio vero illius 
nominis est alia atque alia.' c. ii. ' Univoca describuntur in hunc 
modum : univoca sunt res vel entia quorum nomen est commune, 
et ratio illius nominis est una et eadem in omnibus quibus nomen 
convenit '). Similarly, it would have been not the word ' foot ', but 
the man's and the mountain's foot that would have been called 
analogous. In the sense in which terms are not words, but the objects 
of thought intended by the words, we might still say that equivocal 
terms are different objects of thought with the same name, rather 
than the same name with different meanings. But in English usage 
the distinction of names has really displaced that of things : we do 
not even (except for the word analogous) retain both, like the Latin, 
when it was said that ' aequivoca ' were either ' aequivocantia, 
ipsae voces aequivocae ', or ' aequivocata, res ipsae per illam vocem 
significatae '. And even in Aristotle, Rheb. y. ii. 2. 1405 a 1, we find 
an example of the use which calls words synonymous. Cf. also 
Journal of Hellenic Studies, vol. xxix. pp. 28 and 32, where avvwvvfxov 
ovojxa (= synonymous noun) is reported from a school tablet found 
in Egypt and belonging apparently to the third century a. d.] 



CHAPTER III 
OF THE CATEGORIES 

The distinctions between terms discussed in the last chapter are 
not primarily grammatical, like the distinction between substantive 
and adjective (though here and there, as we saw, the forms of 
language have affected the mode in which they have been drawn) ; 
nor do they belong to any special science, like the use in chemistry of 
names in -um to signify metals, and names in -ide to signify com- 
pounds. They may be illustrated from all sciences, and are based 
on certain features that reveal themselves to reflection about any 
subject whatever ; and that is why they belong to Logic. But 
they involve not only features of thinking, like attribution, affirma- 
tion, negation, but also features in what is thought of ; and so far 
they belong to Logic only because the thought which Logic studies 
is thought about things, and we cannot separate the study of 
thought from the study of the most general nature of things thought 
about — such nature as they must have, if they are to be objects of 
thought at all. It is of special importance to remember this in con- 
sidering the Aristotelian doctrine of Categories, out of which some of 
the preceding distinctions take their rise. The Categories present 
a logical, but they present also a real distinction : i. e. a distinction 
in the nature of the reality about which we think, as well as in our 
manner of thinking about it. 

We saw x that reflection on the form of judgement 'A is B ' 
leads us to ask in what sense one thing is another ; that sometimes 
it is meant that the predicate character, B-ness, is incidental to 
the subject A, sometimes that to be A is essentially to be B ; thus 
1 The Emperor is captured ' does not mean that to be Emperor is 
to be captured, but ' Man is an animal ' does mean that to be a man 
is to be an animal. Out of such reflection arose the doctrine of the 
Categories. 2 

The word category, Karriyopia, means predicate 3 ; but its predi- 

1 Cf. supra, pp. 22-24. 2 Cf. Arist. Metaph. A. vii. 

8 The Latin equivalent is Praedicamentum, and Aristotle occasionally writes 
Karriyoprjfia instead of Karriyopia, which means predication as well as pre- 
dicate : v. Bonitz, Index Aristot., s. vv. Karrjyopr/pa and Karriyopia. 



OF THE CATEGORIES 



49 



cate is what any subject is ; and the categories may be described as 
a list of predicates, one or other of which declares the mode of its 
essential being belonging to any subject that exists. In Aristotle's 
complete list there are ten, viz. 



ovaCa 


substantia 


substance 


irocrov 


quantitas 


quantity 


TTOLOV 


qualitas 


quality 


7rpoy tl 


relatio 


relation 


TTOV 


ubi 


place 


TTore 


quando 


time 


K^lcrdai. 


situs 


situation 


Ixew 


habitus 


state 


7roieu> 


actio 


action 


itaaytiv 


passio 


passion (being acted on) 



These Aristotle calls both ' kinds of predicate ', yivr\ tS>v Kar^yopi&v, 
and ' kinds of being ', yevq tG>v ovtcov. We must examine the 
latter phrase first, if we wish to understand his doctrine. 

In the form of proposition ' A is B ', as just observed, the predi- 
cate does not seem equally in all cases to declare what the subject is. 
A man is an animal, and a man is in the kitchen ; Tray is a dog, and 
Tray is happy now ; a musician is an artist, and a musician is break- 
ing my hurdy-gurdy : if we look at these judgements, we shall admit 
that the second does not tell us what a man is so much as the first ; 
that the third is a fuller answer than the fourth to the question 
1 What is Tray ? ' ; and that the fifth is a fuller answer than the 
sixth to the question ' What is a musician ? '. In Aristotle's phrase 
the first, third, and fifth of them declare what their respective sub- 
jects are nad' avro, or per se : the second, fourth, and sixth what 
they are Kara o-v/i/3e/3jjKoy, or per accidens. In other words, the 
predicate is in the one case of the essence of the subject, and ' covers 
its whole being ' l , and the subject could not exist at all without its 
being predicable of him ; in the other case it is an accident of the 
subject. What is predicated of a subject kclO' avro tells you what 
it is necessarily, permanently and constitutively 2 ; what is predi- 
cated of it Kara avnficfir]K6$ tells you indeed something about it, but 
something less important, and perhaps unnecessary, to its being — 

1 Cf. supra, p. 23. 

2 This is not a complete statement of the meanings in which, according 
to Aristotle, a predicate may be said to belong to a subject ko6' avro ; but 
it is, I think, a sufficient account of the sense in which the expression is 
used in this connexion. 

1779 B 



50 AN INTRODUCTION TO LOGIC [chap. 

something of which it could be divested, and still remain the thing 
it is, at least something not constitutive of it as such a subject. 

The ultimate subject of predication is the concrete individual 
thing — you, Socrates, Bucephalus, or the stone in your signet- 
ring 1 ; and if you ask of this what essentially it is, you will have to 
specify in your answer some kind of substance 2 ; you are a man, 
Bucephalus is a horse, the stone in your signet-ring is an agate. All 
these — man, horse, agate — are so many different substances ; in 
saying what you, Bucephalus, or the stone in your signet-ring is 
essentially, or per se, these are the answers I must give ; their 
essential being, therefore, is to be some kind of substance, and the 
predicates which give their essential being are in the category of sub- 
stance. But if I ask what is a substance, I cannot find any more 
general character under which to bring that, as I bring Bucephalus, 
in declaring what he is, under horse, and horse, in declaring what it 
is, under substance. Of substance I can say that it is a kind of 
being ; for substances are one kind of things that are ; but it is of 
no use to treat mere being as a genus, of which substances are a 
species, for to being considered in itself, and not as a determinate 
way of being (e. g. being a substance), I can attach no meaning. 

On the other hand, there are a great many subjects, about which, 
if asked what essentially they are, I could not possibly say that 
they are substances. Large, loud, blue, heavier, here, yesterday, 
fever, horizontal, running, defeat, virtue — each of these is some- 
thing, or nothing could be said to be it : but what are they ? Directly 
or indirectly they all presuppose substances ; if there were no 
animals, there would be no fever : if no fighters, no one could be 
defeated. But they are something incident to substances, attri- 
butes or relations and not things. To say that they are attributes, 
however, only declares their relation to something else, their de- 
pendence ; it does not declare what they are in themselves. If we 

1 This is the true meaning of the statement in Cat. iii. l b 10 orav htpav 

k<i#' erepov <ar r]y oprjTni cos xaB' VTTOKeipivov, o<rn Kara tov Kmr}yopnvp,ivov Xeytrai, 

TTiivm Ka\ Kara t<<v vnoKfitxevov prjfirjaerai ('When one thing is predicated of 
another as of a subject de quo, all that is asserted of the predicate will be 
asserted of the subject as well ') — a statement sometimes erroneously quoted 
as equivalent to the Dictum de Omni et Nullo. Cf. infra, c. xiv. p. 297 n. 

2 But concrete things sometimes receive names implying their possession 
of predicates in some other category than that of substance ; e. g. a threshold 
is a concrete thing, but in calling it a threshold I do not give its substance : 
to do that, I should have to say that it was a stone. It is a threshold because 
it is a stone in a certain situation. 



in] OF THE CATEGORIES 51 

ask that, we shall find ourselves ultimately giving as an answer some 
one of the other categories. 

Thus I may say that ' yesterday was wet ' : but that does not tell 
any one the nature of yesterday in itself. But if I say ' yesterday is 
the day before that on which I am now speaking ', I explain what 
yesterday in itself is. And if next I am asked ' What is that ? ', I 
should reply that it is a certain date or time ; and there I must stop. 
The kind of being then which belongs to yesterday is not being a 
substance, but being a time. Similarly blue is a colour, and colour 
is a quality ; loud also is a quality, and virtue ; so that their being 
is being qualities ; that is what essentially they are. Large is a 
size, i. e. to be large is to be of a certain quantity ; to be heavier is 
to be in a certain relation, here is a place, fever is a state of the body, 
horizontal a situation, running an action, defeat a being acted on. 

There. is nothing then, according to Aristotle, that exists or can 
be thought of, which is not either a substance, or a quality, or a 
quantity, or in some other of the categories. One or other of them 
is predicable of everything ; and they cannot be further reduced, 
or brought under any common head. 1 A quality is not a quantity, 
a time not a place, to do is not to be done to, nor any of these a 
situation : and so forth. It might be thought that state is hardly 
distinguishable from quality, nor situation from place. But they 
are not really the same. A state is something which characterizes 
a whole through the condition of its parts ; thus we call a man 
shod, because he has shoes on his feet ; or healthy, because each 
part of his body is functioning rightly ; the healthiness of his body 
as a whole does not mean that each part of it is qualified alike, 
nor his being shod that every part of him has shoes on. A quality, 
on the other hand, is comparatively simple, and if it characterizes 

1 As a matter of fact, however, the category of relation is not equally 
excluded by the others ; and Xenocrates is said to have reduced them all to 
Substance and Relation. In doing this he would not have effected a real 
simplification, any more than if they were all reduced to Being ; for time, 
place, action, &c, involve irreducibly different kinds of relation ; and mere 
relation, which is not any definite kind of relation, is almost as barren a con- 
cept as mere being. Aristotle probably erected relational predicates into 
a separate class because they tell us less than others what a subject is (cf. 
Metaph. N. i. 1088 a 23). 'Six feet high' would be in the category of irna-nv : 
'taller than his neighbour' in that of 7t/jo? n ; it gives more information 
about what a man is to say that he is six feet high, than that he is taller 
than his neighbour. The latter predicate may change when his neighbour 
changes ; the former only by a change in the man himself. The former 
involves relation also ; but the latter is more plainly and purely relational. 

£2 



52 AN INTRODUCTION TO LOGIC [chap. 

a whole, does so through being present in the same way in its various 
parts ; if a whole surface is blue, that is because the various parts 
of it exhibit the same colour, and if a trader's stock is sweet, that 
is because the things it is composed of are severally sweet. A state, 
therefore, is more complex than a quality ; and so it is with situa- 
tion and place. 'Upside down', 'horizontal', ' sitting', 'standing', 
are in the category of situation — predicates which determine not 
where a thing is, but its ' lie ' or position there. Without place 
there could be no situation ; but you do not determine a thing's 
situation by assigning its place. 

The categories, therefore, are a list of predicates, one or other of 
which must in the last resort be affirmed of any subject, if we ask 
what in itself it is. They are yivr) t5»v Kar^yopiSiv, kinds of predi- 
cate, and equally yhr\ tS>v ovtcov — the kinds of being which we 
recognize, the kinds (if we may put it so) of what things are. 1 These 
things, the ultimate subjects of predication, are individual sub- 
stances, and the categories do not give a classification of these, as 
is given when things are said to be animal, vegetable, or mineral ; 
they give a classification of the kinds of being displayed in and 
predicable of them. Those predicates express most fully the being 
of an individual substance which are in the category of substance, 
like man, rose, gold ; they tell us what essentially it is. But every 
predicate tells us what in some sense it is, and the kinds of being 
displayed in what else it is are the other categories beside substance. 
Thus the distinction between substance and the other categories 
is a prominent feature of the doctrine ; for all the others presuppose 
and are incidental to substance, since predicates belonging to them 
are displayed in the being of individual substances. Terms in these 
other categories may be subjects of predication, as when we say 
that blue is a colour, and that wisdom is rare; but they exist not inde- 
pendently but in concrete individuals. There is no blue except the 
blue of the sea or the sky, of a larkspur or a gentian, &c. ; no wisdom, 
except that of the wise. Concrete individual things are substances 
in the strict and fullest sense. But what is predicated of them is 

1 Cf. At. Met. A. vii, and Apelt, Beitriige zur Geschichte der griechischen 
Philosophie, III. Die Kategorieenlehre des Aristoteles. In the expression yivr) 
rav KaT>]yoptr~.>i>, ' kinds of predicate,' Kar^ynpi> refers no doubt to the predi- 
cates of things, these predicates falling under the kinds enumerated, not to 
the heads or most general predicates under which these fall. Hence the 
concrete individual is not in any category, since it is not what any further 
subject is (cf. Cat. V. 3 a 36 «7ro p-iv yap rrjs TrpoiTrjs ovirias ovdefiia e'crri KiiTrjyopia, 
'for 6rst substances furnish no predicates'). 



in] OF THE CATEGORIES 53 

partly in the category of substance, partly in the other categories. 
We have here that distinction between first and second substances 
which once occupied so much of the attention of philosophers and 
theologians. 1 

First substances are individuals like Socrates or Cicero ; second 
substances are the kinds of these, and terms are in the category of 
substance which, like man, horse, peppermint, parsley, tell what 
kind of thing an individual is. All else that is said of an individual 
tells only some quality or state that characterizes him, his activity 
or situation, his relation to others, &c, and is therefore a predicate 
in one of the remaining categories. 

Undoubtedly it is here that the chief difficulty in Aristotle's 
conception lies. But the difficulties are not gratuitous ; they 
arise naturally in our reflection upon the nature of things. 2 We 
naturally incline to think, in considering any concrete individual, 
that out of all that characterizes it some part is more essential than 
another, goes more to make it what it is. This we call its kind, 
and Aristotle called it also its substance ; and language contains 
names that are evidence of this, kind-names like man, horse, gold. 
It is indeed very hard to say exactly what constitutes the kind ; 
kind-names, as we shall see later, present special obstacles to 
definition ; and a positive account of the substance of an individual 
seems beyond us. But negatively there is a great deal which we 
should say does not belong to the substance — the place where the 
individual is, what it momentarily does or suffers, all in fact that 
we can refer to other categories. All these we tend to think of as 
attributes which the individual has, but that it can exist irrespec- 
tively of them : whereas, irrespectively of its kind, it would no 
longer be at all. And yet the kind is universal ; it is predicated of 
more things than one ; Socrates, Plato, and millions more are men ; 
the lumps of iron in the world are uncountable. Hence follow two 
lines of reflection. 

First, because the kind, though universal, is at the same time 
more substantial than the other predicates of an individual are- 
more concrete, in fact, than they— the kind, or ' second substance ', 
comes to be thought of as having some special claim to independent 
existence. Other modes of being, other predicates, depend on it ; 
but it is thought of as depending on nothing else for its existence. 

1 This mode of expressing the distinction comes from Cat. v. 2 a 11-19. 
8 Cf. supra, pp. 28, 35. 



54 AN INTRODUCTION TO LOGIC [chap. 

True that we only find the kind realized in some concrete indi- 
vidual ; nevertheless it is not a mere attribute of the concrete 
individual, as are predicates in other categories. And some have 
held that these ' second substances ', though displayed in divers 
individuals, are each not only genuinely one and single, but 
real, whether there be any concrete individual of their kind or 
not. 1 

But secondly, because the kind is universal, it is predicated of 
the concrete individual, like predicates in other categories. And 
as the individual is something which has them, so it is something 
to which its kind is attributed. It cannot be identified with its 
kind ; for then there would be nothing to distinguish one indi- 
vidual from another. Man is predicated equally of Socrates and 
Plato, and if each as an individual substance were just man, Socrates 
would be the same as Plato. Therefore we must look elsewhere for 
what distinguishes them. If we find it in the other predicates of 
the concrete individual, and say that he is the kind plus all his par- 
ticular attributes, we resolve the individual into an assemblage of 
universal predicates. If we do not do this, but suppose that his 
kind and all his particular attributes as well belong to the individual, 
the individual, to which they all belong, becomes a mere uncha- 
racterized something. For in saying what it is, we should merely 
assign to it a fresh predicate ; whereas we want to get not at its 
predicates but at that which ' has ' them. Thus we should reach 
a new way of considering the subject of predication. Originally 
it was the concrete individual, Socrates or Plato ; but of what he is, 
one part was distinguished as what he is essentially, and the rest 
reduced to be attributes or ' accidents ' of him, not necessary to his 
being, and not to be included in an account of his essence. Now, 
what he is essentially is also reduced to the position of attribute and 
mere predicate, and the subject becomes a mere subject of which as 
such nothing more can be said except that it exists and is unique in 
each individual. This mere subject of predicates, which cannot in 
itself be described as specifically of this kind or of that, Aristotle 
called matter. 2 We only know matter in conjunction with form ; 
bricks and timber are the matter or material of which a house is 
built, but a brick is in turn clay to which a certain form has been 
given ; clay again is matter of a certain form ; but matter by itself — 

1 Cf. supra, p. 32. 

2 Cf. Ar. Phys. a. vii. 191» 8-12, Z. iii. 1029 a 23. 



in] OF THE CATEGORIES 55 

that which is found in various forms, but has no form of its own — 
is unknowable. 1 

It may be questioned whether Aristotle was justified in his 
use of the conception of matter. He started by thinking of the 
material out of which a thing is made. Now the material of any- 
thing is always something quite determinate. Economists know 
in how many ways the products of one industry are ' raw material ' 
to another ; but the raw material which is rawest, i. e. which has 
itself been least worked up, is still matter of a perfectly definite 
kind. Timber is the raw material of the carpenter, but trees of the 
lumberman : pig iron of the ironmaster, but iron ore of the smelter ; 
and neither trees nor iron ore are any nearer being formless matter 
than timber or pig iron. In these cases, the matter (or material) 
is a concrete thing, in a different state no doubt from that into which 
it is worked up, but perfectly familiar to us as existing in that state ; 
but in the philosophical antithesis, the matter is not a concrete thing 
at all, is in no state, is quite unfamiliar and indeed incapable of 
being known to us as such ; and this relation of matter to form has 
no real analogy with the relation of matter to what is made out of it 
in the arts. 2 It is true that in using the metaphysical analysis of the 
concrete individual into matter and form in order to find in different 
individuals different subjects of the same form, I may not at first 
sight seem to need the conception of a quite indeterminate matter. 
The matter of a house, says Aristotle, is stones and timber ; the 
form — what makes the stones and timber the matter of a house — 
is ' to be a shelter for men and goods '. Stones and timber are 
determinate material, as ' to be a shelter for men and goods ' is a 
determinate form. But suppose two houses built to the same 
specification ; what distinguishes them ? We say, that they are 
built of different materials — different stones and timbers. But 
what distinguishes these ? Not their form, since ex hypothesi they 
are of the same form. We may say that they just are different, 
and leave it at that. But if we are going to use the analysis into 
matter and form to explain their difference, since they are not dis- 
tinguished by what they are, their predicates, we must find the ground 
of their difference in the difference of the matter ; and this dis- 
tinguishing matter must be taken as something divested of predi- 

1 fj v\ n ayvoxnos *«#' uvttjv, Met. Z. x. 1036 a 8. Cf. supra, p. 35. 

2 In the foregoing criticism I am particularly indebted to lectures of 
Professor Cook Wilson. 



56 AN INTRODUCTION TO LOGIC [chap. 

cates, because in respect of predicates they are the same. The 
outcome of this line of reflection would seem to be that what makes 
possible different individuals of the same kind is the indeterminate 
matter of which what they are is predicated ; and this at times 
Aristotle says, 1 and he admits that in one sense matter is substance. 
But the corollary, that the nature of Socrates, as predicated of this 
matter, is something that may be common to another, and universal, 
he does not draw ; and it would seem to be his considered doctrine 
in the Metaphysics (however hard to reooncile with some of his 
other statements) that what makes Socrates Socrates is his form, 
or what he is, and not the matter in which this form is realized. 2 
This form is really his substance, or substantial being ; and it is 
neither merely the specific form of men, nor does it include all that 
can be predicated of him ; but we are not told how to distinguish 
it from predicates in the other categories. We need not pursue the 
Aristotelian doctrine further ; so much has been said in order to 
illustrate the difficulty of determining what is in the category of 
Substance. We start with the concrete individual, and draw a dis- 
tinction, among all that can be predicated of him, between that 
which declares what he is essentially, and is his substance, or in the 
category of substance, and that which declares about him some- 
thing not essential, and belonging to one of the other categories. 
But a predicate in the category of substance seems universal, as in 
any other ; and if it belongs to several individuals, these must be 
distinguished otherwise than by it ; hence the tendency to say that 
what individualizes is material substance, not universal, nor capable 
of figuring as predicate. But then the kind, what is predicated of 
individuals in the category of substance, ceases to be essential to 
them, for they would still be, and be individually different, without it. 
Thus the attempt to distinguish what is from what is not essential 
to the individual must either be abandoned in a doctrine of indi- 
vidual forms — for if we suppose that there is something about 
Socrates which makes him Socrates, we have no principle on which 
to select this from among the sum total of all his predicates ; or else 
it leads us to distinguish the individual both from his essential and 
from his non-essential attributes, and then he is individualized by 

1 Cf . Met. Z. viii. 1034 a 5-8 ; and v. Bonitz, Index Arist. s. v. vXt}, 786 a 52-58. 
But individuality cannot be explained by difference of mere matter: cf. infra, 
p. 90. 

2 Cf. Met. Z. x. 1035 b 27-1036 a 9, xiii. 1038 b 8-15; H. i. 1042 a 28-9. But 
one cannot really support any statement on the point except by reference 
to his whole discussion. 



in] OF THE CATEGORIES 67 

neither, and neither is essential to his being the very individual he is. 
The ' first substance ' is at the outset the whole concrete individual. 
We try to distinguish within what it is what is essential to it, and 
we only really find what is essential to its being of a certain kind. 
Taking this as what is essential to it, we regard it as constituting 
the individual, and so as possessing a substantiality of its own and 
being a sort of ' second substance '. But then we find that a second 
substance will not individualize. 

We shall be met later with the same difficulty, when we consider 
the doctrine of the Predicables, and the problem of definition. The 
metaphysical issue raised is fundamental. But for the present it is 
enough to have called attention to it. Logical and metaphysical 
problems have a common root. We cannot reflect upon the being 
which is asserted in all predication, without asking how things can 
be conceived to exist. And it may readily be shown, with regard 
to the different categories in particular, that we could not use predi- 
cates in them, except so far as we conceived subjects to exist in certain 
ways. Thus no predicates in the category of quantity can be used 
of the mind, because the mind is not extended ; if it were, it might 
have a capacity of 3 or 30 cubic feet, and an area and maximum 
diameter ; since it is not, we cannot apply such epithets to it at all ; 
and it is only because the existence of material things is existence 
in space, that we can call them large or small, three feet square or 
four feet long. In the same way, if it were not for the fact that 
the world is spatial, there could be no predicates in the category of 
place ; and space also renders possible predication in the category 
of situation ; for it contains the distinctions of up and down, front 
and back, right and left ; and it allows the parts of a body to alter 
their relations to certain fixed points above and below, behind and 
before, to the left and right of them, while the whole body remains 
within the same limits. This is what happens when a man lies on 
the sofa where he was formerly sitting, or when an hour-glass is 
inverted on the table. And a perfectly homogeneous sphere, though 
it may change its place, can be situated only in one way ; and if 
we are to distinguish a right and wrong way up in it, we must mark 
or single out some point in the circumference, whereby it ceases to 
be perfectly homogeneous ; and this again illustrates how the dis- 
tinction of categories arises out of the distinguishable modes of 
being in things. For it is because it is a figure of a certain kind, 
that such a sphere does not admit of the same varieties of situation 



58 AN INTRODUCTION TO LOGIC [chap. 

as a cylinder ; and because it does not admit of these, they cannot 
be predicated of it ; and if nothing could be perceived or imagined 
to admit of them, predicates in the category of situation, and 
therefore the category of situation, would not exist. Again, there 
are predicates in iroielv and -nda-xetv because things act one on 
another ; and the two categories are distinguishable because there 
are two terms, agent and patient, in all causal interaction. And 
the different tenses of verbs, which make a difference to a predica- 
tion in time, though it remains in the same category of irotelv or 
ttcktxciv, e'xei^ or Keladai, 1 presuppose that things exist in time ; 
otherwise, how could we distinguish the meanings of vytaivti and 
vytavev, vapulat and vapulabit, vivit and vixit, sits and sat ? Of 
that which had no continuous existence through differences of time, 
predication would be possible only for a moment in the present. But 
reciprocally, as we could not predicate in these categories unless 
things existed in certain ways — as substances, with qualities, ex- 
tended in space, persisting in time, &c. — so we cannot predicate 
about things except in one or other category ; in other words, if 
we think of anything, we must think it to be determined in one or 
another of these ways. 2 That which was not conceived as a sub- 
stance, or a quality, or a state, and so forth, would not be conceived 
at all ; and a concrete thing that was no substance, had no quality 
or state, and so forth, would be just nothing. And therefore the 
consideration of these distinctions belongs to logic, since the thought 
of them is involved in our thought about objects in general ; and 
though logic is not interested in the indefinite variety of existing 
qualities — blue, green, sour, shrill, soft, &c. — (because a substance, in 
order to be a substance, need not have any one of these qualities in 
particular, but only one or other) yet it is interested in the category 
of quality, or in noticing that a substance must have some quality 
or other : in the category of relation, or in noticing that it must 
stand in relations to other things : and so on. 

1 i.e. action or being acted on, state or situation. It is to be observed that 
the predicate of the same proposition may determine its subject in more 
than one category. In the proposition ' The other disciple did outrun Peter ' 
the predicate is in the category of time, for the past is a time, and the event 
is referred to the past : and of action, for running is an activity : and of 
relation, for ' faster than Peter ' is a relation. But of course, if we distinguish 
these different elements in the predicate, we can refer them, considered 
separately, to different categories. 

2 It is not necessary, however, to hold that Aristotle's list of categories is 
complete. 



in] OF THE CATEGORIES 59 

The problem underlying Aristotle's doctrine of Categories may be 
expressed thus — to discover the forms of existence which must be 
realized in some specific way in the actual existence of anything 
whatsoever. His classification may exhibit defects, but the impor- 
tance of his undertaking must be admitted. And many of the 
distinctions between terms insisted on by those who attach least 
importance to the Aristotelian doctrine of Categories express an 
attempt to solve part of the problem which he was attacking, and 
are derived from his doctrine. Those distinctions, as was pointed 
out in the last chapter, rest upon certain fundamental features of 
the existence which we conceive the objects of our thought to have. 
The distinction between singular and general concrete terms corre- 
sponds in the main to that between irpu>Trj ovcrCa, the concrete 
individual, and predicates in the category of substance ; for the 
most noticeable of general concrete terms are in the category of 
substance, as man, stone, or beast, though some (which might be 
called substantives oflin attributive kind) are in other categories, 
as, for instance, officer and organist. The distinction between con- 
crete and abstract terms corresponds roughly to the distinction 
between substance and the other categories. That relative terms are 
predicates in the category of relation is plain. The attention paid to 
collective terms reminds us that we can consider not only things 
severally, but what they are in certain groupings or combinations ; 
and the distinction between quality and state involves the same fact. 1 
The logical divisions of terms rest on differences apprehended in the 
being of things ; this is apt to be overlooked when the subject is 
approached from the side of names ; Aristotle's doctrine of Categories 
has this advantage, that throughout it fixes our attention on things. 

[The Aristotelian doctrine of Categories bulks large in the history 
of Logic ; such conceptions are instruments of thought ; the instru- 
ments forged by one generation are handed on to the next, and 
affect subsequent thinking. On that account alone therefore it is 
fair to give some attention to it ; but it is still valuable as serving 
to express and distinguish certain important features recognized by 
our thought about things. That a quality is not a quantity is a 
truth which those overlook who think that sound can be a wave- 
length in the vibration of the air ; they forget that it is not possible 
to define terms of one category by another. 2 Moreover a conception 

1 It is not meant that collective terms are in the category of State. 

2 Except as terms in a derivative category involve terms in those from 
which it is derived. 



60 AN INTRODUCTION TO LOGIC [chap. 

[of categories not very far removed from that of Aristotle has, 
through Kant and Hegel, become one of the chief doctrines of 
modern metaphysics. 

These admissions do not bind us to consider Aristotle's list as 
perfect. One important remark on it would perhaps hardly have 
been regarded by him as a criticism. The different categories are 
not all equally distinct or ultimate. Thus the distinction between 
Ttov 1 and 7rore 2 is far more fundamental than that between -noulv 3 and 
irdaxzt-v- 4 A thing need not have a place because it has duration, 
nor can any one doubt under which category such predicates as ' at 
home ' and ' belated ' respectively fall. But to be acted on implies 
something acting ; indeed, if action and reaction are equal and 
opposite, for a thing to be acted on implies that it acts itself ; and 
it is often difficult to say to which of these categories a predicate is 
to be referred. A ship travels : are we to attribute the motion to 
the ship, and say that she acts, or to the engines, and say that she 
is acted on ? or shall we say that the engines in turn are acted on 
by steam ? Aristotle in a measure recognized the mutual implication 
of these two categories, for in one place he includes them together 
under the single term kiVtjo-i?. 5 Language bears traces of it also, 
in deponent verbs, which have a passive form with an active meaning, 
and neuter verbs, which have an active form with sometimes a 
passive meaning. We cannot admit, as Trendelenburg and others 
have maintained, that the distinctions of categories were derived by 
Aristotle from the grammatical distinctions between parts of speech ; 
but undoubtedly they are reflected (though in an imperfect way) in 
grammatical forms. Again, as we have seen, the notions of ex*^ 6 
and Keladat 7 are derivative : state presupposes the distinction of 
whole and part, which, in material things at least, implies the 
category of iroaur, 8 and it presupposes also the categories of 7roiet^ 3 
and -nao-yjtiv*, and of ttolov 9 ; for a whole is in a certain state 
through the interaction of parts having certain qualities, as when 
the body is well or ill ; or through something done to certain parts of 
it, as when the body is shod or clad ; a situation presupposes the 
distinction of whole and part also (a point can have place, but no 
'situation'), as well as the categories of ttov 1 and irpos n 10 ; for 
when a thing changes its situation, some part that was formerly 
above another comes to be below it, and so on. On these two deri- 
vative categories Aristotle lays least stress ; they are only twice 

1 Place 2 Time. 3 Action. * Being acted on. 

6 Movement, or change : v. Met. Z. iv. 1029 b 25. See for a conspectus of 
the lists of the categories found in different parts of the Aristotelian corpus 
O. Apelt, Beitrdge zur Geschichte der griecJiischen Philosophie, Kategorienlehre, 
pp. 140-141. 

6 State. 7 Situation. 8 Quantity. 

• Quality. 10 Relation. 



in] OF THE CATEGORIES 61 

[included in his enumeration. But though derivative, they are 
peculiar, and contain something not in the notions from which they 
are derived ; it is quite impossible to treat a state like health as 
being of the same nature with a quality like sweetness, or place with 
situation in that place. Kant made it a ground of complaint against 
Aristotle that he had included derivative conceptions in his list 
along with pure or underivative ; but it would probably be a fairer 
criticism, that he had not taken account of all the derivative con- 
ceptions which call for recognition. 

A word may be added upon Kant's doctrine of Categories, and 
its relation to that of Aristotle, though it is very difficult to put the 
matter at once briefly and intelligibly in an elementary treatise. 
Aristotle had sought to enumerate the kinds of being found in the 
different things that are ; Kant was interested rather in the question 
how there come to be objects of our experience having these 
diverse modes of being. He maintained that in the apprehension of 
them we are not merely receptive and passive ; on the contrary, all 
apprehension involves that the mind relates to one another in various 
ways the elements of what is apprehended ; if the elements were not 
so related they would not be elements of one object ; and they 
cannot be related except the mind at the same time relates them ; 
since relation exists only for a mind. Kant called this work of 
relating a function of synthesis ; and he desired to determine what 
different functions of synthesis are exhibited in the apprehension, 
and equally in the existence, of objects ; for the objects in question 
are not Dinge an sich, things by themselves, existing out of relation 
to the perceiving and thinking mind ; of these, just because they 
are out of relation to it, the mind can know no more than that they 
are, not what they are ; the objects in question are objects of ex- 
perience, and their being is bound up with the being of experience 
of them. He maintained in the first place, that the mere perception 
of anything as extended, or as having duration, involved certain 
peculiar ways of relating together in one whole the distinguishable 
parts of what is extended or has duration. These modes of synthesis 
we call space and time. As to time, I know that I am the same in the 
succession of past, present, and future ; I could not do this unless 
I distinguished as different the moments in which I am (as I realize) 
the same ; I could not distinguish them except by the differences 
of what I apprehend in them ; but unless these differences were 
conceived as differences in the being of something persistent and 
identical, I could not hold them together ; hence through my function 
of synthesis there come to be objects combining manifold successive 
states into the unity of one and the same thing. It is the same 
with any spatial whole. I must be aware at once of its parts as 
distinct in place, and yet related together in space ; space is a 
system of relations in which what is extended stands ; but the 
relations are the work of the mind that apprehends that manifold 



62 AN INTRODUCTION TO LOGIC [chap. 

[together. But these two modes of connecting in an unity the parts 
of what is manifold Kant attributed to sense, for reasons which 
we need not now consider ; thinking, the use of general conceptions, 
did not enter into them ; and therefore he did not include them in 
his list of categories, which were to be the most general conceptions 
by which in understanding we connect into an unity the manifold 
parts of an object, and so make it an object for ourselves. The 
perception of an object involved space and time ; but perception 
was not enough. We think of it in certain ways, or conceive it, in 
apprehending it as an object. Now this conception of an object 
involved, according to him, four things : (1) its having quality : and 
quality can only exist in degrees, each of which is distinguished 
from and related to the other degrees of the same quality ; heat 
only exists at a definite temperature and blue must be of a definite 
shade and saturation : (2) its having quantity, or being a whole 
composed of parts : (3) that it should be a substance having attributes, 
one or permanent through its changing and successive states, and 
that its changes should be determined according to laws by its 
relation to other substances with which it stood in interaction : 
(4) that every such object conceived to exist should be conceived as 
connected with every other existing object in a way that knowledge 
could apprehend, and express in the form of necessary inference. 
The various peculiar relations involved in these requirements Kant 
called Categories ; and he pointed out that, in all the sensible 
diversity of concrete objects as we know them, these categories or 
forms of relation exemplify themselves. Let something be pre- 
sented to me ; if there is nothing which I can call it, or regard it as 
being (for the question is one of thought and not of names), it is 
so far nothing for me ; but if I call it sky-blue, I am thinking of 
it as qualified ; I am ' taking it in ' by help of that conception of 
quality (realized in a specific mode of quality, sky-blue) which is 
one of the notions by which I relate together all that is sensible in 
what objects are. Of course it might have a colour unlike any 
colour I had seen hitherto, which I had no name to indicate ; but 
I should still be apprehending it as coloured in a certain way, though 
I could not name the colour, and therein I should be using the 
conception of quality. If I call it a sky-blue tassel, I am using in 
a specific form the notion of a whole of parts ; for to one who 
could not connect distinguishable parts in one whole a tassel would 
not be apprehensible as one thing ; I am also using the conception 
of substance and attribute, when I regard it as a thing, one of whose 
qualities it is to be sky-blue. I cannot call it woollen, without 
connecting its existence by causality in a definite way with the life 
of a sheep ; and so forth : the forms of space and time being 
presupposed in my apprehension of it throughout. It is not meant 
that these notions or categories are abstractly grasped, and con- 
sciously applied as guides in our apprehension and description of 



in] OF THE CATEGORIES 63 

[objects, as a doctor who had recognized that height, weight, chest 
measurement, and state of the teeth were important characters in 
determining the health of children at a given age might use these 
headings in a statistical description of the health of children in 
London schools. We only become aware of the part which these 
notions play in our apprehension of objects by reflection upon the 
use we have unconsciously made of them ; just as we become aware 
in the abstract of using certain forms of inference, by reflecting upon 
the inferences we have drawn in divers fields. But as there would be 
no men if there were no animals, and no circles if there were no figures, 
so we should not judge anything to be coloured if we could not 
conceive quality ; we should never think that a horse pulled a cart, 
if we could not conceive a substance to have attributes and to 
determine changes in another substance ; we should never call the 
movement of the cart necessary, if we could not think of the different 
real things in the world as so connected that we could infer one thing 
from another. And in all these different ways, we are relating, 
or distinguishing and connecting, features and parts of what we 
apprehend : what is merely sensible is not the work of the mind ; 
but the mind effects a synthesis in what would otherwise be a mere 
chaos or confusion of manifold sensations or sensibilia. 

Now it has been seen that Aristotle also noted that what, by 
making them subjects of predication, we recognize as existing are 
sometimes substances with attributes, sometimes attributes of 
various kinds ; we recognize the existence of qualities ; of quantities 
in things that are wholes or parts of such and such a size ; of rela- 
tions and positions in place and time ; of what things do and have 
done to them ; of their states and situations. Eut Aristotle ap- 
proached the matter from the side of the object ; he asked what 
modes of being we can distinguish in that which we recognize to be. 
Kant approached it from the side of the knowing subject, and 
asked what were the modes of synthesis on the part of our mind, 
through which objects are apprehensible by us as the sort of objects 
they are. If Kant is right in thinking that there could be no objects 
known to us, except through the mind's activity in relating according 
to certain principles their manifold differences, then we should expect 
that when we reflect upon the modes of being which these objects 
exhibit, we should find just those which the mind by its synthetic 
or relating activity makes possible for them. Hence the two lists 
of categories should correspond ; and in the main they do ; and the 
differences between them can be readily explained. Aristotle's list 
we have seen. Kant recognized four classes of category, those of 
Quality, Quantity, Relation and Modality. Now Quality and 
Quantity appear in Aristotle's list as well (though in Kant's they 
are each analysed into three aspects, or ' moments ', which here 
need not concern us). But in Kant the category of Relation covers 
the three relations of Substance and Attribute, Cause and Effect, 



04 AN INTRODUCTION TO LOGIC [chap. 

[and Interaction (which last really involves the other two) ; the dis- 
tinction of substance and attribute is present in Aristotle's doctrine, 
when he says that the rest presuppose Substance, and in iroulv 1 and 
ttaayjeiv 2 we have the recognition of the relation of cause and effect ; 
but there is nothing in Kant corresponding to the Aristotelian 
category of Trpos n 3 . The reason of this is that all predicates in 
the category of -npos tl 3 really involve some other category as well ; 
larger involves ttoo-o'i/ 4 , earlier irore 5 , slave Trao-^eiv 2 , farthest ttov 6 , 
and loudest ttolov 7 ; reciprocally, all categories involve relation, 
and Kant's whole point is that the relational functions involved are 
different. For Kant, who was interested in distinguishing these 
functions specifically, it would have been absurd to treat predicates in 
which relating, no matter how, is especially prominent, as involving 
a special kind of relating 10 ; or to suppose that there was any other 
kind of relation involved when I say that Socrates was more scrupu- 
lous than Crito, or taller than Tom Thumb, than when I say he 
was scrupulous or four cubits high. All scrupulousness must be of 
some degree, and all height of some quantity, so that as far as 
the function of relating in the way of quantity or degree is con- 
cerned, it is equally present whether my term is positive or com- 
parative. But from the side of the object, there are predicates 
which relate it particularly to some definite other object ; and these 
Aristotle placed under the category of -npos tl 3 . It might perhaps 
be objected to him that all predicates in the category of -npos tl 3 were 
also in ttov 6 or ttot4 5 , ttolov 1 or irocrov*, TtoLfLV 1 or -nacryjtLV 2 , Hxeiv* 
or KtlaOaL 9 ; but he would have replied that they were referred to 
the category of relation not because they involved qualitative or 
quantitative, spatial, temporal, or causal relations, but because they 
determined a thing as standing in some relation (of any one of these 
kinds) to some other thing, and they were predicated of it not so 
much in itself as in relation to something else n . Again, terms in 

I Action. 2 Passion. 3 Relation. 
* Quantity. 6 Time. 6 Place. 

7 Quality. 8 State. • Situation. 

10 The reason why Kant gave the name of Relation to the three syntheses 
of Substance and Attribute, Cause and Effect, and Interaction was historical. 
He quite recognized that all his categories were really modes of relating 
a manifold. 

II Ta npos n are defined first in Cat. vii. 6 a 36 as ' what are said to be that 
which they are of another' — bo-a avra amp (<jt\v iripoiv thai XtytTai, and more 
closely later in 8 a 32 as that ' for which to be is the same as to be related 
in some way to another ' — oh r6 thai ravrov tort tQ> irpos W nms (X etv ' The 
implication of n^k n with some other category is recognized in particular 
cases, but not stated generally; cf. vii. 6 b 11, ix. ll a 20-38, and esp. 37-38 
fTt el Tvyyuvot to uvto 7rpos ti koi jrowv ov, ouftep aronov tv dfx(poTepois rots ytveaLP 
airo KnTapiQptlcrQai ('besides, if the same thing happen to be both related 
and of such a quality, there is nothing strange in its being counted in both 
kinds '). Cf. Met. N. i. 1088 a 21-25, where it is said that relation pre- 
supposes quality and quantity. 



in] OF THE CATEGORIES 65 

[irorrov 1 , like 'three-foot' or 'year-long', involve space or time as 
well as the relation of whole and part ; and Kant thought right to 
distinguish the perceptual syntheses of space and time from the con- 
ceptual synthesis of whole and part ; hence also he objected to the 
presence of ttov 2 and irori 3 in the Aristotelian list at all. But Aristotle 
cared only to notice the modes of being that were to be found, the 
kinds of predicate that concrete things had, and was not interested 
to distinguish the parts which sense and thought respectively 
play in rendering the apprehension of them possible. Once more, 
Aristotle included the 'derived' notions of e'xetf 4 and Keln-dai 5 
with the rest, because they certainly are different modes of being ; 
Kant, who thought them to involve only the co-operation of func- 
tions of synthesis already recognized, gave no place to them. The 
most considerable difference between the two doctrines is the absence 
from Aristotle's of anything at all corresponding to the Kantian 
categories of modality, i. e. to the notions of actual, possible, and 
necessary as determinations of our thought about things ; but their 
absence will not surprise us if we consider that to the question, what 
essentially a subject is, no one would ever answer that it was actual, 
possible, or necessary. Speaking generally, however, we may put 
the relation of the two doctrines in this way, that whereas Aristotle 
had classified the products, Kant distinguished the processes of that 
synthesis or relating, through which (as he held) objects in all their 
manifold variety, however much they may materially or sensibly 
differ one from another, are all alike objects of knowledge and so 
far formally the same. Merely to be, said Aristotle, is not possible : 
ov is not a significant predicate 6 ; what is must be in a particular 
way, and its being thereby fall under one or other of the yivt\ tG>v 
Ka.Tr]yopi£>v, the kinds of predicate, which he enumerated ; and all 
the modes of being characterize in the last resort some concrete 
individual thing, which exists in and through them. An object, 
said Kant, cannot be an object of experience, and therefore cannot 
exist in the world of our experience, except through being perceived 
and thought in certain ways : the general ways in which an object is 
perceived or thought, the forms of perception and conception in- 
volved (one or another of them) in every predicate through which 
an object is known, are the ' forms of the sensibility ' — viz. space and 
time — and the ' categories of the understanding'. 7 ] 

1 Quantity. 2 Place. 8 Time. 4 State. « Situation. 

6 Unless in the sense of otaia or Substance ; but that is one of the 
categories. 

7 Kant may have been wrong (as Mr. H. A. Prichard has powerfully argued 
in his Kant's Theory of Knowledge) in supposing that the ' formal ' characters 
which belong to all objects of possible experience are not merely apprehended 
in them by the mind, but are there to be apprehended through the mind's 
activity. Nevertheless what has been said above will still express the relation 
which, on his doctrine, subsists between Aristotle's categories and his own. 

1779 F 



CHAPTER IV 

OF THE PREDICABLES 

The distinctions to which our attention was directed in the last 
chapter are distinctions of terms according to the nature of their 
meaning ; and if we understand what a term means, we may know 
to what category to refer it, without waiting to learn the subject 
of which it is predicated ; large, for example, is in the category of 
quantity, whether it be predicated of a triangle or of a gooseberry, 
and just in the category of quality, whether it be predicated of 
Aristides or his actions. Such difficulty as may exist in determining 
the category to which a term is to be referred arises through defect 
in the list of categories (i. e. of the conceptions under which we are 
to classify all possible predicates), or through the complexity of 
meaning in the term itself, whereby it involves more than one 
category at once, like a verb with tense ; but not through the fact 
that we are considering the term by itself and without reference to 
the subject of which in a particular proposition it may be affirmed 
or denied. And the treatise called the Categories indicates this when 
it puts forward the list of ten categories as a division of terms out 
of construction. 1 

In the present chapter we have to consider another division of 
terms, based upon the relation in which a predicate may stand to 
the subject of which it is predicated. Aristotle recognizes four such 
relations, and one of them he subdivides, obtaining five in all ; later 
logicians give five, but their list is in one important respect different. 
According to Aristotle, in every judgement the predicate must be 
either the definition (opos), the genus (yivos), the differentia (bt-acpopd), 
a property (Ibiov), or an accident (o-vpLfiefirjKos) of the subject. The 
later list, 2 losing sight of the principle on which the division was 

Tcov kuto. firjdeniau (TVfXTr\o<rjV Xeyo/ievcov eKnarov t'jrot oiaiav armnivei r) noaov 
r) 7TOIOV rj tti>6 ti fj ttov rj nore r) KelaBai t] %X eLV h TOieiv r) ndcr^tiv, Cat. iv. l b 25 

( ' what is said out of construction signifies either substance or quantity or 
quality or relation or where or when or situation or state or action or being 
acted on '). 

2 The Aristotelian list is given in the Topics, a. iv. 101 b 17-25. At the 
outset Aristotle names yivos, Ibiov and <jvpj3epr)K6s ; he then says that Siacpopd 



OF THE PREDICABLES 67 

made, omits definition, and includes instead species (eI8o?), running 
therefore as follows — genus, species, differentia, proprium, accidens. 

The distinctions are known as the Five Predicables, or more 
strictly as the Five Heads of Predicables. The words have passed 
into the language of science and of ordinary conversation ; we ask 
how to define virtue, momentum, air, or a triangle ; we say that 
the pansy is a species of viola, limited monarchy a species of consti- 
tution ; that one genus contains more species than another ; that 
the crab and the lobster are generically different ; that man is 
differentiated from the lower animals by the possession of reason ; 
that quinine is a medicine with many valuable properties ; that the 
jury brought in a verdict of accidental death ; and so forth. The 
fact that the employment of the words is not confined to any special 
science suggests that the consideration of them may belong to Logic, 
as expressing something recognized in our thought about all kinds 
of subject. 

' Predicable ' here means a predicable character, i. e. not an 
individual substance, but what it is ; all kinds, qualities, states, 
relations, &c. ; and these may be exemplified in and belong to more 
than one individual subject, and so we may say that they are 
universal. 1 All terms, therefore, except proper names may be 
brought under one of these five heads of predicables in relation to 
the subject of which they are predicated ; but proper names are 
not included 2 ; they may indeed be predicates in a proposition (in 
Aristotle's view only improperly) ; but they stand for individuals, 
and an individual is not the character of anything. The Par- 
thenon, for example, is not the genus or species of anything ; 
nor is it that which differentiates any species from another species ; 
nor is it a property or accident of anything. It is a particular 
building ; and the name denotes that building, with all that it is — 

may be ranked with y«W, as ov<rav yeviKi)i', i.e. presumably, as being a 
modification of that ; and he distinguishes 18101-, as what is common and 
peculiar to the subject, into o^os, which gives the essence, and 18101- sensu 
strictiore, which does not. In c. viii he offers a proof that the five-fold 
division is exhaustive. The later list passed into modern Europe from a little 
work by Porphyry (b. A. d. 233), the Elaayayi) or Introduction to the Categories, 
through the medium of a Latin version and commentary by Boetius, who 
lived in the last quarter of the fifth and first quarter of the sixth century a.d. 

1 Except when they are what no second subject can be ; e.g. there can 
be only one Omnipotent, and only one superlative in any kind. Professor 
Cook Wilson has called attention in an unpublished paper to the fact that 
there may be universals with only one instance. 

2 Nor designations, though what is general in a designation may be. 

F2 



68 AN INTRODUCTION TO LOGIC [chap. 

a temple, Doric, of Pentelic marble, beautiful by the simplicity of 
its lines and the magnificence of its sculptures, the work of Pheidias 
and his assistants, the glory of Athens. All these things are pre- 
dicable about it, and they are universals ; for might not another 
building be a temple, in the same style, of Pentelic marble, and so 
forth ? It, however, is not predicable ; nothing else can be the 
Parthenon. We may ask what kind of thing is the Parthenon, but 
not of what things is it the kind. The distinctions which we have 
to consider, therefore, do not afford a classification of things, but of 
concepts * : and (unlike the categories) of concepts considered not 
in themselves but in their relation one to another. 

But things are known to us through these concepts ; and an 
enquiry into the relation of concepts is an enquiry into the nature 
of things. There is indeed another sense of knowing. It has been 
frequently pointed out that the English language uses only the one 
verb, ' know,' to represent two different acts, which in some lan- 
guages are distinguished by different verbs 2 : the knowledge of 
acquaintance with a thing, and the knowledge about it. In Latin, 
the former is signified by cognoscere, the latter by scire ; French 
uses respectively the cognate words connaitre and savoir ; German 
the words kennen and wissen. Knowledge of acquaintance does 
not come barely through conceiving ; however much may be 
told me about Napoleon, and however clearly I may have 
succeeded in conceiving the features of his character, I never 
knew him, and never shall know him, in the sense of being 
acquainted with him : such knowledge comes only by personal 
intercourse, and separate intercourse is needed with each indi- 
vidual that is to be known. But knowledge about a thing comes 
by concepts ; and this too is necessary to real acquaintance, 3 
though it does not by itself amount to acquaintance. I may know 
a great deal about a man, without having ever met him : but 
I may in fact once have met him, without knowing who he was or 

1 To use a phrase of Mr. F. H. Bradley's, it is the ' what ' and not the 
1 that ' of things which we have to consider. 

2 Cf. e. g. J. Grote, Exploratio Philosophica, Pt. I, p. 60 — a work and by an 
author less known than they deserve to be ; the expressions ' knowledge of 
acquaintance ' and ' knowledge about ' are borrowed thence. 

3 Though not to such familiar recognition as a dog may show of its master, 
or a baby of its mother. The less developed mind acts in ways very difficult 
to describe, because it does not shew completely what mind is ; but it is 
wrong in principle to ' interpret the more developed by the less developed ', 
as Herbert Spencer would have us do. 



iv] OF THE PREDICABLES 69 

anything about him ; and I am no more acquainted with him in 
the latter case than in the former. 

Now most of our knowledge is knowledge about things ; things are 
useful and important to us for the most part not because they are 
such particular individuals but because of what they are ; this is not 
equally the case with persons ; and yet with persons too it is very 
largely the case. ' Wanted, a good coat-hand ' : it is not Smith, 
who is taken on, that is wanted, but only the coat-hand : the 
master-tailor is satisfied to know that he has engaged a coat-hand, 
and very often does not desire his acquaintance : if he knows about 
Smith, he can regulate his business accordingly, without knowing 
Smith. 

Through concepts, then, i. e. through what we conceive of their 
being, we are not acquainted with things individually, but we know 
and think and reason about them thereby. And a concept may be 
said to differ from a thing in being universal, not individual : an 
object of thought and not of sense : fixed and not changing : com- 
pletely knowable and not partially 1 . Take, for example, the con- 
cept of a timepiece : a timepiece is a machine in which the move- 
ment of wheels is so stimulated and regulated as to cause a hand or 

1 The characters recognized and named in things are often imperfectly 
understood ; but they might be understood completely, whereas the individual 
thing cannot be. Hence we may say that a concept is completely knowable, 
though not completely known. About the unchangeableness of a concept 
certain difficulties arise. (1) It is said that men's concepts change as their 
knowledge increases, e.g. there are now timepieces indicating the time by 
cards on which the hour and minute are printed, and which displace each 
other in proper succession ; and therefore we must modify our concept of 
a timepiece. But this only means that we must change the meaning of 
a name. What was conceived does not alter ; it is still displayed in the 
instruments to which the name was hitherto given ; now, when the name 
is also given to instruments which effect their purpose in a different way, 
something different is conceived when the name is used (cf. infra, c. vi). So, 
if we arrange a row of books according to height, we may say that the height 
increases along the shelf ; but no book is getting higher. (2) But we may 
conceive a changing character ; and here, what is conceived is not unchanging. 
In a body moving with an acceleration, the velocity changes. Cannot we 
then conceive velocity ? In the growth of an organism, perhaps we ought 
to say that the specific form changes ; yet this, one would say, is only known 
by conceiving. We must remember here the distinction between an universal 
and its instances. The velocity of this bullet may change ; but velocity is 
one in all these momentary velocities. When it is said that we know things 
through concepts, that means, through what they are ; but what they are 
is an instance of an universal nature. Between instances of these universals 
relations hold which do not hold between universals ; Juvenal's indignation 
may cause his activity in verse-making, but one universal does not cause 
another. So in the instances there may be change, but not in the universal. 



70 AN INTRODUCTION TO LOGIC [chap. 

hands to move at an uniform rate (usually twice in twenty-four hours) 
round a dial, and by pointing to the divisions marked upon the dial 
to indicate the time of day. That is the concept of a timepiece : it 
is clearly universal, for it applies to all timepieces ; it is an object of 
thought, and cannot be seen or felt, like the watch in my pocket ; 
it is fixed and unchanging, while my watch wears out or gets broken ; 
and it is completely knowable or intelligible, whereas there is a great 
deal about my watch which I do not know or understand : where the 
metals of which it is made were quarried, and by what series of 
events they came into the hands of the maker : why it loses 10" 
to-day and gains 13" to-morrow, and so forth. No one knows the 
whole history and idiosyncrasy of any particular timepiece, but he 
may conceive its general nature satisfactorily for all that. 

It has been asked, as we noticed above, 1 is a concept merely an 
object of thought, with no existence in things (as it is put, outside 
our minds) ? or does it exist in things 2 ? Much ink, and even much 
blood, have been spilt in disputing over this question. An elemen- 
tary treatise must be content to be brief and dogmatic. Concepts, 
we maintained, have existence in things, as well as in our minds. 
The thing which I can pull out of my pocket, and see and feel, and 
hear ticking, is itself a machine wherein the movement of wheels 
causes hands to tell the time of day as set forth in stating the con- 
cept of a timepiece. What I conceive a timepiece to be, that (if my 
concept is a right concept) every particular timepiece is ; what 
I know about things is the nature of the things ; nor would it 
otherwise be they wherewith my knowledge dealt. But though 
the features of things exist in the things, besides being conceived by 
our minds, the manner of their existence is different in an important 
respect from that of our conceiving them. In our minds, 3 each is to 
some extent isolated ; my knowledge of an individual thing is 
expressed piecemeal in many predicates about it ; each predicate 
expressing a different concept, or a different feature in the nature 
of the thing. But in the thing these features are not isolated. 
The individual thing is at once and together all that can be pre- 
dicated of it separately and successively (except indeed as far as 

1 Supra, pp. 25, 31-32. 

2 Or does it (as some have held) exist apart at once from particular things 
and from our minds ? Cf. supra, he. cit. 

3 What is conceived by the mind is sometimes said to be in the mind. To 
be in the mind means to be the object of a conceiving, thinking, remembering, 
or imagining mind : not of course to be in the brain, or inside the skull. 



iv] OF THE PREDICABLES 71 

predicates are true of it successively — a man, e. g., is successively 
awake and asleep). Thus in thinking of my watch I may think of it 
as a timepiece, as an heirloom, as being two inches in diameter, and 
bo on : between these concepts there is no connexion thought of ; 
they are as it were separate from one another ; but they and much 
besides are united in the thing. 1 The individual thing is all that 
can be predicated of it (and there is no end to what might be pre- 
dicated, if we knew its whole nature and history) ; but one thing 
that can be predicated of it is not another. 

An object comes into the room, which I call Tray : what is 
Tray ? it is a dog, an animal, yelping, at my feet, mine ; Tray is 
all these : but is a dog all these ? A dog (that is, any dog) is an 
animal, and a dog yelps ; but I cannot say that a dog (meaning 
any dog) is mine, or at my feet ; and though a dog is an animal 
it is not equally true that an animal is a dog, or that what is at my 
feet is mine, or that what is mine is at my feet. 

What, then, is the relation of those various concepts to one 
another, which can all be predicated of the same individual ? Are 
they united in it like stones in a heap, where the stones together 
are the heap ? or like almonds in a stewed pippin, where the pippin 
is not the almonds ? or like links in a coat of mail, where the links 
indeed are the coat, but only because they are peculiarly looped one 
into another ? It is easily seen that none of these analogies is 
appropriate. According to Aristotle they are related in one of five 
ways. Take any proposition, ' A is B,' where the subject A is 
not a proper name, but a general concrete term, or an abstract term. 
The predicate B must be either definition, genus, differentia, 
property or accident 2 of A : one or other of these relations must 
subsist between the two concepts A and B, in any individual 
characterized by them. 

The statement just advanced clearly concerns our thought about 
subjects generally : the technical terms have yet to be explained, 
but it is the actual procedure of our thought which they profess 
to indicate. Logic invented the terms, but it discovered the 
relations denoted by them. 

1 The word thing here is used first of the concrete subject of predication, 
then of the character predicated. It has been used already in both these 
senses. The English idiom allows both uses — we may say, for example, 
' about that thing I know nothing ' ; and it may be worth while to use the 
word closely together in both senses, in order to direct notice to the ambiguity. 

2 But cf. pp. 76, n. 1, 104, n. 1, infra. The Porphyrian list of predicates 
Will be considered later. 



72 AN INTRODUCTION TO LOGIC [chap. 

If we take any term that is general, and not singular, and make 
it the subject of a proposition, then the predicate must be either 
commensurate with the subject, or not. One term is said to be 
commensurate with another, when each can be predicated of 
everything whereof the other can be predicated x ; equilateral 
triangle and equiangular triangle are commensurate terms, because 
every equilateral triangle is equiangular, and every equiangular 
triangle equilateral ; but the term equiangular is not commen- 
surate with equilateral, for there are figures equilateral which are 
not equiangular. It may be pointed out (for it is important to 
bear in mind that we have to deal now with the relation between 
the different ' universals ' predicable of the same individual, and 
not the relation between them and the individual of which they 
are predicated — with the relation of ' animal ' and ' mine ', &c, 
to ' dog ', and not with the relation of these terms to Tray) — it 
may be pointed out that when the subject of a proposition is 
singular, the predicate is hardly ever commensurate 2 : for the 
predicate is an universal, and so commonly predicable of other 
subjects besides this individual : mine is predicable, for example, 
of other subjects than Tray ; whereas this individual is predicable 
of none of those : nothing else that I can call mine is Tray. Now 
where the predicate of a proposition is commensurate with the 
subject, there it is either the Definition or a Property of it : where 
it is not commensurate, there it is either part of the Definition, 
i. e. Genus or Differentia 3 , or an Accident. 

The definition of anything is the statement of its essence 4 : 
what makes it that, and not something else. In the following 
propositions, the predicate claims to be the definition of the subject : 
1 An organism is a material body, of which the parts are reciprocally 
ends and means ' ; ' a church is a building devoted to the service 

1 And therefore, of course, neither of anything of which the other cannot 
be predicated. Here and in some later passages I put triangle as equivalent to 
rectilinear triangle. Spherical and other triangles are ignored for the sake of 
simplicity. 

2 Only if it is a predicate which from its nature can belong to no more 
than one individual : cf. supra, p. 67, n. 1. 

3 But sometimes a differentia is commensurate : v. p. 74. 

* 'Opurpos nev yap tov ri i<TTi Kai ovaias, Ar. Anal. Post. /3. iii. 90 b 30. We 
may ask the question ri etm ; — what is it ? — of an attribute (like momentum) 
as well as a substance (like a man or a lobster) ; and the answer will be 
a definition. In strictness we can define the ovaia of an individual, if at 
all, only as meaning the kind to which it belongs ; cf. the previous ch., 
pp. 53-57, and also p. 28. 



iv] OF THE PREDICABLES 73 

of God according to the principles of the Christian religion ' ; 
1 momentum is quantity of motion ' ; ' wealth is that which has 
value in exchange ' ; 'a triangle is a three-sided rectilinear 
figure ' ; ' a line is the limit of a superficies '. The predicate states 
what it is that makes anything an organism, a church, a line, 
a triangle : what constitutes momentum or wealth, as distin- 
guished from everything else, such as apathy or architecture. 
In these judgements it is clear that the predicate, in claiming to 
be a definition, claims to be commensurate with its subject ; if 
an organism is a material body of which the parts are reciprocally 
ends and means, then my dog Tray, being an organism, must be 
that, and whatever is that must be an organism : for to be such a 
body is to be an organism. If wealth is that which has value in ex- 
change, then gold, having value in exchange, is wealth, and so forth. 
The genus is that part of the essence of anything which is pre- 
dicate also of other things * differing from it in kind. 2 Each of 
the definitions above given begins by declaring the subject some- 
thing, which other and different subjects are besides ; an organism 
is a material body — so is a machine, or a block of stone ; a church 
is a building — so is a stable ; a triangle is a rectilinear figure — ■ 
so is a square ; a line is a limit — so is a point, but of a line ; wealth 
is that which has value — so is honesty, but not in exchange, for 
you cannot transfer it 3 ; momentum is quantity — of motion, but 
not of matter. These (building, rectilinear figure, limit, &c.) are 
the genus, in each case ; and the genus, being predicable of other 
subjects, is clearly not commensurate. 4 Genus is sometimes 
explained as a larger class including the class defined within it ; 
figure, for example, as a class including triangles, squares, cones 

1 ' Thing ' here again does not mean only a concrete thing. 

8 Vivos 8 y earl to Kara irXeiovoop Knt duicfjepovTav ra e"8ei ev rep ri icm KnTt}yo- 
poifxevou, At. Top. a. v. 102 a 31. The notion of a kind is here presupposed. 
Some discussion of it will be found below, pp. 91-103. In botanical and 
zoological classification, genus is not merely correlative to species, but marks 
a certain degree of affinity, lower than specific, higher than that of families, 
orders, &c. Hence a genus, and even a family, may contain only one species, 
if that diverges as far from the species nearest it as do the species of different 
genera or families ; Homo Sapiens is in the zoological genus Homo and family 
Hominidae, and is alone in them. (I borrow the latter part of this note from 
Miss Augusta Klein.) 

3 The honest man, however, commands in many situations a higher price, 
and so far some economists would reckon honesty as wealth. 

4 This must be received subject to modification from what is said below 
as to the genus being in itself indeterminate, and actually different in each 
of its species. Cf. pp. 83-88, 138. 



74 AN INTRODUCTION TO LOGIC [chap. 

and many other subordinate classes besides : building as a class 
including churches, stables, barracks, and so forth. This explana- 
tion cannot be considered a good one, for reasons to be presently 
stated 1 ; but it may put some into the way of grasping a better. 

The differentia is that part of the essence of anything — or, as 
we may say, of any species — which distinguishes it from other 
species in the same genus ; it is the differentia of an organism 
that its parts are reciprocally ends and means — in this it differs 
from other material bodies ; it is the differentia of a church, to 
be for the service of God according to the principles of the Christian 
religion — in this it differs from other buildings ; and so forth. The 
genus and differentia (or differentiae 2 ) between them constitute 
the species, or make up the essence of that which is defined. The 
differentia, like the genus, need not be commensurate with its 
subject. The Book of Common Prayer is for the service of God 
in accordance with the principles of the Christian religion, but not 
being a building, it is not a church. On the other hand the 
differentia is commensurate with the subject of which it is pre- 
dicated in cases where no genus except that to which the subject 
belongs is susceptible of the particular attribute which serves as 
differentia ; thus a vertebrate is an animal of a particular structure 
which cannot exist except in an animal, so that the differentia of 
vertebrate is commensurate with it. And it is only where this is 
the case that the ideal of definition is attained, because only there 
is it precisely the common genus which is shewn to be realized 
in the several species. 

Those who speak of the genus as a larger class containing the 
species or smaller class within it sometimes explain the differentia 
as the attribute, the possession of which marks off the smaller 
from the rest of the larger class. If squares and rhomboids, 
triangles and pentagons, &c, are all placed in the class of plane 
rectilinear figures because they have that character in common, 
triangles, on the other hand, are differentiated from the remaining 
classes included within that of plane rectilinear figure by possessing 
the attribute of being three-sided. Provided it is not supposed 
that the differentia is added to the common character of the 

1 v. infra, pp. 83-84. 

2 In the plural if the genus has divers determinable points, some or all of 
which have to be specified differently in the different species. Cf. infra, 
pp. 100-101. In the rest of the paragraph, the singular must be taken as 
covering a complex of differentiae. 



iv] OF THE PREDICABLES 75 

' larger class ' in the same extraneous way that sugar is added to 
tea, there is no fresh harm in this mode of expressing oneself. 

A property is an attribute common and peculiar to a subject 1 
(and therefore obviously commensurate with it), but not part of 
its essence, and so not included in the definition of it. This is 
Aristotle's original account of a property, though we shall see that 
he also used the term with a less restricted meaning. 2 An organism, 
for example, is contractile, irritable, assimilates food, reproduces 
itself after its kind : these are attributes of every organism, and 
of nothing else, and therefore common and peculiar to the subject 
organism ; but they are not in its definition. A triangle, again, 
has its interior angles equal to two right angles, and its area half 
that of the parallelogram on the same base and between the same 
parallels ; a line is either straight or curved (here the alternatives 
together are common and peculiar) ; and so forth. 

All other attributes of any subject are accidents. An accident 
is defined as a non-commensurate predicate not included in the 
essence : or as an attribute which equally may and may not belong 
to a subject. The latter is the better definition, because it tells us 
what an accident is, whereas the former only tells us what it is not. 3 
It is an accident of an organism to be used for food ; for it may 
be so used, but need not. It is an accident of a church to be a 
cathedral ; some churches are cathedrals, and some are not. It 
is an accident that a contractor should be an honest man, and an 
accident that he should be a rogue ; for roguery and honesty are 
both compatible with being a contractor. 

The doctrine just illustrated presents many points for considera- 
tion, of which the following are perhaps the most important : — 

1. the antithesis between accident on the one hand and all the 
other heads of predicables on the other ; 

1 The subject being indicated, it must be remembered, by a common, not 
a singular term. I cannot speak of yelping as an attribute common to Tray, 
but I can speak of it as an attribute common to the dog— i.e. belonging to 
every instance of dog. Aristotle sometimes spoke of an attribute peculiar 
to an individual, and not to a kind or universal, as a property ; and also of 
attributes peculiar to one out of a certain definite number of kinds, and 
therefore serving to distinguish it from the rest (though found perhaps again 
outside their number) as relatively properties ; thus it is a property of man 
relatively to any quadruped to go on two legs ; but so also does a bird. He 
recognized that this use of the term 'property' was not the same as that 
given in the text, and not (in his view) so proper a use. Cf. Top. c i. 

2 Cf. infra, pp. 80-81, 104. , _ 

8 Cf. At. Top. a. v. 102 b 4-14. Cf. Top. e. i. The former also includes 
generic properties : cf. infra, p. 104, n. 1. 



76 AN INTRODUCTION TO LOGIC [chap. 

2. how to understand the analysis of a definition into genus and 
differentia ; 

3. the ground of the distinction between the essence of anything 
and its properties. 

(1) When we classify the members of a genus or class, we some- 
times, after specifying as many distinct species as we can think of, 
add another to include anything that does not fall within any of 
these ; I may classify my books, for example, according to subject 
into historical, philosophical, philological, scientific, and mis- 
cellaneous — the last division being merely added in order to 
receive any book which does not fall within the others, though the 
miscellaneous books have no common character that distinguishes 
them all alike from the rest. Now Accident is a head of predicables 
which includes any predicate that is neither definition, genus, 
differentia, nor property of its subject 1 ; but it is not a heading 
like ' miscellaneous ' ; there is a very definite and important differ- 
ence between the relation of those predicates to their subject 
which are classed as accidents, and that of those which fall under 
the other heads ; the latter belong to their subject necessarily and 
universally, the former do not. 

Of any individual, as we have seen, an infinity of predicates 
may be asserted. Some of them are seen to be connected, or (as 
we may express it) have a conceptual connexion ; i. e. if we rightly 
conceive one predicate, we see how it involves another. Tray, for 
example, is a dog and an animal ; and these predicates are con- 
ceptually connected, because the concept of a dog involves that of 
animal. My watch has hands, and there is a conceptual connexion 
between having hands and being a watch, since without hands 
a watch could not fulfil the task of telling the time, which is part 
of the concept of it as a timepiece. But there are also many 
predicates which coincide 2 in one and the same individual, without 
being conceptually connected. Besides being a dog, Tray is mine, 
and was born at Bishop Auckland ; now there is no reason in the 
nature or the concept of a dog, why it should belong to me, nor in 
a thing being mine, why it should be born at Bishop Auckland, 
nor in being born at Bishop Auckland, why it should be mine, or 
be a dog. No doubt in the case of this particular dog Tray, there 

'SvfxfiftfrjKos 8- (cftiv o fxrjdev fiev rovrav e'o~ri, p;re opos Ui]TC iSiop prjTf y(POs t 
Ar. Top. a. v. 102 b 4. 

2 Cf. supra, p. 24. Coincident is really a better translation of av/i.Se^Kos 
than accident. 



iv] OF THE PREDICABLES 77 

is a reason why he is mine and a reason why he was born at Bishop 
Auckland ; but the reason for the first fact (which may be that he 
was given me) has nothing to do with the reason for the second 
(which is that his mother was there at the time) ; nor has the 
reason for either anything to do with his being a dog ; he would 
have been a dog still, if he had never been given to me, or if he 
had been born at Bishop's Lydeard. 

Of course with more knowledge the coincidence of attributes 
in an individual may often be explained ; but the explanation 
will always be largely historical, connecting the coincident attri- 
butes severally according to laws with other facts which are found 
conjoined but not seen to be connected. We have here the great 
difference between science and history. In science we seek to 
ascertain the connexion of universals. Sometimes we can only 
do this inductively ; by noticing how attributes are historically 
found conjoined or disjoined in divers individuals we determine 
which must be supposed to be connected 1 ; but having established 
these ' laws ', we trace out by mere thinking their consequences in 
divers situations of fact. Sometimes, without the appeal to experience 
which induction makes, we can, as in geometry, trace necessary 
connexions between one character and another in things. But 
history is interested in individuals in whose total being we find 
characters coincident, the conjunction whereof we can never wholly 
see to be necessary. Even where they are so far of a kind that we 
know how they must behave in a given situation, yet each situa- 
tion presents different conjunctions. No doubt the scientific and 
historic interests interpenetrate. Some sciences, like geology, are 
largely occupied in applying what they know of the connexion of 
universals to the elucidation of the history of individual things, 
or aggregates, if we hesitate to call a mountain range or a coal 
formation one thing. And the historian attempts to trace con- 
nexions among the events that make the history of individuals, 
or groups of individuals, and so far to be scientific. Perhaps, even 
if we started with complete historical knowledge of the conjunction 
of individuals at a given time, the subsequent course of history 
could never be wholly explained this way ; it may be that the 
nature of individuals cannot be exhaustively given in terms of 
universal characters, but that there is in each something unique. 

1 The illustration of this forms a considerable part of what is called Inductive 
Logic ; we shall find that many connexions are inductively established whose 
necessity remains unconceived. 



78 AN INTRODUCTION TO LOGIC [chap. 

But anyhow there will always be the bare conjunction of facts 
in the historic situation, which cannot be deduced except from 
the previous conjunction in another historic situation. 

That the accidental should be opposed to what is necessary and 
universal conforms to the usage of common speech. Sir Robert 
Peel was killed by a fall from his horse, and we say his death was 
accidental. Why ? he was a man, and for a man it is necessary 
to die, and for any one who falls in that particular way it may 
be necessary to die ; but it is not necessary that a man should fall 
in that way ; that is not predicable universally of man. We 
sometimes dispute whether there is such a thing as chance in the 
world, or whether everything has a cause, and happens necessarily. 
Few people really believe that anything happens without a cause ; 
but chance is not the negation of cause ; it is the coincidence of 
attributes in one individual, or events in the same moment, when 
each has its cause, but not the same cause, and neither helps to 
account for the other. 

If we bear in mind this fundamental contrast between the 
accidental and the necessary, we shall not be inclined to think that 
Aristotle was engaged in a trivial pursuit when he attempted to 
classify the various relations in which a predicate might stand to its 
subject. Discussions as to what we mean by cause occupy much 
space in many modern treatises. Now the causal relation is also 
grounded in the nature of universals : Tray yelps not because he 
is this individual Tray, but because he is a dog, and unless any dog 
yelped, it would not be because he is a dog that Tray does so. 
But when we call this the cause of that, the relation intended is 
not always the same ; just as when we say that A is B, the relation 
of B to A is not always the same. It might be supposed that if 
one thing X is the cause of another Y, then you could not have 
X without Y, nor Y without having had X. And yet we say that 
molecular motion is the cause of heat, that the heat of the sun is 
the cause of growth, that starvation is sometimes the cause of 
death, that jealousy is a frequent cause of crime. We should in 
the first case maintain that the cause and effect are reciprocally 
necessary ; no heat without molecular motion, and no molecular 
motion without heat. In the second, the effect cannot exist 
without the cause, but the cause may exist without the effect ; 
for the sun shines on the moon, but nothing grows there. In the 
third, the cause cannot exist without the effect, for starvation 



iv] OF THE PREDICABLES 7B 

must produce death, but the effect may exist without the cause, 
since death need not have been produced by starvation. In the 
fourth case, we can have the cause without the effect, and also the 
effect without the cause ; for jealousy may exist without producing 
crime, and crime may occur without the motive of jealousy. It is 
plain, then, that we do not always mean the same by our words, 
when we say that two things are related as cause and effect ; and 
any one who would classify and name the various modes in which 
two things may be causally related would do a great service to clear 
thinking. Now that is the sort of service that Aristotle attempted 
in distinguishing the heads of predicables. Many predicates are 
asserted of the subject A. Those of them are accidents, whose 
cause does not lie in its nature as A, or which, when they belong to 
any individual of the kind A, do not belong to it because it is A. 
The rest are in some way or another connected causally with A, 
and are predicable of any individual because it is A. Whether 
Aristotle's account of the different modes of connexion between 
a subject and a predicate is satisfactory is another question, in- 
volved principally in that of the value of his account of ' property '. 
But that the theory of predicables is closely akin to the question 
of the various senses in which one thing can be the cause of another 
may be seen by this : whenever science tries to find the cause not 
of a particular event, such as the French Revolution (whose cause 
must be as unique as that event itself is), but of an event of a kind, 
such as revolution, or consumption, it looks in the last resort 
for a commensurate cause. What is that exact state or condition 
of the body, given which it must and without which it cannot be 
in a consumption ? What are those conditions in a political 
society, given which there must and without which there cannot 
be a revolution ? 

The kindred nature of the two enquiries will be further seen, 
by looking at certain cases where it is disputable whether a pre- 
dicate should be called an accident of its subject or not ; for an 
exactly parallel difficulty may arise in determining whether one 
thing shall be called the cause (or effect) of another or not. An 
accident is a predicate of a subject A, the ground for whose exist- 
ence in that subject does not lie in its nature as A. Hodge drives 
a plough ; and a full knowledge of his history would show me 
why he drives a plough, and the ground for it therefore lies in the 
history of the subject Hodge ; it is not of him that driving the 



80 AN INTRODUCTION TO LOGIC [chap. 

plough is predicated as an accident. But a man drives a plough. 
That is an accident ; for the subject now is not Hodge wholly, 
but a man, and it is not in his nature as a man that the ground 
or reason of his driving a plough lies ; else should we all be at the 
plough-tail. And yet no animal but man can drive a plough : so 
that it is partly because he is a man that Hodge drives it ; and 
therefore, when it is said that a man may drive a plough, the 
relation of the predicate to the subject seems not completely 
accidental. Contrast the statement that a cow may be knocked 
down by a locomotive. There the nature of the subject, as a cow, 
contributes nothing ; it is in no wise necessary to be a cow, in order 
to be knocked down by a locomotive 1 ; and the relation is purely 
accidental. 

If we consider these two examples, we see that our account of 
an accident, just given, may be interpreted in two ways. A pre- 
dicate may belong accidentally to the subject of which it is pre- 
dicated either 

(i) when the ground for its existence in the subject does not lie 
completely in the subject-concept, 2 or 

(ii) when the ground for its existence in the subject does not lie 
at all in the subject-concept. 2 

The first interpretation would rank as accidents of a subject 3 all 
predicates that are not either part of its definition, or else common 
and peculiar to that subject, i.e. properties in the strictest sense; 
and such, if we take him at his word, is Aristotle's view. But we 
are then required to say that it is an accident of money to be 

1 So far as a cow is a body, and only a body can be knocked down, it must 
be allowed that the nature of a cow contributes something to the accident ; 
but the second sentence will stand without qualification. 

2 When a general term is subject of a proposition, though the proposition 
concerns individuals (designated individuals or not, according as the general 
term is or is not combined with a demonstrative), yet these are characterized 
only by the general term. The character by which they are thus distinguished 
is the subject-concept. If I say that a cow was knocked down by a loco- 
motive, the subject is an individual cow ; it is distinguished in my proposition 
from other obstacles by being a cow; this being a cow, or cowness, is the 
subject-concept. What is knocked down is a cow, not cowness ; but being 
knocked down is accidental to cowness in the cow ; and I can therefore say that 
the relation of accident lies between universals, though exhibited between 
the instances of them in this cow. It would of course be absurd to say that 
the particular cow contributed nothing to the accident, since it could not 
have been knocked down if it bad not been there. Students of Professor 
Cook Wilson's lectures will remember this distinction between subject and 
subject-concept. 

8 i.e. of the subject as distinguished by the subject-concept. 



ivl OF THE PREDICABLES 81 

valuable, since it would have no value if there were nothing to buy 
with it : or of coal to burn, since it would not burn in a vacuum. 
The second interpretation would refuse the name of accident to 
anything that could be said about a subject, however rare and 
unconnected the conjunction of circumstances through which it 
came about, where the nature of the subject contributed anything 
at all to the result. Thus we could hardly call it an accident that 
an animal should die of overeating itself, since it must be an animal 
in order to eat. In practice we make a compromise between these 
extreme interpretations. We call it a property rather than an 
accident of belladonna to dilate the pupil, though the result depends 
as much upon the nature of the muscles as on that of belladonna ; 
we call it an accident rather than a property of the plough to be 
a favourite sign for country inns, though its necessary familiarity 
to countrymen accounts for its selection. The further pursuit of 
these difficulties does not concern us now ; but it remains to be 
shown that they arise also in regard to the relation of cause and 
effect. Is the cause of an effect that, given which and without 
anything besides, the effect follows ? in other words, must it contain 
the whole ground of the effect ? then a spark is never the cause of 
an explosion, for it will produce no explosion without powder. Is 
the cause anything, however slight, without which the effect could 
not have occurred ? in other words, is that the cause which con- 
tributes anything whatever to the effect ? then are cooks the cause 
of health, since there would be little health without them. 

(2) The antithesis between accident and the other heads of pre- 
dicates needs perhaps no further illustration. We may pass to 
the second of the three points enumerated on pp. 75-76, viz. how 
to understand the analysis of definition into genus and differentia. 

It should first be noticed that definition is never of an individual, 
but always of what is universal, predicable of individuals — whether 
it be what we call their ' kind ', or some state or attribute of them, 
or relation in which they stand. For what is defined is thereby 
marked off and fixed in our thought as a determinate concept ; 
but the individual is made the individual he (or it) is by an infinity 
of attributes ; he is as it were the perpetual meeting-place of con- 
cepts ; we can neither exhaust what is to be said of him, nor make 
a selection, and declare that this is essential to him, and that 
unessential. Moreover, even if we could, we should still only have 
settled what he in fact is, but a second person also might be ; for 

1779 a 



82 AN INTRODUCTION TO LOGIC [chap. 

every concept is universal. What makes him this individual and 
not another we should not have denned, nor could we ; for there 
is something which makes me me over and above what can be 
predicated of me ; else, what makes me me might also make you 
you ; for what can be predicated of me might be predicable of 
another, you for example ; and then why does the same character 
make me me and you you, and not rather make me you and you 
me, or each of us both ? 

We can only define then what is universal, or a concept. But 
we have already said that concepts are the natures of things ; 
and therefore in defining concepts, we may define things, so far as 
they are of a kind, but not as individuals. It is sometimes main- 
tained that definitions are not of things, but only of names x : that 
they set forth the meaning (or, as it is also phrased, the connotation ^ 
of a name, but not the nature of a thing. Yet the names are only 
used to convey information about things ; and to explain what the 
name means, is to explain what the thing is said to be. Definitions 
then are not really of names ; but we shall see later the difficulties 
which drove men into saying so. 

Now when we define we analyse ; and the elements into which 
we analyse that which is defined are called, as we saw, genus and 
differentia. These might be called attributes of the subject : it 
might be said, for example, that rectilinear figure and three-sided 
are attributes of a triangle. But the expression is not quite appro- 
priate ; for an attribute implies a subject beyond itself, to which it 
belongs ; but the parts of a definition themselves make a whole, 
and coalesce into the unity to which they belong. This may be 
best explained by a contrast. We may take any attributes we 
like — say far, sour, pink, soft and circular — and we may give one 
name to the aggregate of these. But they do not form one notion ; 
they remain obstinately five. If we took a single name to signify 
the possession of these attributes, we could explain the name as 
meaning that assemblage, but we should feel that in so doing we 
were merely explaining a name, and not defining any unity. But 
when we analyse into genus and differentia, this is otherwise ; 
then we feel that the two together really make a single notion. 
They have such a connexion in their own nature as makes one fit 
the other, so that they constitute the essence of one thing, or state, 

1 e.g. Mill, System of Logic, I. viii. 5. 

2 On ' connotation ' cf. infra, c. vi. 



iv] OF THE PREDICABLES 83 

or action, or quality, or relation. And the reason for the parts of 
a definition being one l is this : that they are not attributes inde- 
pendent but coincident, but the genus is the general type or plan, 
the differentia the ' specific ' mode in which that is realized or 
developed. Take again the definition of a (rectilinear) triangle. It is 
a rectilinear figure ; but to be merely that is impossible, because 
incomplete. There cannot be a rectilinear figure without a definite 
number of sides, though any definite number above two will do ; 
and if the number in a triangle is three, then three-sidedness is 
the specific mode in which the general plan, or as we may say the 
potentialities, of rectilinear figure are realized in the triangle. 
We may say that the genus and differentia are one, because they 
were never really two. Three-sidedness can only be realized in 
a figure, rectilinear figure can only be realized in a definite number 
of sides. The genus therefore never could exist independently of 
a differentia, as soft may of sour : nor the differentia of the genus. 
It may be said perhaps that though three-sidedness can only exist 
as the form of a figure, rectilinear figurehood exists independently 
of three-sidedness in the square, the pentagon, &c. But it is not 
quite the same thing in the square or pentagon as it is in the 
triangle. So intimately one are the differentia and the genus, that 
though we refer different species to the same genus, yet the genus is 
not quite the same in each ; it is only by abstraction, by ignoring 
their differences, that we can call it the same. Triangle and square 
and pentagon are all rectilinear figures ; but in the sense in which 
they actually are such, rectilinear figure is not the same in them 
all. Thus the differentia modifies the genus. And the genus also 
modifies the differentia. It might be said that three-sidedness is 
not confined to the genus figure ; for a triangle is a three-sided 
figure, and N is a three-sided letter. And doubtless, so far as the 
genus is the same in two species, the differentia may be the same 
in the species of two genera. But three-sidedness is plainly 
different in the figure, where the sides enclose a space, and in the 
letter, where they do not ; and the genus as it were fuses with the 
differentia, so that each infects the other through and through. 

For this reason the genus is not well described as a larger class 
including the smaller class or species within it. For the word class 

1 That the parts of a definition are one is a thing on which Aristotle fre- 
quently insists, and says that the main problem about definition is to show 
how that can be. Cf. e.g. Met. Z. xii, H. vi. 

G2 



84 AN INTRODUCTION TO LOGIC [chap. 

suggests a collection, whereas the genus of any species is not a collec- 
tion to which it belongs but a scheme which it realizes, an unity 
connecting it with things different from itself. It may seem at 
first plain-speaking, without any metaphysical nonsense, to say that 
a genus is a class of things that all have certain features in com- 
mon ; and that its species is a smaller class composed of some of 
those things, which all possess not only the features common to the 
whole genus, but others not belonging to the other members of it. 
But what is really meant by being included in a class ? The phrase 
is sometimes put forward as if it were simple, and presented no 
difficulty ; but such is not the case. The words ' to be within ', or 
1 to be included in ', have many meanings, and we must know what 
meaning they bear in the phrase ' to be included in a class ', before 
we can know what that phrase signifies. We may distinguish in 
particular two meanings, which are quite inapplicable to the relation 
between a genus and its species ; but they are more easy to grasp 
than the meaning in which the species can be said to be included in 
the genus, because they can be in a manner represented to the 
senses ; whereas the relation of genus to species can never be repre- 
sented to the senses, but only apprehended by thinking. Because 
one of these inapplicable meanings is readily suggested to the mind, 
when we are told that the genus of a thing is a class in which it is 
included, we fancy that the expression helps us to understand what 
a genus is ; for these inapplicable meanings are easily understood. 
But as they are inapplicable, they help us not to understand but to 
misunderstand the logical relation of genus and species. 1 

In the first place, one thing may be included in another as a 
letter is included or enclosed in an envelope, or 
as Mr. Pickwick and the wheelbarrow were en- 
closed in the pound. In this case, all that is 
included may be removed, yet that in which it 
was included will be left. Such is clearly not 
the sense in which species are included in a genus ; 
for there would be no genus left if the species 
vanished. Yet the logical relation is often represented by a diagram, 
which inevitably suggests this sense. Two circles are drawn, one 

1 Though the relation of a species to individuals is not the same with that 
of genus to species in all respects, yet what is said here upon the vice of 
calling the genus a class in which species are included applies also to the 
habit of calling the species a class including individuals. 




iv] OF THE PREDICABLES 85 

enclosing the other ; the genus being represented by the outer and 
the species by the inner circle. It is not impossible to use such 
diagrams without being influenced by their obvious suggestions ; 
yet their obvious suggestions are false, and to avoid them is difficult. 

Secondly, a thing may be included in an aggregate, which is 
constituted by that and all the other things included along with it. 
In this sense a cannon-ball is included in a heap, and a particular 
letter in the pile on my table. We do actually use the word class 
on some occasions to indicate a total formed in this way ; in 
a school, for example, a class is a certain number of boys taught 
together, and when a boy is moved from one class to another, he is 
sent to do his work with a different set of boys. Here we have 
a notion which is so far nearer the logical notion, 1 as that the class 
would disappear upon the disappearance of what is included in it. 
But a little reflection will show that the logical relation of genus 
to species is no more like that of an aggregate to its members than 
it is like that of an envelope to its contents. 

If Tom Smith is in the first class in his school, I should look for 
him among the boys in a particular class-room ; but if a triangle is 
in the class figure, or a Red Admiral in the class lepidoptera, that 
does not mean that I should look for either in a collection of figures 
or of lepidoptera ; it is true that a collection of these objects would 
include specimens of the triangle or the Red Admiral ; but they do 
not belong to their respective genera because they are in the collec- 
tion ; specimens of them are placed in the collection because they 
belong to the genera. Were it otherwise, I could not say that 
a triangle is a figure, or that a Red Admiral is a lepidopteron, any 
more than I can say that Tom Smith is the first class ; I could 
only say that as Tom Smith is in the first class, so a triangle is in 
the class figure, and a Red Admiral in the class lepidoptera ; 
whereas it is characteristic of this to be a lepidopteron, and of that 
to be a figure. 

The ' class ' to which species (or individuals) are referred is apt 
not to be thought of as something realized in its various members 
in a particular way ; but the genus is something realized in every 
species (or, if it is preferred, in the individuals of every species) 

1 i.e. the notion which the phrase 'to be included in a class' must bear 
in logic, if it is to be used in any applicable sense at all. And note that even 
a class at school is not a chance collection, but a collection of boys supposed 
to share the same level of attainments. 



86 AN INTRODUCTION TO LOGIC [chap, 

belonging to them, only realized in each in a special way. The diffe- 
rentia carries out as it were and completes the genus. Individuals 
are not included in one genus because agreeing in certain attributes, 
and then in one species within the genus because agreeing in certain 
other attributes that have no connexion with the first ; as you 
might include in one island all men who had red hair, and then 
rail off separately within it those of them who had wooden legs ; 
wooden-legged could not be a differentia of the genus red-haired ; 
it must be some modification of red-hairedness itself, and not of the 
men having it, which could serve as a differentia to that genus. 
It is therefore a phrase that may mislead, to say that the differentia 
added to the genus makes the species, or makes up the definition. 
For adding suggests the arbitrary juxtaposition of independent 
units ; but the differentia is not extraneously attached to the genus ; 
it is a particular mode in which the genus may exist. And hence, 
when we distinguish the various species of one genus, in what is 
called a logical division, 1 assigning to every species the differentia 
that marks it off from the rest, our several differentiae must be 
themselves homogeneous, variations, as it were, upon one theme 
and, because each cognate with the same genus, therefore cognate 
with one another. If rectilinear triangle, for example, is regarded 
as a genus, and one species of it is the equilateral, the others will 
be the isosceles and the scalene : where each differentia specifies 
certain relations in the length of the sides ; if one species is the 
right-angled, the others will be the obtuse- and the acute-angled : 
where each differentia specifies certain relations in the magnitude 
of the angles. The principle that the differentiae must be thus 
cognate is technically expressed by saying that there must be one 
fundamentum divisionis ; this, however, has its proper place of 
discussion in the next chapter. 

To define anything then per genus et differentiam is to put forward 
first a relatively vague notion and as it were the rough plan of the 
thing, and then to render this definite by stating in what way the 
rough plan is realized or worked out. And the differentiae are of 
the essence of the things, because they belong to the working out 
of this rough plan. In the definition of organic species (inorganic 
kinds we will consider later) this is what we aim at doing. We 
start with the general notion of a living body, and classify its 
various forms in such a manner as to show how this scheme is 

1 Cf. infra, c. v. p. 115. 



iv] OF THE PREDICABLES 87 

realized in successively more complex ways. Our first division is 
into unicellular and multicellular organisms (protozoa and metazoa) : 
the former obviously admit of no composite cellular structure ; in 
a multicellular organism there must be a method of constructing 
the system of parts. Hence we proceed to differentiate these 
according to the principal modes of structure which they exhibit ; 
on this basis is founded for example the division of the metazoa in 
the animal kingdom into coelentera and coelomata ; of coelomata 
into a number of ' phyla ' (cpvXa, tribes), the platyhelmia or flat- 
worms, annelida or worms, arthropoda, mollusca, echinodermata 
and chordata ; of chordata, according to the form which the noto- 
chord assumes, into hemichorda, urochorda, cephalochorda and 
craniata ; and of craniates, according to the different forms 
which the general principle of craniate structure may assume, into 
fish, dipnoi, amphibia, reptiles, birds and mammals. 1 When it is 
said that we start with the general notion of an animal body, it 
is not of course meant that historically we conceive that, before 
becoming acquainted with individuals. We first become acquainted 
with individual plants and animals. But the use of general names 
shews that some apprehension of their common nature comes 
to us from the beginning along with our experience of individuals ; 
only we may long remain unable, or not endeavour, to formulate 
it. This also applies, at a higher level, to the common nature of 
various species — horse, dog and fox, oak, elm and apple — with 
which we have become familiar ; we may detect that there is 
such an identity, before we know what it is, and call them all 
by a generic name, like animal or tree. The genus is that with 
which, when we have acquired an insight into the nature of these 
various kinds, we then start ; it is first in the order of our thought 

1 The extent to which, in subordinating species and genera to a superior 
genus, a common type or plan can be definitely traced through them all, 
may vary at different stages of a classification. The same functions of animal 
life are diversely provided for in protozoa and metazoa ; and within the 
comparative complexity of metazoa, in coelentera and coelomata ; but it 
would be impossible to give any one diagrammatic representation of the 
structure of all these, or even of all metazoa. Such representations are given 
for coelentera in general, and coelomata in general ; yet they are a mere 
outline, in which even the principal organs of many important types are 
sacrificed. On the other hand, for each separate phylum among the coelo- 
mata zoologists can give a representation, in which a place is found for every 
principal organ that all the species of that phylum, though with manifold 
variation of development, at some stage of life or other alike exhibit ; and 
for the subdivisions of the craniata this can be done more adequately than 
for the subdivisions of the chordata. 



88 AN INTRODUCTION TO LOGIC [chap. 

about them when we understand them, not in the order of our 
acquaintance with them when we perceive them. According to 
the Aristotelian formula, it is (pvuei irporepov, or Aoyw Trporepov, not 
7]p2v -nporepov : first or fundamental in the nature of the thing, or 
in an account of it, but not what strikes us first. And Aristotle 
also expressed its function by saying that the genus is, as it were, 
the matter, vk-q, of the species or kind. 

In saying that a genus is related to its species as matter to form, 
the relation of matter to form is conceived as that of the less 
developed to the more developed, the potential to the actual. 
A word of caution is necessary here. We often compare two 
particular objects, say a ' bone-shaker ' and a modern bicycle, and 
observing that one carries out more completely certain features 
imperfectly present in the other, call them respectively more and 
less developed. The same thing may be observed in the arrange- 
ment of a picture gallery, where the pictures are placed in such an 
order as will exhibit the gradual development of an artist's style, 
or of the style of some school of artists : and in a museum, where 
the development of the art of making flint implements is illustrated 
by a succession of specimens each more perfect than the last. Now 
in all these cases, the more and the less developed specimens are all 
of them concrete individuals : each has an actual existence in space 
and time. But with genus and species it is otherwise. They are 
not individuals, but universals ; the genus does not exist side by 
side with the species, as the bone-shaker exists side by side with 
the best bicycle of the present day ; and you cannot exhibit genus 
and species separately to the senses. It is our thought which 
identifies and apprehends the generic type, say of mammal, in the 
different species, man and horse and ox ; and in thinking of them, 
we may say that the single type is developed in so many divers 
ways ; but genus and species do not exist in local or temporal 
succession, the less developed first, and the more developed later, 
like the specimens which illustrate the development of a type or 
style. Obvious as these remarks may seem, they are not super- 
fluous, if they help to guard against the idea that a genus is some- 
thing independent of its species. 

[It would be travelling too far beyond the limits of an elementary 
work to enquire into the meaning of arranging individuals in an 
order of development : whether (like plants and animals) they 
proceed one from another in a true genealogical series, or are manu- 



iv] OF THE PREDICABLES 89 

[factured independently, like bicycles or arrowheads. A criticism 
of the conception of development is however of great importance ; 
for the complacent application of the notion to disparate subjects, 
under the influence of the biological theory of evolution, by writers 
like Herbert Spencer has diffused many fallacies. Perhaps it may 
be suggested that, if we wish to know what we mean when we 
apply the conception of greater and less development to the relation 
between individual things, we should first examine what we mean 
by the conception in the relation of genus and species. We cannot 
throw any light on the relation of genus and species by comparing 
it with what subsists between individuals at different stages of 
' evolution ' ; but we may get some light upon the conception 
of evolution from reflection on our conception of the relation of 
genus to species. For the ' evolution of species ' is generally 
supposed to be not mere change, but development ; yet it is often 
supposed also to involve nothing of the nature of purpose, or design. 
Now unless we find, in considering individual things, that there 
is a character or form suggested to us in what we call the less 
developed, but not adequately exhibited there as we conceive it, and 
that this same character or form is more adequately exhibited 
in what we call the more developed thing, we have no right to call 
them more and less developed at all. The relation therefore is not 
between the things as individual, but between their characters ; 
we cannot identify with the less developed individual the character 
or form which is less developed in it ; there is the same at 
different levels of development in each individual ; and the evolu- 
tionary history of the series of individuals must be a manifestation 
of such a character or form in them, unless we are to say that 
there is no real development, but only change, and that to call this 
change development is to read into things a fancy of our own. The 
example of such development best known to us is in the activity of 
the intelligence.] 

[In the first chapter, the antithesis of form and matter was 
employed in explaining how a common character might belong to 
divers things. Two shillings, we saw, may be said to be of the 
same form, while the matter in them is different : and two proposi- 
tions to be of the same form, so far as each asserts a predicate of 
a subject, while their matter varies with the difference of subject 
and predicate. But in saying that genus is related to species as 
matter to form, it is implied, as between two species, that their 
common genus, the ' matter ', is that in which they agree : while 
the specific form assumed by this matter in either is the basis of the 
distinction between them. Indeed, the phrase ' specific differences ' 
implies that their differences constitute their form. It may seem 
strange that whereas in one sense matter is that which is different 



90 AN INTRODUCTION TO LOGIC [chap. 

[in things of the same form, in another it is that which is the same 
in things of different form. 

A little consideration will show that the common notion in both 
these uses of the term matter is the notion of something undeveloped. 
With regard to the phrase that calls the genus the matter of the 
species, this point has already been illustrated. And when we 
contrast, in a shilling, the matter (silver) with the form, it is still 
so. We regard a shilling as an object having a certain form (that 
might also be stamped in gold or copper) impressed upon a certain 
matter, silver : and say that both are necessary to its being a 
shilling. But the material which the minter takes has a shape as 
much as a shilling has, though one geometrically less simple ; 
whereas the matter which the metaphysician contrasts with form is 
really silver as of no shape, or without regard to shape (cf. pp. 55-56 
supra). Now in thinking of silver in abstraction from any shape, 
our thought of it is incomplete. As the genus only exists in the 
species, so the matter, silver, only exists in some form. It is 
however true that there is no special relevance between the nature 
of silver and the shape of a shilling, whereas the specific form of 
man can only be realized in the genus mammal ; and hence the 
conception of development applies more closely to the relation of 
genus and species, than to the relation of matter and form in 
a concrete thing. 

Many controversies have been waged over what is called the 
principium individuationis. What is it that makes one individual 
distinct from another individual of the same species ? Some of the 
schoolmen held that, being of the same species or form, they were 
distinct in virtue of their matter ; and it followed, since angels have 
no matter, that every angel is of a different species : except their 
species, there is nothing by which they can be distinguished from 
each other. We may be less ready to dogmatize with confidence 
about angels than were the schoolmen ; but the fashion of deriding 
their speculations because they were exercised in solving that kind 
of questions is fortunately in diminished vogue. The problem of 
the principium individuationis is a serious philosophical problem. 

It may throw some further fight on what has been said of the 
antithesis between matter and form, to point out that matter cannot 
really be the principium individuationis. Two shillings which have 
the same form are said to be of different matter. Now their matter 
is silver : but it is not because it is made of silver that one shilling 
is different from another shilling. In that respect all shillings 
agree ; it is because they are made of different masses or pieces of 
silver that they are different shillings. But if so, it follows that to 
be of silver is a character common to both pieces (quite apart from 
their being from the same die) ; and though we say they differ in 
matter, we mean that though of the same matter, they are different 



iv] OF THE PREDICABLES 91 

[pieces of it. The problem of the principium individuationis is not 
therefore solved by the distinction of matter and form ; the shillings 
are different, though of the same form, because in each that form 
is stamped upon a different piece of silver ; but the pieces of silver 
themselves present the same problem, of a common form (the 
nature of silver) in different individuals. Matter is indeed, strictly 
speaking, not a particular thing or an aggregate of particular 
things, but a generic concept. We recognize various species of 
it, which we call elements : the elements are different forms of 
matter ; and in calling them so, we imply something common to 
them all, as we imply something common to man and ox in calling 
them both animals ; though we are less able in the former case 
than in the latter to conceive the common or generic character in 
abstraction from its specific differences.] 

It hardly needs now to be pointed out, that where the predicate 
of a proposition defines the subject, it is related to its subject far 
otherwise than where it is an accident. We realize (or we should 
realize, if our definitions were what we aim to make them) that the 
genus, modified or developed in the way conceived, is the subject ; 
the definition and that which is defined are not two but one. Of 
course, when a green thing is square, the same particular thing is 
both square and green ; the green thing and the square thing are 
one thing ; but here the subject is not an universal, and we have 
only to recognize the coincidence of attributes in the same indi- 
vidual. Being green and being square are not one, as being a square 
and being a four-sided rectangular and rectilinear figure are x ; there 
is a conceptual unity between these ; between those only an 
accidental. 

It follows that there is a conceptual connexion between any 
subject and its genus or differentia ; he who understands the 
nature of the subject sees that it must be what is predicated of it 
as its genus or its differentia. What belongs to the essence of any- 
thing must belong to it ; for else it would not be that kind of thing, 
but something different. 

(3) We may now take up the last of the points raised on pp. 75-76, 
viz. the ground of the distinction between essence and property ; 
since the last paragraph suggests the question, What do we mean 
by the essence ? If the essence of anything be what makes it what 

1 Aristotle would express this by saying that to xXopoVmay be r? rpayavov, 
but to x^wpw rival is not to TiTpayiovai elvai — the green is square, but green- 
ness is not ' squareness ; whereas triangularity is three-sided-rectilinear- 
figurehood. Cf. supra, pp. 15, n. 1, and 22-23. 



92 AN INTRODUCTION TO LOGIC chap. 

it is, of course it would be something different, were any element 
in its essence wanting ; but what makes it what it is ? 

Those who hold the view, already mentioned, that definition is of 
names only and not of things, have an answer ready here, agreeable 
to that view. They say that we cannot tell what makes anything 
what it is, but only what makes it to be called by a certain name ; 
and that the world might have been spared much useless con- 
troversy, if men had realized that by the essence of anything they 
meant no more than the attributes which they agreed should be 
signified by a general name : or, as Locke called it 1 , the nominal 
essence. The essence is on this view determined arbitrarily, i.e. 
by human convention, though doubtless not without regard to 
human convenience — in particular, the convenience of conforming 
our nomenclature to what experience shews us of the grouping 
of qualities in things. The view is readily suggested by a con- 
sideration of material things. If we were to regard only the 
definitions of geometry, it would appear paradoxical to maintain, 
that men determined arbitrarily what to include in the definition 
of circle or rectilinear triangle, and what to omit. Manifestly 
you declare better what a rectilinear triangle is by saying that it 
is a three-sided rectilinear figure than by saying it is a rectilinear 
figure whose angles are equal to two right angles ; or a circle, by 
saying that it is the figure generated by the revolution of a straight 
line in one plane round one of its extremities remaining fixed, than 
by saying that it is a plane figure having a larger area than any 
other of equal perimeter. What has led men to suppose that 
definition is a matter of fixing the meaning of names is chiefly the 
difficulty found in defining natural kinds, i.e. the various species 
of animal, plant, or inorganic element; in despair they have looked 
to the signification of the name for the only meaning of the essence 
of the thing. Our procedure with abstract notions like wealth 
or crime or liberty has lent support to the same view. In these 
cases, the subject defined cannot be presented to the senses in an 
example, as can gold, or the holm-oak, or the buffalo ; we cannot 
be sure therefore that different men intend to define the same 
thing, when they offer definitions of such notions ; and instead of 
settling first by its appearance that a given act is a crime, or an 
object wealth, or a state one of liberty, and then arguing to its 
nature from our definition, we have rather to determine whether 
1 v. Essay concerning Human Understanding, Bk. III. c. iii. § 15. 



iv] OF THE PREDICABLES 93 

it is to be called a crime, or wealth, or a state of liberty by con- 
sidering whether its nature is such as mankind, or particular 
writers, have agreed to signify by those names. Hence it might 
appear that in the case of abstract terms x at any rate, convention 
settles what the essence of them shall be ; in the main it is not 
really so, even with them ; for the understanding of facts would 
not then be facilitated as it is by the substitution of ' better ' for 
' worse ' definitions of abstract terms ; but the plausibility of the 
view here adds weight to the arguments which are drawn, in the 
manner we must now proceed to show, from the definition of 
natural kinds. 

Suppose that we wish to define the natural substance dog, or 
gold. The forms of language recognize a difference between a sub- 
stance and its attributes ; for we say that Gelert is a dog, but not 
that he is a faithful ; and speak of a piece of gold, but not of a piece 
of heavy. Yet when we define a substance we can only enumerate 
its qualities or attributes, 2 and leave out of account what it is that 
has them. What attributes of Gelert then are we to enumerate, 
to explain what we mean by calling him a dog ? or what attributes 
of a wedding-ring, to explain what we mean by calling it gold ? 
In each case a certain fixed nucleus, as it were, of attributes, holding 
together in repeated instances and through great varieties of cir- 
cumstance, is included in our concept of a thing called by such 
a general concrete name. But which attributes are to form this 
nucleus, and on what principle are we to make our selection ? If 
it be said that we are to include every attribute common to all 
dogs, or all gold, two difficulties arise. The first is, that we should 
include in our notion of dog or of gold all the properties, as well as the 
attributes that are to constitute the definition : for the properties 

1 Such complex abstract notions were called by Locke ' mixed modes ' ; 
which he said we could define, because we had first made them by putting 
together simple notions (or in his language, simple ideas) with which we 
were perfectly acquainted. The expression ' mixed mode ' has not estab- 
lished itself ; perhaps because the words are not well adapted to convey the 
meaning which Locke intended by their combination ; but it would be useful 
to have an appropriate expression to indicate what he meant. Cf. Essay, 
Bk. II. c. xxii. 

2 We have, however, seen, in discussing genus and differentia, that these 
cannot well be called attributes. But it might be urged, that although they 
cannot be attributed to any other 'universal ' as qualifying it, they must 
be attributed to something which in any individual is what has the sub- 
stantial character, in virtue of which we call it a dog or gold, as well as 
having such other attributes as mangy or fine-drawn ; cf., however, pp. 54-57, 
supra. 



94 AN INTRODUCTION TO LOGIC [chap 

of a kind are the predicates common and peculiar to all the indi- 
viduals of that kind ; and hence we should still lack a principle 
upon which to discriminate between property and essence. The 
second difficulty is more serious. We are to include in our defini- 
tion of a kind every attribute common to all individuals of that 
kind ; but until we have defined the kind, how can we tell whether 
a particular individual belongs to this kind or another ? Let the 
definition of gold be framed by collecting and examining every 
piece of gold, and noting down the attributes common to them all ; 
the task is impossible in practice, but that might be overlooked ; 
it is, however, vicious in theory ; for it implies that we already 
know what gold is, or what makes a particular thing a piece of 
gold, and can by that knowledge select the things which are to be 
examined, as specimens of gold, in order to determine the nature 
of that substance. Thus we seem to be moving in a circle ; what 
is gold we are to settle by an examination of the things that are 
gold ; what things are of gold, by knowing what gold is. 

Hence our selection must be arbitrary ; for we have no principle 
on which to make it. We may take a particular atomic weight, the 
power to resist corrosion by air, ductility, malleability, and solu- 
bility in aqua regia ; and say these constitute gold, and are its 
essence. And in that case its colour is a property, or for all we can 
tell, an accident ; for we can see no necessary connexion between 
a yellow colour and all or any of those attributes, and if we found 
a white metal with those five attributes we should have to call it 
gold. But if we chose to include yellow colour with them in our 
definition, then nothing could be gold that was not yellow ; yellow 
would be of the essence of gold ; but only because we had decided 
to give the name to no metal of another colour ; it would be the 
meaning of the name that fixed the essence, and the essence would 
be only ' nominal '. 

It has been assumed in the above that the attributes included in 
the definition may be not only arbitrarily selected, but without any 
perceivable connexion among themselves ; so that any attribute 
omitted from the definition should drop at once into the rank of 
accident ; the essence is only a collection of attributes comprised in 
the signification of the same name, and there are no properties at 
all. And some logicians have maintained that we can never see any 
necessary connexion between different attributes ; and that when 
we speak of them as universally connected, we really mean no more 



iv] OF THE PREDICABLES 95 

than that they have been very frequently found accompanying one 
another. Without for a moment agreeing with this opinion (which 
denies any sense in the distinction between a connexion that is 
necessary and universal, and a conjunction that is accidental) it 
may be admitted that we often regard attributes as necessarily and 
universally connected, because we believe that with fuller know- 
ledge we might see into the necessity of the connexion, when as yet 
we cannot actually do so. This is markedly the case with the 
various properties of an inorganic substance ; and the kinds of plant 
and animal also present us with many instances where different 
peculiarities in a species are inferred to be ' correlated ', because 
the same conditions seem to affect them both, or because within 
our experience they are uniformly present and absent together, 
without our being able to understand the connexion between 
them. 

The difficulty of determining what attributes are essential to 
a substance, and therefore of discriminating between essence and 
property, does not however arise entirely from the seeming discon- 
nexion among the attributes of a kind. It arises also, at least in 
the organic, from the great variation to which a species is liable 
in divers individuals. Extreme instances of such variation are 
sometimes known as border varieties, or border specimens ; and 
these border varieties give great trouble to naturalists, when they 
endeavour to arrange all individuals in a number of mutually 
exclusive species. For a long time the doctrine of the fixity of 
species, supported as well by the authority of Aristotle and of 
Genesis, as by the lack of evidence for any other theory, encouraged 
men to hope that there was a stable character common to all 
members of a species, and untouched by variation ; and the 
strangest deviations from the type, excluded under the title of 
monstrosities or sports or unnatural births, were not allowed to 
disturb the symmetry of theory. Moreover, a working test by 
which to determine whether individuals were of different species, 
or only of different varieties within the same species, was furnished, 
as is well known, by the fertility of offspring ; it being assumed 
that a cross between different species would always be infertile, 
like the mule, and that when the cross was uniformly infertile, the 
species of the parents were different. But now that the theory 
of organic evolution has reduced the distinction between varietal 
and specific difference to one of degree, the task of settling what is 



96 AN INTRODUCTION TO LOGIC [chap. 

the essence of a species becomes theoretically impossible. It is 
possible to describe a type ; but there will be hundreds of charac- 
teristics typical of every species. Who is to determine what degree 
of deviation in how many of these characteristics will make a 
specimen essentially or specifically different ? Will it not have 
to be decided arbitrarily at the last ? so that here again our use 
of names will settle what is essential to the species. Everything 
will be essential that we require in a specimen in order to call it by 
a certain specific name. 

Such are the reasons for saying that the essence of anything is 
settled by the meaning that we give to names, and if the essence 
is thus arbitrary or fixed by convention, the distinction between 
essence and property is similarly infected. But that distinction is 
obnoxious to another objection, already noticed on p. 93 : that if 
the property is common and peculiar to the kind, it ought to be 
included in the essence, because connected with it universally and 
necessarily. It is as little possible for a rectilinear triangle not to 
contain angles equal to two right angles, as not to have three sides ; 
as little possible for a line not to be straight or curved, as not to be 
the limit of a superficies. If the property of a subject is grounded 
in the nature of that subject alone, why is it not regarded as a part 
of its nature ? if it is grounded partly in the nature of the subject, 
partly in conditions extraneous to the subject, then the subject 
only possesses it in a certain conjunction, and it ought to be 
called an accident. 1 

Having thus presented our difficulties, we must endeavour their 
solution. 

The inexpugnable basis of truth in the theory of the predicables 
lies first in the distinction between the necessary and the acci- 
dental : secondly, in the analysis of definition into genus and 
differentia. The first underlies all inference ; the second, all classi- 
fication. But the notion of essence, and the distinction between 
essence and property, are not applicable in the same way to every 
subject. 

They present at first sight no difficulty in geometry. The 
essence of any species of figure includes so much as need be stated 
in order to set the figure as it were before us : whatever can be 
proved of such a figure universally is a property. Thus the 
definition is assumed, the properties are demonstrated ; and 

1 Cf. supra, pp. 80-81. 




iv] OF THE PREDICABLES 97 

that is the true Aristotelian distinction between essence and 
property. 

But how are the properties demonstrated ? Only by assuming 
a great deal else besides the definition of the figure of which they 
are demonstrated. We assume, for example, the postulates ; and 
that means that we see that we always can produce a straight line 
indefinitely in either direction, or join any two points, or rotate 
a straight line in one plane about its extremity. We assume the 
axioms ; and that means that we see, e. g., that any two right angles 
must be equal ; and that if a straight line 
AB falling on two other straight lines CD, 
EF makes the sum of the angles CAB, 
EBA equal to the sum of the angles DAB, 
FBA, CD and EF must be parallel, and 
if not, not ; we assume also in one proposition all that we have 
already proved in others. It is seldom from considering merely the 
definition of the figure which we contemplate that the perception 
of its properties follows ; we must set the figure into space-relations 
with other lines and figures, by an act of construction ; and the truth 
of our conclusion involves not solely the essence of the figure as set 
out in its definition, but that taken together with the nature of 
space ; for it is really the nature of space which we apprehend when 
we realize that the sum of the interior angles made by two particular 
parallel straight lines with a line that cuts them is the same on either 
side of it, or that a given straight line can be produced to meet 
another with which it is not parallel. Another point must be noticed. 
It was said that whereas the properties are demonstrated, the 
definitions are assumed ; but that does not mean that they are 
arbitrarily taken for granted. They are assumed, because they are 
what we start with. But they are not arbitrarily taken for granted, 
because it is self-evident to us that the existence of a figure as defined 
is possible ; and this is self-evident, because in the process of defining 
we realize in an actual or imaginary example that such a figure can 
be constructed. We know that three straight lines are enough to 
make a figure, because we make it of them in imagination ; we 
know that a figure may have five sides, because we see the pentagon 
before us. It is this power which geometry possesses of creating in- 
stances of the objects of its own study that distinguishes it from the 
non-mathematical sciences. And it creates its objects by construct- 
ing them — i. e. by drawing lines and surfaces ; and in this possesses 

177» H 



98 AN INTRODUCTION TO LOGIC [chap. 

a natural principle upon which to distinguish between property 
and essence. For though commonly, in geometry, properties are 
commensurate with their subjects, and may be reciprocally demon- 
strated, yet everything depends upon the power mentally to see the 
lines and surfaces ; thus the angles of a triangle determine the position 
of its lines as much as the position of the lines determines its angles ; 
but it is only through dividing space by lines that the angles can be 
realized. The visible figure is therefore our necessary starting- 
point. A definition which fails to determine that waits for applica- 
tion until the figure can be pictured. Let a circle be a plane figure 
having a larger area than any other of equal perimeter ; that does 
not set a circle before us ; an infinity of figures can, we see, be made 
by a line that returns upon itself and is flexible at will ; and the 
property specified will not, previously to demonstration, afford us 
any means of selecting the figure intended. But say that a circle is 
the plane figure generated by the revolution of a straight line about 
one of its extremities remaining fixed, and then we have it before 
us ; then we understand what it is about which the property of 
having a larger area than any other figure of equal perimeter is 
affirmed. Once again, in geometry there are no happenings, no 
conjunctures. It is true that in order to geometrize we have, 
actually or in thought, to draw the figures : but our process of 
drawing only renders visible space-relations which we conceive are 
eternally present everywhere in space. Therefore the circle or the 
triangle is not subject to mutation on different occasions ; there is 
nothing to prevent it at one place or time from being the same as at 
another ; and the conditions under which it exists do not vary ; 
the general nature of the space in which it is is uniform and constant. 
Hence the properties of any geometrical figure, though, as we have 
seen, we must take the general nature of space into account, as well 
as the definition of the figure, in order to realize their necessity, may 
yet without risk of any false deduction be regarded as if they were 
grounded in the essence of that figure alone. For the general nature 
of space is a ' constant ' ; it is everywhere the same, and conditions 
every figure alike ; it is not because that ever changes, that different 
figures have different properties, but because the figures are different. 1 
Geometry therefore deals with subjects capable of definition : 

1 Some deny that we know Euclid's axioms ; they are only the most 
convenient assumptions. Even on this view, though we shall have demon- 
strated the properties which in Euclidean geometry are demonstrated of the 



iv] OF THE PREDICABLES 99 

in which the definition serves to set the subject before us : and 
in which the distinction between essence and property, though 
from one point of view questionable, is from another sound. It is 
questionable, so far as the properties of a figure are as necessary 
to it as its definition, and do not really any more depend on the 
definition than the definition on them. But it is sound, so far as 
the essence is that with which we must start, in order to have the 
figure before us, and say anything about it, while the properties 
are what we can demonstrate. The process of demonstration may 
require that we should make a further construction than what the 
figure itself demands ; but this further construction is not necessary 
in order that we may apprehend the figure itself ; and hence the 
definition, which as it were constructs the figure, gives us what is 
essential, the demonstration what is necessarily bound up therewith. 1 

Now the science of geometry, both in Aristotle's day and since, 
has been apt to seem the model of what a science should be ; and 
that deservedly, so far as its certainty and self-evidence go. But 
though we may desire an equal certainty and self -evidence in other 
sciences, we must not ignore the differences between their subject- 
matter and that of geometry ; nor must we assume that the dis- 
tinction of essence and property will have the same applicability to 
concrete bodies as to figures in space. The subjects which we study 
in chemistry, in botany, or in zoology, are not constructed by us ; 
they are complex, and for all we know may differ much in different 
instances ; and they exist under conditions which are not con- 
stant (like space) but infinitely various. Hence in them we cannot 
expect to find the determination of the essence, and the separation 
between that and its properties, as soluble a task as in geometry. 

Let us consider first the definition of inorganic kinds. Here, 
since a compound may be defined by specifying its composition, 
our problem deals with the elements. It will be instructive to look 
for a moment at the Greek treatment of this question. There were 

figures defined only subject to these assumptions, the definitions of the figures 
will have the function stated above. So far as non-Euclidean geometry 
deals with what cannot be constructed or imagined, the above statement of 
the distinction between essence and property will for it have to be qualified. 
In analytical geometry, the distinction between essence and property is 
harder to draw ; yet it must be remembered that unless we could envisage 
the figure, there would be nothing to analyse. Cf. also infra, p. 333. 

1 Yet where there are alternative modes of constructing a figure (e.g. an 
ellipse) it will be arbitrary which of them we select to define it by ; we can 
only say that the definition must enable us to construct the figure. 

H2 



100 AN INTRODUCTION TO LOGIC [chap 

two main attempts to define the famous four elements of Empedocles, 
earth, air, fire, and water. Plato supposed that they differed in the 
geometrical construction of their particles, those of earth being 
cubic, of air octohedral, of fire tetrahedral, and of water eicosihedral. 
If these were their differentiae, what was their genus ? We can only 
reply, solid. 1 They were something filling space, of different figures. 
In assuming the concrete things which he defined to fill space, Plato 
did what every one who defines a natural substance does. We do not 
always mention this character in our definition ; we might define a 
scabius, for example, as a certain kind of composita ; but to be a com- 
posita involves it ; and it is necessary if the definition is to furnish 
the conception of a material thing at all. In taking geometrical 
figures as his differentiae, he attempted to gain in physics the 
advantages which geometry derives from our power of constructing 
its objects ; but he failed to show how the sensible properties of the 
different elements were connected with their respective figures. 
Aristotle preferred the method of those who distinguished the 
elements not by the figure of their particles, but by the mode in 
which they combined certain fundamental sensible qualities, heat, 
cold, moisture, and dryness. Fire he thought was the hot and dry 
substance, water the cold and moist, earth the cold and dry, air the 
hot and moist. These definitions have the disadvantage of using 
terms that possess no very precise signification. How hot is un- 
mixed fire, and how moist is pure water ? 

Modern science recognizes in each element a whole legion of 
common and peculiar attributes. Some of these, such as its atomic 
weight, are conceived to be constant or to characterize the element 
in all conjunctures ; others it only exhibits upon occasion ; this is 
the case, for example, with its reactions towards other bodies. We 
have very little insight into the inter-connexion of the various 
attributes thus characterizing each element ; but unless we are to 
regard everything in nature as accidental, we are bound to believe 
them interconnected. 2 It is impossible to include in its definition 
all that is known to be characteristic of an element ; and for the 
mere purpose of identification, many of the attributes of an element 
would serve equally well. But we prefer to select as differentiae, 
and include in the definition, such attributes as appear, in some 

1 Or perhaps, regular solid. 

a On what kind of evidence particular attributes are held to be connected, 
it is the business of the theory of the inductive sciences to show. 



iv] OF THE PREDICABLES 101 

form or another, in all or a large number of elements ; because we 
are thus able to exhibit the divers elements as related to one another 
upon a scheme, or in other words to classify them. Thus the atomic 
weight of a substance is more suitable for defining it than some 
peculiar reaction which it exhibits, although perhaps less useful for 
identifying it ; because all elements must have some atomic weight, 
but no other need exhibit the same sort of reaction. If, however, 
a reaction is common to a number of substances, it may serve as 
a ground for collecting those into one class, like the acids : the 
common reaction being a generic character ; especially when for 
any reason, such as the number of attributes that are commensurate 
with it (i. e. are found where it is found, and not where it is absent), 
such reaction seems to count for much in the being of the substances 
to which it belongs. 

Such considerations may guide us in choosing what to include 
in our definition ; and we shall also ceteris paribus prefer for diffe- 
rentiae those attributes that are continuously exhibited to those 
that an element only exhibits in a rare conjuncture. Nevertheless 
it is plain that our procedure is in great measure arbitrary ; and 
the distinction between essence and property is not applicable as it 
was in geometry. For among the constant attributes of an element 
we cannot start with some and demonstrate the remainder ; and 
those which it exhibits only in particular circumstances are not pro- 
perties in the full sense. We may indeed call it the property of an 
element to exhibit a certain reaction in certain circumstances 1 ; but 
whereas the ' circumstances ' under which geometrical figures exist 
and possess their properties are in every case the same (being their 
existence in space), the circumstances relevant to the manifestation 
of the several properties of an element are different ; hence we 
cannot afford to omit the statement of them in stating its properties ; 
and since they are often very numerous and complex, and involve 
many other substances, it may be more natural to refer the property 
to a compound, than to one element. Nevertheless, since causal 
connexion is fundamental in the notion property, we rightly regard 
these attributes as properties rather than accidents. For although 
the subjection of an element to any particular conditions rather 
than others is strictly speaking accidental, since it depends upon 

1 Cf. Ar. Top. e. i. 128 b 16 oVoSi'Sornt te to t'^iov fj k«0' avTo Kai afi rj npos 
trepov Kal nore (' a property is ascribed to a subject either per se and always 
or in a particular relation and time '). 



102 AN INTRODUCTION TO LOGIC [chap. 

historical causes that are independent of the nature of that element, 
yet its behaviour when subject to those conditions is not accidental : 
so that it is fairly called a property of gold to be soluble in aqua 
regia, though very little gold be so dissolved. On the other hand, 
we call it an accident of gold to lie in the cellars of the Bank of 
England ; for though it is not accidental that it should lie where it 
is placed, but its doing so is connected with other features in the 
nature of gold, yet that the particular place should be the cellars 
of the Bank of England no more illustrates a general principle, 
than that the aqua regia in which it is dissolved should have been 
bought in Cheapside. No reasonings that apply to gold universally, 
but only historical reasons, will show that certain parcels of gold 
must be lying there. 

The use of the singular without the article (as in a proper name) 
when we say that gold is malleable, or iron rusts, or silver tarnishes, 
is worth remark. It implies that we think of gold, or silver, or 
iron as one and the same thing always : that we are looking to the 
unity of kind, and not the particular specimens. Different parcels 
of the same element may be found in divers states, solid, liquid or 
gaseous, crystallized or uncrystallized, in molecules of different 
numbers of atoms, and so forth. But we conceive that any one 
sample is capable of all states whereof any other sample is capable ; 
they have no ' individuality \ Even when we investigate the 
properties of a compound, so far as the composition is really known 
with accuracy, we have the same confidence in attributing to that 
compound universally the properties discovered in a particular 
sample. But in organic kinds, though we may know the chemical 
composition of the parts, we cannot know with the same accuracy 
the composition of the heterogeneous parts into the whole. Hence 
we do not know how far different individuals are capable of the 
same behaviour. And if an organism has a real unity, the differences 
between one and another individual of the same kind will never be 
fully explicable from their composition. 

Indeed the problem of distinguishing between essence and property 
in regard to organic kinds may be declared insoluble. If species 
were fixed : if there were in each a certain nucleus of characters, 
that must belong to the members of any species either not at all or 
all in all : if it were only upon condition of exhibiting at least such 
a specific nucleus of characters that the functions of life could go on 
in the individual at all ; then this nucleus would form the essence 



iv] OF THE PREDICABLES 103 

of the kind. But such is not the case. The conformity of an 
individual to the type of a particular species depends on the fulfil- 
ment of an infinity of conditions, and implies the exhibition of an 
infinity of correlated peculiarities, structural and functional, many 
of which, so far as we can see (like keenness of scent and the property 
of perspiring through the tongue in dogs), have no connexion one 
with another. There may be deviation from the type, to a greater 
or less degree, in endless directions ; and we cannot fix by any hard- 
and-fast rule the amount of deviation consistent with being of the 
species, nor can we enumerate all the points, of function or structure, 
that in reality enter into the determination of a thing's kind. Hence 
for definition, such as we have it in geometry, we must substitute 
classification ; and for the demonstration of properties, the discovery 
of laws. A classification attempts to establish types ; it selects some 
particular characteristics as determining the type of any species ; 
these characteristics should be (a) of the same general kind for each 
type within one genus, or, as it was expressed on p. 86, variations 
upon the same theme, in order to exhibit the mutual relations of 
agreement and divergence among the various types : (b) important, 
or, as one might say, pervasive : that is, they should connect them- 
selves in as many ways as possible with the other characters of the 
species. It will be the description of the type, drawn up on such 
principles as these, that will serve for definition. It is avowedly 
a mere extract from all that would need to be said, if we were to 
define (upon the supposition that we could define) any species of 
plant or animal completely. 

The full nature of an organic species is so complex, and subject 
to so much variation in different individuals, that even if it could 
be comprised in a definition, the task of science would hardly con- 
sist in demonstrating its properties. To discover the properties 
of kinds belongs to the empirical rather than to the scientific stage 
of botany or zoology. Science proceeds to ask what it is in any 
kind on which a particular property belonging to it depends. 
Herein we break up or analyse the complex character of the kind, 
in order to determine what we call the laws of organic life. If a 
species, for example, is keen-scented, that must depend upon 
conditions that are but a small part of what would be included in 
a complete account of its nature. In order to find the commen- 
surate subject of which a property is predicable, we must abstract 
from all in the species which is not relevant to that one property ; 



104 AN INTRODUCTION TO LOGIC [chap. 

and our subject will not be the concrete kind, but one determined 
by a set of conditions in the abstract. The property whose conditions 
we have found is of course the property not of those conditions, but 
of anything that fulfils those conditions ; keen-scentedness, for ex- 
ample, is not a property of a particular construction of the olfactory 
organ (though we should call it an effect of this), but of an animal in 
whom the olfactory organ is thus constructed ; the laws of organio 
life suppose of course that there exist organisms in which they 
are exhibited. We may still speak therefore of properties of kinds ; 
but the demonstration of them considers the nature of the kind 
only so far forth as it concerns the property in question. The 
property is not common and peculiar to the kind, if other kinds, as 
may well be the case, agree with it in those respects on which the 
property depends ; or if it depends on conditions which cannot 
be fulfilled except in an individual of that kind, but are not fulfilled 
in every individual thereof. 

Such reflections led the schoolmen to distinguish four senses of 
the term property — 

1. id quod pertinet omni sed non soli : thus it is a property of the 
cow to give milk ; but other animals do the same ; and to give milk 
is the commensurate property not of a cow but of a mammal ; being 
causally connected with a feature which though present in a cow is 
present in other species besides. 1 

2. id quod pertinet soli sed non omni : thus it is a property of 
man to write poetry, but not universally ; for the writing of poetry 
requires powers which no creature but man possesses, but which 
also one may not possess and yet be a man. 

3. id quod pertinet omni et soli, sed non semper : in this sense it is 
a property of the male egret to grow a certain kind of feather, much 
used by ladies in their hats ; but only to grow it at the pairing season. 

4. id quod pertinet omni et soli et semper : in this sense it is a pro- 
perty of a rectilinear triangle to have its angles equal to two right 
angles ; but it is difficult to find an example of such a property 
among organic kinds, for a feature so constant and universal would 
be regarded as part of the essence : unless like the schoolmen we 
call it a property in this sense to be capable of exhibiting a property 

1 If all the subjects possessing the property are in one genus, it is called 
a generic property. Aristotle's definition of property as a commensurate 
predicate not included in the essence places a generic property under the 
head of accident. Cf. p. 126, infra. 



iv] OF THE PREDICABLES 105 

in sense 3 ; they often gave it as an illustration of property in the 
third sense that man laughs ; and in the fourth sense, that he is 
capable of laughter ; for the capacity is permanent, but the exer- 
cise of it occasional. 

In all these uses of the term property the notion of a necessary 
or causal connexion is retained ; but commensurateness with the 
subject is not insisted on in all. No doubt a commensurate subject 
for every predicate is to be found ; but only by specifying the 
precise conditions (in an organism or in whatever it may be) on 
which the property depends ; but the concrete thing is the subject 
about which we naturally make propositions, naming it after its 
kind ; and kinds being complex may agree together in some points 
while differing in others with intricate variety ; so that when we 
have distinguished the species to which things conform, and the 
attributes which they possess, we cannot divide the latter among 
the former without overlapping. 

Many general and abstract terms, which form the subjects of 
propositions, designate neither natural substances nor mathematical 
entities. There are names of qualities and states of things, like 
softness or putrefaction : or psychical states and processes, like 
pleasure, anger, volition : of the material products of human or 
animal skill, like pump, umbrella, bridge or nest : of natural features 
of the earth's surface, like beach or valley : of determinate parts of 
an organism, like cell or sympathetic nerve : of forms of human 
association, like army, university, democracy, bank. It would be 
tedious to proceed further with such an enumeration. About all 
of these terms it is to be observed that the notion of them involves 
a certain abstraction. Bridge and pump are concrete terms, but 
they are names given to material things because they serve a cer- 
tain purpose, or exhibit a certain structure ; and all else in the 
nature of the thing is disregarded, in considering whether it is 
a bridge, or whether it is a pump. In attempting to define an 
element on the other hand, or an organic species, we have to wait 
upon discovery, in order to know the nature that a thing must 
possess as gold, or as a crab ; the whole nature of the concrete 
thing forms the subject of our enquiry. It is the abstract character 
of the terms which we are now considering, or the limited extent 
of their signification, that renders them more capable of satis- 
factory definition ; they are least definable, where that which 
they denote is most complex ; thus it is easier to define army 



106 AN INTRODUCTION TO LOGIC [chap. 

than democracy, and rigidity than putrefaction. The more complex 
any subject, the less is it possible to exhaust its nature in any 
brief compendium of words, and the greater also are its capacities 
of various behaviour under varying conditions ; all these are part 
of the notion of it, and no definition will really be worth much to 
any one who cannot realize how different the thing defined would be 
in different circumstances. Thus a definition of democracy means 
most to him whose mind is most fully stored with a knowledge of 
history and of institutions and of human life ; he can realize what 
government of the people by the people for the people (if that were 
our definition) really involves. But comparatively little knowledge 
is needed in order that the definition of a bridge may be fully under- 
stood. It will be readily seen, that what has been said of the diffi- 
culty of determining either property or essence in regard to natural 
kinds applies also to such terms as we are now considering in pro- 
portion to the complexity of the notion to be defined ; the more 
complex the subject, and the greater the range and variation of the 
modes in which it manifests itself, according to the conditions under 
which it exists, the more arbitrary becomes our choice of characters 
to be included in the definition, and the less can properties be com- 
mensurate attributes. 

We have now reviewed the theory of predicables as it was first 
propounded ; we have seen that the scheme of knowledge which it 
implies cannot be realized upon all subjects ; that it is best exem- 
plified in mathematics, and in other sciences which deal with 
abstractions. But we have also seen that it contains distinctions 
of great value and importance. These are 

1. the antithesis between an accidental conjunction (or coinci- 
dence) and a necessary or conceptual connexion ; 

2. the conception of the relation of genus and differentia, and of 
the unity of genus and differentia in a single notion ; 

3. the resting the distinction of essence and property upon the 
distinction between that which we start with and that which we 
demonstrate therefrom ; though this use of the term property 
cannot always be adhered to in practice. 

It remains to say a few words upon the Porphyrian doctrine. 

It differs to appearance in one point alone ; the Porphyrian list 
of predicables substitutes Species for Definition. But that difference 
implies a change in the point of view. It implies that we are to 
find the meaning of these five terms — Genus, Species, Differentia, 



iv] OF THE PREDICABLES 107 

Property, Accident — in the relations which its predicates bear to 
an individual subject not as an individual of a certain sort, but barely 
as that individual ; for it is of individuals as individuals, not as of 
a certain sort, that their species (such as man, or horse, or parrot- 
tulip) are predicated. 1 And various inconveniences arise from this 
change. First and foremost we have to determine what is a true 
species, and what only a genus within a wider genus. 2 Do I pre- 
dicate his species of Cetewayo when I call him a man, or when I call 
him a Zulu ? if Zulu be a species, man is a genus, though included 
within the wider genus of mammal, craniate, or animal ; but if 
man is the species, Zulu is an accident. The question thus raised 
is really insoluble ; for species, as is now believed, arise gradually 
out of varieties. It gave rise to many great controversies, as to 
whether a species were something one and eternal, independent of 
individuals, or on the other hand no more than a name. These 
opposite views were indeed older than Porphyry or the mediaeval 
thinkers who discussed them so earnestly ; nor can any philosophy 
refuse to face the controversy between them. But it was a mis- 
fortune that the theory of predicables should have got involved in 
the controversy ; partly because it led to a mode of stating the 
fundamental issue which is not the best : partly because the true 
value of the theory of predicables, as a classification of the relations 
between universals predicated one of another, was lost sight of in 
the dust of the dispute between the realists and the nominalists. 

A second inconvenience in the Porphyrian doctrine is that while 
beginning by distinguishing the relations of its predicates to an 
individual, it cannot continue true to this standpoint. Species is 
properly predicated of an individual ; we ask what is the species not 
of man, but of Cetewayo ; and if the species can be analysed into 
genus and differentia, it is possible to regard these as predicated of 

1 There is a suggestion in Aristotle's Topics of this point of view, for he 
allows that tBiov may mean a peculiarity that distinguishes an individual 
from others ; cf. the passage quoted, p. 101, n. 1, supra, and e. i. 129 a 3-5. 
But his doctrine as a whole implies that the subject term is general. 

2 In technical language, what is an infima species and what a species 
8ubalterna ; it was said that a species subalterna ' praedicatur de differentibua 
specie ', an infima species ' de differentibus numero tantum '. But it is clear 
that this does not help us to solve the problem : how are we to determine 
whether men differ in number only and not in kind ? It is no easier than to 
determine whether man or Zulu is the infima species ; being in fact the samo 
problem restated. Looked at from the other side, the species subalterna 
can of course be called the genus subalternum: of. Crackenthorpe's Logic, 
Bk. I. c. iv. 



108 AN INTRODUCTION TO LOGIC [chap. 

the individual belonging to the species. Nevertheless they are his 
genus and differentia not as this individual, but as an individual of 
this species. And similarly with property and accident : a property 
is necessary to its subject, either absolutely or under definite condi- 
tions, i. e. it belongs to a subject of a certain sort because it is of 
this sort, or of this sort under these conditions ; an accident is not 
thus necessary ; it belongs in a given instance to a subject of this 
sort, but not because it is of this sort, and so need not belong in 
a second instance. But of a subject indicated by a proper name x — 
of an individual as this individual — we cannot thus distinguish the 
predicates. A predicate which is connected with one character in 
the being of an individual is merely coincident with another ; but 
a proper name does not signify one character to the exclusion of 
the rest. Without such selection, we cannot say whether a predicate 
is property or accident. If it is asked whether it is a property of 
Cetewayo to talk, or fight, or be remembered, we must demand, of 
Cetewayo considered as what 1 Considered as a man, it is a property 
of him to talk ; considered as an animal perhaps it is a property of 
him to fight ; but considered as a man, or as an animal, it is an 
accident that he should be remembered, though perhaps a property 
considered as a barbarian who destroyed a British force. So long 
as we consider him as Cetewayo, we can only say that all these 
attributes are predicable of him. They all help to constitute 
his being as Cetewayo, though not all as a barbarian who destroyed 
a British force. 

Thirdly, the Porphyrian doctrine gave rise to a division of acci- 
dents into separable and inseparable which, if a singular term be 
the subject, is confused, if a general, self-contradictory. 2 An in- 
separable accident of an individual is an accident of the species 

1 Or by a designation, unless we regard only the general terms in the 
designation, and not the demonstrative which makes it singular. ' The king * 
is a designation ; if I say that it is a property of the king to be exempt from 
prosecution, I mean of a king, and therefore of George V. 

Ifiuoy fie dictffiepeiv Ae-yerai ertpov crepov, orav dj^apiaroa crvp^f^rjKOTi to erepov 
tov trtpov 8ia<ftepei. dx<x>piCTOV fie av^fif^iTjKos olov yXavKorrjs r) ypvnoTijs fj oiXf) 
(k rpavfiaros (vo-Kippa>6(7cra, Porph. Isag. c. iii, init. ('One thing is said to differ 
peculiarly from another when it differs by an inseparable accident. And an 
inseparable accident is such as greyness of the eye, hook-nosedness, or the 
scar of a wound.') Porphyry indeed says that accidents in general subsist 
primarily in individuals — kcu to. pev <rvpfi(^rjK(Wa ini tg>v cnoputv npnijyovpevuis 
vcpiararai, ib. c. x ; and also that they are predicated primarily of individuals — 

aXXa irp<>T]yovptva)S pfv tcov nropwv (sc. Kar^yopetrat, from the context) and 

secondarily of the species containing these, Kara dfCrepov fie Xoyov /cat twi/ 



iv] OF THE PREDICABLES 109 

under which he is considered, but inseparable in fact from him. 
Thus it is an inseparable accident of a man to be born in England, 
but a separable accident to wear long hair ; because he can cut his 
hair short, but cannot alter his birthplace. Now this notion of an 
inseparable accident is confused, because the attribute is called an 
accident in relation to the species, but inseparable in relation to the 
individual ; the whole phrase therefore involves two standpoints at 
once. And the distinction between separable and inseparable acci- 
dents thus understood has really nothing to do with the doctrine of 
the predicables as a classification of conceptual relations between 
a subject and its predicates. There are, properly speaking, no 
accidents of an individual as the complete concrete individual. The 
Old Pretender might have been born elsewhere than in England, 
and might have cut his hair shorter : regarding him as the son of 
James II, each of these things is an accident ; but regarding him 
completely as the man he was, there was reason for each, and 
neither could have been otherwise without certain historical cir- 
cumstances being different, though history does not usually concern 
itself with tonsorial incidents in the lives even of princes. That 
one thing was alterable while he lived and the other unalterable 
leaves them equally accidents from one standpoint, and equally little 
accidents from the other. If however the subject of which a pre- 
dicate is said to be an inseparable accident be a general term, 
then the expression is self-contradictory. Porphyry said that 
blackness is an inseparable accident of the crow. But if it is an 
accident at all, then it is a mere coincidence that all crows are black, 
and there is nothing in the fact that a bird is a crow requiring it to 

7reptex<n'T(ov ra (irofia, ib. c. vi. But he does not seem to see that it is not 
from their relation to the individual that they are called accidents. For 
his account of the distinction between separable and inseparable accidents, 
cf. C. V crvfifiejiriKos 8e ecrriv 6 yivtrai Kal anoyivtTai X^P 15 T *l s T0 ^ vnaKtinevov 
(pdopas. Siaipetrat 8e (Is 8vo' to fiev yap avTov xutpio-rop eort, to 8e a^coptarof. 
to fiep ovv Ka8ev8eiv x^P^tov o~vpl3ej3r]K6s, to 8e fie\av elvai ax a) P' a " ra,s T< P "opaKi 
Kai to) kldiotri o-vuftefirjKe, SiWrai 8e iirivor)8r)vai Kal *opa£ \tv<6s Kal AWio)\}s 
drro^aXoiv rrjv xpotav ^copir (f>8opas tov vTroKeipevov. ('Accident is what comes 
and goes without the destruction of the subject. It is of two kinds, separable 
and inseparable. To sleep is a separable accident, to be black is an inseparable 
accident of a crow or an Ethiopian ; a crow can be conceived to be white 
or an Ethiopian to have lost his colour without the destruction of the sub- 
ject.') That he regarded inseparable accidents as predicated both of species 
and of individuals as subject is clear from c. vi to 8e peXav tov ts (18ovs to>u 
Kopcixaiv Kai tocv Kara /xepos (sc. KaTrjyopeiTai), o-vfxfieftrjKos ov a^copccrroi/, Kai to 
KiviicrOai dvdpinrov re Kal 7mrov f x a> P l0 ~ T0V ° v o~vp@e(3r)K6s. ( To be black is pre- 
dicated both of the species of crows and of crows severally, being an inseparable 
accident, and to move of man and horse, being a separable accident ) 



110 AN INTRODUCTION TO LOGIC 

be black ; it cannot therefore be inseparable, however constant in 
our experiences the conjunction may have been. Per contra, if it 
is inseparable, that must be because the nature of a crow as such 
requires it, and then it cannot be an accident. The so-called in- 
separable accident of a species is really an attribute which we rind 
to characterize a species so far as our experience extends, without 
knowing whether its presence depends on conditions necessary to 
the being of the species, or partly on conditions in the absence of 
which the species may still exist. That amounts to saying that we 
do not know whether it is an accident or a property ; and so a phrase 
is adopted which implies that it is both. 

It would be well therefore to abandon the division of accidents 
into separable and inseparable ; and it would be well to abandon 
the Porphyrian list of predicables in favour of the Aristotelian. 1 
Either list raises very difficult questions ; but those which have 
been discussed in this chapter are questions that must be raised, 
whether we attach little value or much to the use of the terms 
Genus, Species, Differentia, Property, and Accident. The attempt 
to think out the connexions between one thing and another is so 
vital a feature of our thought about the world, that Logic may not 
ignore the consideration of it. Abstract terms, and general con- 
crete terms, signify not individuals as such, but as of a kind. We 
do regard attributes as connected with one another, and with the 
kind of a thing, sometimes necessarily and universally, sometimes 
through a conjuncture of circumstances in the history of an in- 
dividual. We need a terminology in which to express these differ- 
ences. We do conceive substances, attributes and states, that cannot 
be anatysed into mere assemblages of simple qualities, but only 
per genus et differentiam. These are the facts which justify this 
somewhat difficult part of logical theory. 

1 Mr. C. C. J. Webb has called my attention to the following interesting 
passage in John of Salisbury, Metalogicon, iii. 5 ' Proinde quid genus aut 
diffinitio, quid accidens sit aut proprium, docet [Aristoteles] longe commodius 
his qui in Porphirio aut Categoriis explanandis singuli volumina multa et 
magna conscribunt. In consilium illorum non veniat anima mea, nee aliquia 
emicorum meorum praeceptoribus his utatur.' 



CHAPTER V 

THE RULES OF DEFINITION AND DIVISION : 
CLASSIFICATION AND DICHOTOMY 

In the last chapter the nature of Definition was discussed at some 
length ; but nothing was said of the technical rules in which the 
requirements of a good definition have been embodied. The process 
of dividing a genus into species was also mentioned, but neither 
were the rules given which should be observed in that. It seemed 
better to defer to a separate discussion these and one or two cognate 
matters. Treated first, they would have been less intelligible. 
But what has been said about the relation of genus and differentia, 
the practical difficulties that lie in the way of adequately defining 
certain — indeed most — terms, and the homogeneity which ought to 
characterize the differentiae of the several species in one genus, 
should serve to render the present chapter easily intelligible. 

The rules of definition are as follows : — 

1. A definition must give the essence of that which is to be defined. 

The essence of anything is that in virtue of which it is such 
a thing. It is in virtue of being a three-sided rectilinear figure that 
anything is a rectilinear triangle : in virtue of being an institution 
for the education of the young, that anything is a school : in virtue 
of having value in exchange, that anything is wealth. We have 
seen, however, that in the case of natural kinds, and in some degree 
of highly complex abstract notions, the essence cannot be comprised 
in the compass of a definition, or distinguished very sharply from 
the properties of the subject. In these cases one must be content 
to do the best he can : remembering — 

(a) That the attributes included in the definition should always 
be such as are the ground of others rather than the consequences. 
Thus the higher species of mammal are better defined by the char- 
acter of their dentition than of their habitual food ; since the kind 
of food that an animal can eat depends on the formation of its 
teeth, and not vice versa. 

(6) That we must not give only some comparatively isolated 



112 AN INTRODUCTION TO LOGIC [chap. 

attributes of the subject, but also indicate the kind of subject which 
these attributes qualify. This is done by giving its genus, 1 and 
hence our second rule is : 

2. A definition must be per genus 2 el differentiam (sive differentias). 
The better the definition, the more completely will the differentia 

be something that can only be conceived as a modification of the 
genus : and the less appropriately therefore will it be called a mere 
attribute of the subject defined. Thus a lintel is a bar placed to 
form the top of a doorway ; it can hardly be called an attribute 
of a lintel that it forms the top of a doorway, for that implies that 
having already conceived a lintel, I notice this further as a charac- 
teristic of it ; whereas really, until I have taken this into account, 
I have not conceived a lintel. On the other hand, if sodium 
be defined as an element exhibiting line D in the spectrum, the 
differentia here may fairly be called an attribute. For one may 
have a pretty definite notion of sodium without knowing that it 
exhibits this line in the spectrum. The complexity of the subject 
under definition is in this case such that whatever be taken to serve 
as differentia can be only a small part of its whole nature ; we have 
a pretty substantive concept (if the phrase may be allowed) without 
the differentia ; and therefore this appears as a further charac- 
teristic, which is really selected because it is diagnostic, i.e. it is a 
feature by which instances of the subject can be readily identified. 

3. A definition must be commensurate with that which is to be 
defined: i.e. be applicable to everything included in the species 
defined, and to nothing else. 

4. A definition must not, directly or indirectly, define the subject by 
itself. 

A subject is defined by itself directly, if the term itself or some 
synonym of it enters into the definition. The sun might, for 
example, be thus defined as a star emitting sunlight ; or a bishop 
as a member of the episcopate. Such error is a little gross ; but 
in the indirect form it is not uncommon. It arises with correlative 
terms, and with counter-alternatives, 3 where one is used to define 

1 Cf. Ar. Top. (. v. 142 b 22-29. But properties, according to Aristotle 
(An. Post. £. x), are defined per causam et subjectum, i.e. by specifying the 
subjects in which they inhere, and the cause of their inherence in their subjects. 

2 Where there is a series of terms in subordination, per proximum genus. 

3 Where a subject occurs in two forms, and every instance must exhibit 
either one or other, then these forms may be called counter-alternatives. 
Thus in number, the counter-alternatives are odd and even ; in a line, 
straight and curved ; in sex, male and female ; in property, real and per- 



v] RULES OF DEFINITION AND DIVISION 113 

the other. A cause, for example, is ill defined as that which pro- 
duces an effect, or an effect as the product of a cause ; for correla- 
tives must be defined together, and it is the relation between them 
that really needs to be defined ; this is the ground of applying both 
the correlative terms, and in defining this, we define them. The 
objection to defining a term by help of its counter-alternative is 
that the latter may with equal right be defined by it. If an odd 
number is a number one more than an even number, the even is 
similarly that which is one more than the odd. It sometimes 
happens, however, that counter-alternatives cannot reallylae denned 
at all ; if a man does not immediately understand from examples 
that a categorical proposition either affirms or denies, there is no 
other knowledge to which we can appeal in order to explain to him 
the nature of the distinction, for it is unique ; and in the same way 
there is no defining the difference between straight and curved. 
In such cases, to explain one counter-alternative by the other, 
though not definition, is sometimes the best course we can adopt ; 
for their mutual contrast may help a man to apprehend them both, 
and he may be more familiar with one than with the other. 

There are subtler modes of defining a thing indirectly by itself. 
We may use a term into whose definition that which we profess 
to be defining enters. Aristotle illustrates this by a definition 
of the sun, as a star that shines by day ; for day is the period during 
which the sun is shining. 1 J. S. Mill's 2 definition of a cause as the 
invariable and unconditional antecedent of a phenomenon errs in 
this particular ; for unconditional cannot really be explained without 
presupposing the conception of cause. 

It should be noticed that where the thing defined is designated by 
a compound word, it may be legitimate to employ in its definition 
the words that form parts of the compound. Thus a ball-race is 
the hollow way between the axle and the wheel in which the balls 
run that are used to take the thrust of one against the other. The 
term ball, used in this definition, is not of course what had to be 
defined. 

5. A definition must not be in negative where it can be in positive 
terms. 

The propriety of this rule is obvious. A definition should tell us 

sonal, &c. Contraries, and opposites generally, may be wrongly used to define 
one another in the same way. 

1 Top. (. iv. 142* 34. * System of Logic, III. v. § 6; cf. infra, p. 405. 

1779 I 



114 AN INTRODUCTION TO LOGIC [chap. 

what the thing defined is, not what it is not. This it must do up 
to a point in naming the genus ; but unless the species is distin- 
guished by lacking altogether some character which, in one form 
or another, other species possess, it should continue doing so in 
naming the differentia. An acute-angled triangle, for example, 
should be defined, not as one containing neither a right angle nor 
an obtuse angle, but as one containing three acute angles. In this 
case it is true that a very little knowledge of geometry would 
enable any one to extract from the negative information of the 
former definition the positive characterization of the latter. But 
the negative differentia is in itself inadequate, and such would 
in most cases leave us quite uncertain what the subject positively 
is. If real property were defined as property that cannot be trans- 
ferred from place to place, we should not necessarily gather that it 
was property in land. If anger be defined as an impulse not 
directed to obtaining for oneself a pleasure, who is to understand 
that it is an impulse to repay a hurt ? But for the reason indicated 
in the exception above, a definition with negative differentia is 
not always faulty. In defining a privative or negative concept 
it is inevitable. A bachelor is an unmarried man ; and the very 
meaning of the term is to deny the married state. Injustice, 
said Hobbes, is the not keeping of covenant. A stool is a seat 
for one without a back to it. 1 And short of this, definition by 
a negative differentia is justifiable, in defining a species which 
is distinguished from other species in its genus by lacking what they 
possess. 2 Thus Amoeba proteus is an amoeba without a nucleus ; 
the melancholy thistle (Carduus heterophyllus) is differentiated by 
the absence of prickles. But it must not be assumed that because 
a term is negative in form it need be negatively defined ; intem- 
perance is the excessive indulgence in strong drink. 

6. A definition should not be expressed in obscure or figurative 
language. 

The use of obscure words where plain and familiar words are 
available is a fault in definition, because it militates against the 

1 From Watts's Logic. In the definition of injustice, the genus, conduct, 
is not stated. 

2 My attention has been called to this class of cases by Miss Augusta Klein, 
from whom I borrow the illustrations ; such definitions are diagnostic. The 
subject so defined exhibits the generic character as determinately as other 
species. But the definition, instead of stating in what ways that character 
is positively determined, names a part or feature whose absence makes a 
notable difference. For positive and negative terms cf . supra, c. ii, pp. 40-46. 



vj RULES OF DEFINITION AND DIVISION 115 

object of definition — viz. that one may understand the nature of the 
thing defined. The use of figurative, or metaphorical, language is 
a graver fault, because metaphors, where they are intended to do 
more than merely to embellish speech, may suggest or lead up to a 
right understanding of a subject, but do not directly express it. 
Memory, for example, is ill defined as the tablet of the mind ; for 
though knowledge is preserved in memory, so that we can recover it 
again, and writing is preserved in tablets for future reference, yet 
the two things are very different, and the actual nature of what we 
call memory is as little like that of a tablet as possible. 

It must be remembered that language is not necessarily obscure 
because it is technical. Every science is bound to use ' terms of art ' 
which will be obscure to the layman, but may express the matters 
belonging to that science clearly and precisely. The obscurity 
forbidden is that which would be acknowledged by those acquainted 
with the field of study to which the definition belongs. 

In the process of Definition, we take some species, or other 
concept, and distinguish in it its genus and differentia. Thus 
wealth is that which has value in exchange. There may be things 
which have value, but not in exchange — the air, for example, which 
has value in use ; these are not wealth, and with them, in defining 
wealth, we are not concerned ; though they belong to the same 
genus. But we might be interested in distinguishing the different 
species which all belong to one genus ; and this process of dis- 
tinguishing, or of breaking up a genus into, the species that belong to 
it is called Logical Division. 

Logical Division is a process of great importance in science. 
Things belonging to one genus will be studied together ; and the 
aim of our study will be to discover all the general propositions 
that can be made about them. But though there may be some 
statements that will apply to everything contained within the 
genus, others will only be true of a portion. And the better our 
division of the genus into its species, the larger will be the number of 
general propositions that can be made about its species or parts. 

Division * is closely allied to Classification ; and both to Defini- 
tion. The difference between Division and Classification seems to 

1 In Logic, if Division is spoken of without any qualification, Logical 
Division is meant ; though there are other operations of thought, to be 
mentioned later (pp. 132-133), to which the name Division is also applied. 

12 



116 AN INTRODUCTION TO LOGIC [chap. 

be principally this, that we divide the genus, but classify the parti- 
culars belonging to it. In other words, Division moves downwards 
from the more general to the more special, Classification upwards 
from the particulars through the more special to the more general. 
This, at least, is the difference which one would intend to indicate 
if he contrasted the two operations ; but in actual practice our 
thought moves in both directions at once ; and the process of 
dividing a genus is at the same time one of classifying the things in 
the genus. If, for example, one were asked to divide the genus 
novel, he might suggest a division into the novel of adventure, of 
character, and of plot ; but he would at the same time run over in 
thought the novels that he had read, and ask himself if they could 
be classed satisfactorily under these three heads. 

The close connexion between Division or Classification and 
Definition is obvious. If we divide a genus into species, it must be 
by the help of differentiae, which serve to define the species we are 
forming. If the genus rectilinear figure, for example, be divided 
according to the number of a figure's sides into those with three, 
with four, and with more than four sides, we obtain the definitions 
of triangle, quadrilateral, and polygon. In a classification also, the 
classes established must be distinguished by characters that will 
serve to define them. 

A division may be carried through several stages, i.e. the species 
into which a genus is first of all divided may themselves be sub- 
divided into species ; and this may be continued until the species 
reached no longer require subdivision. The species with which a 
division stops are called infimae species ; the genus with which it 
starts, the summum genus ; and the intermediate species, subaltern 
genera, i. e. genera (for they are genera in respect of the species 
next below them) subordinated to another genus. 1 The proximum 
genus of any species is that next above it in the series ; and the 
words superordinate, subordinate, and co-ordinate are used to indicate 
respectively the relation of any genus to those below it, above it, or 
standing on the same level with it (i. e. having the same proximum 
genus). These terms are also used in reference to a classification ; 
for a classification when completed may be regarded as a division 
and vice versa. The co-ordinate species into which a genus is 

1 Cf. p. 107, n. 2, supra. According to one doctrine, nature has determined 
where division should stop, and infimae species are fixed by nature ; according 
to the other, they are fixed by us with reference to our purpose or con- 
venience. Cf. p. 95, supra. 



v] RULES OF DEFINITION AND DIVISION 117 

divided are sometimes called its constituent species, 1 as together com- 
posing or making up the genus. 

A division, or a classification, may be set out in a scheme, some- 
what after the manner of a genealogical tree. The following is an 

example : — 

Nebula 



I I 

Irresolvable Resolvable 

(i.e. clusters of stars) 



Spiral Lenticular Irregular Containing variables Not known to con- 
tain variables 

The following are the rules which should be observed in a logical 
division : — 

1. A division must be exhaustive : i. e. there must be a place for 
everything belonging to the genus in one or other of the constituent 
species into which it is divided. This rule may also be expressed 
by saying that the constituent species must be together equal to the 
' totum divisum '. 

The necessity of this rule hardly needs indicating. The aim of 
division is to set out in orderly relation whatever is included within 
a certain genus ; and if the division is not exhaustive, this is not 
done. Suppose that an income-tax is introduced ; it is necessary 
that the Act imposing it should state what forms of wealth are to be 
regarded as income, and taxed accordingly. The rent of land and 
houses is clearly a form of income, and would be included in the divi- 
sion of that genus ; but if the owner of a house lives in it instead of 
letting it, he receives no rent. Nevertheless, he enjoys an income, in 
the shape of the annual value of the house he lives in, just as truly as if 
he had let that house, and received for it a sum of money sufficient to 
hire himself another ; and he ought to be taxed if he lives in his own 
house as much as if he lets it. But if the income-tax Act omitted to in- 
clude among the species of income the annual value of houses occupied 
by their owners, he would escape payment on that head altogether. 
Such is the practical importance of making a division exhaustive. 

2. The constituent species of the genus must exclude each other. 
Unless Ave secure this, we do not properly divide ; for the parts 

of that which one divides must be separate from each other. 

1 In Latin, membra dividentia, as the species are conceived to share the 
genus amongst them. 



118 AN INTRODUCTION TO LOGIC [chap. 

There are two ways in which a breach of this rule may come 
about. We may co-ordinate with a species another which ought 
properly to be subordinated to it ; as Dr. Johnson is said to have 
divided the inhabitants of the country north of the Tweed into 
Scotchmen and Damned Scotchmen ; or as the proverb distin- 
guishes ' fish, flesh, fowl and good red herring '. In these instances 
the logical error points a sarcasm ; but in itself it is comparable to 
the procedure of the philosopher, who cut two holes in his door, 
a large one for the cat and a small one for the kitten. 

The second mode in which this rule is broken is by a cross- 
division ; the nature of this will be explained in connexion with the 
rule now following. 

3. A division must proceed at every stage, and so far as possible 
through all its stages, 1 upon one principle, or fundamentum divisionis. 

The fundamentum divisionis, the principle or basis of a division, 
is that character of the genus, in respect of which the species are 
differentiated. 2 Let the genus be soldier ; in a soldier we may 
look to the mode in which he fights, the military rank which he 
holds, or the conditions of service by which he is bound. Proceeding 
upon the first basis, we should divide into artillery, cavalry, infantry, 
engineers, and flying corps; perhaps staff and commissariat ought 
to be added. Proceeding upon the second, we should divide into 
officer and private, officer being again divided into commissioned 
officer and non-commissioned. Proceeding upon the third, into 
regulars, reserve, and territorials. When the division is carried 
further than one stage, the same fundamentum divisionis should 
be retained in the later stages which was used in the first. If the 
division of soldier into artillery, cavalry, infantry, engineers, and 
flying corps be prolonged, we might divide artillery into horse- 
artillery, field-artillery, garrison-artillery, and mountain-battery ; 
cavalry into light and heavy dragoons, lancers, and hussars ; 
infantry into mounted and unmounted. But it would not be 
proper, unless we wish to distinguish our species by combinations 
of differentiae, after beginning with the mode of fighting as our 
fundamentum divisionis, to proceed with that of military rank, and 
divide artillery into officers and privates ; for that is a division of 
soldier generally, and not of artillery any more than of cavalry, 
infantry, or engineers ; so that if it is applied to one of these species 
it must equally be applied to the others. 

1 Of. infra, p. 131. * Cf. supra, c. iv. pp. 86, 10L 



V] RULES OF DEFINITION AND DIVISION 119 

A division which proceeds on more than one fundamentum 
divisionis at once is called a cross-division ; as if one were to divide 
soldier into artillery, cavalry, privates, and territorials. It is called 
a cross-division, because the grouping required by one basis cuts 
across that required by another ; in distinguishing privates, for 
example, from other soldiers, we disregard the distinction of cavalry 
and artillery, taking all members of both those arms who are not 
officers. A cross-division is worse* than useless; for instead of 
assisting to an orderly arrangement of things in thought, it intro- 
duces confusion. 

It is plain that in a cross-division the constituent species will 
not exclude each other. The only security for their being mutually 
exclusive lies in their being formed upon one basis ; for then they 
are distinguished by the different modes in which they exhibit the 
same general character. But if different characters A and B are 
taken, both of them belonging to the genus, everything within the 
genus will exhibit some mode of both these characters ; and the same 
individuals which are included in a species that is constituted by the 
particular mode a' in which it exhibits the character A may also be 
included in a species constituted by the particular mode b' in which it 
exhibits the character B ; hence a' and b' may not exclude each other. 

There are two apparent exceptions to be considered to the state- 
ment that, where more than one fundamentum divisionis is employed, 
the resulting species do not exclude each other. 

The ancient division of matter into the four elements, already 
alluded to as having been adopted by Aristotle, 1 proceeds (or 
appears to proceed) upon a double basis, of temperature and of 
humidity. Matter is either hot or cold ; matter is either moist or 
dry ; and hence four species were established, the hot and dry (fire), 
the hot and moist (air), the cold and dry (earth), the cold and moist 
(water). But there is not really a cross-division here. We do not, 
while professing to divide upon the basis of temperature, at the same 
time introduce species founded upon the basis of humidity (as if 
we were to distinguish the hot, cold, and moist elements) ; our real 
basis is neither humidity nor temperature, but the combination of 
the modes of temperature with the modes of humidity. And such 
a basis offers a peculiarly favourable opportunity for a good division. 
For given a certain number of characters in a genus, each found in so 
many different modes, and granted that every member of the genus 

1 Cf. supra, c. iv. p. 100. 



120 AN INTRODUCTION TO LOGIC [chap. 

must exhibit each character in some mode, and no character in more 
modes than one, then the possible alternative combinations are 
discoverable with mathematical precision. But it is only where the 
combination of certain characters happens to be of primary impor- 
tance, that such a basis of division can be profitably adopted. There 
would be no advantage in applying the method in such a case as 
the division of the genus soldier, where, if we took the three bases 
of mode of fighting, military rank, and conditions of service together, 
assuming five alternatives under the first head, three under the 
second, and three under the third, we should obtain a division into 
forty-five members. These would be mutually exclusive ; yet 
such a result would for most purposes be valueless ; for the three 
bases of division are not such as it is useful to attend to together ; 
though in a particular connexion, as, for example, in drawing up 
a scale of rates of pay, it might be advisable to proceed thus. 1 

In the above case, a cross-division seemed to be employed when 
it was not ; in the next it might seem not to be employed when it is. 
It may happen that in respect of the individuals belonging to them, 
the constituent species into which a genus is divided upon one basis 
coincide respectively with those into which it is divided upon another. 
Thus angiosperms, or plants whose seed is contained in a pericarp, 
may be divided according to the method in which they form new 
wood into exogenous and endogenous ; and according to their mode 
of germination in the seed into dicotyledonous and monocotyle- 
donous. It happens that all the exogena are dicotyledonous, and 
all the endogena monocotyledonous ; so that if the genus were 
divided into exogena and monocotyledons, there would not in fact 
be any plant that fell within both members. Nevertheless, the 
division is logically a cross-division, for there is nothing that we can 
see to prevent the existence of such a plant, and we can imagine 
endogena which are dicotyledonous ; and therefore that our con- 

1 Dr. Venn, Empirical Logic, c. xiii. pp. 318-321, points out the part played 
by this method in Symbolic Logic. Suppose a class S, whose members are 
characterized by the presence or absence of each of the attributes X, Y, Z; 
but not all combinations are found. Then we may work out mathematically 
the class-compartments determined by the different possible combinations of 
differentiae ; and if we symbolize the absence of X by X', there will be 
XYZ, X'YZ, XY'Z, XYZ', and so on. Then the statement that whatever 
is X and Y is Z is equivalent to saying that the class-compartment XYZ* 
is not 'occupied', and can be written symbolically ' XYZ' = '. Such 
methods of symbolization may facilitate the working out of the implications 
of a number of propositions relating to the same genus. But they do not 
express the common character of all reasoning. 



v] RULES OF DEFINITION AND DIVISION 121 

stituent species do not overlap must be regarded as our good fortune, 
whereas it ought to arise out of the necessity of the method on 
which our division proceeds. And even if we came to understand 
the connexion between these differences in mode of wood-formation 
and of germination, such a division would still be vicious ; for it 
would not exhibit our species as necessarily excluding each other ; 
and this because (what is more important) it would not exhibit 
them as alternative developments of a single, or common, notion. 1 

There is a form of division called Dichotomy, which is of necessity 
exhaustive, and the species yielded by it of necessity exclude each 
other ; for it divides the genus at every stage into two members 
(as the name implies), which respectively do and do not possess 
the same differentia ; everything in the genus must therefore belong 
to one side of the division or the other, and nothing can possibly 
fall into both. Animal, for example, may be divided into vertebrate 
and invertebrate, body into animate and inanimate, substance into 
corporeal and incorporeal ; each of these divisions is exhaustive, 
and its members mutually exclusive. 

Some logicians have held that in order to secure these advan- 
tages all divisions ought to proceed by dichotomy. But the truth 
seems rather, that when a division is undertaken with the view of 
classifying or arranging all that is contained in the genus, dicho- 
tomy should not be used. Its use is in analysing or defining some 
one subordinate species. It may, however, sometimes be used to 

1 A cross-division is in fact a defect of principle, which is not removed 
because practical inconveniences are avoided. H. Sidgwick, in his Methods 
of Ethics, holds that it is reasonable for a man to seek his greatest private 
happiness, and also to seek the greatest happiness of the greatest number; 
and he admits that, so far as happiness in this life is concerned, these principles 
would conflict in their application to many situations. He thinks however 
(v. Concluding Chapter) that this ' fundamental contradiction ' would be 
removed, if the Deity by a system of rewards and punishments hereafter 
made it for the greatest happiness of the individual to promote the greatest 
happiness of the greatest number. But the theoretical difficulty, that reason- 
able action is conceived in two ways, between which we see not only no 
necessary connexion, but possible collision, would still remain. So in the 
division of angiosperms into endogenous and dicotyledonous, the specification 
proceeds disparately, and the absence of collision is an ' uncovenanted mercy \ 
If a genus were merely 'items of connotation', to which differentiae were 
added as further items (cf. Venn, op. cit., c. xii. p. 310), such procedure in 
dividing it would have no impropriety : angiosperms X ( = abc) could be 
divided into Xd and Xe. Thus we see the impropriety is evidence that we 
do regard the relation of genus and differentia in the way described in the 
previous chapter : that the alternative species of a genus are bo many ways 
in which the same nature is realized or carried out. 



122 AN INTRODUCTION TO LOGIC [chap. 

show that a division which is not dichotomous is nevertheless exhaus- 
tive, and the constituent species exclusive of each other. 

The reason why dichotomy is out of place as the principle of 
a classificatory division is that we desire in a division to exhibit our 
various species as alternative developments of a common notion ; 
at every stage the genus is further particularized by the differentiae 
which we introduce in constituting its species ; thus the division of 
the genus soldier, according to mode of fighting, into artillery, 
infantry, cavalry, engineers, and flying corps, was carried further 
by particularizing the way in which the artillery may be con- 
stituted for different fighting purposes, or the cavalry armed, &c. 
But one side of a dichotomy is always characterized negatively, by 
the non -possession of the attribute which characterizes the other 
side ; and there is therefore no positive notion, except the original 
genus, which we can develop in the subdivision of this side. Now 
it may be sometimes convenient to use negative differentiae in the 
course of a classification, when one species or subaltern genus is dis- 
tinguished from the rest by lacking a character which they exhibit. 1 
But this is not done upon any principle of dichotomy ; for there 
might be several co-ordinate species or subaltern genera distinguished 
by different forms of that character which the one lacked ; and then 
the division would not be dichotomous, but as manifold as the facts 
required. Thus albinism might be co-ordinated with several varieties 
of pigmentation. And the further differentiation of the subaltern 
genus differentiated negatively would be made by means of some 
fresh generic character ; whereas when dichotomy is adopted as 
a principle, the negative differentia is introduced before exhausting 
the co-ordinate forms of the generic character first used as a basis ; 
so that at each stage the remainder of these appear as variations of 
the lack of the last form taken as a positive differentia. Thus the 
land of a country may be divided, according to the use to which it is 
put, into building-land, farm-land, forest, means of communication, 
pleasure-ground, and waste ; each of these ' subaltern genera ' 
may be subdivided, farm-land for example into arable, pasture, and 
orchard : orchard again according as bush-fruit, tree-fruit, or hops 
are cultivated. But if we were to proceed by dichotomy, we should 
divide land into building-land and land not used for building : the 
latter into farm-land and non-farm-land : non-farm-land into forest 
and not forest, and so forth. Now such a division would not only be 

1 Cf. supra, p. 114, n. 2. 



v] 



RULES OF DEFINITION AND DIVISION 



123 



far more cumbrous than one unhampered by the method of 
dichotomy, as may be seen by setting both out in scheme as 
follows : — 



1. 



Land 



Building-land Farm-land Forest Means of com- 
munication 



2. 



Arable Pasture Orchard 

Of bush-fruit Of tree-fruit Of hops 

Land 



T 1 ri 

Pleasure- Waste 
ground 



Building-land Land not used for building 



Farm-land 
I 



Non-farm-land 



Arable Not arable Forest Not forest 



Pasture Not pasture Means of communication Not means of communication 



Orchard Not Orchard 



Pleasure-ground Not pleasure-ground 



Of bush-fruit Not of bush-fruit 



of bi 



Waste Not-waste 



Of tree-fruit Not of tree-fruit 



1 I 

Of hops Not of hops 

but it fails entirely to exhibit its species as alternative developments 
of a common notion, or (as it was put in the last chapter) variations 
on a common theme. To build on it, to farm it, to let it grow 
timber, &c, are so many ways of using land ; to plough, to graze, 
and to raise fruit from permanent stocks on it are three ways of 
farming, and therefore of using it ; to grow bush-fruit, tree-fruit, 
and hops on it are three ways of raising fruit on it from permanent 
Btocks, and therefore of farming and therefore of using it. 1 But 

1 Perhaps orchards (if they may be held to include all ground used for 
raising fruit from permanent stocks) should be divided according as they 



124 AN INTRODUCTION TO LOGIC [chap. 

to farm land is not a way of not building on it ; a forest is not a 
form of not being a farm ; roads and railways, which occupy land 
that is used as a means of communication, are not modes of not 
being a forest ; to use land as pleasure-ground is not a particular 
way of not making a road or a railway along it ; to leave it waste 
is not a particular way of not using it as pleasure-ground. Neither 
again is grazing a particular way of not ploughing land, nor growing 
tree-fruit a particular way of not growing bush-fruit on it. The 
positive differentia of any subaltern genus negatively characterized 
is therefore really a differentia of the nearest positive genus : 
forest-land and farm-land, e.g., are species of land, not of non- 
farm-land and land-not-used-for-building. A negative concept 
affords no basis for further subdivision, and in a division which 
attempts to classify by dichotomy half the differentiae are useless 
for the development of the generic notion. 

[This is the main objection to a classificatory division by dicho- 
tomy ; which is strangely defended by Jevons, Principles of Science, 
2nd ed., c. xxx, pp. 694-698, and Elementary Lessons in Logic, 
Lesson XII. Other objections, which it seemed unnecessary to add 
in the main text, since the first is fatal, may nevertheless be pointed 
out. The proper division co-ordinates concepts of the same degree 
of speciality ; but the division by dichotomy subordinates them in 
several stages ; so that waste-land is placed level with orchards of 
bush-fruit. The serial order in which the subaltern genera are placed 
(except where a positive concept is divided) is also quite arbitrary ; 
building on land might as reasonably be called a way of not farming 
it, as farming it a way of not building on it. Lastly, it is claimed 
for division by dichotomy that it is the only method which secures us 
from possible oversight of a species : if man be divided into Aryan, 
Semitic, and Turanian, a race may turn up that is none of these ; 
whereas if it be divided into Aryan and non- Aryan, non- Aryan into 
Semitic and non-Semitic, and non-Semitic into Turanian and non- 
Turanian, we have a class ready (non-Turanian) for any new race 
that may turn up. But it must be observed that to say that a race 
is non-Turanian does not characterize it ; that the Aryan and 
Semitic races are also non-Turanian (so that the constituent species 
are not mutually exclusive) ; and that if the last objection is con- 
grow bush-fruit, tree-fruit, or bines ; and bine-orchards might be subdivided 
into hop-yards and vineyards. Even then it is not clear where strawberry- 
gardens would come. Such are the practical difficulties of making a perfect 
division. In the text something has been sacrificed to compendiousness, else 
nursery-grounds, brick-fields, and other varieties of land distinguished 
according to use would need to be included. 



v] RULES OF DEFINITION AND DIVISION 125 

[sidered captious, because the non-Turanian is expressly made a 
branch of the non-Semitic, and that in turn of the non-Aryan, then 
it means what is neither Aryan, Semitic, nor Turanian ; now if we 
are uncertain that our division is exhaustive, and wish to reserve 
a place for things that may fall within none of the species we set 
up, it is easy to do that without the pains of all this dichotomy ; we 
may divide man into Aryan, Semitic, Turanian, and anything that 
is none of these ; this last heading expresses what non-Turanian 
means in the dichotomy, and stands, as it should, upon a level with 
the rest.] 

For this reason, a classificatory division should never use dicho- 
tomy as a principle ; the numbers of species into which a summum 
or subaltern genus is to be divided can be determined not on any 
general logical grounds, but solely with reference to the nature of the 
genus in question. Even where, as in the case of the four elements, 
the basis of division is the combination of attributes, the number of 
possible species that can be formed by different combinations is 
determined, under the restriction that contraries cannot be combined 
together, not by logic but by mathematics. Of course, if a genus 
falls naturally into two species, it ought to be divided in two ; as 
number is divided into odd and even, and line into straight and 
curved. But this is not mere dichotomy ; for it is not the same 
to divide number into odd and even as to divide it into odd and not 
odd. The claim made for dichotomy is that its branches exhaust 
the genus and exclude each other in virtue of the mere form of the 
division * ; since everything in a genus must either be or not be, 
and cannot at once be and not be, characterized by any differentia 
that can be taken. And this is true ; and we need realize no more 
than this, in order to see that number is either odd or not odd ; but 
in order to see that it is either odd or even we need to understand the 

1 Cf. S. H. Mellone, Introductory Text-book of Logic, c. v. § 10, who points 
out that although division by dichotomy ' has been adopted by the mediaeval 
and formal logicians because it appears to provide a theory of division which 
does not make the process depend entirely on the matter of our knowledge, 
as classification does ', yet this appearance is illusory. I know on formal 
grounds that of any genus x the species either are or are not characterized 
by any attribute a ; but I cannot therefore divide x into the two species 
a and not-a, since in fact a may be an attribute never found in the genus at 
all. Every circle must be either rectilinear or not ; but there are not two 
species of circle, the rectilinear and the non-rectilinear. For this reason, in 
Symbolic Logic (cf. supra, p. 120, n. 1), XYZ, X'YZ, &c, represent not classes 
but class-compartments, which may be necessarily empty; and some writers, 
like Mr. Bertrand Russell, recognize by the name of null-class a class which 
has no members. 



126 AN INTRODUCTION TO LOGIC [chap. 

peculiar nature of number, and not merely the general ' laws of 
thought ', as they are called, that hold of every subject. The com- 
pleteness of the division of number into odd or even is not therefore 
vouched by logic, any more than the completeness of the division of 
rectilinear triangle into equilateral isosceles and scalene ; nor in the 
fact that it is twofold does the first possess any guarantee which the 
second lacks in being threefold. And if a genus is seen to fall into 
thirteen species instead of three, it should be divided into thirteen ; 
just as rectilinear triangle should be divided into three and not two. 
Unfortunately there are few subjects where we can see at once that 
a genus contains necessarily so many species and no more ; and 
that makes our divisions precarious, but there is no remedy in the 
use of dichotomy. 

It may, however, occasionally be possible to show by dichotomy 
that a division which is not dichotomous is exhaustive or its species 
mutually exclusive. Aristotle thus supported his list of predicables. 

Predicable 



Commensurate Not commensurate 

I I 

Essence Not essence Part of essence Not part of essence 1 

(Definition) (Property) (Genus or Differentia) (Accident) 

But there is no particular logical interest attaching to this mode 
of establishing a division ; it is in principle the same as where our 
basis is the combination of certain attributes, and we show the 
division to be exhaustive by showing that no other possible com- 
binations remain, as in the case of the four elements already given. 

Element 



hot cold 



moist dry moist dry 

(Air) (Fire) (Water) (Earth) 

Dichotomy is really appropriate when we are seeking not to divide 
a genus but to define a species. There are two contrasting ways in 

1 But generic properties would have to be ranked in this division as acci- 
dents. Cf. p. 104, n. 1, supra. 



v3 RULES OF DEFINITION AND DIVISION 127 

which we may set about to seek a definition. We may take instances 
of that which is to be defined, and try to detect what they have in 
common, which makes them instances of one kind, and on the 
strength of which we call them by the same name. This is the 
' inductive ' method. We might thus define ' snob ', comparing 
those of our acquaintance to whom we could apply the name, or 
those whom Thackeray has drawn for us ; and if we thought that 
among all their differences they agreed in prizing rank or wealth 
above character, we might accept that as our definition. The other 
method is that of dichotomy, and in this we try to reach our defini- 
tion rather by working downwards from a genus, than upwards 
from examples. Some genus is taken, to which the subject we 
wish to define belongs. This genus we divide into what possesses 
and what does not possess a certain differentia. The differentia 
taken must be something predicable of the subject to be defined ; 
and if genus and differentia together are already commensurate 
with that subject, the definition is reached ; if they form only 
a subaltern genus predicable of it, this subaltern genus must be 
again divided in the same way : until we reach a commensurate 
notion. At every stage of our division, the differentia taken must 
either be a modification of the differentia next before it, or at least 
be capable of combining with those that have preceded it in the 
construction of one concept in such a way that we are throughout 
specifying the general notion with which we started ; and there 
should be so many steps of division as there are stages which our 
thought recognizes as important in the specification of this concept. 
At every stage also we proceed by dichotomy because we are only 
interested in the line that leads to the subject we are defining ; all 
else contained within the genus we thrust aside together, as what 
does not exhibit the differentia characterizing that subject. Had 
we further to consider and subdivide it, we could not be satisfied 
with characterizing it only negatively ; for a negative notion 
furnishes, as we have seen, no basis for any further specification. 
But we may disregard, or cut it off : a step to which the technical 
name abscissio inflniti has been given, i. e. the cutting off of the 
indeterminate. 

The following example of definition by dichotomy will illustrate 
what has been said. The term to be defined is tuber ; the genus 
to which it is to be referred is stem. 

1 Cf. infra, pp. 130-131, 133-134. 



128 AN INTRODUCTION TO LOGIC [chap. 

Stem 



creeping not creeping 
underground not underground 

/\ 

much thickened not much thickened 



possessing buds in the not possessing buds in the 
form of ' eyes ' form of ' eyes ' 



In this process, we reach as our definition of a tuber ' a stem 
creeping underground, much thickened, and possessing buds in the 
form of eyes '. At every stage by an abscissio infiniti we rejected 
from further consideration a large part of the genus we had so 
far reached : first all stems not creeping, then all creeping stems 
not underground, then all underground creeping stems not much 
thickened, &c. ; and at every stage we subdivided that part of 
the genus which we had retained by a differentia that specified 
further the form to which we had so far brought it. 

It might have happened, that creeping stems had a name to 

denote them, say Chthamala l ; and that underground Chthamala 

had a special name, say Hypochthamala ; that these when much 

thickened had again a different name, say Pachysmata ; and that 

tubers were pachysmata that possessed buds in the form of eyes. 

In this case, the matter would be set out in somewhat different 

form, as follows — 

Stem 



creeping not creeping 
Chthamalon 



underground not underground 

Hypochthamalon 

/\ 

much thickened not much thickened 

\ 

Pachvsma 



possessing buds in the not possessing buds in th« 
form of eyes form of eyes 

\ 

xSanaXa. Tuber 



v] RULES OF DEFINITION AND DIVISION 129 

This mode of setting out the definition of anything implies a 
classification, in which names have been given to every wider and 
narrower genus, and the differentia which distinguishes each within 
its proximum genus has been settled. It may indeed be regarded 
as an extract from a classification, made for the purpose of exhibit- 
ing the nature of a single species. And this is more or less the 
character of all definition by dichotomy ; though the classification 
may be only in the making, in the very process by which we seek 
for our definition. It is only after considerable study of the parts 
of flowering plants, enabling us to group them by their less super- 
ficial characters, that a tuber would be referred to the genus stem 
at all, instead of root ; by that time, the distinction between 
creeping and other stems, between those that creep above and 
those that creep below the ground, would have been already made ; 
so that the method of dichotomy does not so much help us to 
discover, as to set out and arrange what we know of, the definition 
of a tuber. There may, however, be cases where the method will 
guide us in the construction of a definition of that whose nature 
has not yet been carefully investigated ; the genus to which a term 
is to be referred may be clear, but the appropriate differentiae 
unconsidered ; snob, for example, belongs clearly to the genus man ; 
but even here, the process of finding a differentia, by which to 
distinguish snobs from other men, is classification in the making. 
Let us take the prizing of rank or wealth ; if that by itself does 
not constitute a snob, we need some further differentia, to 
distinguish snobs from other men who prize rank or wealth ; 
say they are distinguished by prizing these beyond character ; 
we then have a definition of a snob, but in getting it, we 
have taken note of a wider class of men within which they are 
included. 

There are three things which Aristotle 1 says that we must look 
to, in reaching definitions by the division of a genus. All the terms 
(the summum genus and the successive differentiae) must be of the 
essence of the subject defined, they must be placed in their right 
order, and none must be omitted. These are requirements also of 
an ideal classification, though in the practice of classification, as 
of definition, many compromises are necessary ; but just as a study 
of the general form of classification does not enable us to classify 
any particular set of things, so we are not enabled to define any 

x Anal. Post. 0. xiii. 97 a 23 sq. 
177» K 



130 AN INTRODUCTION TO LOGIC [chat. 

particular subject, merely by familiarizing ourselves with the scheme 
of definition by dichotomy. 

[A definition of man, displaying the series of subaltern genera to 
which he may be assigned below the summum genus substance, and 
the differentia by which each subaltern genus is successively dis- 
tinguished within the genus next above it, was long known in 
logical textbooks by the name of Arbor Porphyriana. It may be 
transcribed here. That of tuber given above on p. 128 is in the same 
form. 

Substantia 



Corporea Incorporea 

\ 

Corpus 



Animatum Inanimatum 

Vivens 



Sensibile Insensibile 

\ 

Animal 
Rationale Irrationale 

\ 

Animal Rationale 
Mortale Immortale 

\ 

Homo 

/l\ 

Socrates, Plato, &o. 

The material for the scheme is to be found in Porphyry's Isagoge, 
c. iii ; where the writer points out that the same differentia which is 
divisive (SicupeTiK?/) of one genus is constitutive (avarariK-q) of that 
immediately below it. The scheme has the advantage of exhibiting 
the series of differentiae by which the definition of the species is 
reached from the summum genus. Aristotle in Met. Z. xii. discusses 
how many differentiae there really are constitutive of the species ; 
and decides that if each differentia is itself a true differentia of the 
one before it, then the species has only one differentia, namely the 
last. For example, if animal is divided into footed and footless 
(vttottovi and avow) and if the footed are divided into biped and quad- 
ruped, the latter differentia biped is a differentia of footed as such ; 
for to be a biped is a particular way of having feet. In the species 



v] RULES OF DEFINITION AND DIVISION 131 

[animal bipes therefore, the correct analysis is into animal and biped, 
and not into footed animal and biped, and though we may proceed 
through successive stages to biped, there is nothing in the thing 
corresponding to the serial order. If, on the other hand, at any 
stage we introduce a differentia which is not merely a further 
specification of that which we have used before (as e.g. if we were 
to divide biped into feathered and featherless, or rational and irra- 
tional), then the species is constituted by more differentiae than 
one ; e. g. if we take animal again as the genus, the species man, 
defined as a featherless or rational biped, would really be constituted 
by two differentiae. We might endeavour to avoid this conclusion 
by calling biped the genus and featherless or rational the differentia ; 
but that ignores the fact that biped is obviously not summum genus 
of man. And if we select a fresh basis of differentiation at more 
than one stage, we are each time adding to the number of differ- 
entiae that must be recognized in the species. In doing so we 
ignore the precept, to proceed throughout any division upon one 
basis ; and Aristotle certainly speaks of the introduction of a differ- 
entia which is not continuous with that before it as dividing Kara 
to <rvixj3e/3 x\ko ? and not Kara to opOov. We may notice too, that 
where a differentia which is a continuation of that before it would 
be inapplicable to the other member of the preceding genus (e. g. 
biped is not applicable to footless, the other member along with 
footed of the genus animal), a differentia which is not of that nature 
might, for all that we can tell a priori, be applicable to both members 
(e. g. feathered and featherless might be applicable to footless no less 
than to footed animals) ; hence we shall characterize our species by 
the combinations presented in them of the various alternative modi- 
fications of several generic attributes. 1 The fullness and complexity 
of natural kinds constantly leads to the introduction of funda- 
mentally new differentiae, especially where, as in the classificatory 
sciences often happens, our differentiae are intended as much to be 
diagnostic — i. e. features by which a species can be identified — as to 
declare the essential nature of the species. Cf. pp. 133-135.] 

Before distinguishing Logical Division from the other processes 
to which the name Division is applied, it may be well to emphasize 
that it deals entirely (like the doctrine of Predicables) with concepts 
or universals. The genus which we divide is divided into kinds ; 
itself a universal, the specification of it by various differentiae can 
only give rise to more determinate universals. The division of it 

1 Some of these may be attributes not of the summum genus but only of 
some subaltern genus ; and in some combinations, a particular generic 
attribute may be altogether absent ; hence the occurrence of negative dif- 
ferentiae in scientific classifications. Cf. supra, p. 114, n. 2. 

K2 



132 AN INTRODUCTION TO LOGIC [chap. 

stops therefore with infimae species, and never proceeds to the 
enumeration of individuals. For if the infima species could be 
logically divided into individuals, we must apply some fundamentum 
divisionis ; and that means, that we should have to distinguish 
individuals according to the different modes in which the common 
character of the species appeared in them ; and to do that would be 
to distinguish these modes themselves, which are not individual bub 
universal, for many individuals might exhibit the same mode. But 
individuals of any species are in fact distinguished from each other 
by the coincidence of innumerable attributes ; it is not any attri- 
bute singly, but the particular combination of them, that is unique 
in each instance ; and whether or not they are sufficient to constitute 
individuality, unique combinations of innumerable attributes cannot 
be exhibited in a logical division as differentiae of one species. 1 

There are two processes which have been called division, besides 
the division of a genus into its species. They are known as physical 
and metaphysical division. In Physical Division, we distinguish 
the parts of which an individual thing or aggregate is composed : 
as in a man head, limbs and trunk : in a flower bract, sepal, petal, 
stamen and pistil. This process is also called Partition. It is still 
a process of thought that is meant — not the actual tearing of 
a flower to pieces, or quartering and beheading of a man ; it may 
be applied to the distinction of the parts composing either a deter- 
minate individual, or any individual of a kind : as Great Britain 
on the one hand can be divided into England, Scotland, and Wales, 
a tree on the other into root, stem, branch, leaf, and flower, or 
a forest into its component trees. 

In Metaphysical Division, we distinguish in a species its genus 
and differentia, in a substance its different attributes, in a quality 
its different ' variables ' or ' dimensions ' ; thus we may distinguish 
in man animality and rationality, in sugar its colour, texture, 
solubility, taste and so forth, in a sound its pitch, timbre, and 
loudness. This is obviously a division that can be carried out in 

1 Thus in the Arbor Porphyriana the enumeration of the Srofia Socrates, 
Plato, &c., in the infima species man is no part of the logical division. Cf. 
Porph. Isag. C. ii anpa de Xeyerat ra roiavra, on e£ tStor»;TO)i' <rvvi<jTi]Ktv eicatrrov, 
L>v to ti6))m(Tfia ovk av en aXXou TWOS nnre to avTo yevoiro twv Kara ^epos" at yap 
~2(CKpnTO\ii ihiuTT^Tit ovk av eV tiXXov rtvbs tg>v Kara, peput yivot"T av at avrai. 
('Such things are called individuals because each is constituted by peculia- 
rities, the precise collection of which would never be the same in any other 
particular instance ; for the peculiarities of Socrates would never occur identi- 
cally in any other particular.') 



vj RULES OF DEFINITION AND DIVISION 133 

thought alone. In Physical Division, the parts of an individual 
man or plant may be physically separated ; and in Logical Division, 
when the genus is concrete, individual specimens of the infimae 
species may be exhibited in different cases in a museum. But in 
Metaphysical Division, the ' parts ' cannot be exhibited separately ; 
though the colour of sugar may be exhibited without its taste in 
a thing of another kind — e. g. in a sample of salt — it can never be 
exhibited by itself. 

It should be further observed, for the better distinguishing of 
these different kinds or senses of division, that in Logical Division 
the whole which is divided can be predicated of its parts — animal, 
e. g. of man, ox, &c. — and indeed unless it is so predicable of all its 
parts, the division is at fault ; in Metaphysical Division the parts 
can be predicated (paronymously, to use the Aristotelian expres- 
sion, 1 or attributively) of the whole — e. g. whiteness, sweetness, &c, 
can each be predicated of sugar, in saying that sugar is white, is 
sweet, &c. ; in Physical Division, the parts can neither be predi- 
cated of the whole nor the whole of the parts — we cannot either 
say that a leaf or stem is a tree, or that a tree is a leaf or stem. 

[A few words may be added on the relation of Logical Division, 
and its rules, to the practical work of Classification. Just as the 
theory of Definition, with its sharp distinction of essence and pro- 
perty, breaks down amidst the complexity and variety of concrete 
things, so it is with the theory of Division. Ideally when a genua 
is divided into species, whether once or through several stages, we 
ought at each stage to see that just such and so many species are 
possible in that genus ; we do see this in geometry, in the division 
for example of conic sections into hyperbola, parabola, ellipse, and 
circle ; but in other sciences for the most part we must wait upon 
experience. Now we do not in experience find that things fall into 
kinds which fit into any perfect scheme of logical division. Any 
actual division that can be made therefore of animals, or plants, 
or forms of government, would exhibit many logical defects ; every 
classification involves compromise ; the things, which it puts into 
the same class from one point of view, from another claim to be 
placed in different classes ; all that was said in the last chapter 

1 napowvpa be Xiyerat ocra airo nvos 8ia(pe povra rfj nroxrei rrjv Kara rovvopa 
Trpoo-rjyopiav «X«, olov anb TVS ypapp-aTUcrj? 6 ypap-p-ariKot Ka\ atro ttjs avbpeias 
6 dvSpe'ios, Cat. i. l a 12. ('That is paronymous which receives its designa- 
tion from something with a difference in inflexion, as a grammarian from 
grammar and a courageous man from courage.') The Latin for n-apairv/oov 
is denominatum or denominativum, according as the subject or its attribute is 
meant. 



134 AN INTRODUCTION TO LOGIC [chap. 

[about the difficulty of defining concrete natural kinds might be 
repeated to show the difficulty of classifying them ; and the same 
reasons which prevent our satisfactorily continuing a division down 
to a point at which it would find a separate specific concept for 
every individual prevent our satisfactorily classifying them at all. 
Classification is, as Jevons called it, 1 a tentative operation ; its 
results are provisional ; discovery may reveal new species, and 
show that characters which have been supposed always to go 
together may be separated, or those hitherto considered incom- 
patible combined in the same individual : there are limits indeed 
to this, for there are ' laws of nature ' with which all particulars 
must be consistent ; but many so-called ' laws of nature ' them- 
selves rest on the same evidence on which our classifications are 
constructed. 

Thus the ideal which Logical Division sets before us is very 
different from anything which Classification achieves. The first 
is or would be an a priori process ; by which is meant that it would 
fain develop specific from generic concepts not indeed prior to 
any experience of that which belongs to the various species of 
the genus divided, but with a perception that the species revealed 
in experience are such as must necessarily have existed in that genus. 
Classification is an a posteriori process ; it appeals for support to 
the facts which we are classifying, and argues that they reveal such 
connexions of attributes as we take to mark the classes proposed ; 
it does not attempt to show that attributes could be connected in 
individuals of the genus in nO other ways than these. Logical 
Division again would fain be exhaustive, and establish constituent 
species which do not overlap ; but a classification may have to 
acknowledge that there are individuals or whole classes which 
might with equal right be referred to either of two co-ordinate 
genera, or seem to fall between them, or outside them all. For 
these reasons, Division, as treated in a textbook of Logic, is apt 
to seem unreal and fanciful to any one familiar with the work of 
scientific classification ; its rules seem framed to suit not the world 
he has to deal with but a fictitious world of the logician's imagina- 
tion ; the consideration of a process which, outside geometry, can 
scarcely be illustrated by examples except by mutilating facts, is 
denounced as a barren pastime. And there is justice in the denuncia- 
tion, when Division, or Definition, is studied without reference to 
the recalcitrant facts, and on its formal side alone. But if we 
realize with what great abatements the rules of Definition and 
Division can be fulfilled in the actual classification of concrete facts, 
we may yet profitably study these rules, as counsels and not pre- 
cepts. That is the best classification which conforms to them most 
closely. The case of the logician may be compared with that of the 

1 Principles of Science, c. xxx. p. 689, 2nd ed. 



v] RULES OF DEFINITION AND DIVISION 135 

[geometer. The geometer studies such figures as he conceives, and 
he believes that his conclusions are true of the squares or triangles 
that exist eternally in space, bounded by the distances between 
points therein ; but he does not imagine they would apply without 
qualification to a square table, or a triangular lawn. The figures 
of these concrete things are much more complex than a simple 
square or triangle. So (though the cases are not identical) the 
logician studies the problem of classification as it presents itself to 
thought ; but is prepared to expect that real things are cross - 
related to each other in far too complicated a manner for any single 
and simple scheme of classification to embrace them as they stand. 
We must consider aspects of them, and attempt to ascertain what 
various forms some particular property may assume, and under 
what conditions. In tracing a property through all the phases in 
which it appears in different instances, we are in a sense pursuing 
a genus into its species ; we are realizing its generic identity under 
divers forms, and this is part of the business of a logical division. 
The things themselves which we have to classify, if we take them 
in their completeness, cannot be caged in a neat logical arrange- 
ment ; yet even so, the ranking of them in genera and species at all, 
which is not the work of logic, but the natural bias of our thought 
(for the distinction of man and animal is older than that of species 
and genus), implies an effort at such arrangement ; the logician 
does no more than render explicit the aims which underlie all 
classification : except that the form of his theory takes too little 
account of the modifications which are imposed by the particular 
nature of the subject-matter with which we may have to deal. 1 ] 

1 Some useful remarks on Classification, on the difference between so- 
called natural and artificial classifications, and on the relation of different 
classifications of the same set of facts to our different purposes, will be found 
in J. Venn's Empirical Logic, c. xiii. 



CHAPTER VI 

OF THE INTENSION AND EXTENSION OF TERMS AND 
OF THEIR DENOTATION AND CONNOTATION 

We are now in a position to consider certain distinctions in 
regard to terms which, owing to the erroneous identification of 
them, have become involved in much confusion. These are the 
distinctions (1) between Extension and Intension, (2) between 
Denotation and Connotation. It was observed by Aristotle, 1 that 
in one sense the genus is in the species, in another sense the 
species is in the genus. ' Animal ' is in ' man ', in the sense that 
you cannot be a man without being an animal, so that being 
animal is included in being man. ' Man ' is in ' animal ', in the 
sense that among the forms of animal nature, man is included. 

In the technical language of later Logic, this distinction may be 
expressed by saying that in intension the species includes the genus, 
in extension is included in it. 

The intension of a term is what we intend by it, or what we 
mean by it when predicating it of any subject 2 : the extension 
is all that stands subordinated to it as to a genus, the variety of 
kinds over which the predication of the term may extend. 3 Or, if 
by term we mean purely the concept, we may say that the extension 
is the variety of species in which a common character is exhibited, 
the intension the common character exhibited in this variety. The 
distinction may be more readily apprehended, if it is noticed that 
we analyse the intension of a term in denning it, and its extension 
in dividing it. 

It is clear that as between two terms subordinated one to the 

1 Phys. S. iii. 210 a 17-19. Cf. p. 133, supra. 

* I do not wish to imply that we may not ' intend ' the same by a term 
when it is subject of a proposition, as when it is predicate. But as in the 
subject the extension may be more prominent than the intension, while 
the predicate is always understood primarily in intension, the expression in the 
text is less ambiguous than if I said ' What we mean by it in a proposition '. 
Cf. infra, c. ix. 

8 For another use cf. p. 143 sq., infra. 



INTENSION AND EXTENSION OF TERMS 137 

other in a classification, the higher, or superordinate, will normally 1 
have the greater extension ; animal, for example, is a term of 
wider extension than man, and conic section than ellipse ; for the 
concept ' animal ' extends or applies to much besides man, and 
that of ' conic section ' to hyperbola and parabola, as well as to 
ellipse and circle. 2 Many hold also, that the superordinate term, 
as it is of greater extension, so is of less intension ; less being 
meant by calling anything an animal than by calling it a man ; 
or by the term ' conic section ', than by the term ' ellipse '. Hence 
it has been said that the extension and intension of terms vary 
inversely : ' when the intent of meaning of a term is increased, the 
extent is decreased ; and vice versa, when the extent is increased, 
the intent is decreased. In short as one is increased, the other is 
decreased.' 3 

This inverse relation of intension and extension in terms may be 
illustrated not only by reference to classification, but in another 
way. We may take any term, such as Christian, and qualify it by 
an adjective or adjectival phrase : as if we were to say ' Armenian 
Christian ' or ' Christian of Caesar's household ' ; by the qualifica- 
tion we clearly make a term of narrower extension than ' Christian ' 
simply, for we conceive that there may be Christians not Armenians, 
or not of Caesar's household ; and at the same time we add to 
the intension, for it is no part of the concept of a Christian to be 
an Armenian, or of the household of Caesar. 

Still, when we thus qualify a general or an abstract term, we are 
instituting a sort of classification ; we make an Armenian species 
within the genus Christian, or a class, say, of bright colours within 
the genus colour. Therefore we may say generally that it is only 
to terms in a classification, and in one ' series of subordination ' in 

1 Occasionally, as we have seen (supra, p. 73, n. 2), we find in a classification 
Bpecies whose members differ from their nearest kindred as widely as members 
assigned to different genera in it differ, so that they are referred to a distinct 
genus, although no other species is found belonging thereto ; as in zoology 
men are placed in the species Homo Sapiens, which is the only species of the 
genus Homo and of the class Hominidae. But that means that we think there 
might be other genera of Hominidae, and species of Homo : and if there were, 
the relation stated in the text would hold. 

2 Porph. Isag. c. viii Ire ra fieu yevr] nXeovafci rrj rfov wr' nvra elftav nepioxTJ, 
ra 8e tlbr) rav yevuv 7r\(ova(d rais olKeiais Sta^opals-. ('Further, genera exceed 
species in the compass of the species under them, species genera in the 
differentiae belonging to them.') 

3 Jevons, Principles of Science, 2nd ed., c. ii. p. 26. Of. Sir W. Hamilton, 
Lectures on Logic, viii. U xxv ; Thomson, Laws of Thought, § 28 ; Bain, 
Logic, Deductive, p. 51 (' the greater the one the less the other '). 



138 AN INTRODUCTION TO LOGIC chap. 

it, that the doctrine of the inverse relation of intension and extension 
applies. It would be ridiculous to compare in this respect such 
different concepts as democracy and steam-engine ; it is even un- 
meaning to compare terms belonging to the same classification but 
to different lines, or ' series of subordination ', in it ; bird and 
reptile, for example, both belong to a classification of animals, but 
are not subordinate one to the other, and nobody can well tell 
which has the greater intension, nor if that were decided would he 
be able to infer from the decision, which had the greater extension, 
or comprised the larger number of subordinate species. 

Applying only to terms subordinated one to another in a classi- 
fication, the doctrine is an attempt to explain the nature of 
classification, as a series of terms so related that each is of wider 
extension and narrower intension than the next below it. 

Now it may be questioned whether the doctrine is just. The 
generic term undoubtedly exceeds the specific in extension, but does 
it fall short in intension ? This question may be put in another 
form : is the process of classification one of mere abstraction 1 do 
I reach a generic concept from specific concepts merely by leaving 
out part of the latter, and attending only to the remainder ? If 
our concepts of species and genus were constituted by sets of 
attributes disconnected but coincident, then this would be the case. 
The generic concept would be formed by picking out from several 
sets those attributes, or marks, which occur in them all ; it would 
contain fewer marks, or be of less intension, in the same sort of 
way as one man may have fewer decorations than another. On 
these principles the nature of a classification might be satisfactorily 
expressed by the following symbols : — 



I 



ab 



ac ad 

t 



abe abf abg ach aci adj adk adl 

But we have seen 1 that the genus is not something which can be 
got by any process of subtraction from the species ; it is not the 
same in all its species, and does not enter unchanged into them all 
as water into every pipe that leads from a common cistern. You 

1 Cf. p. 83, supra. 



vi] INTENSION AND EXTENSION OF TERMS 139 

cannot form a concept of it apart from all the species, as a can 
be read and written apart from other letters with which it may be 
combined. Attributes that are really independent, such as blue, 
and sweet, and heavy, can be thus conceived apart ; but they 
cannot stand to each other in the relation of genus and species. 1 

If we look at terms which are really in a relation of genus and 
species, it is not clear that the wider term has the less meaning. 
Take animal and man ; if I say of anything that it is an animal, 
I certainly convey less information about it than if I say it is 
a man ; but it does not follow that the concept animal is of less 
intension than man. For it must be noted, that I should not say 
of anything that it is animal, but an animal ; which implies that 
I am aware of other animals, and that the concept animal includes 
alternatives, among which I cannot or do not at present choose. 
But if so, the generic concept would seem to exceed the specific 
in intension ; ' animal ' means ' man, or horse, or crab, or jellyfish, 
or some other form in which the general nature of an animal may 
manifest itself '. As we become familiar with the infinite variety 
of animal life, the term comes to mean not less to us, but more. 

Or take another illustration. Say that a boy first makes acquain- 
tance with the steam-engine in the form of railway locomotives. 
For a long time the term means that to him ; but by and by he 
meets in his experience with traction-engines, ship's -engines, and 
the stationary engines of a factory. His earlier concept of a steam- 
engine — the earlier intension of the term for him — will alter ; much 
which he included at first in it, because he found it in all railway 
locomotives, he will learn to be unessential — first running on rails, 
then the familiar shape, then the moving from place to place. And 
according to the doctrine before us, he will leave out from the 
concept one point after another, and at the end his notion of 
a steam-engine will be the unexcised residuum. But surely his 
notion of a steam-engine will have become richer and not poorer 
in the process ; it is not that he finds that a steam-engine need 
not run on rails, so much as that it may run on the roads, nor 

1 And therefore the introduction of differentiae into a division which are 
not differentiae of those before them is not Kara to 6p6nv (cf. supra, p. 131), 
though they may still be such of which only the genus from which we started 
is susceptible ; and the introduction of them may be justified as well by 
considerations of practical convenience as on the ground that species are 
distinguished by variously combining the variations of many generic charac- 
ters, or characters not pervading the whole genus. 



140 AN INTRODUCTION TO LOGIC [chap. 

that its familiar shape is unessential, so much as that it may be 
built in quite a different manner ; nor that it need not move from 
place to place, so much as that it may work as a stationary engine. 
It becomes a genus to him, because it becomes a thing of alter- 
native possibilities ; and the experience which leads him to extend 
the term to new kinds of subjects leads him to use it with a wider 
range of meaning. It is true that in becoming generic, the term 
comes to have a less definite meaning, when applied to any subject ; 
but it does not therefore come to have less meaning. 

The doctrine of the inverse relation of extension and intension 
in terms may seem therefore to misrepresent the nature of a classi- 
fication. But a doctrine which has been accepted so widely, 1 and 
is at least at first sight so plausible, must have some degree of 
justification. Its justification, or excuse, seems fourfold. 

1. The thought which general terms suggest to the mind is 
often vague, and the more so in proportion as they less suggest 
a definite sensible object. We do not realize all the alternative 
possibilities involved in animal nature each time that we use the 
term 'animal '. So, because in the term of wider, as compared with 
that of narrower, extension there is often little definite, we are apt 
to suppose instead that there is a definite little. This error is 
encouraged by mistaking for thought the imagery that accompanies 
thinking. The nature of this imagery differs with different people, 
and any illustration can be only arbitrary. But it might well be 
that when one thought of man or horse, he pictured to himself the 
look of either with fair completeness ; but that with the notion of 
animal there went the kind of image which a child would draw of 
a quadruped — four lines sticking out of an elongated trapezium, 
with a few more for the head and tail. There is less detail in such 
an image than in that of a horse or a man ; and it is not impossible 
that one might hence be led to suppose there was less intension in 
the term. 

2. Our actual classifications, as we have seen, fall short of per- 
fection in many respects ; we often do not understand the inter- 
dependence of the various characteristics of an organic kind, or of 
the various properties of an elementary substance. In these circum- 
stances, we are compelled at times to fix on certain characters as 

1 There are, however, eminent names on the other side, e. g. Mr. F. H. 
Bradley, Professor Bosanquet, and R. L. Nettleship. Cf . especially section xi 
of the ' Lectures on Logic ' in The Philosophical Remains of R. L. Nettleship. 



vi] INTENSION AND EXTENSION OF TERMS 141 

constituting a genus, and then distribute into species the subjects 
in which they are found by means of attributes whose connexion 
with these characters we cannot conceive. For example, there is 
a far-reaching division of angiosperms (already referred to) into 
monocotyledons and dicotyledons, based on the number of the seed- 
leaves ; but in these two classes the sub-classes are distinguished 
by various characteristics of the calyx and corolla, of the mode in 
which the stamens are inserted, &c. Now we are ignorant why 
a plant with two seed-leaves should be capable of one series of 
flower-developments, and a plant with one seed-leaf of another 
series ; the number of seed-leaves is, for all we can see, an irrelevant 
character, though it cannot really be so ; and the concept of 
dicotyledon or monocotyledon is complete, without reference to 
the character of the flower. Here therefore the intension of the 
wider term is less than that of the narrower. To the botanist 
the term Dichlamydeae, whose extension is less than that of Dicoty- 
ledon, means plants which in the first place have two seed-leaves, 
and over and above that have both calyx and corolla ; the term 
Dicotyledon means merely a plant with two seed-leaves. Such 
cases give colour to the doctrine, that where terms are subordinated 
one to the other, the intension varies inversely with the extension ; 
but they do not embody the true spirit of a classification. 

3. We have seen that a term may be qualified by an adjective 
which is really an accident of it : by which is meant that the ad- 
jectival concept is an addition to the original concept, rather than 
a further determination of it ; as when we qualify the term Christian 
(which implies a certain religious belief) with the adjective Armenian 
(which implies a certain nationality) — there being no necessary 
connexion between creed and race, but any variety of one being 
capable of coinciding in individuals with any variety of the other. 
These cases (to which those considered in the last paragraph ap- 
proximate) bear out the doctrine of inverse relation, so far as they 
go. But it may be observed that they only bear it out, because 
they have been as it were constructed to do so. We take a term, 
and qualify it by an adjective which in the first place is known 
not to be applicable to all instances (and therefore narrows the 
extension), and in the second place is not implied by the term in any 
way as a possible development of the genus : so that it is a sheer 
addition to whatever intension the original term possessed. Then 
we call attention to the fact that in the original term, and the term 



142 AN INTRODUCTION TO LOGIC [chap. 

composed of it and of an adjective, extension and intension vary 
inversely. Of course they do, because we have carefully arranged 
it, by so qualifying the original term that they must. But it is 
ridiculous to infer from this, that in all terms, where one is of wider 
extension than the other, its intension is less. Because this holds 
where the terms are not related as genus and species should be, 
it must not be concluded to hold where they are so related. 

4. It may still be felt that there is more truth in the doctrine 
than has been conceded. Take the most unimpeachable examples 
of genus and species, such as rectilinear triangle, with its species 
equilateral, isosceles and scalene. Can we not and do we not con- 
ceive a rectilinear triangle with regard to those points in which 
equilateral, isosceles, and scalene agree, and without regard to 
those in which they differ? and may not this notion be perfectly 
precise and definite ? and if such be the intension of the genus - 
term, is it not less than that of the species-term ? We must admit 
that this is possible. In the words of R. L. Nettleship, 1 * we may, 
for convenience' sake, mentally hold apart a certain fraction of the 
fact ; for instance, the minimum of meaning which justifies us in 
using the word " triangularity ". We may call this the generic 
triangle, and distinguish it from particular forms of triangle.' But 
the true intension of the term is not the ' minimum of meaning ' 
with which we can use it, but its ' full meaning \ 

What has been so far said with regard to the relation of intension 
and extension in terms may perhaps be rendered clearer to some 
as follows. Wherever we have species of a genus, or distinguishable 
varieties of a common nature, we may contrast the unity which they 
present with the variety. To attend to the intension is to attend 
to the element of unity : to attend to the extension is to attend 
to the element of variety. Sometimes we are more interested in 
one, and sometimes in the other. When Socrates in the Meno 
asks what is virtue, and Meno begins describing the virtue of a man, 
the virtue of a woman, and so forth, Socrates explains that he wants 
to know what virtue is as one in all these, and not what the divers 
virtues are ; in later language, he wished for the intension and not 
the extension of the term. Aristotle remarks 2 that an enumeration 
of these different virtues and a description of them severally are 
more valuable than a vague statement of their common nature : 

1 Philosophical Remains, i. p. 220. The italics are mine. 

2 Plat. Men. 71 D-72 D ; Ar. Pol. a. xiii. 1260 a 20-28. 



vil INTENSION AND EXTENSION OF TERMS 143 

i. e. that here at any rate the element of variety is more worth 
consideration than the element of unity, if either is to be neglected. 
But if the two are realized together, the unity of the superordinate 
whole must be seen as the more comprehensive unity, not as the 
more jejune extract. So far however as we cannot realize them 
together, and see their necessary connexion, it will have the character 
of the jejune extract and be a whole of less meaning, even although 
we know that the variety of species into which it enters is great ; 
and in these conditions, it may be said to be of less intension. 

It follows that the infima species (or the term denoting it), in the 
unity of whose being we recognize no variety, has properly speaking 
no extension. Equilateral triangles may differ in the length of 
their sides, and we may if we like regard this difference as con- 
stituting a variety in their common nature. But if we do not — 
if we conceive the particular length of the sides to constitute no 
difference in equilateral triangularity — then we recognize no such 
variety in the unity as makes it possible to distinguish from the 
intension the extension through which it ranges. The term equi- 
lateral triangularity will denote to us a certain unitary nature, but 
no varieties of such. 

Logicians have been withheld from acknowledging these terms 
to have no extension by two reasons, by one justifiably, by the 
other through a confusion. Justifiably by this, that the point at 
which logical division stops is generally arbitrary, and what are 
treated as infimae species are capable of subdivision into lower 
species, which would be their extension ; ellipses may vary in their 
ellipticity according to focal length, Christians in their Christianity 
according to faith as well as practice. The consciousness of the 
variability of the specific nature which forms the intension of the 
term makes us regard it as still having extension, though less than 
its superordinate terms. Terms within whose intension there is 
no variety, like point, or none recognized, like equilateral triangle, 
are rare. 

The other reason is this, that even where there is no variety 
within the intension of a term, there is multiplicity of instances. 
Though no species of equilateral triangle are distinguished, innu- 
merable equilateral triangles are. Two such triangles interlaced 
are a favourite symbol in the decoration of churches ; and the 
number of them delineated on church-walls and windows must be 
past counting. If the individual instances make the extension, 



144 AN INTRODUCTION TO LOGIC [chap. 

the infima species will have plenty, though still less than its super- 
ordinate terms, because there are more instances of the genus than 
of any one species l — more triangles, for example, than equilateral 
triangles. 

It is plain that this reason involves a confusion between two 
different things, between the variety of kinds over which the pre- 
dication of a term may extend — the variety of which we conceive an 
unity to be susceptible, and the various individual instances in 
which a common nature is manifested. On the former view, the 
extension of man is Aryan and Semitic, Negro and Berber, &c. : of 
triangle equilateral, isosceles and scalene ; on the latter, that of man 
is Socrates and Plato, Alexander and Caesar, you and I, &c, that 
of triangle every triangle on a church wall or on a page of a copy of 
Euclid's Elements. But the relation of genus to species is not the 
same as that of universal to individual, of a kind to its instances, 
and the antithesis of intension and extension ought therefore not 
to be used indifferently in respect of both. We might perfectly 
well understand by the extension of a term either the various forma 
or the various instances in which the common nature that is its 
intension is manifested ; but we ought not to understand both 
indifferently. 

It is easy to see how the confusion arises. Though the antithesis 
between the intension and the extension of terms is based on that 
between the unity in wJiat different individuals are, and the variety 
in which that unity is displayed, most of the terms in which this anti- 
thesis is illustrated are general terms predicated of individuals, like 
man or ox and animal, gold or silver and metal, axe or hammer and tool, 
musician or painter and artist, triangle or square and figure. 2 They 
are predicable of individuals, but in respect of their common nature. 
The superordinate term — animal, metal, &c. — is predicable of more 
individuals, the subordinate — man or ox, gold or silver, &c. — of 
fewer. Sometimes there are also proper names predicable of the 
individuals singly, but all alike are names of individuals. The 
distinction in the meaning of a general name between the individuals 
whereof it is predicable and the common nature in respect of which 
it is predicable of them is important and obvious. Language 
allows us to say that Caesar is a man, and that a man is an animal, 

1 Except in a species which is sui generis : cf. p. 137, n. 1, supra. 

2 In the last two instances the terms though substantival are attributive 
in meaning : cf. supra, p. 37, n. 1. 



vi] INTENSION AND EXTENSION OF TERMS 145 

that Beethoven is a musician and that a musician is an artist, that 
this is gold, an axe, a triangle, and that gold is a metal, an axe a tool, 
a triangle a figure. Hence it is supposed that the relation of man 
to Caesar, or musician to Beethoven is the same as that of animal 
to man, or artist to musician ; the relation of axe or triangle to 
' this ' the same as that of tool to axe, or figure to triangle. For 
we are misled by the common form of the proposition, A is B, and 
do not reflect sufficiently on the different senses in which one thing 
is said to be another. 1 When I say that a man is an animal or 
a triangle a figure, I mean that being a man is a way of being an 
animal, to be a triangle is to be a figure ; and I could say instead 
that humanity is animality or triangularity figurateness. But 
when I say that Caesar is a man, or this a triangle, I do not mean that 
Caesarness is a way of being a man, or that thisness is triangularity ; 
the concrete individual is something more than can be comprised in 
any concept. 

With abstract terms and names of universals we are not 
tempted to make this confusion. We should not feel the same 
hesitation in allowing that ' equilateral triangularity ' as that 
' equilateral triangle ' has no extension ; and if we hesitated to 
deny extension to humanity or democracy, it would be only 
because we are conscious that these concepts are capable of 
further specification, that humanity is something different in 
different men, democracy in France and in the United States. No 
doubt attributes and relations have their instances, and abstract 
terms are names of attributes and relations ; they are predicable 
of the several instances, and as such are general. But the instances 
can only be distinguished by referring to the particular subjects 2 
in which the attributes inhere or between which the relations 
hold ; and in abstraction we commonly ignore these, and consider 
the attribute or relation by itself ; we may be interested in the divers 
forms that it may take, and have separate names for these, for the 
diversities of colour or constitution, consanguinity or proportion ; but 
to be interested in the instances would be to be interested in the con- 
crete individuals that display them, and from these we are abstract- 
ing. Hence it is that the abstract term becomes the name of the 
attribute or relation, of whose instances it is predicable as a general 

1 Cf. supra, pp. 23-24. 

2 Generally concrete individuals, but not always ; I might e. g. direct 
attention to instances of degree by mentioning colour and heat, without 
reference to particular coloured or hot things. 

177» L 



146 AN INTRODUCTION TO LOGIC [chap. 

term, and that even when we use it as a general term, e. g. when 
we speak of so many deaths, in the plural, we are still apt to think 
of the attribute or relation as identical in all its instances ; indeed, 
as we saw, it has been denied that there are instances of relations. 1 

It is plain then that by the extension of a term we should not mean 
indifferently species and individuals ; to be specified in divers ways 
is not the same as to be found in many instances. And there is the 
less necessity for using the word extension thus confusingly, that 
another word, denotation, will serve where the instances are meant. 
A word denotes anything of which it can be predicated as a name ; 
man denotes Socrates and Caesar, artist Beethoven and Giotto, 
triangle this and that triangular figure. It is true that universals 
are denoted also by their names ; animality, triangularity, proportion, 
each denote something; and abstract terms denote not only instances 
of attributes and relations, but the attributes or relations con- 
sidered each as one in its several instances. 1 But this fact need not 
disturb us. We use denote in the same sense, in each case. 

It will be observed also that the inverse relation of extension 
and intension does not hold equally when by the extension of a term 
we mean the forms in which the intension is displayed, and when we 
mean the instances. We saw how the intension of the term animal 
might from one point of view be said to increase, as one becomes 
acquainted with fresh forms of animal life ; and how from another 
point of view, because what at first one might have regarded as 
essential to an animal turns out not to be indispensable, it might 
be said to diminish, shrinking to a jejune residuum. But M'hichever 
way we look at it, it is only acquaintance with fresh forms of animal 
that produces this result ; a mere increase in the number within one's 
acquaintance would not produce it. It is said that you cannot 
widen or narrow the extension of a term without restricting or 
enlarging its intension, and vice versa. But change in the meaning 
of a term comes by extending its application to new kinds of subject, 
or confining it to some kinds only of those to which it was before 
applied. The intension of the term baby does not increase and 
decrease with the fluctuations of the birth-rate. 2 A change in the 
intension of a term will indeed commonly affect its denotation as 
well as its extension, just as the superordinate term in a classification 
commonly denotes more individuals than the subordinate, besides 
having a wider extension ; but only a change in the extension, that is, 
1 Cf. supra, pp. 27, n. 3, 33-35. 2 F. H. Bradley, Principles of Logic, p. 158. 



vi] INTENSION AND EXTENSION OF TERMS 147 

in the kinds of individual denoted, not in the mere denotation, will 
affect the intension. 1 

In place of the terms Extension and Intension, various writers 
have used others to mark either what is, or what they wrongly 
thought to be, the same distinction ; and in particular, since the 
publication of Mill's System of Logic? the antithesis of Denotation 
and Connotation has come into favour. Mill regarded this antithesis 
as identical with that of Extension and Intension ; but he claimed 
for his expressions that they possess an advantage lacking to others, 
in the existence of the corresponding verbs, to denote and to connote ; 
we may speak of a term denoting or connoting this or that, but with 
other expressions we must use a periphrasis and say, e. g., that so and 
so is included in the extension, or constitutes the intension, of a term. 
This advantage and the jingle of the antithesis have combined with 
Mill's authority to bring the word connote into common use ; for 
we do require at times, as the passage above referred to in the 
Meno shows, a word that will distinguish a term's meaning in inten- 
sion from its meaning in extension. In other respects Mill's ex- 
pressions are less appropriate ; for extension suggests, and denotation 
does not, the range through which the intension is manifested ; 
intension suggests, and connotation does not, what we intend by a 
term; and connotation contains a suggestion, inappropriate in many 
cases, of additional meaning. But the trouble is that the two antitheses 
are not really equivalent. A term may denote, which has no exten- 
sion; and may have intension, which, in the prevalent meaning 
of the word, has no connotation. Mill drew his distinction with his 
eye mainly on two classes of terms, attributives and general concrete 
names. The functions of denoting and connoting which he found in 
these he thought to be the only functions of any term. Then, 
because certain terms do not connote like them, viz. proper names 
and the names of infimae species of attributes or relations 3 (like 
length and whiteness), he thought they only denoted ; and he made 
a division of ' names ' into connotative and non-connotative (by which 
he understood unmeaning), which he described as ' one of the most 
important distinctions which we shall have occasion to point out, 
and one of those which go deepest into the nature of language '. 

1 Of course, when the term denotes kinds, its intension will be affected by 
a change in the denotation. 2 v. Bk. I. ii. § 5. 

8 Mill does not mention relations, but the argument applies equally in 
their case ; and if they are not always mentioned in the following discussion, 
that is only for brevity's sake. 

L2 



148 AN INTRODUCTION TO LOGIC [chap. 

As he expounded it, however, it has been a source of little but error 
and confusion. He confounded different distinctions, and raised 
a controversy about the connotation of proper names, to which 
there has been no satisfactory issue, because he never clearly realized 
to himself what he meant by connotation, nor that it was something 
different from intension ; and so the word has been used in the 
controversy in different senses. 

In order to clear up the ambiguities of the word, we must examine 
the passage in which Mill expounds his doctrine. It runs as follows. 
' A non-connotative term is one which signifies a subject only, 
or an attribute only. A connotative term is one which denotes 
a subject, and implies an attribute. By a subject is here meant 
anything that possesses attributes. Thus John, or London, or 
England, are names which signify a subject only. Whiteness, 
length, virtue, signify an attribute only. None of these names, 
therefore, are connotative. But white, long, virtuous, are connotative. 
The word white, denotes all white things, as snow, paper, the foam 
of the sea, &c, and implies, or in the language of the schoolmen, 1 
connotes, the attribute whiteness. The word white is not pre- 
dicated of the attribute, but of the subjects, snow, &c; but when 
we predicate it of them, we convey the meaning that the attribute 
whiteness belongs to them . . . All concrete general names are con- 
notative. The word man, for example, denotes Peter, Jane, John, 
and an indefinite number of other individuals, of whom, taken as 
a class, it is the name. But it is applied to them, because they 
possess, and to signify that they possess, certain attributes. . . . The 
word man, therefore, signifies all these attributes, and all subjects 
which possess these attributes. . . . Even abstract names, though 
the names only of attributes, may in some instances be justly con- 
sidered as connotative ; for attributes themselves may have attributes 
ascribed to them ; and a word which denotes attributes may connote 
an attribute of those attributes. Of this description, for example, 
is such a word as fault ; equivalent to bad or hurtful quality. This 
word is a name common to many attributes, and connotes hurtful- 
ness, an attribute of those various attributes. 2 . . . Proper names are 

1 Mill means that in the case of such terms as these, the schoolmen spoke 
of attributes being connoted ; but not that his use of the word connote 
conforms generally with that of the schoolmen : cf. infra, pp. 156-158. 

2 Mill instances ' slowness in a horse ' as an attribute denoted by the word 
1 fault '. It is clear that if ' fault ' is connotative, ' virtue ' should not lmve 
been given as an example of a non-connotative name. The italics in this 
quotation are his. 



vij INTENSION AND EXTENSION OF TERMS 149 

not connotative : they denote the individuals who are called by 
them ; but they do not indicate or imply any attributes as belonging 
to those individuals.' 

Thus Mill considers three classes of terms to be connotative — 

(a) attributive terms, like white, long, virtuous, &c. ; 

(b) general concrete names, like man, snow, &c. ; 

(c) abstract terms, if they are names of a genus of attributes, like 
fault ; 

and two classes to be non -connotative — 

(a) proper names ; 

(6) abstract terms, if they are names of infimae species of attributes, 
like length, whiteness, &c. Designations, i. e. phrases indicating an 
individual that contain connotative terms, he regards as connotative. 

Now it is true of all his ' connotative ' terms, that they signify 
more or less of what that is, whereof they are predicated ; and they 
are therefore said to denote the subjects of which they are predicable, 
and to connote whatever character x they indicate these subjects to 
possess. But further, they are used of these subjects because of their 
possessing such character. Mill means then by the denotation of 
a term the subjects of which it can be predicated, by the connotation 
that character, to indicate the possession of which we use the term 
of any subject. 

It might seem that we could say simply, that the connotation of 
a term is its meaning. But there are two reasons why this is not so. 
In the first place, terms have two functions, both of which may be 
called meaning. They direct our thought to some subject, and they 
suggest what that subject is, to which our thought is directed. I 
may be said e. g. to mean by tools either spades, hammers, axes, &c, 
or ' things made in order that we may by their means in handling 
them do what we could not do, or do so well, with our unaided 
hands '. Mill would say that the former is what the word denotes, 
the latter what it connotes. In the second place, a term may dis- 
charge the function of signifying what the subject is, to which it 
directs our thought, in two ways. It may signify the subject in its 
entirety, or some character in the subject, with which the subject 
is not identical. It is only the latter function which Mill calls 
connoting, as in the example tool just given. Terms which mean 
what the subject is in its entirety he calls non-connotative, and he 

1 Mill says attributes, because he regards e.g. being gold as an attribute 
or aggregate of attributes in any piece of gold. 



150 AN INTRODUCTION TO LOGIC [chap. 

does not think that they signify what the subject is at all. And there 
are further differences within both kinds of terms, in their way of 
discharging the function of signifying what the subject denoted by 
them is, which Mill ignores. 

The most important class of his ' non-connotative ' terms is proper 
names. If connotation in a term is signifying some character in 
a subject, to indicate its possession of which we use the term of any 
subject, proper names certainly do not connote. But besides this 
signification in a term Mill recognized no other function, except 
denoting. Hence he thought that proper names only denoted, and 
were ' unmeaning marks '. ' A proper name ', he says, ' is but 
an unmeaning mark which we connect in our mind with the idea 
of the object, in order that whenever this mark meets our eyes or 
occurs to our thoughts, we may think of that individual object ' l ; 
and he contrasts connotative names as ' not mere marks, but more, 
that is to say significant 2 marks.' Now in thinking that a proper 
name merely denotes, and signifies nothing, Mill was wholly wrong. 
It is the sense of this error which has led critics to say that proper 
names have connotation 3 ; and if we had to make the antithesis of 
denoting and connoting cover the ground in regard to the functions of 
every kind of term, that would certainly be the less misleading 
doctrine. But Mill was calling attention to a real difference distin- 
guishing his ' connotative ' from proper names, which may be well 
expressed by saying that proper names have no connotation, if we 
accept the sense of ' connotation ' which may be extracted by con- 
sidering the classes of term to which he ascribes it, and reject his 
identification of it with ' signification ' generally. We may the more 

1 This account of a proper name closely resembles Hobbes's definition of 
a name generally (quoted p. 20, supra), which in the first section of the same 
chapter Mill approved. Hobbes says that a name is ' a word taken at pleasure 
to serve for a mark which may raise in our mind a thought like to some 
thought we had before '. To say that it is taken at pleasure means that 
it is not taken on account of any pre-existing signification. This is true at 
the outset of all names, proper and general alike, except derivatives. A 
general name was unmeaning before it was given to anything ; so also is a proper 
name. But a proper name, like a general name, has a meaning after it is 
given. 

2 Mill obviously means by signifying being the sign of what a thing is ; 
else he could not distinguish ' mere marks ' from ' significant marks ' ; for 
a mere mark denotes. It is possible to use the word ' signify ' in the sense 
of ' denote '. But throughout the following discussion it will be used as 
Mill uses it. 

3 e.g. Jevons, Elementary Lessons in Logic, Lesson V : Bosanquet, Essentials 
of Logic, Lect. V. § 6 ; also the first edition of this book. 



vi] INTENSION AND EXTENSION OF TERMS 151 

conveniently do this, because the signification which proper names 
do possess is perfectly well indicated by the word ' intension '. 

A proper name certainly has intension as well as denotation. It is 
a mark directing our thought to an individual ; but that which is to 
be a mark must have meaning. A scratch may be a mark on a coin 
which I am looking at ; it is not a mark of the coin that I am looking 
at, but of its being the same coin which I had put in the way of 
a suspected thief. I may of course be ignorant of the meaning of 
a mark. The broad arrow T which is occasionally seen on gate- 
posts, milestones, &c, is a mark; a traveller might not know what it 
meant ; but he would not call it a mark, unless he guessed that it 
meant something. By enquiry he might learn that it meant that 
the spot where it was placed was the precise spot whose height 
was recorded in that portion of the ordnance survey. Here the mark 
is general. But the mark by which his nurse recognized Odysseus 
was equally significant. In its own nature it was a scar, the conse- 
quence of a wound, and not (like a brand) intended as a mark. Yet 
this scar (its precise form and position being taken into account) to 
those who had observed it in Odysseus became a mark by which to 
know him. He had been absent twenty years, and was changed 
otherwise beyond recognition ; he was supposed to be dead ; but his 
nurse, seeing the mark, knew the man before her to be him — knew 
that about the man before her which otherwise she would not have 
known. How can it be said that it was an unmeaning mark for her ? 
And suppose that instead he had at once told her that he was 
Odysseus ; the name would have given her precisely the same 
information ; how then could the name be unmeaning ? The 
doctrine that proper names have no intension is refuted by every 
criminal who assumes an alias. 

And not only, to any one who knows of what individual it is the 
name, has a proper name meaning, but it has more meaning than 
a general term. The cry ' man overboard ' would have conveyed to 
Aeneas and his companions not more but less information than the 
cry ' Palinurus overboard '. It cannot indeed convey to any one, 
for he cannot know, the whole character of the individual denoted ; 
but it excludes from its meaning designedly nothing of that character ; 
whereas another term, if it is not the name of an infima species of 
attributes, 1 is designedly confined to signifying only some deter- 

1 This is intended to signify the whole character of what it denotes : cf. 
infra, p. 154. 



152 AN INTRODUCTION TO LOGIC [chap. 

minate character in what it denotes. Mill speaks as if, were I to 
point to some individual person or thing, and to ask who or what is 
that, and were another to reply by a proper name, I should only 
learn what it is called, not what it is. And if I now heard the name 
for the first time, that is true. But it is equally true of a general 
name, when I hear it for the first time. If I point in a foreign 
country to an unfamiliar object, and ask what is that, though I am 
answered with a general name, I shall only learn what in that 
language it is called. On the other hand, if a proper name is, and 
I know it to be, the name of something with which I am already 
familiar, either personally or by report, it may be very instructive. 
What would not a man have given to be once truly told, in reply to 
the question ' Who is that ? ' ' Napoleon ' ? Or if I cross a country 
road, and am told ' That is Watling Street ', do I not learn much 
more about it than what it is called, and more than the word 
' road ' conveys ? 

What then is the important difference between a proper name and 
other classes of term, which Mill wishes to indicate by saying that 
proper names have no connotation ? It is that they cannot be used 
to convey information about an otherwise unknown individual. 
A general term, used of any subject, is instructive to those not 
acquainted with the subject. If I ask ' What startled you ? ' and 
you tell me a karait, I shall know that it was a very venomous snake. 
That is because the term ' karait ' is used of a subject merely to 
indicate that it has a certain character, of any subject possessing 
which it might be used equally. It has a signification on the ground 
of which it may be predicated of one fresh individual after another. 
But a proper name is not used of any individual for the first time on 
the ground of a signification which it already possesses ; the son of 
James I and VI was not called Charles on account of his Carolinity. 1 
It acquires its signification from the individual to which it is given. 
Hence it is uninstructive to any one ignorant of the individual 
denoted. If I ask ' What startled you ? ' and you answer ' Glamby ', 
I shall not know in the least what it was, unless I know already 
what that word denotes. On the other hand if I do already know 
that — if I know that Glamby is the name of your dog or your baby 
or the ghost that haunts your house — I shall learn not only what 

1 Hence, as was pointed out p. 47, supra, the name Charles is used equi- 
vocally of him, of his son, of the son of Pepin, &c. But an equivocal term 
is not a term with no meaning ; it is a term with more than one meaning. 



vi] INTENSION AND EXTENSION OF TERMS 153 

kind of individual it was that startled you, but what individual of 
that kind. For this is a further peculiarity distinguishing a proper 
name from terms of any class that Mill calls connotative : it is part 
of the meaning of a proper name that the subject denoted is precisely 
this or that individual. That is why a proper name can be the 
predicate of a proposition ; we make it a predicate when we wish to 
say not of what kind something is, about which information is 
offered, but what individual of some kind. If I were wandering for 
the first time in a country known to me by history, and, coming to 
a village, asked its name, the answer Quatre Bras would not tell me 
that it was a village, but which village it was. And since I may 
point to this village without knowing which it is, I can distinguish 
in a proper name the function of designating or denoting an individual 
from that of signifying which individual, with all its being and history, 
is denoted ; and so I must say that, besides denoting, it has intension ; 
only, part of its intension, concerning what it denotes, is that this is 
such precise individual. 1 Did it signify nothing concerning that 
which it denoted, it would not even have denotation. If you say 
that you have been reading about Quatre Bras, and I do not know 
whether that is a village or a general or a poem or a star, it denotes 
nothing to me. A name could only denote and have no signification 
if that could be discriminated which had no character. 2 

All this indeed only amounts to saying that a proper name has 
not general meaning. Mill really intended by connotation general 
meaning, but thought that to lack it was to lack meaning altogether. 
' General meaning ' is not however a complete account of what he 
intended by the word. Connotation is signifying some character in 
a subject, which can be distinguished from that subject. ' A con- 
notative term is one which denotes a subject and implies an attribute.* 
When a term signifies a subject in its entirety, what it signifies i3 
not an attribute of what it denotes. Hence Mill denied connotation 
to another class of terms, the names of infimae species of attributes. 
He was assisted to do so by confusing the relation of species to genua 
with that of individuals to their kind. Man denotes ' Peter, Jane, 

1 If we had to make the words denotation and connotation express all the 
functions of all kinds of terms, we might say, though a trifle loosely, that 
the denotation of a proper name is part of its connotation. 

2 Mill's confusion between an individual's substantial nature and an attri- 
bute perhaps helped to mislead him here. Because, if I think away its being 
white, snow still remains something that I can discriminate, therefore he 
seems to suppose that, if I think away his being man, John still remains 
something which I can discriminate. 



154 AN INTRODUCTION TO LOGIC [chap. 

John,' and connotes their common character ; fault denotes slow- 
ness, stupidity, &c, and connotes their common character. Man is 
connotative, Peter or Jane or John is not ; and similarly, he thinks, 
fault is connotative, slowness or stupidity not. But this result, 
unlike his similar view about proper names, is both devoid of 
plausibility and in contradiction with his teaching elsewhere. So 
unplausible is it, that some, being unable to bring these terms under 
the formula just quoted, have preferred to deny to them denotation. 
And it flatly contradicts Mill's doctrine, that definition declares the 
connotation of a name. For the name of a species of attribute may 
be definable 1 by giving its genus and differentia, even where that 
of the genus is not ; and yet according to Mill the latter has con- 
notation, and the former none. 

That these terms are unmeaning is clearly absurd. When Wolsey 
says to Thomas Cromwell, ' Cromwell, I charge thee, fling away 
ambition ; By that sin fell the angels ', the word ambition does not 
denote an object of thought, without signifying what that is which 
it denotes, but signifies the nature of the sin which Cromwell is 
warned to avoid. Yet it also denotes it. Such terms are names 
of universals, of the common character in many instances of an 
attribute or relation. 2 But of what they denote they signify the 
entire being ; and what they denote is general. Hence, if to be 
connotative is to have general meaning — and that is why Mill denies 
connotation to proper names — they are connotative. If it is to 
signify something general in a subject of which that is not the entire 
being, they are not. This is the ambiguity which is the source 
of Mill's vacillating language. 

Proper names, then, and the names of infimae species of attributes 
and relations both signify the entire being of what they denote, but 
with a difference, because what the latter signify is general, and may 
be definable. Those are the classes of term which Mill calls non- 
connotative. But the classes which he calls connotative, though he 
offers a single account of them all, are not really alike. An attribu- 
tive term, like long or white, 3 denotes that which, being constitutively 
something else, is long or white also 4 ; and it is connotative because 

1 It need not be ; e. g. blue is a species of colour, but can no more be 
defined than colour, because to know the specific difference presupposes that 
I know the species ; I could only say that it is a blue colour. 

2 Or names of the instances considered merely in their common character. 

3 These terms were called connotative by the schoolmen : v. infra, p. 157. 

4 Hence they are commonly combined with a general term, and we speak 



vi] INTENSION AND EXTENSION OF TERMS 155 

it notes a character found along with the constitutive being of the 
subject which it denotes. 1 Its ' connotation ' is not the constitutive 
or general being of that subject, but some detail in its being, which 
would be denoted by the corresponding abstract term length or 
whiteness. 2 But a general concrete name, like man or snow, does not 
denote that which, being something else, or having some other con- 
stitutive being, is man or snow also ; and it is connotative because, 
besides denoting a subject, it signifies not some detail in its being, 1 but 
its constitutive or general being ; the prefix, if it has any force, has 
not the same force in this case. And those abstract terms which 
Mill calls connotative he calls so because, besides denoting species of 
relation or attribute, they ' connote ' their generic nature. 2 

We may now sum up the results of our investigation into the 
antitheses Intension and Extension, Connotation and Denotation. 
All terms may be said to denote the subjects of which they can be 
predicated, but those most directly which are names of, or can 
stand for, those subjects ; hence adjectives, when used to denote the 
subject of a proposition, are often combined with a demonstrative 
word, such as an article. All terms have intension, or meaning ; 
that is, they signify all or something of what that is which they 
denote. When the intension, or what is thus ' intended ', is some- 
thing displayed in divers forms or species, these are said to be the 
extension of the term ; and sometimes the individuals in which the 
common nature, which is the intension of a concrete general term, 
is found are called its extension ; the latter usage is not extended to 
general abstract terms, for in abstraction the instances are not dis- 
criminated. Either way, proper names have no extension ; names 
of infimae species of substances can only be said to have extension, 
if the individuals are taken as the extension ; names of infimae 
species of attributes can only be said to have it on the same condition, 
that we consider their individual instances. What is commonly 

of long days or long shadows, white sails or white complexions. The fact 
that they may also be combined with proper names, so that we can say 
' the envious Casca ' or ' the melancholy Jacques ', shows that proper names 
have intension. No one would say ' the envious X ' if he did not know in 
the least what that was, which X denoted. 

1 A word like traitor or artist might be said to do this ; but we have seen 
(p. 37, n. 1, supra) that these, though substantives grammatically, are attri- 
butive in function. They also were called connotative by the schoolmen. 

2 Attributive terms also may be predicated of attributes and relations, as 
when we say that impartiality is rare ; here rare connotes an 'accident ' in 
the attribute which it denotes, and not, as virtue would, its generic nature. 
Mill takes no account of this difference. 



156 AN INTRODUCTION TO LOGIC [chap. 

said abont the inverse relation of intension and extension in terms 
refers only to terms subordinated one to another in a classification, 
and does not regard individuals as the extension. Lastly, terms 
have connotation which have general meaning ; the connotation 
of a term is that character through signifying which it denotes the 
subjects of which it can be predicated. 

[It may be added that the instance which Mill takes, on which 
to argue that proper names have no connotation, viz. Dartmouth, 
confuses the issue. He urges that the town would still have the 
same name if the river changed its course, though the name would 
not then connote the town's position ; therefore it connotes nothing 
now. The argument is not good. If a town is called Dartmouth 
because it stands at the mouth of the Dart, so far the name is 
a designation. But meaning or intension in a proper name is not 
dependent on connotation belonging to a connotative word in it. 
Mill should have taken the river's name Dart, or Dartmouth in 
New Hampshire. The latter illustrates yet another point. Most 
proper names are chosen for a reason. A mountain may be named 
after its discoverer or first climber, a town or college after its 
founder, a child after its grandparent or godparent, a society after 
some one of whom its members wish to be considered the disciples. 
But this does not become part of the meaning of the name, which 
is derived from that to which the name is given. A similar remark 
applies to those names in which, as often happens, something may 
give a clue to the nature or nationality or sex of the subject denoted ; 
the guess may be wrong ; but even if it is right, the feature which 
gave the clue functioned as having general meaning ; and the 
meaning which it is important to vindicate for proper names is 
not general meaning. It is however relevant to this vindication, 
that proper names often come to acquire general meaning ; Caesar 
is a familiar instance, and we have all heard of a Daniel come to 
judgement, and that Capuam Hannibali Carinas fuisse. For this 
acquisition comes about through extending to another subject some 
part of the signification which the name derived from the subject 
to which it was originally ' proper '.] 

[For the sake of the curious, a few words may be added on the 
history of the term ' connotative '. In William of Occam a dis- 
tinction is found between absolute and connotative terms. Absolute 
terms have not different primary and secondary significations ; 
* nomen autem connotativum est illud, quod significat aliquid pri- 
mario et aliquid secundaria' He gives as instances relative names 
(for father signifies a man, and a certain relation between him and 
another) : names expressing quantity (since there must be some- 
thing which has the quantity) : and certain other words : v. Prantl, 



vi] INTENSION AND EXTENSION OF TERMS 157 

[GeschicMe der Logih im Abendlande, Abs. xix. Anm. 831, vol. iii. 
p. 364. Johannes Buridanus said that some terms connote nothing 
beyond what they stand for (' nihil connotantes ultra ea, pro quibus 
supponunt'); but ' omnis terminus connotans aliud ab eo, pro quo 
supponit, dicitur appellativus et appellat illud quod connotat per 
modum adiacentis ei, pro quo supponit '.* Thus meus and tuus 
stand for something which is mine or yours ; but they connote or 
signify further and ' appellant me et te tanquam adiacentes ' (id. ib. 
xx. Ill, vol. iv. p. 30). Elsewhere we are told that ' rationale ' 
' connotat formam substantialem hominis ' (xx. 232, vol. iv. p. G3 : 
cf. Anm. 459, p. 109). Elsewhere again album and agens are given 
by Occam (ib. xix. 917, vol. iii. p. 386) as examples respectively 
of connotative and relative terms ; and it is explained (ib. Anm. 
918) that a connotative or a relative term is one which cannot be 
defined without reference to one thing primarily and secondarily 
another ; thus the meaning of album is expressed by ' aliquid habens 
albedinem ' ; and when by any term anything ' connotatur vel 
consignificatur, pro quo tamen talis terminus supponere non potest, 
quia de tali non verificatur ' 2 , such a term is connotative or relative. 
Thus a term was called connotative if it stood for (' supponit pro ') 
one thing, but signified as well (' connotat ') something else about 
it ; as Archbishop Whately says (Logic, II. c. v. § 1, ed. 9, p. 122), 
'it "connotes", i.e. "notes along with" the object [or implies], 
something considered as inherent therein.' The Archbishop sug- 
gests the term attributive as its equivalent ; and though connotative 
terms were not all of them adjectives, since relative terms also 
connote, and so do terms like ' mischief-maker ' or ' pedant ', which 
though adjectival in meaning are substantival in form, yet adjectives 
are the principal class of connotative terms, in the original sense 
of that word. 

Connotation and denotation were thus originally by no means 
equivalent (as they have come to be treated as being) to intension 
and extension. Connotative terms were contrasted with absolute, 
and their function of connoting distinguished from that of standing 
for something. James Mill, who probably by his remarks upon 
the word connote had some influence in directing his son's attention 
to it, says that ' white, in the phrase white horse, denotes two things, 
the colour, and the horse ; but it denotes the colour primarily, the 
horse secondarily. We shall find it very convenient to say, there- 
fore, that it notes the primary, connotes the secondary, signification ' 
(Analysis of the Phenomena of the Human Mind, vol. i. p. 34, ed. 

1 i.e. to use J. S. Mill's terms, it denotes 'id pro quo supponit', and 
connotes ' id quod appellat '. For appellatio cf . Prantl, vol. III. xvii. 59 
(' proprietas secundum quam significatum termini potest dici de aliquo 
mediante hoc verbo " est " '). Cf. also ib. xix. 875. 

2 Occam means that, e.g., snow can be referred to as album, but albedo not. 



158 AN INTRODUCTION TO LOGIC 

[1869). By the schoolmen it would commonly have been said to 
connote the colour, and the primary signification was that ' pro 
quo supponit '. J. S. Mill, in a note to p. 299 of the same volume, 
objects to his father's inversion of the usage. But he himself, by 
extending the term connotative to cover what the schoolmen called 
absolute, and opposed to connotative, names, introduced a complete 
alteration into its meaning. 

John and man are both absolute names in Occam's sense. Man, 
no doubt, according to some (though not according to a nominalist 
like Occam) signifies in John, or anything else ' pro quo supponit ', 
an universal nature ; but John and this are not two things, of 
which it denotes one primarily and the other secondarily, or for 
one of which it ' supponit ', and ' appellat ' the other ; for John 
is a man, and without what the word man signifies would be nothing 
for which that word could stand or by which it could ' call ' him. 
With white it is different ; I have a notion of paper, and a notion 
of whiteness, and whiteness is no necessary part of my notion of 
paper ; and so with any other subject of which whiteness is only 
an attribute and not the essence. Hence the name white may be 
said to signify (or in James Mill's usage to denote) two things, the 
colour, and that which is so coloured ; for these can be conceived 
each without the other, as John and man cannot ; or, if we prefer, 
it may be said to denote or stand for one, and to connote the other. 

(Cf. also on the history of the word Connotative a note in Minto'a 
Logic, Inductive and Deductive, p. 46.)] 



CHAPTER VII 
OF THE PROPOSITION OR JUDGEMENT 

A general acquaintance with the nature of the judgement or 
pioposition has been hitherto assumed. It would be impossible for 
Logic to be written, or if written to be understood, unless the acts 
of thought which it investigates were already in a way familiar ; 
for Logic arises by reflection upon an already existent thought 
of things. Now judgement is the form in which our thought of 
things is realized, and it is primarily in judgement that we use terms. 
Their use in question, command, exclamation or wish presupposes 
earlier judgement. The varieties of terms, the different relations 
of one to another which form the basis of the distinction of pre- 
dicables, would be unintelligible, unless it were realized that, in the 
first instance, terms come before us only as elements in a judgement. 
They live, as it were, in a medium of continuous judging and think- 
ing ; it is by an effort that we isolate them, and considering subject 
and predicate severally by themselves ask in what relation one stands 
to the other, whether they are positive or negative, abstract or con- 
crete, singular or general, and so forth. Without presuming some 
knowledge of this medium in which they live it would be of as 
little use to discuss terms, as to discuss the styles of Gothic 
architecture without presuming some knowledge of the nature of 
space. 

We must now consider more closely what judgement is, and what 
varieties of judgement there are that concern Logic. 

A discussion of judgement raises many metaphysical problems, 
into which such a work as this cannot enter fully. But a few things 
may be pointed out about it. 

To judge, in the logical sense of the word, is not to acquit or 
condemn, but to affirm or deny a predicate of a subject. There is 
however a connexion between the logical and judicial uses of the 
word. Judgement, in the logical sense, is often preceded by what 
must indeed be called thinking, but is not judging, viz. questioning 



1G0 AN INTRODUCTION TO LOGIC [chap. 

or ' wondering ' ; but this process, if we do not give it up, is ended 
or decided by a judgement, as the judge by his judgement after 
considering decides the case. It is true that as the judge may be 
mistaken in the opinion which he reaches on the facts, so we commonly 
in our judgements form fallible opinions only ; and Logic can render 
no greater service than to make us more alive to the distinction, 
which the grammatical form of the proposition fails to reflect, 
between opinion and knowledge. We shall meet it in discussing 
what is called the modality of judgements. So important is it, 
that some would hesitate to bring knowledge and opinion under 
one genus, judgement. But there is much which may be said about 
them in common. 

Every judgement makes an assertion, which must be either true or 
false. Its propositional form claims truth : i. e. I ought not to make 
a statement, such as that the earth is round, unless I think that it is 
so, and mean that it is so ; although in fact we often express in this 
form opinions which we hold doubtfully. This capacity of truth or 
falsehood is the peculiar distinction of judgement, expressed gram- 
matically in a proposition by the indicative mood. Imperatives, 
optatives, exclamations, and interrogations are not propositions as 
they stand, though they imply the power of judging. ' I say unto 
this man " Come ", and he cometh.' Here the indicative sentence 
' I say unto this man " Come " ' may be true or false, the indicative 
sentence ' He cometh ' may be true or false, and both these are 
propositions, and express judgements ; but we cannot ask of the 
imperative ' Come ', is it false or true ? — it is not a proposition. 
Again the question ' Art thou he that troubleth Israel ? ' is not 
a proposition ; it is not itself true or false, but enquires whether 
the judgement implied is true or false. An optative, as in the line 
' Mine be a cot beside the rill ', is not as it stands a proposition ; it 
could hardly be met with the rejoinder ' That 's true ', or ' That 's 
a lie ' ; if it were, and we were to ask ' What is true ? ' or ' What is 
a lie ? ' the answer would be ' That you really wish to live in a cot 
beside the rill ' ; so that, although an assertion is implied about the 
wishes of the person speaking, it is not so expressed in the optative. 
Exclamations may in like manner imply an assertion which they 
do not express, as when we say ' Strange ! ' or ' Incredible ! ' They 
may also be mere modes of expressing feeling, like an action and 
a gesture ; and in such cases, though something doubtless ' passes in 
the mind ', the exclamation can hardly be regarded as an attempt 



vn] OF THE PROPOSITION OR JUDGEMENT 161 

at asserting 1 anything. It is not, however, necessary to go into any 
subtleties ; the same grammatical form may indicate different acts 
of mind, and the same act of mind be indicated by different gram 
matical forms ; ' Let the king live for ever ' may be called imperative 
or optative : ' Angels and ministers of grace, defend us,' imperative, 
optative, or exclamatory : ' I would that I were dead,' optative or 
indicative. It is enough for us to realize that a judgement being 
an assertion, capable of truth and falsehood, the full and proper 
expression of it is in the indicative mood. 

In judging, I affirm or I deny ; in either case, I assert. I can 
express doubt — ' matter may be eternal ' ; and herein I neither 
assert that it is nor that it is not eternal ; still, I assert something, 
though it is not so easy to say what. 2 Propositions of the simple 
form ' S is P ', or ' S is not P ', are called categorical, but in all there is 
a categorical element. We can best elucidate the general character 
of judgement by considering examples of this form in the first place. 

A proposition makes one assertion 3 ; an assertion is one, when 
there is one thing said of one thing — ev *a0' kvos, i. e. when the 
subject is one, and the predicate one ; though the subject and 
predicate may be complex to any degree. Thus it is one proposition 
that ' The last rose of summer is over and fled ' ; but two that ' Jack 
and Jill are male and female ' ; for the latter is equivalent to ' Jack 
is male and Jill is female ' ; one thing is asserted of Jack and another 
of Jill ; one grammatical sentence expresses two judgements. 

Subject and predicate are terms which have already been explained, 
as that about which something is asserted, and that which is asserted 
about it. A proposition — at least a categorical proposition — is often 
said to be composed of three parts, subject, predicate, and copula ; the 
copula being the verb substantive, is, l<rTiv,est, ist(or is not, ovk €<ttiv s 
non est, ist nicht), sometimes, though mischievously, represented in 
Logic books by the mathematical sign of equation, = (or not — ). We 
may consider at this point the nature and function of the copula, and 
the propriety of thus reckoning it as a third member of a proposition. 

Common speech does not always employ the copula. Take the 

1 The reasoning which would make all exclamations imply a judgement 
was extended to actions by Wollaston, when in his Religion of Nature 
Delineated (first published 1724) he regarded all wrongdoing as a particular 
mode of telling a lie. 

2 Cf . infra, pp. 197 sq. 

3 Some difficulties about the singleness of judgement are discussed in 
Mr. F. H. Bradley's Essays on Truth and Reality, c. xiii. pp. 393 sq. 

1779 M 



162 AN INTRODUCTION TO LOGIC [chap. 

line ' It comes, it comes ; oh, rest is sweet '. Here in the proposi- 
tion ' Rest is sweet ', we have subject (rest), predicate (sweet) and 
copula all severally present ; whereas in the proposition ' It comes ', 
we have the subject (it, referring to the omnibus), and for copula 
and predicate together the one word, comes. But that word contains 
what is said about the omnibus (for it is said to be coming, as rest 
is said to be sweet) ; and it also contains, in the inflexion, a sign 
that this is said about a subject ; and the judgement may, if we like, 
be put in a form that exhibits predicate and copula separately, viz. 
' it is coming '. It is true that this change of verbal expression may 
sometimes change the sense ; it is not the same to say ' he plays the 
violin ', and to say ' he is playing the violin ' ; we must say, ' he is 
one who plays the violin ', or ' he is a violinist '. But it is clear that 
what the copula expresses is present as much in the proposition ' he 
plays the violin ' as in the proposition ' he is a violinist ' ; just as it 
is present alike, whether I say Beati immaculati in via or Beati sunt 
immaculati in via. The inflexion of the predicate verb, or the in- 
flexion of the predicate adjective together with the form and balance 
of the sentence, replaces or renders superfluous its more precise ex- 
hibition by the copula ; which is, however, always understood, and 
if we set down the subject and predicate in symbols whose meaning 
is helped out by no inflexion, we naturally insert it. We symbolize 
the judgement generally by the form ' A is B ' 2 ; we may write it 
' A B ', but that is an abbreviation ; to write it ' A =B ' is an error. 

If the copula thus expresses something present or implied in 
every judgement, what is its function, and can it be regarded as 
expressing one of three parts composing a proposition ? Its 
function is to express that the subject and predicate are brought 
into the unity of a judgement : that the predicate is asserted of the 
subject, and that the subject is qualified by the predicate. I may 
think of rhetoric and I may think of trickery, but they may 
remain apart in my thought — subjects successively contemplated, 
like breakfast and a morning's work ; if I say that ' rhetoric is 
trickery ', I show that they are not unconnected, to my thinking, 
but that one qualifies the other. 

Is the copula then a third member in the judgement, distinct from 
subject and predicate ? Strictly speaking, no. For two terms are 
not subject and predicate, except in the judgement ; and the act 

1 C. S. Calverley, Lines on the St. John's Wood Omnibus. 

2 Or ' A is not B ', if the judgement is negative ; and so elsewhere, mutatis 
mutandis. 



vii] OF THE PROPOSITION OR JUDGEMENT 163 

of judging, whereby they become subject and predicate, is already 
taken into account in calling them subject and predicate ; it ought 
not therefore to be reckoned over again in the copula. In the verbal 
expression of judgement, which we call a proposition, we may dis- 
tinguish as a third member a word showing that other words are 
subject and predicate ; but the whole proposition 'A is B' expresses 
a single act, in which though we may distinguish subject and predicate 
from the predicating, we cannot distinguish them from it as we can 
from one another. To think the copula is the synthesis (or linking) 
of judgement : it is the form of the act, as distinguished from 
thinking the subject and predicate ; this is the matter, for judge- 
ment varies materially with variation of the subject and predicate. 
The copula is a word used to express the performance of that act. 
Is it of any consequence how that act is expressed — (1) whether 
by an inflexion or by an independent word ; (2) if the latter, whether 
by the verb substantive or some different word or sign (such as the 
mathematical sign of equality) ? 

(1) Every categorical judgement is analysable into subject and 
predicate ; in the act of judgement we affirm or deny their unity ; 
but, whether in affirming or denying it, they are distinguished; 
and the predicate may in its turn become a subject of thought. The 
separation of the sign of predication from the predicate (as in the 
proposition ' He is a violinist ', compared with ' He plays the violin ') 
frees the predicate, as it were, from its immersion in the present 
judgement. If therefore we wish to set out a judgement in a form 
that shows clearly what is the subject, and what the predicate, each 
separately considered, an independent word is better, as a sign of 
predication, than an inflexion. For the purposes of a logical example, 
we should prefer to express a judgement in a form that shows this ; 
but it would be pedantry to do it, where, owing to the idiom of the 
language, it perverts the sense ; and we do not need to do it at all 
when we have no such need to extricate the predicate. 

(2) Different languages agree to use the verb substantive, or 
verb of existence, as the sign of predication : Homo sum, I am 
a man : Cogito, ergo sum, I think, therefore I am. 1 The use of the 
verb of existence as copula suggests that every judgement predicates 

1 Propositions in which the verb of existence was predicate used to be 
called propositions secundi adiacentis ; and those which had some other 
predicate, where the verb to be was present or implied as copula only, were 
called propositions tertii adiacentis. 

M2 



164 AN INTRODUCTION TO LOGIC [chap 

existence, that if I say ' government is a science ', I declare not only 
that it is a science, but that it is or exists ; on the other hand, the 
content of many judgements seems to negative this ; for in saying 
' a griffin is a fabulous monster ', or ' Queen Anne is dead ', I do not 
assert that a griffin or that Queen Anne exists. Hence some have 
boldly said that the verb ' to be ' is a mere equivocal term employed 
sometimes to signify existence, and sometimes to signify predication : 
with no more identity of meaning in these two uses than there is 
between est = ' is' and est = ' eats \ x From this it would follow, 
that there is no special appropriateness in using the verb to be as 
sign of predication, rather than any other sign. 

Yet if there were no special appropriateness in the verb to be, as 
the sign of predication, it is strange that so many languages should 
have agreed to use it. The case seems to be thus : that every 
judgement does imply existence, but not necessarily the existence of 
the subject of the sentence. The distinguishing characteristic of 
a judgement is, as we have seen, that it is true or false. With the 
false we need not here concern ourselves ; for the man who makes 
a judgement, unless he says what he does not really think, says 
what he thinks to be true, and therefore intends to declare the truth. 
All judgements therefore, besides affirming or denying a predicate 
of a subject, implicitly affirm themselves as true. 2 But a judgement 
which affirms itself as true claims to express, so far as it goes, the 
nature of things, the facts, or the realit} 7 " of the universe. In doing 
this it maybe said to imply existence, not of its grammatical subject, 
but of the whole matter of fact asserted in it. 

When I say that a griffin is a fabulous monster, I do not affirm 
that griffins exist like pigs and cows. But my judgement implies 
the existence of a mass of fable, in which griffins have their place as 
fables too. If there were no fables, I could not say that griffins 
were fabulous ; but fables are an element in reality — i. e. in the 
totality of what is real — no less than pigs and cows. Again, when 
I say that Queen Anne is dead, I do not affirm the present existence 
of Queen Anne ; I do imply her existence in the past ; and the 

1 Cf. James Mill, Analysis of the Phenomena of the Human Mind, vol. L 
p. 174 (ed. 1869) ; J. S. Mill, System of Logic, I. iv. 1. 

2 Cf. F. H. Bradley, Essays in Truth and Reality, p. 382 : * We cannot, 
while making a judgement, entertain the possibility of its error.' It may 
be noted that a lie is not a judgement, but rather an action intended, through 
the use of words that commonly express a judgement, to influence the action 
or opinion of others. 



vii] OF THE PROPOSITION OR JUDGEMENT 165 

copula therefore still has the meaning of existence. It may be 
asked why it should be in the present tense, when the existence 
meant is past. The answer is, first, that the predicate corrects this 
so far as is necessary ; but secondly, that the past (like fable) has 
a kind of existence. If I am the same to-day as I was yesterday, 
then I do somehow unite in me at once the present and the past ; 
the past has ceased to be present, but it still somehow belongs to 
me. What is true of me is true of others, and of reality as a whole. 
Its history is in time ; but it is one through that history ; and the 
past belongs to it now, as well as the present. Queen Anne, it may 
be, does not exist now ; but that exists now in whose past the life 
and death of Queen Anne have their place. They belong to the 
whole system of things which we call the universe ; therein they 
exist, and only in belonging to it can they or anything else exist. 
The moon, if it had no place there, would not be ; neither would 
justice, nor triangularity ; though these different things play different 
parts in the whole. 1 When I say what triangularity is, the present 
tense is not used because it is contemporary with the time of the 
utterance; for it is not temporal at all. Not everything real 
belongs to the succession of events in time. 

Every judgement then that I make claims to declare some portion 
of the whole truth that is to be known about the universe : in what 
form (so far as its purview goes) the universe exists. Hence it is no 
accident that the verb of existence is employed to express the act 
of judgement. There is a kind of thinking called questioning or 
wondering, in which we think of various things, and imagine them 
connected in various ways, without deciding in our minds whether 
they are so connected or not. Thus I may think of Public Schools, 
and ask myself whether they are liable to stifle originality in their 
pupils ; and I shall be thinking also of that liability, and of the 
relation of subject and attribute, and imagining that relation to be 
exemplified between these terms. But if I judge one way or the 

1 Some writers have used the notion of a ' universe of discourse ' or ' limited 
universe ' to express the foregoing contention. In the whole universe fact 
and fable, savages and Rousseau's conception of savages alike have their 
place ; but I can make statements which are true about Rousseau's concep- 
tion which would be false about savages themselves. It is said that these 
are different ' limited universes ' ; and that propositions which do not assert 
the existence of anything in the material universe may assert it in some 
other. ' The royal dragon of China has five claws ' — I do not affirm its 
existence in the universe of zoology, but in that of Chinese heraldic design. 
Cf. p. 44, n. 2, supra. 



166 AN INTRODUCTION TO LOGIC [chap. 

other, that public schools are or are not liable to stifle originality 
in their pupils, then I believe that this relation really holds, or does 
not hold, between these terms, and that what I think of exists 
independently of my thinking. And to express that a combination 
of which I think is real, I use the verb to be. * Public schools are 
liable (or not liable) to stifle originality in their pupils ' ; i.e., the 
liability of public schools to do so, or their freedom from such 
liability, exists. 

[It will be observed that on p. 164 the copula was said to imply, 
not to predicate, existence. For existence by itself is not a significant 
predicate, as we have already seen, 1 and therefore cannot strictly 
speaking be predicated. We may ask, for example, whether griffins 
exist, as we may ask whether ostriches fly ; but whereas in the 
latter case the subject is assumed to exist, and the question is 
whether it possesses a certain predicate, in the former case we do 
not assume that there are griffins, and enquire whether they possess 
the predicate of existence. Their existence would consist in being 
griffins, and not merely in being ; and to ask whether griffins exist 
is to ask whether anything existing has the character intended by 
the term griffin. The existent is thus assumed as the subject of 
our judgement, and the judgement claims to declare its nature ; 
we do not assume its nature as a subject of which to predicate 
existence. Hence it has been said that reality is the ultimate sub- 
ject of every judgement ; that, as the distinction of its terms is 
not a distinction of two independent things, but of two factors in 
the being of one, this whole being, conceived by us in subject and 
predicate together, is really one ' content ', and though judgements 
differ in their content, these contents are all predicated of the one 
reality ; and the contents of all true judgements are factors co- 
existing in the being of that reality. To ask ' Is such and such 
a proposition true ? ' is to ask whether in its subject and predicate 
together I apprehend in part the nature of reality ; and it is because 
of this ' reference to reality ' in every judgement that we use in 
expressing it the verb to be. 

This view that reality is the ultimate subject of every judgement 
is wrong if it be understood to mean that it is the logical subject, 
or be taken as destroying the force of the logical distinction between 
subject and predicate. We may distinguish in fact three subjects, 
the logical, the grammatical, and the ultimate or metaphysical. 
That the logical subject is not the same as the grammatical subject 
of the sentence is readily apprehended. The proposition ' Bella- 
donna dilates the pupil ' may be an answer either to the question 
1 What dilates the pupil ? ' or ' What do you know of belladonna ? ' 

1 Cf. supra, p. 65. 



vn] OF THE PROPOSITION OR JUDGEMENT 167 

[In either case the grammatical subject is belladonna ; but the 
logical subject is in the former case ' dilating the pupil ' ; that is 
what we are thinking about, and about that the judgement informs 
us that belladonna will effect it ; in the latter case, the logical 
subject is belladonna, and about that the judgement informs us 
that it produces this effect. This distinction of logical subject and 
predicate is always present in thought when we judge, though 
sometimes the logical subject may be very vague, as when we say 
' it rains ' or ' it is hot '. But subject and predicate together may 
qualify something further. This is easily seen when the subject is 
an abstract term. ' Jealousy is a violent emotion ' : jealousy may 
be the logical subject here, but it only exists in those who are 
jealous. It is not then the ultimate subject, for it inheres in some- 
thing else. Where then do we reach the ultimate subject ? Accord- 
ing to our ordinary way of thinking, in concrete individuals ; and 
this is the view also of many philosophers, who have thought (and 
Aristotle seems to have been among them) that there was no single 
metaphysical subject, but as many as there are concrete individuals. 
In the Categories 1 the concrete individual is defined as that which 
can neither be predicated of nor inhere in anything further. 2 

But the doctrine which makes Reality the ultimate subject of 
every judgement holds that in a sense the metaphysical subject is 
always one and the same : i. e. that there can be only one real 
system, to which all judgements refer, and which they all contribute 
to determine and qualify. That a particular thing should exist or 
be real means that it has its place in this system ; and what is 
called the existential judgement — the judgement whose predicate 
is the verb to be, in the sense of to exist — as in ' Sunt qui non 
habeant, est qui non curat habere ', or ' Before Abraham was, 
I am '—declares a part of the nature of the one system of reality. 
The content of an existential judgement cannot indeed be pre- 
dicated of reality as a quality or attribute. When I say that 
jealousy is a violent emotion, I think of it as an attribute of jealous 

1 ii. l b 3-9, v. 2 a 11-14. Cf. supra, pp. 50 sq. 

2 It is true that a singular term may appear as predicate of a judgement, 
as, for example, if we say ' The greatest epic poet is Homer ' or ' The first 
man was Adam '. But in such a case Aristotle regards the predicate as only 
accidentally predicate, or Kara avfi^e^KOi (cf. Met. A. vii) : by which he 
means that the concrete individual does not really qualify or belong to what 
figures as its subject, but that because these two come together, or because 
it befalls Homer to be the greatest epic poet, and Adam to have been the 
first man, therefore you can say that one is the other, as you can also say 
that a grammarian is a musician when the two characters coincide in one 
individual, though ' musician ' is not what ' being a grammarian ' is, any 
more than Homer is what being the greatest epic poet is, or Adam what 
being the first man is. In fact, in making a judgement whose predicate is 
a singular term, we cannot help at the same time thinking of the predicate 
as qualified by what figures as subject. But cf . supra, p. 153. 



168 AN INTRODUCTION TO LOGIC [chap. 

[men ; when I say ' Est qui non curat habere ', I do not think of 
Horace as an attribute of reality. Nevertheless, his existence is 
bound up with the existence of the whole universe ; the universe 
of reality is found (when we think the matter out) to be presupposed 
by the existential judgement as much as by any other ; and though 
in it existence appears to be first affirmed in the predicate, and 
therefore not assumed in the subject, yet this cannot represent 
the true course of our thought. We could make no judgement at 
all, if we did not presume a reality about which it was made. 
Even the negative existential — ' Joseph is not, and Simeon is 
not ' — implies this ; for not to be means to have no place in that 
which is. 

We are indeed accustomed to think of things and persons as if 
each were complete and independently real ; and in that case, the 
metaphysical subject of any judgement would be some concrete 
individual or other. The doctrine we are considering carries the 
question further, and holds that, since what is predicated of the 
concrete individual is not true of him in complete isolation from 
all else, therefore he is not, metaphysically speaking, or in the last 
resort, the subject of which it is true. There is no desire to deny to 
individuals a relative independence, or to pretend that the relation 
of attributes or universals to the concrete individual is the same 
relation as that of an individual to the system of reality which 
includes him. The judgement ' Jealousy is a violent emotion ' can 
be so restated as to make the concrete subject man the logical 
subject of the judgement ; I may express it, for example, by saying 
that jealous men are violent in their jealousy. I cannot so restate 
the existential judgement, or any other in which the logical subject 
is already a concrete term, as to make Reality the logical subject 
instead. But it is the metaphysical subject in the sense that it is 
presupposed and referred to even in those judgements. We cannot 
maintain the view that the metaphysical subject of every judge- 
ment is always in the last resort a particular individual. ' Civiliza- 
tion is progressive.' Doubtless civilization is only seen in the fives 
of men ; but it is seen in the lives not of this and that man singly 
but of the communities to which they belong. We have to think 
of men as forming a system and an unity, if we are to give meaning 
to a judgement like this. We saw too that the process of biological 
evolution, which seems in some way single, yet cannot be exhibited 
in any single organism ; nor is it easy to know what is a single 
organism. What is contended is, that all judgements involve us in 
the thought of one all-embracing system of reality, whose nature 
and constitution none can express completely, though each true 
judgement declares a part of it. Logic, as has been said before, 
cannot be rigidly separated from metaphysics ; indeed, it derives 
its chief importance from its connexion therewith. If it had merely 



vii] OF THE PROPOSITION OR JUDGEMENT 169 

[to work out the scheme of syllogistic inference, and such -like 
matters, the problem which the present note has raised would be 
superfluous ; but it investigates what is involved in thinking ; and 
whether we must think of the universe as a sum of independent 
reals or as a system is a fundamental problem. 1 ] 

In the act of judgement, the subject 2 with which we start is 
thought of as modified or enlarged by the predicate, and in that 
form declared to be real. We end with the subject with which we 
began, differently conceived. 3 The thought of a combination of 
elements, and the affirmation of its reality, 4 are common features 
of every judgement, and the copula expresses them always, and so 
far has always the same meaning. Whatever sign be used, whether 
an inflexion, or the verb substantive, or the mathematical symbol 
for equality, or anything else, this combination, and the affirmation 
of its reality, must be meant. The verb to be naturally lends itself 
to this meaning. The mathematical symbol of equality has a dif- 
ferent meaning ; it is not a sign of predication, but an incomplete 
predicate ; it expresses, of one thing, quantitative identity with 
some other. If I say A = B, the predicate is not B but ' equal to B ' : 
the special force of the sign ' = ' is ' equal to ' ; I must still perform 
in thought the act of predication, whether I say ' A is equal to B \ 
or ( A is the first letter of the alphabet ' ; and if = were adopted as 
the sign of predication, the equation ' A=B ' (which means ' A is 
equal to B ') must be written ' A = = B '. 

A judgement then contains subject and predicate ; subject and 
predicate in their combination are declared real. To the words 
which signify the subject and the predicate separately is added 

1 The view that Reality is the ultimate subject of judgement is of course 
familiar to all readers of Mr. F. H. Bradley's or Professor Bosanquet's logical 
work. Cf. Bradley, Principles of Logic, c. i. pp. 12-14, and Essays on Truth 
and Reality, c. ix. pp. 253-254. Mr. Bradley does not distinguish between 
logical and metaphysical subject. 

2 i. e. the logical subject. 

8 Sigwart has pointed out that the movement of thought in a judgement 
is different for a speaker communicating information and tor his hearer. The 
speaker knows the whole fact, when he starts putting forward one aspect of 
it in enunciating the subject, and supplements it with the other by adding 
the predicate : if I say ' This book took a long time to write ', the whole 
fact is present to my mind in its unity before I begin speaking. To the hearer 
I present a subject of thought, ' this book ', which awaits supplementation : 
to him the predicate comes as new information, which he has now to combine 
with the concept of the subject hitherto formed by him. v. Logic, § 5. 1. 

* Even in a negative judgement, subject and predicate are elements thought 
of together, as standing in a relation of mutual exclusion. 



170 AN INTRODUCTION TO LOGIC 

a word which signifies that these are thought to be combined in the 
real. This word is called the copula ; it may be omitted in speech 
or writing, or be replaced by an inflexion ; but the act of thought 
which it indicates cannot be omitted, if there is to be a judgement. 
This act, however, is not a part of the judgement in the same way 
that subject and predicate are. It is the act or form of judging, and 
they determine the matter. Hence it is, at least generically, the 
same, while subject and predicate change ; and for this reason the 
scheme of a proposition 'A is B ' represents subject and predicate 
by symbols, but retains the ' copula ' itself. We write A and B for 
subject and predicate, 1 because they represent indifferently any 
subject and predicate, being themselves none ; we write ' is ', and 
not another symbol in its place, because whatever be the subject and 
predicate, the act of judgement is, generically, the same. 

But judgements are not all so much alike that they can all be 
equally well expressed in propositions of the form ' A is B ' ; they 
do not differ merely as the places of these symbols are taken by 
different terms. For some propositions are of the form ' A is not B '; 
and A may be replaced by a singular or by a general term ; and if 
by a general, we may judge either that all or some A is (or is not B), 
and this difference is one of form, in the sense that it is not a differ- 
ence in the terms that replace our general symbols A and B. And 
there are other differences in propositions which are not differences 
in their terms. Having got some notion of what judgement is in 
general, we must now turn to the differences which are expressed in 
these differences of propositional form. With differences merely 
of the terms, as between ' men are animals ' and ' roses are plants ', 
we are not in Logic concerned. 

1 Of course any other indifferent symbols will serve, such as X and Y or 
S and P. 



CHAPTER VIII 
OF THE VARIOUS FORMS OF THE JUDGEMENT 

Judgements, or the propositions in which they are expressed, 
have for long been commonly distinguished according to Quality, 
Quantity, Relation, and Modality : — according to Quality, into 
affirmative and negative : according to Quantity, into singular, 
universal, and particular : according to Relation, into categorical, 
hypothetical, and disjunctive : according to Modality, into assertoric, 
problematic, and apodeictic. The distinctions in Quality and 
Quantity, as the simplest and most familiar, will be discussed first ; 
they can only be fully illustrated in categorical judgements or pro- 
positions. 

In respect then of quality, categorical judgements are distin- 
guished as affirmative or negative. An affirmative categorical 
judgement assigns a predicate to a subject ; a negative puts it from 
it. But the distinction between affirming and denying is too familiar 
to need and too simple to admit of being expressed in any other way, 
in order to indicate what is meant. 

There are certain difficulties connected with negative judgements, 
which have already met us in dealing with negative terms. Judge- 
ment, as we have seen, refers to the existent, whose manner of being 
(so the judgement declares) is as we conceive. But the real is 
positive ; it only exists by being something, not by being nothing. 
A negative judgement declares what it is not, and how can this 
express it as it is ? Dead-nettles don't sting. How does that tell me 
anything real in dead-nettles ? You may say that I formed an idea 
of a stinging dead-nettle, and in the negative judgement declare it 
false, an idea of nothing real. But that only means that I had 
thought that, or asked myself whether, dead-nettles sting, and in 
correction or reply now judge that they do not. My ' idea ' means 
my opinion, or a supposed opinion ; I may reflect on that, and say 
that the opinion is false ; but in the example I am judging about 
dead-nettles, not about any past opinion about them. And 
when I say that they do not sting, what am I saying about them ? 



172 AN INTRODUCTION TO LOGIC [chap 

in them, what is this property of not stinging ? surely, it may be 
urged, just nothing : so that in the negative judgement I assert 
nothing real. 

These misgivings are sometimes, though unfairly, met by ridicule. 
Still, in face of them, we must assert, that everything finite is what 
it is, by not being something different : and at the same time, that 
it is not something different, in virtue of what it positively is. Hence 
we must accept the negative judgement as expressing the real limita- 
tion of things ; but we must allow that it rests upon and presupposes 
the affirmative. If dead-nettles do not sting, there must be some 
characteristic which they do possess, incompatible with stinging. 1 
There is always a positive character as the ground of a negation. 
Snow is not hot, because it is cold ; this is not indeed an explanation 
of the temperature of snow ; but it means that a material body 
(which must have some temperature) can only not have one degree 
of temperature through having another. If snow had no other degree 
of temperature, it would have 212° Fahr. ; if it had none but 32° 
Fahr., it must have that. And it may be noticed how often in the 
building up of knowledge we use negative judgements to reach 
affirmative : to know what anything is not is frequently a help to 
discovering what it is. In the inductive sciences this procedure 
is constant, and we shall find it a fundamental feature of the 
induction in them. 

To say that negative judgements presuppose affirmative does not 
however get rid of the difficulties to which we have referred. If 
snow is not hot because it is cold, then the cold is not hot. No one 
will deny that ; some people will think it a mere tautological pro- 
position. But it is not tautological, though it is superfluous. It is 
tautological to say that the cold is cold ; to say that it is not hot 
because it is cold informs us that hot and cold are mutually exclusive 
attributes. Cold is no more identical with not-hot, than odd with 
not-even ; though the numbers which are odd are the same numbers 
as are not even. The reciprocal exclusiveness of certain attributes 
and modes of being is the real truth underlying negation. But for 

1 A critic (Miss Augusta Klein) has objected that this is only a negative 
character, viz. the absence of glandular stinging hairs. But the tissues 
forming any part of a leaf can only not be glandular stinging hairs if they 
ire something else. A body can only not be here if it is elsewhere. However, 
a difficulty arises with empty space ; by being what, is it not occupied by 
some body ? is emptiness purely negative ? Democritus, and Plato, called 
space fi>) ov, not-being. Some have denied that a vacuum can exist. 



vin] VARIOUS FORMS OF THE JUDGEMENT 173 

that, everything would be everything else ; that is as positive, as 
these several modes of being themselves. 

Negation, as Plato saw, 1 is as necessary as affirmation, if there are 
to be any differences or discriminations within reality ; that A is not 
B means that it is different from B, and not that it is non-existent. 

[The further pursuit of this subject would take us too far into 
metaphysics. It may be pointed out in passing that the notion of 
an infinite (or, as philosophers sometimes say, an absolute) being 
is of a being who is everything that there is to be ; of whom it 
cannot be said that he has one attribute by lacking another ; 
whereas finiteness comes by limitation and exclusion : whence 
Spinoza's Determinatio est negatio. Whether this is a tenable con- 
ception is another matter. In particular it raises the problem of 
the meaning, and reality, of evil. For if an infinite being is all 
things, and evil is something real, he ought inter alia to be evil. 
It has been contended therefore that evil is in reality just nothing, 
a view against which there are obvious objections on the surface : 
or at least that it is a mere appearance incident to limitation, but 
in itself no more than limitation ; what is absolute and all-inclusive, 
having nothing outside it to limit it, would not be evil, though it 
would include what, taken in improper isolation, appears evil.] 

It has sometimes been proposed to treat the negative judgement, 
A is not B, as an affirmative judgement, A is not-B, 2 by combining 
the negative with the predicate. But inasmuch as the reciprocal 
exclusiveness of certain attributes and modes of being is a positive 
fact, it is no use trying to ignore it by a verbal manipulation. 
Nothing will make A is not-B an affirmative judgement, unless not-B 
is something positive ; and if not-B is something positive, say C, the 
judgement is true because B and C are counter-alternatives ; e. g. 
the fact that the path of a bullet is not straight may be expressed 
by saying that it is a curve, but only because straight and curved 
are mutually exclusive and sole alternative determinations of a fine. 
It follows that C is not B, and B is not C ; and these negative judge- 
ments cannot be evaded by writing ' C is not-2? ', ' B is not-C '. 
For if C means the very same as not-B (e. g. curved as not-straight), 
then not-C means the very same as not-not-B, and the proposition 

Soph. 256 E 7T(p\ €Kci(ttop cipa Tu>v elSa>i> 7roXv pev eori to ov, arretpov 8e nXr/da 
to pr/ ov. 257 B onorav to p,f] ov \eywpev, if coiKfv, oIk ivavrinv ti \eyoptv tov 

oVto?, a\\' ercpov povov. ('About each Form then there is much that it is, 
but an infinite amount that it is not. . . . When we speak of not being, 
we speak, it seems, not of what is contrary to being but only of what is 
different.') 

2 Such judgements, with an infinite term (cf. p. 42, n. 2, supra) for predicate, 
have been called infinite judgements. 



174 AN INTRODUCTION TO LOGIC [chap. 

B is not-C means no more than B is not-not-B (' straight is not-not- 
straight '). That however is absurd ; for G is positive, and the 
consciousness of the distinction between it and B and of their 
reciprocal exclusiveness cannot be reduced to the consciousness that 
B cannot be denied of itself. The above argument could equally 
be illustrated if we took for B not one of two counter-alternatives, 
but a term like dog ; only then not-B would leave us to select in the 
dark among a large number of still remaining alternatives. 

In respect of quantity, categorical judgements are said to be either 
singular, or universal, or 'particular. But the differences at the 
bottom of this distinction are not in reality purely quantitative, 
though they have sometimes been represented as being so. 

The subject of a proposition may be either a singular term like 
' Socrates ' or ' Caesar ' or ' the present Cabinet ', or a common 
term like ' man ' or ' triangle '. In the former case, the proposition 
too is called singular. In the latter, the proposition may affirm 
or deny the predicate of the subject either universally, i. e. in every 
instance of it, e. g. ' All equilateral triangles are equiangular ', 
' Nemo omnibus horis sapit ' : in which case it is called universal ; 
or partially, i. e. in particular instances, or of a part of the subject, 
only, e. g. ' Some larkspurs are perennial ', ' Some animals cannot 
swim ' : in which case it is called particular. The judgements which 
these propositions express * are correspondingly distinguished as 
singular, universal, or particular. 

Now these three kinds of judgement may clearly be represented 
as concerned respectively with one individual, with all individuals of 
a certain kind or description, or with some part of such aggregate 
or class. For though when I say that all acids contain hydrogen, or 
that some larkspurs are perennial, I may be thinking primarily 
of the kinds or species of acid, or of certain species of larkspur, yet 
the statements, if true, are true in every instance of those species. 2 

1 We judge, commonly, not about words but about what they stand for, 
but we express our judgements in words. A common term stands for and is 
predicable of not a common nature in things, but things in respect of their 
common nature. These things are the subject of the judgement, when 
a common term is the subject of a proposition. 

2 i. e. of the whole or part of the denotation, as well as of the whole or part 
of the extension of the subject-term, if the distinction made on p. 146, supra, 
be adopted. It should be remembered that the singular term has no extension ; 
and that an individual cannot be called the whole denotation of a singular 
term in the same sense in which the divers individuals of a class can be called 
the whole denotation of a general or class-term. 



vin] VARIOUS FORMS OF THE JUDGEMENT 175 

And so they may be represented as concerned with all or part of 
what their subject terms denote. And as a singular term denotes 
only one individual, the singular proposition is also concerned with 
all that its subject-term denotes. Hence it has sometimes been said 
that propositions are of two kinds in respect of quantity, universal 
when they refer to the whole denotation of the subject-term, 
particular when they refer to part of it. We shall see later, when 
dealing with syllogism, that in some connexions it is unnecessary to 
distinguish between singular and universal judgements or pro- 
positions, because they both equally make certain inferences possible. 
But at present it is important to realize that what are called differ- 
ences of quantity in judgements or propositions, are not primarily 
differences in respect of how much of the denotation of the subject 
term is the subject of our thought. 

The subject of a singular judgement is individual (though it may 
be an individual collection) ; that of an universal judgement may 
be an universal, or concept, e. g. ' Fear is contagious ' ; or, though 
not a concept, it may be determined by a concept, 1 e. g. ' Letters 
in transit are the property of the Postmaster-General.' The latter 
statement, though it concerns individual letters, applies to them not 
as this or that individual, but as possessing the character signified 
by the words ' letter in transit '. The difference therefore between 
it or the former and a singular judgement lies not in the quantity 
of the individuals to which they refer (i. e. in the singular referring 
to one individual and the universal to all individuals of a certain 
collection), but in the logical character of the subject, which in the 
singular judgement is a determinate individual, in the universal 
judgement a concept or anything characterized and determined by 
a certain concept. We may include both these in the expression 
1 a conceptual subject '. No doubt an universal judgement has 
a quantitative aspect, for it does concern all individuals that share 
the subject-concept ; but this aspect is secondary. Primarily, in 
making it, we have before us a relation between one character and 
another in individuals, not between individuals and a certain char- 
acter. Neither therefore is the difference between an universal 
and a particular judgement primarily quantitative. A particular 
judgement refers to part only of the denotation of some conceptual 
subject, an universal to all ; but this is because in the latter the 

1 The totality of things exhibiting a certain character is called a class, 
and the character which determines membership of the class a class-concept. 



176 AN INTRODUCTION TO LOGIC [chap. 

relation of concepts is taken to be necessary, and therefore the 
subject-concept sufficiently determines the application of the judge- 
ment ; in the former it is not, and we indicate by the word some 
that the application of the judgement is not completely determined. 1 
A criticism of the forms in which language expresses judgements 
of these different types will throw further light on what has just 
been said. 

It is common to indicate an universal judgement by the words 
all or no (none) prefixed to the subject, according as the judge- 
ment is affirmative or negative ; a particular judgement by the 
word some, similarly prefixed ; these are called signs or marks of 
quantity. The idiom of language will indeed often express a uni- 
versal judgement in other ways ; we can say Man is mortal, as well 
as All men are mortal : A barometer will not work in a vacuum, as 
well as No barometer will work in a vacuum. But in the absence 
of a mark of quantity, it is not always clear whether a proposition 
is meant to be universal or particular ; if I say Women are jealous, 
A flower is a beautiful object, I need not mean all flowers, or all 
women. Precision requires the quantity of a judgement to be 
expressly indicated : particularly where (as in logical examples) the 
proposition is taken out of context and we lack the help which 
context often affords us in divining the writer's intention ; and at 
least where the subject is in the plural, 2 the words all, none, some 
are appropriated to that service. A proposition without any mark 
of quantity is technically known as an indefinite proposition ; 
because it is not clear whether the whole, or only a part, of the 
extension or denotation of the subject is referred to, and so the 
scope of the proposition is undetermined ; the examples just given, 

1 The Aristotelian division of political constitutions (or rather Platonic — 
for it occurs in Plato's Politicus) is another example in which differences 
not really quantitative have been presented under a quantitative form. 
A monarchy, an aristocracy, and a democracy, though said to differ according 
as power is in the hands of one man, of the few, or of the many, really differ, 
as Aristotle himself pointed out, in quality or kind. It must be added that 
Aristotle does not put forward a purely quantitative division of judgements 
(cf. de Interpr. vii. 17 a 38 eirei 8' tar\ ra fiev kci66\ov to>v 7rpaynora)v to 8e xad 
tKatTTov — 'since of things some are universal and some several'), though in 
expounding the syllogism in the Prior Analytics he often lays stress on the 
quantitative implications of the contrast between universal and particular 
judgements. 

2 ' Man is mortal ' is clearly universal ; but represented in symbols as 
' A is B ' it will not unambiguously show its universality. For ' Iron is 
found in Lancashire ' might be represented by the same symbols, but is as 
clearly particular. 



viii] VARIOUS FORMS OF THE JUDGEMENT 17? 

Women are jealous, A flower is a beautiful object, are therefore 
indefinite propositions. 

At the same time, the words all and none, as signs of the uni- 
versality of a judgement, have disadvantages of their own. For 
a judgement is really universal, when the subject is conceptual, and 
the predicate attaches to the subject (or is excluded from it) neces- 
sarily ; but if it is found to attach to the subject (or to be excluded 
from it) in every existing instance without any necessity that we 
know of, we use the same expressions, all and none. Thus we may 
say that No American poet stands in the first rank, or that All the 
French ministries are short-lived ; but neither of these is really 
an universal proposition. Each expresses a judgement made about 
a number of individuals : it states an historical fact, and not a 
scientific truth. It would be convenient to call such propositions 
collective x or enumerative ; for they really collect in one the state- 
ments which may be made about every instance of a certain class, 
and make their assertion on the strength not of any conceptual 
necessity, but of an enumeration. 

We must of course distinguish the question whether a proposition 
is meant as universal, in the strict sense, from the question whether 
we have a right to enunciate it universally. If instead of saying All 
the French ministries are short-lived (where the article the shows that 
I am referring to all of a certain number of things), I were to say All 
French ministries are short-lived, it might be contended that the 
proposition no longer referred primarily to individuals or instances, 
but affirmed a necessary character of French ministries as such. In 
truth the statement is not clear, and a man would have to ask me, 
whether I meant it as an historical summary, or an universal truth ; 
but the ambiguity of the statement is the very point to be noticed ; 
for the two interpretations indicate the difference between a merely 
enumerative, and a true universal, judgement. The difference is 
plain in suitable examples : contrast, for instance, ' All, all are gone, 
the old familiar faces ', and ' All lovers young, all lovers must, like 
chimney-sweepers, come to dust.' 

We have seen that there is a marked distinction between a sin- 
gular judgement, whose subject is an individual, and an universal 
or particular judgement, whose subject is conceptually determined 
by a general or abstract term. The enumerative judgement (and 

1 Cf. Bradley, Principles of Logic, Bk. I, c. ii. §§ 6 and 45. In the Table 
of Contents he speaks of ■ collective ' judgements in this sense. 
1779 N 



178 AN INTRODUCTION TO LOGIC [chap. 

this is true in some degree of the particular also) approximates to the 
type of the singular rather than of the universal. 1 For though the 
subject of the proposition be a general term, and I predicate about 
all the members included under that term, yet I do so because I have 
examined them severally and found the predicate in them all, 
or at least, on good evidence or bad, believe it to attach to them 
all, not because of any necessary connexion between the predi- 
cate and the common character of these individuals which the 
general term signifies. French ministry is a general term ; but (for 
all that I see) it is not because being a French ministry involves 
being short-lived, that all the French ministries are short- 
lived ; I assert it because I have noted each case ; just as it 
would be upon the strength of noting the individual case that 
I should assert the first ministry of M. Jules Ferry to have been 
short-lived. At the same time, the enumerative judgement, though 
thus approximating to the type of the singular, gives the hint of 
a true universal judgement. It suggests that the ground for the 
predicate may lie in the common character signified by the general 
term under which all these instances are collected. If I say Luther 
was hated, there is nothing to indicate what about him was hateful : 
with which of all the coincident attributes in Luther his hatefulness 
is universally connected. If I say All reformers have been hated, 
though that is as much an historical statement as the first, and there- 
fore enumerative only, it suggests that the reason why all those 
men have been hated (Luther and Calvin, Cromwell and Gladstone 
— the statement implies a possible enumeration) lies in the fact 
that they were reformers. Thus from an enumerative judgement 
we may pass to an universal ; from a study of individuals to the 
assertion of an universal connexion of characters. When we enun- 
ciate enumerative judgements, we are on that road : sometimes 
farther, and sometimes less far. 

The difference between a true universal judgement and one 
merely enumerative is exceedingly important. The one belongs 
to science, the other to chronicle or history. An universal judge- 
ment concerns any and every instance, alike past, present and 
future, examined or unexamined. An enumerative judgement 
concerns only those instances which have been examined, or have 
existed, and which are summed up in the subject. All reformers 
are hated : if that is merely enumerative, it does not require me to 
1 Cf . Bradley, Principles of Logic, Bk. I. c. ii. § 45. 



vin] VARIOUS FORMS OF THE JUDGEMENT 179 

anticipate hatred if I undertake reform ; it affords me no explana- 
tion of the hatred with which these men have been met. But if it is 
a true universal, it explains the past, and predicts the future. 
Nevertheless an universal judgement has nothing, as such, to do with 
numbers of instances ; if the connexion affirmed in it be necessary, 
the judgement is still universal, whether there be a million instances 
of its truth, or only one 1 ; so that the form ' All A is B ' hardly does 
justice to it. An enumerative judgement contemplates a number 
of instances, and refers to all of them ; and the form ' All A is B * 
or ' All the A's are B ' expresses it adequately. 

The particular proposition may be interpreted as referring either 
to individuals not enumerated or to an universal not fully deter- 
mined ; and it will approximate more to the enumerative, or more 
to the universal, accordingly. If I say Some women have ruled 
kingdoms, I mean women whom I could enumerate — Semiramis, 
Cleopatra, Zenobia, Elizabeth, Christina, &c. : not women of such 
and such a type, but this and that woman. If I say Some pigments 
fade, I do not mean pigments that I could enumerate, but any pig- 
ments of a certain kind ; and supposing that I could specify or 
determine the character of pigment, I could say that all pigments 
of that character fade. There is nothing in the verbal form of a 
particular proposition to show whether the speaker is thinking 
rather of individuals whom he does not name, or of conditions 
which he does not specify ; though content and context will often 
guide us on this point. 

It will be readily seen that there is the same sort of difference 
between the particular proposition interpreted of individuals not 
enumerated, and the particular proposition interpreted of conditions 
not fully specified, as exists between the enumerative and the true 
universal proposition. If the women vaguely referred to as some were 
enumerated, I could say All the women on my list have ruled kingdoms ; 
if the pigments vaguely referred to as some were characterized, 
I could say All such pigments fade. The former is the enumerative, 
the latter the universal All. And this difference, whether between 
the two interpretations of the particular proposition, or between the 
enumerative and the universal, may be expressed by saying that in 

1 Or, as some logicians would add, none. Such a view makes the universal 
judgement, however, purely hypothetical : cf. Leibniz, Nouveaux Essais, 
IV. xi. 14 ; Bradley, Principles of Logic, Bk. I. c. ii. §§ 43-6 ; Bosanquet, 
Logic 2 , vol. i. pp. 263-266; v. also Bradley, Appearance and Reality, p. 361. 

N2 



180 AN INTRODUCTION TO LOGIC [chap. 

the one case the subject of the proposition is interpreted in extension 
or denotation, in the other case in intension. The subject of a pro- 
position is interpreted in extension or denotation, when we are 
thinking primarily of the various species or individuals included in 
the subject to which the predicate refers ; it is interpreted in intension, 
when we are thinking primarily of the subject as of a certain kind, 
of the character implied by the subject-term, with which the pre- 
dicate is connected. ' Some A is B ' is interpreted in extension or 
denotation, if I think of this, that and the other A : in intension, if 
I think of ^L's of a certain character. ' All A is B ' is interpreted 
in extension or denotation, if I think of every one of the A's : in 
intension, if I think of the character of ^4's as such. 

What has been said on the quantity of judgements and propositions 
may be summed up as follows. Categorical judgements may be 
made about either individuals or universals. If about individuals, 
these may be indicated either by a proper name or designation — 
and then the judgement is called singular — or by a general term. 
In the latter case, if the judgement concerns all that is included in 
the extension or denotation of its subject-term, it is called universal ; 
but a distinction must be made between a true universal judgement, 
in which the predicate is affirmed (or denied), without respect of 
individuals, of whatever exhibits the subject-concept (or intension 
of the subject -term) and one only enumerative or collective, in 
which it is affirmed or denied of all of certain species or individuals, 
which might be enumerated, but which the subject-term enables us 
to indicate collectively. If the judgement concerns an unspecified 
part of the extension or denotation of the subject-term, it is called 
particular. Judgements about an universal are universal. Pro- 
positions are denominated after the character of the judgement 
which they express. A true universal judgement can be indicated 
by the same words (All and None) as an enumerative, and is often 
confused with it. A particular judgement is really incomplete ; it 
may be an incomplete enumerative, or an incomplete universal 
judgement, according as we think rather of the instances we im- 
perfectly denote, or the conditions we imperfectly specify, in the 
subject. We make particular judgements chiefly in opposition to 
the universal statements of others, to which we ' take exception ', 
or in approach towards universal judgements ; and their value 
for knowledge is subsidiary and instrumental. The subject of 
a categorical proposition may be viewed primarily in intension. 



viii] VARIOUS FORMS OF THE JUDGEMENT 181 

if the proposition affirms or denies a connexion of characters, 
or in extension or denotation, if it affirms or denies a certain 
character in individuals. 1 The former aspect predominates in 
the universal, the latter in the enumerative : in the particular, 
sometimes the former and sometimes the latter, according as we 
think more of the conditions imperfectly specified, or the instances 
imperfectly denoted : the singular proposition merely affirms or 
denies in an individual a certain character. 1 Sometimes these 
distinctions, though we are conscious of them in our thought, are 
not expressed in language ; and for certain purposes of inference, 
it is enough to consider propositions simply as either universal or 
particular : universal, when the whole extension or denotation of 
the subject-term or when an individual is referred to, particular 
when a part of the extension or denotation is referred to only. 

Judgements are distinguished according to relation into categorical, 
hypothetical, and disjunctive. We have been considering hitherto 
categorical judgements. A categorical judgement merely alfirms 
or denies a predicate of a subject : dogs bark, dead men tell no tales. 
An hypothetical judgement connects a consequent with a condition 
which it does not, however, assert to be fulfilled : if money is scarce, 
the rate of discount rises. The condition is called sometimes the 
antecedent (in grammar, the protasis), as what is connected with 
it is called the consequent (in grammar, the apodosis). A disjunc- 
tive judgement affirms alternatives : bees are either male, female, or 
neuter. 2 The hypothetical judgement is sometimes called con- 
junctive, as conjoining the truth of the consequent with that of the 
antecedent : while the disjunctive disjoins the truth of one alter- 
native from that of the others. 3 Both are sometimes called com- 
plex judgements, in contrast with the categorical, which is called 
simple. 

In an hypothetical judgement, the antecedent and consequent 
may have the same, or different, subjects or predicates : the scheme 
of the proposition may be either ' If A is B, it is C ' (If corn is scarce, 
it is dear), or ' If A is B, C is D ' and (// the dead rise not, we are of 

1 The singular proposition whose predicate is a proper name does not 
assert a character of its subject. 

2 For any given bee, these are alternatives : for bees collectively, they are 
three forms which are all realized : cf. p. 188. 

3 The term hypothetical has also been used by some generically, with con- 
junctive and disjunctive to denote the species. 



182 AN INTRODUCTION TO LOGIC [chap. 

all men most miserable), or ' If A is C, B is C ' (Si tu et Tullia valetis, 
ego valeo). Again, antecedent and consequent may be either nega- 
tive or affirmative : but these differences make no difference to the 
character of the judgement as hypothetical : it still affirms the 
dependence of a consequent on a condition : hence the alternative 
of affirmative and negative, though applying to the antecedent and 
consequent severally, does not apply to the hypothetical judge- 
ment as a whole. 

It is sometimes said that hypothetical propositions can be reduced 
to categorical. So far as the verbal form is concerned, this can often 
be done. ' If A is B, it is C ', in which antecedent and consequent 
have the same subject, may be written ' A that is B is C ' ; If com 
is scarce, it is dear becomes Scarce corn is dear : If that dog is teazed, 
he bites becomes That dog bites when teazed. Even where antecedent 
and consequent have different subjects, a little ingenuity may 
produce from the hypothetical a proposition categorical in verbal 
form ; If no war is toward, the temple of Janus is closed might be 
written The temple of Janus is closed in peace time : If men are not 
free, blame is unjust might be written Men who are not free are not 
justly blamed. But whether a judgement is hypothetical or cate- 
gorical cannot be determined merely from the verbal form of the 
proposition in which it is expressed. The hypothetical judgement 
asserts the qualification of the subject by the predicate of the 
consequent to be dependent on a condition expressed in the ante- 
cedent ; as has been said, it does not assert this condition to be 
fulfilled. But where this condition is known to be at times fulfilled, 
it may still be expressed by an // (as well as by a When or Whenever) ; 
and if it can also be expressed as a qualification of the subject or 
predicate of the consequent, then that predicate may be asserted 
of the subject so qualified, or the predicate so qualified of that 
subject. Now the first three of the above examples are of this sort. 
Corn is sometimes scarce, that dog is sometimes teazed, Rome i3 
sometimes (though rarely) free from war. And the proposition 
// corn is scarce, it is dear, regarded as a statement about scarce corn, 
must be ranked as categorical, notwithstanding its form ; while 
Scarce corn is dear, regarded as a statement about corn whose scarcity 
it leaves in doubt, must be regarded as hypothetical. We are so 
well aware that corn is from time to time scarce, that we naturally 
interpret categorically in this instance. But in an argument con- 
taining the proposition Men who are not free are not justly blamed we 



vni] VARIOUS FORMS OF THE JUDGEMENT 183 

might see that it was not intended to deny that all men are free, 
but only to point out a consequence that would follow from denying 
it ; and then the judgement remains hypothetical. Otherwise, and 
if taken as implying the existence of men not free, the categorical 
proposition is not the equivalent of an hypothetical in which their 
existence is not implied. 1 The reduction to categorical form is only 
justified when the hypothetical proposition is meant merely to 
affirm a connexion of one character with another existing in a given 
subject or in all subjects of a certain kind. 

The difference between the two types of judgement — between 
affirming or denying a predicate of a subject, and affirming the de- 
pendence of a consequent on a condition not asserted to be fulfilled — 
becomes clear where the judgement concerns an individual situation, 
and particularly if it contains an unfulfilled condition, in past or future 
time, i/ he is insane, he cannot make a will implies, no doubt, a con- 
nexion between insanity and testamentary incapacity, but not be- 
tween the individual and either. // / had served God as diligently as 
I have done the king, He would not have given me over in my grey hairs : 
no doubt this implies the categorical judgement God does not forsake 
those who serve Him diligently ; but it cannot be reduced to this ; for 
it implies also Therefore He would not have forsaken me, if I had served 
Him diligently ; and we cannot ehminate this hypothetical judge- 
ment. Kpotaos "Akvv 8ta/3as y.eyahrjv apyj]v /caraAucrei, If Croesus 
crosses the Halys, he will ruin a great power 2 ; here it is not stated 
whether Croesus will cross the river or not ; so that, as the fulfilment 
of the condition upon which the event in the consequent depends is 
left in doubt, there is nothing but a dependence categorically asserted. 

It may be urged that, as this at least is asserted categorically, the 
hypothetical judgement is categorical after all. And against any 
one who attempts to abolish the distinction between the two kinds 
of judgement by saying that all judgements are really hypothetical, 
it is a good answer to point out that the hypothetical thus involves 
the categorical. But that does not invalidate the distinction between 
them ; for the distinction rests on the difference between asserting 

1 The form ' Men who are not free would not be justly blamed ' retains in 
the would the expression of hypothetical judgement, and cannot be regarded 
as a categorical proposition. 

2 More literally, Croesus by crossing the Halys will ruin a great power, which 
might be taken to mean that Croesus will cross the Halys and ruin a great 
power. So taken, the oracle is categorical ; and the line well illustrates how 
the grammatical form is no sure guide to the logical character. 



184 AN INTRODUCTION TO LOGIC [chap. 

a dependence of consequent upon condition not asserted to be 
realized, and asserting (affirming or denying) a predicate of a sub- 
ject. If it be granted that the hypothetical judgement asserts the 
former, though it does so categorically, yet it differs from the 
categorical. 

It has been said x that the very reason just given for maintaining 
the essential difference of these two types of judgement excludes the 
consideration of that difference from Logic. For both assert ; they 
differ in what they assert ; the difference is therefore in the matter 
and not the form of judgement. We have the same form, A is B, 
whether for A we write Croesus, and for B a king of Lydia, or for A 
the destruction of a great power, and for B must follow on Croesus 
crossing the Halys. But it will be readily admitted that the dis- 
tinction between categorical and hypothetical assertion is formal 
in the sense that it is illustrated in our thought about all kinds of 
subjects ; and to exclude it from Logic on the ground that, as com- 
pared with the common form of assertion in both, it is material, only 
shows the impossibility of making Logic a purely formal science. 
It is claiming to consider the genus, and refusing to consider the 
species : a procedure which would be tolerated in no other subject, 
and cannot be tolerated in Logic. 

[There is however a difficulty about the meaning of saying that 
a consequent depends on a condition, when that condition is unful- 
filled. // Hannibal had marched on Rome after Cannae, he would 
have taken it. This proposition makes an assertion ; in doing so, 
it asserts something about the real, for it claims to be true. But 
what does it assert about the real, and what historical fact (as we 
may put it in such an instance) does it affirm ? Not that Hannibal 
marched on Rome after Cannae, for he did not ; nor that he took 
Rome, for he did not ; nor therefore that one event was due to 
the other, for neither happened. How then can we say that one 
depended on the other ? In the sense, it may be answered, that 
if he had marched on Rome at that time, he would have taken it. 
But this is the original proposition whose meaning we are trying 
to discover. And it does not state a fact in Hannibal's history, 
or in the history of Rome, but what is called an unfulfilled con- 
tingency ; and how can that be asserted of the real ? Every 
hypothetical judgement presents this problem. For its truth does 
not require that either condition or consequent be realized, and 
yet, if true, it is true of reality ; and reality, we may urge, is 
actual. What then does it affirm to be actual in the real ? Mr F. H. 

1 Cf. Mansel, Prolegomena Logica, pp. 232, 251. 



vm] VARIOUS FORMS OF THE JUDGEMENT 185 

[Bradley x replies that it ascribes to reality a character which is the 
ground of the connexion stated in the hypothetical judgement. 
Rome was in such a state that it could not have resisted Hannibal 
after Cannae. This is true ; but it still leaves us with the question, 
How can there be the ground in the real universe of something 
which nevertheless does not happen ? Or we may put the problem 
a little differently by asking how there can be a dependence between 
a consequent and a condition that do not exist. 

Professor Cook Wilson holds that an hypothetical proposition 
affirms the dependence of the solution of one problem upon the 
solution of another. ' And they sent the coat of many colours, 
and they brought it to their father ; and said, This have we found : 
know now whether it be thy son's coat or no. And he knew it, 
and said, It is my son's coat ; an evil beast hath devoured him ; 
Joseph is without doubt rent in pieces.' 2 Here the hypothetical 
proposition is imiDlied, If this is thy son's coat, he has been killed ; 
and this means that the determination in the affirmative 3 of the 
question whether it is his coat involves the like determination of 
the question whether he has been killed. Where the condition is 
an unfulfilled condition in past time, this dependence of the solution 
of one question on that of another is affirmed not to exist now, but 
to have existed. The determination of the question whether Rome 
would fall directly after Cannae did depend on that of the question 
whether Hannibal would march on Rome. And such a proposition 
implies also the assertion that the condition was not fulfilled. 

What Professor Cook Wilson points out seems true and important. 
An hypothetical proposition does assert the solution of one problem 
to be connected with the solution of another. But the particular 
difficulty before us is not removed by that doctrine. For neither 
problem need be solved or by us soluble, and yet the hypothetical 
proposition may be true, as in the instance // the ' Phaedo ' is historical, 
Socrates believed in the immortality of the soul. Now our difficulty 
concerned the affirmation that a ground exists for what yet does 
not happen, or that there is a connexion between terms which yet 
do not exist. And there is the same difficulty in asserting one 
solution to depend on another, when neither is made. It concerns 
the meaning of saying that something is possible, which is not 
actual. 

It is a partial answer to say that connexions, or principles of 
connexion, exist in a different way from the particular things and 
events in which they are displayed or illustrated. They are, even 
when they are not exemplified. ' If you put a match to that powder, 

1 Principles of Logic, Bk. I. c. ii. §§ 50-53. 2 Gen. xxxvii. 32, 33. 

8 The determination in the negative of the question in the antecedent 
leaves the question in the consequent undetermined, unless the antecedent 
is the sole condition of the consequent. Cf. infra, p. 33b. 



186 AN INTRODUCTION TO LOGIC [chap. 

[it will explode.' Why ? because of a connexion between rise of 
temperature and detonation in compounds of a certain kind, which 
is not dependent for its being upon the actual process of those 
changes. The explosion then is possible, because there are certain 
connexions, and some of the things, given which these connexions 
are exemplified, exist. These connexions, which somehow are, 
even though the conditions for their display do not exist, are the 
' ground ' which the hypothetical judgement ' affirms of the 
real ' But the connexions whose affirmation is implied need 
not be such as are repeatedly illustrated. Sometimes the reason 
why the solution of one problem carries the solution of another 
lies in principles of connexion displayed in situations that are 
repeated ; so it is with the connexion between rise of temperature 
and detonation in gunpowder. But sometimes the conditions are 
apparently unique, and we cannot resolve them into an assemblage 
of repeatable elements ; so it is often with complex historical 
situations where all seems to turn on the action of a great per- 
sonality. And in some hypothetical propositions the connexion 
between the solutions of two problems seems to be the only con- 
nexion affirmed, as in the instance already given, ' If the Phaedo 
is historical, Socrates believed in the immortality of the soul ' ; 
though doubtless this implies an assertion of certain particular facts 
about that dialogue of Plato. 1 ] 

The disjunctive judgement may be expressed schematically in the 
forms ' A is either B or C ' (Every man at forty is either a fool or 
a physician), * Either A is B or C is D ' (He either fears his fate too 
much, Or his desert is small, 2 Who dares not put it to the touch, To 
gain or lose it all), ' Either A or B is C ' (Either the Pope or the King 
of Italy should retire from Rome). As the hypothetical judgement 
always affirms a dependence of consequent on condition, so this 

1 The reader must not suppose that these paragraphs deal at all completely 
with the problems raised by hypothetical judgement. Nothing, for example, 
has been said about distinctions of quantity in them. It has been urged 
by some that they are all universal. But though without necessary con- 
nexion in the real no hypothetical judgement would be true, such implied 
connexion may be remote from the actual hypothetical judgement made. 
Again, some hypothetical judgements are concerned with certain individual 
consequents and conditions, some with any of a certain kind ; or the 
condition may be of the former sort and the consequent of the latter, or 
vice versa. These differences however are not of first-rate importance. 

2 This might be equally expressed ' He either fears his fate too much, or 
deserves little ' : indeed in sense the alternative predicates are predicated of 
the same subject, not (as in the proposition Either Tacitus was a slanderer 
or Tiberius a villain) of different subjects. This affords another example of 
the fact that the logical character of a judgement cannot always be inferred 
from the grammatical form of the proposition. 



vhi] VARIOUS FORMS OF THE JUDGEMENT 187 

always affirms a disjunction, whether the alternatives themselves 
be given affirmatively or negatively. So far as the nature of the 
disjunction goes, there is no difference between ' A is either B or G ', 
and ' A is either not B or not G ' : between ' Either A is B, or C is 
D ', and ' Either A is not B, or C is not D ' : between ' Either A or B 
is G ', and ' Either A or B is not G \ But it should be noted that 
' Neither . . . nor ' is no disjunction at all, but a conjunction of 
negations. On St. Paul's voyage to Rome ' neither sun nor stars in 
many days appeared. ' ; there is no choice between alternatives here, 
but two statements — the sun did not appear, and the stars also 
did not. 

There may be any number of alternatives in the disjunction ; but 
that clearly does not alter the character of the judgement. 

It is not always clear in a disjunctive proposition whether the 
alternatives offered are meant to be mutually exclusive. If A is 
either B or G, then it cannot be neither ; but may it be both ? The 
question concerns the right interpretation of a form of speech, rather 
than the nature of disjunctive judgement. Sometimes from the 
nature of the case we may know that the alternatives exclude each 
other : as if we are told that Plato was born either in 429 or 427 b. c. 
Where this is not so, it is perhaps safer to assume that they are 
intended as mutually exclusive, unless the contrary is stated ; a legal 
document is careful so to write it, where ' A or B or both ' is meant, 
or to write ' A and/or B ' with that signification. 

If has been suggested that the disjunctive judgement is in reality 
a combination of hypotheticals ; that ' A is either B or C ' means 
' If A is not B, it is G ; if A is not C, it is B ; if A is B, it is not G ; 
if A is C, it is not B '. Doubtless these four propositions are in- 
volved (supposing B and C to exclude each other) : but we do not 
therefore get rid of the peculiar nature of the disjunctive judge- 
ment. For they are not four independent hypothetical judge- 
ments ; and their force is not appreciated, unless it is seen that 
together they make up a disjunction, that they offer us a choice 
between alternatives. Thus disjunctive judgement at once includes 
and goes beyond hypothetical, in the same sort of way as hypothetical 
judgement includes and goes beyond categorical. An hypothetical 
proposition makes an assertion, like a categorical ; but what it 
asserts is a relation of a consequent to a condition. A disjunctive 
proposition involves hypotheticals, which it presents as true together, 
but it asserts the truth of one (or, if they are not mutually exclusive, 



188 AN INTRODUCTION TO LOGIC [chap. 

of at least one), without specifying which one, among alternative 
caiegoricals. 

The disjunctive judgement also raises a metaphysical problem, 
when we ask what real fact corresponds to it. ' Plato was born 
either in 429 or 427 b. o.' cannot state the actual fact about Plato : 
he was born definitely in one year, not merely in one or other ; 
it is because we do not know in which, that we state an alternative, 
and there was no alternative in the event. Here, therefore, the 
disjunctive proposition seems rather to express the state of our 
knowledge, than the state of the facts. On the other hand ' Number 
is either odd or even ' seems to express a disjunction in the facts x ; 
and the species of the same genus are a kind of real disjunction. 
If a colour is to exist, it must be blue, or red, or some other colour, 
and if it is one, it can be none of the others. We come back here 
upon the same truth which met us in considering negative judge- 
ments, that a thing is definitely this or that by not being some- 
thing else ; we have to recognize also that there is often a limited 
number of possibilities, in the way, for example, of colour, or of 
animal species, but why or how there should be a limit to what is 
possible in the universe is a hard question. 2 

We come next to the distinctions of modality in the judgement. 
In respect of modality, categorical judgements are distinguished as 
assertoric, problematic, and apodeictic (or necessary) ; the first is 
sometimes opposed as pure to the other two as modal ; but we shall 
find that if judgements are divided into pure and modal, the assertoric 
can be regarded as a form of modal judgement. Propositions of 
the form ' X is Y ', ' X is not Y ' are assertoric — ' the train is late ', 
' the train is not late ' ; of the form ' X may be Y ', ' X may not 
be Y ', problematic — ' the train may be late ', ' the train may not 
be late ' ; of the form ' X must be Y ', ' X cannot be Y ', apodeictic 
— ' the train must be late ', ' the sun cannot be late '. The dis- 
tinctions are also expressed by adverbs : X actually, possibly, 
necessarily is (or is not) Y. 

In the sense of the word to which we have so often called atten- 
tion, these distinctions are clearly logical : i. e. they belong to no 

1 Of course there is a disjunction in the facts, in the former case as well, 
bo far as that the 429th and the 427th years from any point of time whence 
we choose to begin our reckoning are distinct years. 

2 For the fuller treatment of this form of judgement also the reader is 
referred to more advanced works. 



vml VARIOUS FORMS OF THE JUDGEMENT 189 

special science, but recur in our thought about all kinds of subject. 
Whatever X and Y may be 1 , we may find ourselves asserting that X 
is, that it may be, or that it must be Y. 2 But their logical character 
is specially manifest in this, that they raise a fundamental question 
about the nature of the thinking activity, viz. that of the difference 
between opinion and knowledge 3 , just as the distinction of judge- 
ments according to quality raises the question of the difference 
between affirming and denying. And as the latter difference cannot 
be reduced to a difference in the predicate affirmed, by combining 
the negative with the predicate, so neither can the former. Still, 
we found a ground for the existence of the two ' qualities ' of judge- 
ment in a certain fact about the being of things, viz. that each is 
positively what it is by exclusion of all else, by difference. It i3 
not so easy to find a ground for the existence of the ' modalities ' 
of judgement in the being of things. 

Let us take three judgements differing in modality and expressed 
in propositions of the form ' X is Y ', ' X may be Y ', * X must be 
Y ' — ' the train is late ', ' the train may be late ', ' the train must be 
late \ We can express the same judgements by saying that the 
train is actually, or possibly, or necessarily late. But it is clear 
that we have not here three judgements with the same subject, the 
train, and different predicates, actually late, possibly late, necessarily 
late ; for those are not three kinds of lateness. The modality of 
a judgement cannot be something qualifying its predicate. ' Nor- 
man mouldings were possibly coloured ' : ' Norman mouldings were 
actually coloured ' ; the adverbs do not express a mode of colouring, 
as if we said that the mouldings were brilliantly coloured, or coloured 
blue. ' Water runs down hill ' : ' water must run down hill ' ; 
these are not different ways of running, like running fast or run- 
ning slowly. Grammarians tell us that adverbs qualify verbs and 
adjectives, but adverbs of modality seem to be an exception. 4 

1 Except so far as in some subjects, like arithmetic, a judgement is nearly 
always made with consciousness of its necessity : cf. infra, p. 196. Even 
here however I might say, before I had made the calculation, that 37596 
may be a square number. 

2 For the sake of brevity, I shall not throughout consider negative as well 
as affirmative judgements. It should be noted that the problematic affir- 
mative ' X may be Y ' is not contradicted by the problematic negative 
' X mav not be Y \ but by the apodeictic ' X cannot be Y ' : and similarly 
the problematic negative by the apodeictic affirmative. 

3 Cf. p. 160, supra. 

* Unless indeed they qualify the copula, the verb to be, as some have said. 
Cf. next page. 



190 AN INTRODUCTION TO LOGIC [chap. 

Again, it is not the judgement, in the sense of the act of judging, 
that the modal words qualify ; if I judge ' the train may be late ', 
my judging is actual ; it is the lateness of the train that is possible. 
That, however, as we have just seen, does not mean that its lateness 
is a certain sort of lateness, as if we said that the lateness of the 
train is scandalous. 

Once more, we cannot say that the modal words qualify the matter 
judged. I judge that the train may be late, or that the window 
may be open ; the judgements have the same form, which I can 
express symbolically in the formula ' that X is Y is possible ' ; 
the assertoric and apodeictic may be similarly expressed — ' that 
X is Y is actual ', or ' necessary ' ; or more compendiously, instead 
of the words ' that X is Y ' I can write '17'. But X Y is certainly 
not the matter judged ; for when I judge it possible that the train 
is late, I do not judge X Y, that the train is late, at all. The matter 
judged is that which is judged to be, the subject qualified by the 
predicate. X and Y are not the subject and predicate in these 
three judgements, as indeed the formulae in which the modal words 
are predicates indicate. The affirmative and negative judgements, 
1 X is Y ' and ' X is not Y ', can have the same subject and pre- 
dicate, but differ in quality ; so we are apt to speak as if the 
assertoric, problematic, and apodeictic judgements could have the 
same subject and predicate, but differ in modality. The analogy 
is false. The true analogy is rather this, that as in a negative 
judgement the matter judged is ' that X is not Y ', and is therefore 
different from the matter judged in the affirmative, so in the 
modal judgements the matter judged is that X is actually, or pos- 
sibly, or necessarily Y. But here what actually, possibly, or 
necessarily is, as there what is not, is said to be. Hence as Plato 
asked what is meant by saying that not being is, so we must ask 
what is meant by saying that possible being, or actual or necessary 
being, is. 

To ask this is the same as to ask whether modality can qualify 
the copula. We use the verb to be as the sign of judgement, because 
the predicate expresses some further being of the subject than is 
expressed already by the subject-term. I look up and say ' the 
window is open ', because that is of the being of the window. But 
whatever the window is, it is actually, and not possibly ; and 
perhaps what it is actually, it is necessarily. If so, what is possible 
being, and how can we distinguish actual from necessary being ? 



vih] VARIOUS FORMS OF THE JUDGEMENT 191 

The modal words cannot indicate different ways in which X is Y, 1 
any more than differences in Y. What then do we mean by them, 
and why do we use them ? 

We use them to mark the distinction between knowledge and 
opinion, and the differences in the certainty with which we hold an 
opinion. This is not a complete answer, because the modal words 
are used in divers senses ; but the difference in the modality of 
'udgements is the difference between knowledge and opinion, and 
between certainty and uncertainty in opining ; and so far as these 
words are marks of modality, they mark that. It is no objection 
to this view, but rather a confirmation of it, that men often use the 
modal forms expressive of knowledge or certainty, when they do not 
really know, or are not certain. They may assume a virtue, if they 
have it not ; and unless these forms had such meanings, there would 
be no motive to use them. But we must turn to a closer examina- 
tion of their use. 

In the history of thought the assertoric form, 'X is Y\ seems to 
come first. Certainty or conviction precedes doubt, and precedes 
the reflective consciousness of knowledge. What Bain called 
primitive credulity cannot make us know, but it can make us assert. 
Our early assertions, however, are made without reflection ; we 
do not ask whether they are consistent with others that we have 
made, or whether it is possible to doubt them. When we ask such 
questions, we may find that different assertions which we have made 
are inconsistent, and that they cannot all be true, though we do not 
know which are false ; or we realize that we can doubt one, but 
not another. Our assertoric thinking is thus displaced by problem- 
atic thinking, or by necessary thinking — i. e. the apprehension of 
necessity, or knowledge. 

But the assertoric proposition itself, ' X is Y ', may express two 
different mental attitudes. 2 We may hold and express an opinion 
without doubt before question has been raised ; after question has 
been raised, we may still hold and reassert the opinion as confidently 
as before, although we have not been able to prove or see into the 
necessity of the fact asserted. There are several kinds of example 
that may be given of this. It occurs in regard to sensible facts. 

1 Or is not. I have not complicated the discussion by taking also negative 
examples. 

2 We shall see that it h also often used where the judgement expressed is 
apodeictic : v. infra, p. 196. 



192 AN INTRODUCTION TO LOGIC [chap. 

A man walking up Eskdale in a fog and having lost his way says 
that he hears Cam Spout ; if challenged, he may listen again, and 
say that he is sure he hears the sound. Or his opinion is asked about 
a proposed act, and he condemns it ; another dissents and asks his 
reasons ; and he replies that he cannot give any reasons, but is sure 
that the act is wrong. Or again (and we shall find this very common 
in the inductive sciences) we assert as a fact something which we 
cannot explain or understand, because we have had experience of 
events that seem only explicable if it is true. Some men detect water 
with the divining-rod. That is very extraordinary ; how do you 
account for it. I can't, but they detect it. Here the assertoric judge- 
ment is challenged ; events are recalled which seem inexplicable 
unless there is this power ; and so it is reasserted. On the second 
assertion, the word detect would be emphasized in speech ; or 
the emphasis could be given in writing by the words ' they do 
detect it ', or ' they actually detect it ' ; and language has other 
idioms for expressing this assertoric confidence. 

The difference between the two mental attitudes just noted lies in 
this, that whereas in both we feel confident, in the former this con- 
fidence is unreflecting, in the latter it is felt in the face of suggested 
doubt, and so is reflective. It might perhaps be best to call a 
judgement pure, rather than modal, which is made without any 
reflection upon the question of its truth ; and assertoric when, upon 
reflection, we can give no proof of it, nor see the necessity of the fact 
asserted, but are confident of it. The word actually would mark 
a judgement as assertoric, not pure ; but the ordinary categorical 
form can also express it ; we are considering the nature of the acts 
of judgement, but can only contemplate these by the help of propo- 
sitional forms. 

A consideration of the problematic and apodeictic judgements 
will throw further light upon the assertoric. When an opinion is 
challenged, we commonly try to justify it by producing grounds for 
it, though we cannot always do this, and our pure judgements, 
as just observed, are apt to be displaced by problematic or apo- 
deictic. The apodeictic may be taken first ; it is a judgement made 
with a consciousness of the necessity of the fact asserted. But we 
often use the apodeictic form of proposition, ' X must, or cannot, 
be Y* ( ' X necessarily is, or is not, Y '), when we do not apprehend 
a necessary connexion between X and Y ; and there are two classes 
of case to be distinguished when we do apprehend it, viz. those in 



vm] VARIOUS FORMS OF THE JUDGEMENT 193 

which we need, and those in which we do not need, in order to see 
the connexion, to look beyond the content of the judgement X Y. 1 
Both are important, because in both we have knowledge. 

A boy may believe and assert, because he has been taught it, 
or because he remembers to have seen no others, that all lines are 
either straight or curved ; if the assertion is questioned — it matters 
not whether the question comes from himself or another — and he 
asks himself what ground he has for making it, he will realize that 
it belongs to the nature of linearity that every line must be straight 
or curved. Put symbolically, the ground for the judgement ' X is 
T ' is seen to lie within the nature of X. 2 We call such a judgement 
self-evident. There are self-evidently necessary negative judge- 
ments, as well as affirmative, e. g. ' the difference between two 
degrees of quality is not a quality '. 3 What is self-evident need not 
be evident at once, or to everybody ; the intelligible is intelligible 
only to the intelligent. In calling anything self-evident we mean not 
that it is evident without need for understanding, but that we need 
consider nothing but the terms of the judgement, to see its necessity. 

[Logicians of two different schools have denied the existence of 
the self-evident. The one school are the Empiricists, who, rightly 
insisting that there is no knowledge without experience, wrongly 
suppose that we cannot by thinking discover the nature of anything 
that we have not perceived. The child learns the multiplication- 
table by counting marbles, or what not ; but it comes to understand 
that the equality of two groups severally of 3 and 4 marbles to 
two severally of 5 and 2 marbles is independent of the units being 
marbles, or the day Monday, or the place London, or itself the 
person counting — that 3+4=5+2 universally; nor does it need, 
nor could its judgement be increased in certainty by, experimenta- 

1 We may symbolize thus the categorical propositions whose subject and 
predicate are X and Y, and which are so far ' materially ' the same, but 
whose ' formal ' character — modality, quality, quantity — may differ ; remem- 
bering however that in the problematic proposition ' X may be Y ', X and 
Y are not the terms of any judgement made, but of a suggested judgement 
which is not made. Cf. supra, p. 190, and infra, pp. 196-197. 

2 In Aristotle's language, the predicate belongs to the subject icad' alro, 
or per se — in virtue of itself. 

3 A gallon and a quart are two quantities. I can take a quart from a gallon 
of water, and I shall have a certain quantity (three quarts) left. The difference 
between two quantities is in this sense a quantity. But suppose two qualities 
differing in degree, say a darker and a lighter blue, or a more and a less intense 
pain : it is meaningless to say that the quality of lower degree can be takeD 
from that of higher, and leave another quality which is the difference of 
those degrees. This self-evident fact has an important bearing on the so-called 
calculus of pleasures and pains. 

1779 O 



194 AN INTRODUCTION TO LOGIC [chap 

[tion with further particulars ; and from henceforth it sees this 
principle to be as true for countable things of which it has not had 
experience as for those of which it has. It has thus obtained by 
thinking knowledge about things of which it has had no experience 
(though it could not have done so without some experience of 
countable things). The Empiricist, however, denies this, and holds 
that the proposition '3+4=5+2' is a mere generalization from 
experience, entertained so confidently not because it is seen to be 
necessary, but because it is verified in so many instances. He is 
however herein using an argument — ' because this equation holds 
good in so large a number of examined instances, therefore it holds 
good in the unexamined \ Either the conclusion of this argument 
follows necessarily from the premise, or it does not. If it does not 
(and in fact it does not), he cannot justify our confidence in any 
process of arithmetical thinking ; if we have put 3 shillings into 
an empty purse, and then 4, and have taken out 2, we ought not 
to say there are 5 left until we look, or to be surprised if we find 
more or fewer. If, on the other hand, the conclusion does follow 
necessarily from the premise, then here at least is an instance of 
our discovering by thinking a fact about things which we have 
not learnt by experience. Empiricism breaks down over the validity 
of inference ; if it allows that, it gives away its case ; if it dis- 
allows it, it cannot argue. 

The other objection to self-evident truth is more serious. It is 
said that all things are interconnected ; that their relations to each 
other are not 'external ', i.e. that relations cannot change without 
a change in the nature of the things related, being really an 
expression of their nature ; that we cannot know anything in all 
its relations, and that a predicate Y which we ascribe to a subject 
X must be conditioned by what we do not know of the subject 
as well as by that which we have indicated of its nature when we 
call it X. Even so simple a fact as that 2+2=4 is part of the 
whole system of numerical relations ; it could not still remain, if 
per impossibile other numerical relations were different from what 
they are, e.g. if 2 +3 =7 and 314 +228 =56. As it is connected 
with all these, it can only be fully known through them, and when 
seen in its relations to the rest of the system. No particular truth, 
on this view, is absolutely true ; only in apprehending everything 
could we know anything as it is. This doctrine is maintained 
forcibly, and even scornfully, by Mr. F. H. Bradley (e. g. Essays on 
Truth and Reality, c. vii) and by Mr. H. H. Joachim in his book On 
the Nature of Truth, c. iii ; its most famous advocate in modern times 
is Hegel. Something like it was known to Aristotle, and criticized 
by him in the Posterior Analytics (/J. xiii. 97 a 6-22). l It rests on meta- 

1 Professor G. F. Stout has put well the argument against it, in the first 
Essay in Personal Idealism (on Error). 



vm] VARIOUS FORMS OF THE JUDGEMENT 195 

[physical considerations which cannot be lightly dismissed ; and 
they might seem to require us to deny that any truth is st7/-evident, 
because nothing can be understood except through the whole. But, 
even if they are sound, we must still acknowledge that we make 
some judgements with a consciousness of their necessity, and others 
not ; we cannot abolish the distinction between knowledge and 
opinion. Such transformation as complete knowledge would effect 
in the thought expressed by a self-evident proposition must be of 
the same nature as occurs when a geometrician comes to realize 
that a proposition which he has demonstrated about one species 
of figure is but a special case of a much wider proposition capable 
of a general proof. His original proposition is not thereby shown 
to be false, though his insight into the facts was incomplete.] 

More often, however, when we use the apodeictic form of pro- 
position, the fact asserted in seen to be grounded in some other fact 
or facts, not stated in that proposition, which we should assign as 
a reason for it. Water must rise in the common pump, when the 
piston is raised : why must ? because of the pressure of the atmo- 
sphere. Mere observation would lead us to affirm assertorically 
that it does rise ; it is the consciousness of the connexion of that 
fact with the pressure of the atmosphere in a machine constructed 
as a pump is, that makes us affirm it apodeictically. But are we 
sure, it may be asked, that the atmosphere must have weight ? 
for unless we are, we can only assert that the water must rise if and 
when the atmosphere has weight. We cannot here discuss the 
grounds on which we regard the general principles of science as 
established ; that belongs to a consideration of inductive reasoning. 
But two things are clear : first, that if the grounds of the judgement 
X Y can only be affirmed assertorically, X Y itself is necessary only 
upon the condition that those grounds are as we assert ; secondly, 
that, even so, the connexion between those grounds and the fact XY 
may be seen to be necessary. We may call the necessity of a judge- 
ment, which we see to follow from certain grounds, but whose grounds 
we cannot affirm apodeictically, an hypothetical necessity ; when 
the grounds can be affirmed necessarily, then perhaps we may 
say that the judgement is apodeictically necessary. Thus, if two 
straight lines falling on another straight line and making the internal 
angles on the same side of it together equal to two right angles can 
never meet, the angles of any triangle, however large or small, are 
equal to two right angles ; to one who regards the axiom of parallels 
as self-evident, the judgement that the angles of a triangle are equal 

02 



196 AN INTRODUCTION TO LOGIC [chap, 

to two right angles will appear apodeictically necessary ; to one 
who does not, hypothetically. 

It will be seen from this, that there is a close connexion between 
the hypothetical and the apodeictic judgement. But we cannot 
say that all hypothetical propositions are apodeictic, for we often 
use them when we do not see the consequent to be necessarily 
involved with the antecedent, e.g. a public speaker says that if 
a certain measure is carried, certain results will ensue. This is only 
another illustration of the fact that a propositional form which ia 
intended to express a certain kind of judgement may be used when 
we do not really make the judgement which it should express. Every 
deliberate falsehood illustrates this, and every false apodeictic 
proposition, whether deliberately intended to deceive or not. And 
it often happens that the assertoric form of proposition is used to 
express necessary truth, the apodeictic to express doubtful opinion. 
In mathematics every step is seen by the mathematician to be 
necessary 1 > insomuch that it is often summarily said that mathe- 
matics deals with ' necessary matter '. There is consequently no 
need to distinguish apodeictic from other judgements in mathematics, 
and they are all, as a rule, expressed assertorically ; we say '2x2 
is 4 ', not '2x2 must be 4 ' : ' the interior angles of a triangle are ' — 
not ' must be ' — ' equal to two right angles '. And contrariwise we 
use the apodeictic form of proposition to hide our doubts, perhaps 
even from ourselves ; we are conscious of grounds for a judgement 
and grounds against it, but we look to those only which enforce the 
side we wish to take, and in reference to them make our assertion 
apodeictic. ' It must be so : Plato, thou reasonest well ' does not 
express the same confidence as if the speaker had said ' It is so \ 
' Methinks the speaker doth protest too much.' The apodeictic 
formula, X must be Y, thus covers in use diversities of thinking ; 
but it always implies that the speaker has reflected upon the question 
of the truth of his judgement. 

The problematic judgement, X may be Y, similarly involves re- 
flection ; but it does not, like the apodeictic, involve the judgement 

1 Many mathematical statements are made without seeing into, or realizing, 
their necessity at the time, and the thinking is then assertoric ; but because 
their necessity can be seen, we may call them apodeictic. There are a few, 
which mathematicians have believed to be true, but found false — e. g. general 
formulae for the finding of prime numbers, which have finally broken down. 
If it had been seen that the formula must yield a prime for any value, it 
could not have broken down. 



vin] VARIOUS FORMS OF THE JUDGEMENT 197 

that X is Y. He who judges that straight lines making equal angles 
with the same straight line cannot meet judges also that they do not ; 
he who judges that Mars may be inhabited does not judge that it is. 
It involves reflection, therefore, like the apodeictic judgement : but 
reflection upon something suggested, as it were in an attempt to 
judge, which we cannot find sufficient grounds either to affirm or 
to deny. It is an expression of uncertainty. 

The problematic is the most difficult of the three modalities of 
judgement, and its consideration is complicated by the fact that the 
formula X may be Y is sometimes used when there is nothing pro- 
blematic in our thinking, because there is no uncertainty. When 
a genus G has divers alternative species S x , S 2 , S 3 , we say that a 
may be either S 1 , S 2 , or S 3 : a triangle may be equilateral, isosceles, or 
scalene — currants may be black, white, or red. So long as such pro- 
positions are general, they express knowledge of the divers forms 
in which it is seen that a genus must be, or found that it is, realized ; 
and they are not problematic. They are only problematic, if the 
subject is a definite individual of the genus — 'that currant-bush may 
be white, black, or red ' ; for then, they express our ignorance as to 
which it is. Again, we use the problematic formula, X may be Y, 
when we know that, under certain conditions P, the subject X does, 
or must, exhibit the character Y, but we either do not now desire, 
or are unable, to state the conditions. In this sense we say ' Water 
may boil below 212° Fahrenheit ' — the condition omitted being 
a diminution of the ordinary atmospheric pressure ; or ' A man may 
die of joy ', the condition here being one which we could not state 
precisely, though no doubt it is connected with the condition of his 
heart. Disregarding these uses for the present, we must turn to those 
which really express problematic thinking. 

The plainest examples occur where the judgement concerns 
individuals, e.g. 'Rain may fall to-morrow' (this is concerned 
not with a particular thing or person, but still with a particular day) ; 
or again ' The Sultan may behead his vizier to-morrow '. It is 
clear that such judgements imply uncertainty in the speaker. But 
is uncertainty only a state of the mind, or is it also a state of the 
facts ? A necessary judgement is really an apprehension of necessary 
connexion in the facts : is a problematic judgement an appre- 
hension of a less than necessary connexion in them ? There is 
a sense in which we may intelligibly maintain this. Given that 
things of the same kind behave differently in different relations, 



198 AN INTRODUCTION TO LOGIC [chap. 

and given a complex system containing many things of divers kinds, 
whose kaleidoscopic interactions bring different things of the same 
kind into different situations, then we can say that there is no 
necessary connexion between being of the kind X and behaving 
in the way Y. This varying collocation of things is the basis, as we 
saw, of the relation of accident or of the ' coincidental ' between 
predicate and subject ; and a system of things subject to such 
changes may be called not ' necessary matter ' but ' contingent '.* 
Yet in a given situation, as we saw in discussing the accidental, we 
commonly think that what happens is necessary. Is this opinion 
a mistake ? There is one region in which men have been disposed 
to think so — that of voluntary action. It has been thought that 
the freedom of the will implies that a man's action does not issue 
necessarily from his character and circumstances, so that no know- 
ledge of these, however complete, would enable one to say that he 
must act thus or thus. If this is so, there is a ground for the pro- 
blematic character of any judgement about the future actions of a 
voluntary agent in the intrinsic uncertainty, or real contingency, of 
the event. But this uncertainty can only belong, if at all, to future 
actions. If I say ' The Sultan may have beheaded his vizier 
yesterday ', I imply no more uncertainty in the facts than if I say 
' Rain may have fallen yesterday ' ; the same is true of the judge- 
ment ' The Sultan may now be beheading his vizier ', just as much 
as of ' Rain may now be falling '. All these alike are problematic 
only in virtue of my uncertainty about the facts, not of any uncer- 
tainty in the facts themselves. And the same character belongs 
to problematic judgements which are not concerned with an in- 
dividual but a kind of thing. ' Cancer may be incurable ' means that 
though cancer either is incurable or not, and we are aware of certain 
facts inclining us to think it is, we have not sufficient grounds for 
a decision. 

Waiving that case, however, a problematic judgement implies by 
the form X may be Y our belief of certain facts which are not suffi- 
cient ground for the judgement X is Y, though we believe that along 
with other facts they would be. We do not in practice make such 
judgements in the absence of all knowledge. ' The grandfather of 

1 In Aristotle's phrase, evbtxoficva «\Xeo? ?x eiv > ' things that can be other- 
wise ' : but Aristotle does not make it very clear how far he thought 
their variability depended on shifting collocations, and how far on a ' real 
contingency ', which he did not altogether reject. 



viii] VARIOUS FORMS OF THE JUDGEMENT 199 

Pocahontas may have died of diabetes ' : that is possible, because any 
man may ; but as we do not know that in this particular case any of 
those special facts were present which, with others, cause a man to 
die of diabetes, we should never so judge. A problematic judgement 
is provoked by knowledge ; it is problematic because of ignorance. 1 
It follows that further knowledge would lead to its supersession 
by an apodeictic or assertoric judgement, according as our doubts 
were removed by a discovery of conceptual connexions or of historic 
facts. A genuine example of cancer being cured would refute the 
judgement ' Cancer may be incurable ' ; so also would such an 
understanding of the nature of the disease as enabled us to see how it 
could be cured. But though further knowledge would lead us to 
abandon the problematic judgement, we do not, when we make it, 
know whether X is never Y, or alwaj^s Y, or sometimes Y and 
sometimes not. In this there is a difference between a genuinely 
problematic judgement and those expressed in propositions of the 
same form which we noticed and set aside. For in them we imply 
that there are conditions, whether we can fully state them or not, 
under which X is Y. 2 These quasi-problematic propositions have 
therefore an affinity with certain particular propositions. In the 
particular proposition ' Some X is Y ', we saw that we might either 
be thinking of individuals of the kind X, not separately enumerated, 
which are Y, or of some general determination of X, not stated, 
which would involve its being Y ; the former sort is rather of the 
nature of the singular proposition, the latter is on the way to the 
universal. In the latter, the conditions, given which any X is Y, 
may be either known but not stated, or, though unknown, shown to 
exist by examples of X being Y : ' Some triangles have the square 
on one side equal to the squares on the other two ' — viz. right- 
angled triangles ; ' Some children are taller than their parents '— 
doubtless in virtue of certain physiological conditions, but we do not 
know them. Particular propositions like these have been called 
' modal particulars ', because of their close similarity to the quasi- 
problematic propositions just considered. The judgements can 
indeed be as easily expressed in the form ' X may be Y ' as in the 
form ■ Some X is Y ' ; each form implies that under certain con- 
ditions, not specified, though perhaps known, X is Y ; but there 
is this difference between them, that the latter implies that the 

1 Cf. Bosanquet, Logic 2 , vol. i, pp. 315-318, on 'real possibility'. 

1 Or, if the judgement were ' X may not-be Y ', under which it is not. 



200 AN INTRODUCTION TO LOGIC [chap. 

conditions are sometimes actually fulfilled, the former does not 
do so. 1 

We may sum up what has been said of the modality of judge- 
ment as follows. In every judgement I intend to assert truth, 
but not necessarily about the particular reality to which the subject 
of my proposition refers ; the truth I assert may be that I am 
unable to discover the truth about this reality. I may judge 
without pausing to question what I assert ; and in such case my 
judgement is called assertoric, and expressed in the form ' X is 
(or is not) Y ' ; it can, however, also be called pure, as being pure 
or free of any reflection upon the question of its truth. On the 
other hand, I may reflect on this question, and if I see the judgement 
to be true in virtue of the very nature of its terms, or if I find 
that what it asserts is involved in what I already know, or take, 
to be fact, my judgement is called apodeictic, and expressed in 
the form ' X must (or cannot) be Y '. Those apodeictic judge- 
ments which are grounded in facts not forming part of what they 
themselves affirm have a different logical character according as 
these facts can be affirmed apodeictically or only assertorically ; 
if the latter, the judgement resting on them is not strictly apodeictic, 
for only the sequence can be affirmed apodeictically. If I find 
that what I attempt to assert in a suggested proposition is con- 
nected with conditions, some of which I know to exist, while I am 
ignorant whether the others required are realized or not, I assert 
it to be possible ; such a judgement is called problematic, and 
expressed in the form ' X may (or may not) be 7 '. The proble- 
matic proposition does not imply that particular events are 
unnecessary in their happening, though, when general, it does 
often imply that an event of a certain kind depends on a conjunc- 
ture, or contingency, which is not universally necessary. It is 
possible that when reflecting on the question of a judgement's 
truth, we cannot find any ground for asserting what we assert, 
except that we perceive or remember the fact stated, or have 
had it on good authority ; though this may be reason enough to 
convince us of the truth of our assertion ; then the content of 
the judgement is affirmed to be actual, and the judgement called 
assertoric, and expressed in the form ' X is (or is not) Y ', with an 
emphasis perhaps on ' is ', or the addition of the word ' actually '. 

1 e. g. ' A man may call at every public-house from John o' Groats to Land's 
End.* 



vm] VARIOUS FORMS OF THE JUDGEMENT 201 

This assertoric judgement, being not a bare unreflective assertion, 
but expressing besides our mental attitude towards a suggested 
doubt, is different from the assertoric judgement, above called 
also pure, that contains no such reflection ; and as involving such 
reflection, this is modal. 

These distinctions of modality do not then express differences in 
the necessity with which elements connected in reality are con- 
nected x ; yet they do express this, that whereas some connexions 
in reality are seen to be necessary, others, and the existence of 
such elements, and their distribution in time and place, are not. 
Many philosophers have felt it impossible not to believe that the 
existence of all things, and their distribution, and every feature 
of their interaction, are as necessary as those matters which are 
asserted in our really apodeictic judgements ; and if their belief 
could pass into clear vision, judgements at present problematic or 
assertoric would be replaced by apodeictic. 

[Some further questions connected with modality, and in par- 
ticular with the problematic judgement, deserve attention. 

In the first place, in a problematic proposition, do we really 
judge ? In the assertoric or apodeictic, we judge that X is F, 
though there is a great difference between thinking, however con- 
fidently, what we do not see to be necessary, and knowing. But 
in the problematic, we do not at any rate judge that. Is it more 
than an expression of doubt, and of our inability to ' make up our 
mind ' ? It certainly is an expression of doubt. But we do not 
utter such propositions in vacuo, and out of relation to any question 
which we desire to answer ; and if a man were asked whether 
there really is telepathic communication, and replied after con- 
sideration ' It may be so ', he would mean rather more than that 
he did not know. He would mean that there were certain facts 
preventing him from denying it, though insufficient to prove it ; 
that there was some reason for thinking yes. 

If there were no assertion of fact in a problematic proposition, 
we should not judge one event to be more probable than another. 
The whole mathematical treatment of the probability of events 
rests upon the assumption of a limited knowledge of their con- 
ditions. If I say that there is more probability of throwing 7 with 
the dice than 12, it is because I know that there are six ways of 
throwing 7 and only one of throwing 12. In complete ignorance 
of a subject I could not say that anything was probable regarding 

1 Hence we cannot accept such a definition as Aldrich offers of modality : 
' Modalis, quae cum Modo, h. e. vocabulo exprimente quo modo praedicatum 
insit subiecto.' Artis Logicae Rudimenta, c. ii. § 2. 1 (Mansel's 4th ed., p. 47). 



202 AN INTRODUCTION TO LOGIC [chap. 

[it. 1 But the attempt to estimate degrees of probability raises 
a difficulty which the problematic judgement of itself does not 
raise. I say that something may happen on a given occasion, 
because I know (or believe) that some of the conditions required 
for its happening exist ; but if I say that one event A is more 
probable than another B, I do not mean to assert that the con- 
ditions necessary for the occurrence of A are more completely 
realized than those necessary for the occurrence of B ; for that 
implies that the conditions requisite for B are incomplete, and if 
I know (or believe) that, I shall call B not less probable, but 
impossible. More conditions necessary for A than for B are known 
to me ; but as the rest is unknown, it may turn out that the con- 
ditions requisite for B are really complete, and those for A incom- 
plete. Anyhow, if one or other event must occur, one will occur, 
and the other not ; one is necessary, the other impossible ; more 
and less probability do not attach to the events. We say therefore 
that they attach to our judgements ; the judgement that A will 
happen is more probable than the judgement that B will happen. 
But one is true, the other false, and we do not know which is which ; 
is it not foolish to prefer one, as the more probable ? It is the more 
probable judgement, comes the answer, because there are more 
grounds for it, i.e. there are more grounds for thinking that A will 
occur than that B will. But what does this mean ? the grounds 
for thinking that A will occur are the facts, or a knowledge of the 
facts, which necessitate A. Less than this is no ground for thinking 
that A will occur, but only that it may occur ; and similarly with 
B. The real situation then is that there are grounds for thinking 
that A or B may occur, but not for thinking that the one will occur 
rather than the other. An example will make the point clearer. 
Suppose I am to draw from a box, in which there are 5 black balls 
and 1 white, and to bet on the result. I shall be told to bet on 
drawing a black ball, because it is more probable ; yet all the time 
perhaps only the white ball is within reach, and my drawing a black 
is impossible. How can that be the more probable judgement 
which leads me to act upon the expectation of an event which is 
impossible ? The usual answer is, that with the knowledge avail- 
able it was more reasonable to bet on black ; but would it not have 
been more reasonable not to bet at all ? And indeed, is not that 
the only reasonable course ? did I know enough to bet reasonably ? 
And if not, can we defend the statement that the one event was 
more probable ? 

I think we may partially solve this difficulty as follows ; but 
not wholly. We must distinguish between what is reasonable if 
we are to act many times, and if only once. If I am going to 
draw from the box many times, the ball being replaced and the 

1 Cf. infra, pp. 423-424. 



viii] VARIOUS FORMS OF THE JUDGEMENT 203 

[box shaken after each draw, then supposing I always bet on black, 
I shall win more frequently than if I always bet on white. In 
saying this I know that there are five times as many black balls 
as white, and I believe that the movements of shuffling and the 
direction of the thrust of my arm are favourable about equally 
often to each ball. But what is reasonable to do on each of a number 
of occasions is no longer reasonable when there is only one occasion 
of acting. The real meaning of the statement that drawing a black 
ball is 5 times as probable as drawing a white is that in a large 
number of trials black will be drawn about 5 times as often ; but 
I cannot transfer the ratio to the event of a single trial. If there 
are twice as many boys as girls in a village, it is not because each 
child is | boy and § girl ; and it is the same here. Those who call 
it reasonable to ' follow the chances ' in an isolated action are like 
people who think that an average or percentage is displayed in each 
of the items from which it is obtained. An excellent example of 
the difference is provided by life insurance. An insurance company, 
knowing that, out of a great number of persons who have lived 
to 55, so many have died at 56, so many at 57, &c, but that the 
average length of life beyond 55 has been (say) 15 years, and 
believing that the circumstances favourable or unfavourable to 
longevity will continue much as hitherto, offers an insurance policy 
to persons of 55 at a premium based on the assumption that they 
will live to 70. It does not matter to the company that it loses 
on X and gains on Y, provided it makes the calculated profit on 
the average. But it matters very much to X whether the company 
is going to lose or gain on his insurance. If he dies next year, he 
will have made a very good bargain ; if he lives to 90, a very bad 
one. What is reasonable for the company to offer is not reasonable 
for him to accept, if he regards life insurance as a speculation. If he 
insures his life for the sake of the security of his family, the question 
is whether this security is worth the price asked for it. The proper 
price to ask of him may be settled by applying the theory of proba- 
bility ; but you cannot so settle whether a thing is worth its price. 

And yet many a man faced with the question, whether it is worth 
his while to pay the premium asked, would take into account his 
so-called ' expectation of life ' — how long it is ' probable ' that he 
will live. If he lived all the lives of all the insurers, this would be 
reasonable ; as he lives only his own, is it reasonable ? I think, 
applying the same considerations as hitherto, we may justify him a 
little further. 

We allowed that a man making repeated draws from the box 
will draw black more often than white, because black will be more 
often under his hand ; and therefore, though he does not know 
on any given occasion which will be under his hand, he will act 
reasonably if he always bets on black. These occasions of action 



204 AN INTRODUCTION TO LOGIC [chap. 

[are all of the same kind. But life requires us to act in all sorts 
of situations, with very imperfect knowledge of the conditions 
affecting the event in each, wherein it is said that we should follow 
the more probable judgement, or take the course more likely to 
succeed. Our difficulty was to discover what is meant by calling 
one judgement (or event) more probable than another ; both seemed 
equally problematic. But we were considering an isolated judge- 
ment. What is meaningless when our judgement is to guide our 
action only once may not be so when very many actions are in 
question, and we judge always on one principle. Suppose that the 
ratio of the known circumstances favourable to one event to the 
known circumstances unfavourable to it, or favourable to another 
is roughly the same — or even, more nearly directty than inversely 
the same — as the ratio of the existing circumstances favourable to 
the one event to the existing circumstances unfavourable to it, or 
favourable to another : then if men always acted as if that event 
would happen, for which they knew more circumstances favourable, 
they would more often succeed than fail. That is what is meant by 
adopting the course, or acting on the judgement, for which there are 
the better grounds. And the reasonableness of so acting is not dis- 
proved by the fact that all men fail sometimes, and some men even 
most times, when they act on this principle : any more than the 
reasonableness of betting repeatedly on the black ball is disproved 
by the fact that every man sometimes loses, or that some men lose 
on the whole, within the run of their draws. Indeed the reasonable- 
ness is greater in the former case ; for men need not bet, but they 
must act ; and if they must act, and act in the absence of the 
knowledge which would enable them to secure success in each case 
separately, they must act upon a rule which will enable them to 
secure the most success upon the whole, and leave its distribution 
to fortune. 1 

Yet I do not think the above a complete solution of the problem. 
A rule that can be applied without a fresh exercise of judgement 
in each case is only possible in matters like drawing balls from a bag, 
or throwing dice, where the factors whose existence we take into 
account can be treated quantitatively. We may grant that the 
man who acts most prudently on a given occasion may fail on that 
occasion, and the imprudent man succeed, and yet that the man 
who always acts prudently will succeed more than men who always 
act imprudently ; but that does not explain what acting prudently 
on a given occasion is. No doubt it requires study of the ascer- 
tainable facts ; but it also involves an estimate of their importance ; 

1 So, because we do not know enough of the ' merits ' of every case to 
decide each ' upon the merits ', we are often compelled in administration to 
adopt a rule which suits most cases, and acquiesce in its sometimes failing, 
and our not knowing when it will fail. 



vin] VARIOUS FORMS OF THE JUDGEMENT 205 

[and this is something quite different from the thinking which dis- 
covers that out of all possible throws with the dice six give 7 and 
only one 12. We speak of a man having a sound judgement, and 
the collect prays for ' a right judgement in all things \ The exercise 
of such a judgement is not knowledge, and not mere guess-work. 
It is better than tossing up, yet it cannot be justified to another. 
Though a man is prepared to act on his judgement, he is not 
prepared to enunciate it assertorically. It is here, as it seems to 
me, that the real puzzle of the problematic judgement lies. We 
hold that one man is wiser than another, and that, not only in 
reaching opinions on which action is to be based, but also in the 
study of matters that do not admit of demonstration, e.g. in 
historical inquiry or anthropological. And this wisdom does not 
consist in either the advantage resulting from acting as if its opinions 
were true, or their confirmation by subsequently discovered fact ; 
though these things may be evidence of it. And yet how is one 
man wiser than another, when neither knows ?] 

[I have spoken frequently of the grounds for a judgement, and 
in the previous edition of this book it was said (p. 171) that what 
gave modality to a judgement was the presence of the thought of 
grounds for what is alleged, though I think it better to say that 
a modal judgement expresses reflection upon the question of the 
truth of what is judged, or suggested ; for an assertoric, or a self- 
evident apodeictic judgement, has not grounds in the same sense 
as an apodeictic judgement deduced from others, or a problematic 
judgement. By the grounds of a judgement are commonly meant 
grounds given in other judgements ; but they are not these other 
judgements, i.e. the acts of our minds in judging; they are the 
facts which in them we assert. And these alleged facts are only 
grounds of our present judgement in the sense that we see a con- 
nexion between them and the fact which it asserts. The relation, 
however, may be of several kinds. The grounds may be facts 
whose existence is seen to account for that of the fact grounded 
on them ; this occurs in causal explanations. Or they may be 
facts which make intelligible the fact grounded on them, though 
there is no causal relation, as in mathematics. Or, thirdly, they 
may be facts which do not make intelligible to us what is said to 
be grounded on them, but which we think could not exist, but for 
that ; this occurs in inductive reasoning, or when we argue from 
an effect to the existence of its cause ; if I have known water to 
be found by men with apparently no other means of discovering 
its presence, I may infer that the divining-rod informs them of it, 
though I do not thereby understand its action. There is an old 
distinction between ratio essendi and ratio cognoscendi, a reason for 
the being of a fact, and a reason for acknowledging its being, which 
expresses the difference between grounds of a judgement in the 



206 AN INTRODUCTION TO LOGIC [chap. 

[first of these three senses, and in the other two. The grounds 
which justify an apodeictic judgement must be either rationes 
essendi, or such rationes cognoscendi as we get in mathematics ; ior 
we can only judge apodeictically if we have insight into the neces- 
sity of the fact alleged.] 

[There are a few other adverbs (besides possibly, actually, and 
necessarily) which may be introduced into a proposition in order 
to express that we have reflected upon and made our estimate of 
its truth : e. g. probably, truly, falsely, really : although ah 1 but the 
first of these may also be used merely to qualify some term in the 
judgement ; a truly virtuous woman, for example, meaning a woman 
virtuous in a particular way, or a falsely delivered message, one 
not delivered as it was received, whereas a probably dangerous 
undertaking does not mean an undertaking involving a particular 
kind of danger. Such adverbs (if used to express our attitude as 
to the truth of the proposition reached by omitting them from that 
in which they are used) may be called modal, and judgements modal, 
in which they are used. But no adverbs of any other kind make 
a judgement modal, and no qualification of the content, but only 
of the unreflecting directness with which, in a ' pure ' judgement, 
the content is affirmed. Differences of tense, for example, must 
not be reckoned to affect the modality of a judgement 1 ; they 

1 As by J. S. Mill, Logic, I. iv. 2, who rightly rejects the view of those 
who would make every adverb the ground of a modal difference in the 
proposition where it occurs. The distinctions of modality descend from 
Aristotle, de Interp. xii. 1, 21 a 34-37, and Anal. Pri. a. ii. 1, 25 a 1 sq„ but 
the word rponos ( = modus) is said to occur first in the Commentary of 
Ammonius ; v. Ainmonius in Ar. de Interp. 172 r , (quoted in part Prantl, 
vol. i. p. 654) = Berlin ed. p. 214 Tpotvos p.ev ovv cori <ba>vr] o-rjpuivovo-a onus 
vnapx*' to Karrjyopovpevov tu vnoKeififvco, oiov to ra^eo)?, orav heympev ij o~ekrjV7) 
Taxtcos dnoKa&io-TaTai ", fj to KaXco? ev t<o " 'Saxparris kciXcos biaXeyerai ", fj to ndvv 
ev to* " nXaraw Aiuiva trdvv <pi\el ", fj to del ev t<$ " 6 rjXios del Kiveirat ''. dpi6p.os 
he avraiv <pvo~ei ptev ovk eo~Ttv aneipos, ov p.r)v 8e ire piXtjirrds ye rjp.lv, uarrep 6 tu>v 
K.a8ohov vnoKeip-eveov fj KaTTjyopovpevcov, dvapidprjTwv de avTcav ovtu>v. Ttrrapas oe 
pdvovs 6 ' \pio-TOTe\rjs napaXafi^dvei irpbs ttjv Bewpiav to>v p.erd rpojruv npoTdo~eo>v, 
tov dvayKciiov tov dvvarov tov ev8tj(6fi€Vov Kal enl tovtois tov aovvarov. . . S Modi 
is a word signifying how the predicate belongs to the subject, e. g. " quickly ", 
when we say that " The moon waxes quickly ", or " well " in " Socrates 
argues well ", or " much " in " Plato loves Dion much ", or " always " in 
" The sun always moves ". The number of them is not infinite in the nature 
of things, but is beyond our computation, like the number of universals that 
can be subjects or predicates, though they cannot be numbered. Aristotle, 
however, brings into his consideration of modal propositions four modes 
only, the necessary, the possible, the contingent, and further the impos- 
sible. . . .' This statement about Aristotle is based on de Interp. xii, and 
the modalities were often enumerated as these four, sometimes with the 
addition of the true and the false. The same wide definition of rponos is 
given by Michael Psellus (v. Prantl, ii. 269), but he singles out for discussion 
only those which ' determine the connexion ' of subject and predicate, i. e. 
the modalities proper. Cf. Buridanus (Prantl, iv. 22), who explains that the 
qualification which is to make the proposition modal must attach to the 



vin] VARIOUS FORMS OF THE JUDGEMENT 207 

[merely affect the predicate, and not our attitude towards affirming 
the predicate of the subject ; and past, present, and future verbs 
may all occur (as we have seen) in judgements of any modality. 
No doubt differences of tense are a somewhat peculiar affection of 
the predicate. If I say Jehu drives furiously, I predicate a different 
action from what I predicate if I say that he drives slowly ; but 
the action predicated is the same, whether I say that Jehu has 
driven, is driving, or will drive, and only the time of the action 
differs. This, however, merely amounts to saying that the pre- 
dicates of judgements differing in tense differ thereby in the category 
of time, and not in another category. Time is a very peculiar 
feature in the existence of things, but still it is a feature in their 
existence, and gives rise to a great variety of modifications in their 
predicates. There is no more reason for reckoning as modal these 
differences in time, than there is for so reckoning the differences 
in degree, or in place, of which a predicate is susceptible. The 
plague raged last year : it is raging now : it is raging here : it is 
raging in Calcutta. If the plague can exist in different times, so 
also can it exist in different places ; and if judgements do not 
differ in modality by connecting its existence with different places, 
neither do they differ in modality by connecting its existence with 
different times.] 

There are a few other distinctions drawn among judgements, 
which ought to be noticed. We may deal first with a series of 
antitheses whose force is sometimes too readily considered to be 
the same : these are analytic and synthetic, essential and accidental, 
verbal and real. 

' In all judgements,' says Kant, 1 ' wherein the relation of 
a subject to the predicate is cogitated (I mention affirmative 
judgements only here ; the application to negative will be very 
easy), this relation is possible in two different ways. Either the 
predicate B belongs to the subject A, as somewhat which is con- 
tained (though covertly) in the conception A ; or the predicate 
B lies completely out of the conception A, although it stands in 
connexion with it. In the first instance, I term the judgement 
analytical, in the second, synthetical. Analytical judgements 

copula, and not to the subject or predicate. The word modus is of course 
a term of wide signification, but Logic is concerned with certain modi pro- 
positionis ; and it is obviously wrong to suppose that any adverb will make 
the proposition in which it occurs modal ; nor can differences of tense do 
so, though they express a modification of the predicate. 

1 Kritik of Pure Reason, E. T. (Meiklejohn), p. 7. The translator uses 
conception as equivalent to concept (cf. supra, p. 22). 



208 AN INTRODUCTION TO LOGIC [chap. 

(affirmative) are therefore those in which the connexion of the 
predicate with the subject is cogitated through identity * ; those 
in which this connexion is cogitated without identity, are called 
synthetical judgements. The former may be called explicative, 
the latter augmentative 2 judgements ; because the former add in 
the predicate nothing to the conception of the subject, but only 
analyse it into its constituent conceptions, which were thought 
already in the subject, although in a confused manner ; the latter 
add to our conception of the subject a predicate which was not 
contained in it, and which no analysis could ever have discovered 
therein.' Kant's example of an analytic judgement is ' all bodies 
are extended ' : for our conception of body is extended substance, 
and therefore, in order to make the judgement, we need only 
analyse the conception. ' All bodies are heavy ', on the other 
hand, is a synthetic judgement ; for it is not contained in the 
conception of bodies, that they gravitate towards one another. 

Kant's statement of the distinction between analytic and syn- 
thetic judgements has been much discussed and criticized. He 
himself attached to it great importance. For he thought that 
analytic judgements could be enunciated universally in advance of 
experience under guarantee of the law of contradiction ; because 
the predicate was contained in the subject-concept, it could not be 
denied of the subject without self-contradiction. Since I mean 
by calling anything a body that it is an extended substance, I can 
say that all bodies are extended without waiting to examine every- 
thing that falls under that denomination. With synthetic judge- 
ments it is otherwise. It is no part of what I mean by calling 
anything a body, that it is heavy ; and I need experience to assure 
me that whatever falls under the denomination body has weight. 
But there are some synthetic judgements which we know to be 
true universally without appeal to experience ; and how that is 
possible Kant conceived to be the fundamental question of meta- 
physics. 

But we never make judgements analytic in Kant's sense — i.e. 
guaranteed by the mere identity of the predicate with an element 
in the subject-concept. To do so would be tautology ; and to 

1 In speaking of the connexion between the predicate and subject as 
cogitated through identity, Kant means that the predicate-concept is identical 
with some part of the subject-concept : where it is cogitated without identity 
the two concepts are quite distinct. 

2 Or ampliative. 



viii] VARIOUS FORMS OF THE JUDGEMENT 209 

utter a tautology is not to judge, for in all judgement we advance 
to the apprehension of a new element in the being of a subject 
already partially apprehended. Suppose the constituent elements 
of the concept A to be BCD, as those of body are solidity and 
extension. Yet the judgement ' A is B ' (all bodies are extended) 
is not the equivalent of ' BCD is B ' (all extended solid substances 
are extended). This proposition does merely repeat in the predicate 
something contained in the subject-concept ; and inasmuch as 
the subject is already conceived as uniting in its being elements 
whereof the predicate is one, the proposition only goes over old 
ground. But that judgement picks out in the unity of what we 
call a body an element which it recognizes as combined with others 
to constitute a body. And the difference is fundamental. ' A is 
B' means 'to the constitution of A, B must go with CD ' ; all 
bodies are extended means ' to the constitution of body extension 
must go with solidity '. Kant himself tells us that until the judge- 
ment is made, the predicate B is only covertly contained in the 
subject-concept A ; so that it is really the work of the judgement 
to recognize B (as an element along with other elements) in the 
nature of A. And it is this recognition of the necessary implica- 
tion of different elements in one nature, not the law of Contradic- 
tion, which allows us to enunciate the judgement universally. 
Suppose that we did not see that a substance could not be solid 
without being extended : then (1) if we meant by body merely a solid 
substance, we should see no self-contradiction in the statement 
that a body need not be extended : while (2) if we meant by the 
word a solid extended substance, the statement would indeed be 
self -contradictory, as is the statement ' a body need not be a body ' ; 
but the so-called analytic judgement all bodies are extended would 
be as uninstructive as the tautology bodies are bodies. 

In all judgements then — even in those which Kant calls analytic 
— we assert a relation of distinguishable elements. Yet his 
antithesis of analytic and synthetic judgements is not baseless. 
That cats purr is a statement not made on the strength of seeing 
that to purr is necessarily connected with other elements in the 
being of a cat ; and we may think of a cat without including in 
its nature purring. This then he called a synthetic judgement. 
But he also called synthetic such judgements as '5 + 7 = 12', or 
' Two straight lines cannot enclose a space ' (in which the con- 
nexion of the predicate with the subject is seen to be necessary), 

1779 P 



210 AN INTRODUCTION TO LOGIC [chap. 

because in them too the subject can be thought of without the 
predicate — whereby is meant not that we can conceive the subject 
to lack the predicate, for we cannot conceive what cannot be, 1 
but that without thinking of the predicate at all, we can still in 
a measure conceive the subject. Hence the predicate-concept was 
no part of the subject-concept, and, not being included in it, could 
be denied of it without self-contradiction ; and so, since we know 
the judgements to be true universally, without examining every 
instance, we have knowledge of things not guaranteed by the law 
of Contradiction before experience of them. This, to Kant's 
mind, was the great problem, which he expressed by asking how 
synthetic judgements a priori are possible. 2 

But the difference between the two classes of judgements is 
misrepresented when it is said, that in the analytic the predicate 
is merely part of the subject-concept, and the necessary truth of 
the judgement therefore obvious : in the synthetic the predicate 
is no part of the subject-concept, and the necessary truth of a 
synthetic judgement therefore a problem. No judgement is 
analytic in the sense of asserting of anything in the predicate 
what in the subject-concept we have already realized or indicated 
it to be. What Kant has really done is to distinguish those judge- 
ments in which the predicate is part of the definition of the subject 
from those in which it is not. The distinction we may mark by the 
antithesis essential and accidental, if accident be taken, as by 

1 ayvaxrla e£ dvdyKris eVl nr/ ovn ('Of what cannot be we can only be 
ignorant'). Plat. Rep. v. 477 a. 

2 To know anything a priori (f*c Trpnrtpov) means to know it by derivation 
from something prior ; and a general principle is said to be prior to the 
facts, or subordinate principles, that exemplify it ; to know anything a pos- 
teriori means to know it by derivation from the particular facts exemplifying 
or dependent on it. Thus I know a priori that 5 men in buckram and 7 men 
in buckram are 12 men in buckram, for it follows from the general principle 
that 7 + 5= 12 : I know a posteriori that cats purr, through observation of 
many cats. Analytic judgements might in Kant's view be known a priori, 
because their truth followed from the law of Contradiction ; but there was 
no principle from which self-evident synthetic judgements could be derived. 
Kant spoke of knowing these also a priori in the sense of knowing them not 
a posteriori, i.e. not on the evidence of their repeated confirmation in experi- 
ence ; properly, they are the priora from which we derive knowledge about 
unobserved particulars. Thus to know a priori came to mean to know in 
advance of experience ; and his problem comes to this, viz. how, in advance 
of experience of that very thing, and therefore merely by thinking, can we 
know more about anything than what is guaranteed by the so-called ' laws 
of thought ' T Cf . on the meaning of the antithesis a priori and a posteriori, 
pp. 436, 437, infra. 



vin] VARIOUS FORMS OF THE JUDGEMENT 211 

Aristotle in the phrase <ad' avrb o-vfAfieftrjKos 1 ( = essential acci- 
dent, or accident per se), to include attributes belonging to any sub- 
ject of a certain nature in virtue of that nature, as well as those 
coincident in it with that nature. 2 Thus the accidental judge- 
ment might be in Kant's sense synthetic either a priori or a posteriori. 
And we might fairly oppose these, as ' ampliative ' or ' augmenta- 
tive ', to essential judgements as ' explicative ', because a subject 
and a property or accident of it are not one, as it and the definition 
of it are. But the opposition of analytic and synthetic is misleading, 
since that insight into the nature of a subject which definition 
expresses, though it may be called an analysis, is also an apprehen- 
sion of the connexion of elements in an unity, and the necessity 
of this connexion cannot be derived from the law of Contradiction. 
That law is that contradictory propositions cannot both be true ; but 
to know this is not to know which of two given contradictories is true. 

Doubtless a man cannot without contradiction deny of a subject 
anything which by the subject-term he means that it is. But 
how has the subject-term come to have its meaning ? If through 
insight into a necessary connexion of elements in the subject, 
then the so-called analytic judgement expresses this insight. Only 
if definitions were quite arbitrary, mere statements of the mean- 
ing of a name, would the truth of Kant's ' analytic ' judgements rest 
merely on the law of Contradiction. If I choose to mean by body a solid 
extended substance, it is self -contradictory to say that a body is not 
extended. But equally, if I choose to mean by body a solid extended 
and heavy substance, is it self -contradictory to say that a body is 
not heavy. And Kant has forgotten to ask why we regard extension 
as belonging to the definition of body rather than weight. 

We saw indeed, in discussing Definition, that we often have to 
settle arbitrarily what elements shall be included in the intension 
of a term, and therefore implied about those subjects to which we 
apply the term. Let us take an example of a subject in whose 
definition the elements are thus arbitrarily put together. 3 In the 
Elementary Education Act of 1870, § 3, an elementary school is 

1 Cf. e.g. Ar. Post. An. a. vii. 1, 75 a 39- b 2. o-v/iSepriKos in this sense 
includes properties, which are distinguished from accidents in sense of the 
Topics by being ko.6' aW6. 

2 e. g. two straight lines, in virtue of their straightness, cannot enclose 
a space : to be heavy is coincident in bodies (so far as we can see) with their 
nature as bodies. 

3 Arbitrarily, not because there is no motive, but because the elements, 
though compatible, are not necessarily implicated together. 

P2 



212 AN INTRODUCTION TO LOGIC [chap. 

by definition ' a school, or department of a school, at which elemen- 
tary education is the principal part of the education there given, 
and does not include any school or department of a school at 
which the ordinary payments in respect of the instruction, from 
each scholar, exceed ninepence a week '. To say therefore that 
an elementary school charged less than 10c?. per head per week 
in fees was to make an analytic judgement from the standpoint 
of the Education Department in 1870 ; but only because it had 
been arbitrarily settled that none charging 10c?. or over should 
rank as an elementary school, and not because we have such a know- 
ledge of what an elementary school must be, as to see that it could 
not be elementary and charge a fee so high. The proposition then 
is true just because it has been agreed what elementary school 
shall mean ; and while that agreement is adhered to, it cannot 
be denied without self-contradiction. But if I say that a triangle 
has sides, that is true not just because it is agreed to call nothing 
a triangle which has not, but because I see that lines can be put 
together into the unity of, and are required in, a triangle. Kant's 
account of analytic judgements ignores this difference. It implies 
that all definition is arbitrary, and that judgements whose predicate 
is part of the definition of the subject are necessarily true, only 
because what we mean by a name we mean by it. 

Some propositions are indeed true universally by mere con- 
vention as to the meaning of names, because they give us informa- 
tion about the convention. These may be called verbal, and to 
them we may oppose as real all which are intended to give informa- 
tion about the nature of things. But verbal propositions are 
in Kant's sense synthetic. ' Elementary schools charge a fee 
below 10c?.' meant that schools called elementary did so ; and to 
charge a fee below 10c?. is not part of being called elementary, 
but of what was meant by being so called. A proposition about 
the meaning of a name is clearly instructive, and ampliative. It 
is only inadvertently that we make about things statements, whose 
truth rests just on the meaning of words ; and when we discover 
that we have done so, we acknowledge that we have really said 
nothing. Suppose that some one had argued in 1870 that a par- 
ticular school which he knew to give mainly elementary instruc- 
tion had a fee below 10c?., because it was an elementary school ; 
clearly he would have wasted his breath, unless he knew that 
it had a right to be called so within the meaning of the Act ; and 



viii] VARIOUS FORMS OF THE JUDGEMENT 213 

he could not have known this till he knew that its fee was below 
lOd. ; and then the argument would have been superfluous. 

There is another objection to Kant's division of analytic and 
synthetic judgements. In speaking of analytic judgements, he 
had in mind only universal judgements, in which, as he held, we 
analyse a concept ; but there are judgements in which we may 
be said to analyse the sensible object before us, as when I look 
up and say ' the sky is starlit '. These have been called * ' analytic 
judgements of sense ' ; they clearly distinguish in a subject an 
element which they assert to be combined with others in the unity 
of that subject, and so far they are equally analytic with those 
which Kant called so ; but yet they differ greatly. They are 
singular, not universal ; they rest on perception, not conception ; 
and by no possibility could their truth be made to seem dependent 
barely on the meaning of names. 

Analytic judgements then may be analytic either of a sensible 
individual or of a concept : in neither case is their truth guaranteed 
by the law of Contradiction, but they rest on our apprehension of 
the connexion of elements in the unity of one subject. So far 
they do not differ from judgements called by Kant synthetic. 
But those analytic of a concept are essential, where without the 
predicate the other elements in the subject could not form a 
conceivable unity, whereof the predicate could be regarded as 
a further attribute. Judgements called by Kant synthetic, whose 
subject is something which can be thus conceived before the attribu- 
tion of the predicate, may be called accidental (though not in the 
sense of that word in the doctrine of Predicables) or ampliative 
of their subject. They include both analytic judgements of sense, 
and all judgements about the meaning of names. Verbal pro- 
positions are therefore not analytic, and real propositions may be 
either analytic or synthetic. Essential judgements are true by the 
nature of things, not ex vi termini ; or, if we call essential those 
judgements whose predicate is part of the arbitrary 2 definition of 
their subject, they will be essential in a different sense, and instruc- 
tive only as statements about the meaning of a name ; intended 

1 F. H. Bradley, Principles of Logic, p. 48 : cf. Sigwart, Logic, § 18. 4 
(E. T., Helen Dendy, vol. i. p. 108). 

2 Arbitrary (though not therefore settled without good reason) because 
what we are defining is something of our own institution, or because our 
so-called definition is a compromise of the nature explained pp. 99-102, supra. 
In the strict sense of definition, none is arbitrary : things are what they are. 



214 AN INTRODUCTION TO LOGIC [chap. 

otherwise the propositions are mere tautologies, and not expressive 
of any real act of judgement at all. It will be seen therefore that 
the three antitheses, of analytic and synthetic, essential and acci- 
dental, verbal and real, are by no means equivalent ; they are neither 
made on the same fundamentum divisionis, nor do they respectively 
bring together and keep apart the same individual judgements. 

[Some further points deserve notice in regard to the distinction 
of analytic and synthetic judgements. 

1. The terms suggest that we in judgement pick to pieces or put 
together the object of our thought. And some who use the terms 
hold that in the last resort this is true ; that mind by its activity 
constitutes its objects, though not perhaps as individual mind, 
yours or mine. 1 But whatever be the ultimate relation of mind 
to its objects, what the individual means to assert in judging is 
a relation of elements in the real that holds irrespectively of his 
present judgement. A judgement then is analytic in so far as it 
recognizes the distinct elements in what the judger starts by envisag- 
ing as an unity ; synthetic in so far as it recognizes the union — 
whether by way of necessary connexion or of empirical conjunc- 
tion — of elements which the judger starts by envisaging as distinct. 

2. But hence, because the judger does not lose sight of his start- 
ing-point, it has been said 2 that all judgements are at once 
analytic and synthetic. In the sense that in all judgements we 
assert a diversity in unity, a many in one, this is true. But the 
relation of the elements, their mode of combination in the unity, 
is not always the same. 

3. It has also been said that the same judgement may be analytio 
to one person, and synthetic to another : that, e.g., a judgement 
analytic to a teacher stating what he already knows is synthetic 
to a learner receiving information new to him ; and similarly that 
a judgement may be synthetic at one time and analytic at another 
to the same person, and that to any one omniscient all judgements 
would be analytic. But this is an error. The view rests on the 
following consideration, that if, e.g., I learn for the first time that 
diamonds are combustible, I make a synthetic judgement, because 
to be combustible was no part of what I understood by the word 
diamond ; but having learnt it, I include that in what I mean by 
the word, and henceforward, when I judge that diamonds are com- 
bustible, my judgement is analytic. Now, were this so, it is clear 
that the name diamond would have come to be used by me with 
a different meaning, i.e. the subject-concept would be different, in 
the judgement afterwards expressed by the words ' diamonds are 
combustible ', from what it had been in the judgement expressed 

1 Cf. e. g. Bosanquet, Logic 2 , vol. i. p. 84, vol. ii. p. 237, and Bk. II. c. x. 
* e. g. Bosanquet, Logic 2 , vol. i. p. 91. 



vni] VARIOUS FORMS OF THE JUDGEMENT 215 

[by the same words before. The earlier synthetic and the later 
analytic would not therefore be the same judgements, though 
expressed in the same proposition. Thus at best the view would 
involve a confusion between the judgement and the proposition. 1 
But it is not even true that, when I know that diamonds are 
combustible, the meaning of the word diamond must change for 
me. The judgement is synthetic because combustibility is not 
something without which the nature of a diamond would cease to 
be conceivable. That fact is not changed by my learning that 
diamonds are combustible. What I know or think once I may 
know or think again ; and the nature of a judgement is not 
altered by my having made it before. We must, however, acknow- 
ledge that there are certain differences in the state of mind of one 
who makes a judgement for the first time and one who repeats it ; 
there are emotional accompaniments in the former case, or a pre- 
ceding attitude of expectation, not present in the latter.] 

Two comparatively unimportant classes of proposition, exceptive 
and exclusive, may be mentioned before closing this chapter. 
An exceptive proposition is one which excepts from its appli- 
cation a certain part of the extension of the subject 2 : as 
in Clough's satirical version of the Second Commandment — ' No 
graven images may be Worshipped, except the currency.' An 
exclusive proposition is one which confines the application of the 
predicate to the subject of which it predicates it : as in Elijah's 
exclamation, ' I, even I only, am left.' Within a given whole, 
it clearly makes no difference whether a predicate is affirmed 
of one part only, or denied of all but that : Only the brave deserve 
the fair would mean the same as the poet's actual line None but 
the brave deserve the fair. The scholastic logicians treated these 
and some other forms of proposition under the head of Exponibilia, 
i.e. statements whose full meaning could only be expounded in 
more propositions than one. Thus ' None but the brave deserve 
the fan ' or ' Only the brave deserve the fair ' implies two pro- 
positions, that the brave (or some of them) deserve the fair, and 
that those who are not brave do not. The infinite proposition was 
also an exponible ; for if I say that Parliament is not-in-session 
I imply that it is not in session, and is in some other state instead. 

1 v. L. Nelson, Ueber das sogenannte Erkennlnisproblem, pp. 36-40. 

2 In strictness, of what would otherwise be the subject : as the part 
excepted cannot be called part of the subject of a judgement which expressly 
does not apply to it. 



CHAPTER IX 

OF THE DISTRIBUTION OF TERMS 

IN THE CATEGORICAL JUDGEMENT: AND OF THE 

OPPOSITION OF JUDGEMENTS 

We saw in the last chapter that all categorical judgements, 1 in 
respect of their quality, were either affirmative or negative ; and 
in respect of quantity, might be treated as either universal or 
particular. The latter division indeed strictly applies to those judge- 
ments only whose subject is a general term, and therefore not 
to singular judgements ; but for the purposes for which these can 
be reckoned with universal judgements the division is exhaustive. 
These purposes are the determining the distribution of terms, 
together with what depends on that. A term is said to be dis- 
tributed, when it is used in reference to its whole extension, or to 
all that it can denote : undistributed, when not so used. 2 Now the 
subject of a singular judgement 3 denotes one individual only, and 
the judgement 3 refers to that ; the subject of an universal judge- 
ment 3 is general, and may denote any number of individuals, but 
since the judgement is universal, it applies to them all. Therefore 

1 By judgement in this chapter will be meant categorical judgement. 

2 We have already seen, in discussing the extension, or denotation, of 
terms, that confusion may arise between the relation of a generic concept to 
the more specific concepts included under it and the relation of the universal 
to the individual, and that, properly speaking, a singular term has no extension, 
but only denotes. But in considering the distribution of terms, it is not 
always necessary to bear in mind this distinction. I may therefore say 
indifferently that a term is used with reference to its whole extension, or to 
all that it can denote, even if we reserve the latter expression (denotation) 
to signify the individuals of which a term can be predicated. 

3 More strictly, of a proposition expressing a singular, or an universal, 
judgement. It is terms verbal that are distributed or undistributed, according 
as the term of thought, what they cause or help us to think of as subject 
or predicate in a judgement, is or is not all that they can denote. For this 
reason it might seem more proper to speak only of the distribution of terms 
in a proposition. But since it is the act of thought or the judgement that 
gives to the terms of the proposition in which it is expressed their distribution, 
we may also speak of the distribution of terms in a judgement ; and because 
it is important to bear in mind that terms have distribution only through 
our use of them in judging, not through their presence in a sentence, I have 
spoken thus. 



DISTRIBUTION OF TERMS, ETC. 217 

in both singular and universal judgements, all that the subject 
can denote is referred to, or, in other words, the subject is dis- 
tributed ; and, in considering the distribution of terms in a judge- 
ment, we may accordingly rank the singular with the universal. 

As every judgement has both quantity and quality, and in each 
respect there are two alternatives, there are four varieties of 
judgement in respect of these two characters combined. An 
affirmative judgement may be universal or particular : a negative 
judgement may be universal or particular. It is customary in 
Logic to indicate these four forms of judgement by the first four 
vowels, thus : — 

an universal affirmative judgement is indicated by the letter A ; 
an universal negative „ „ „ ,, „ ,, E ; 

a particular affirmative „ „ „ „ „ „ 7 ; 

a particular negative „ ,, ,, ,, „ „ 0. 

Thus the affirmative judgements are A (universal) and 7 (particular) : 
the negative judgements are E (universal) and (particular) ; and 
this may be remembered by noting that A and 7, which indicate 
the universal and particular affirmative judgements, are the first 
two vowels in the verb ' afKrmo ' : E and 0, which indicate the 
universal and particular negative judgements, the vowels in the 
verb ' nego '. 

All universal judgements (A and E) distribute their subject : all 
negative judgements (E and 0) distribute their predicate. No 
particular judgements (7 and 0) distribute their subject : no 
affirmative judgements {A and 7) distribute their predicate. Thus : — 

in A, the subject is distributed, the predicate undistributed ; 
in E, „ ,, ,, distributed, ,, „ distributed ; 

in 7, „ ,, „ undistributed, ,, „ undistributed; 

in O, „ „ „ undistributed, ,, „ distributed. 

It is important to understand and become familiar with these 
characteristics of a judgement. 

A term, as was explained just now, is said to be distributed when 
it is used with reference to all that it can denote. 1 The term ' book ' 
is distributed, when used as subject in a proposition that refers to all 
books : undistributed, when so used in a proposition that does not 

1 i. e. denote univocally : an equivocal term is to be regarded as a different 
term in each sense. 



218 AN INTRODUCTION TO LOGIC [chap. 

refer to all books. It is obvious that an universal proposition about 
books (whether affirmative or negative) refers to all; and that a par- 
ticular proposition does not : all books are written before being printed : 
no book was printed before 1450 1 : some books are published unsewn : 
some books are never published. That the subject of universal pro- 
positions is distributed, and of particular propositions undistributed, 
needs no further illustration. Two cautions, however, may be 
offered. 

1. The subject of a proposition is the whole subject-term ; if 
I say all modern books are printed from movable type, the subject is 
not books, but modern books ; it is true that my judgement does not 
refer to all books, but it refers to all modern books, and so the 
subject is still distributed ; while it is undistributed in the pro- 
position some modern books are printed from stereotype plates. But 
I may restrict a general term like book not by words which leave it 
still general (e. g. modern book, book printed by Elzevir in Leyden), 
and therefore capable of being either distributed or undistributed, 
but by a demonstrative pronoun, or other words which destroy its 
generality (e.g. that book, these books, the first book which I ever 
possessed). In the latter case, the term becomes a designation, and 
is therefore singular, or (like ' these books ') a singular collective ; 
and the proposition should rank with universals. Nevertheless the 
general term which is restricted, by a demonstrative or otherwise, 
to the designation of a particular individual, is not distributed, since 
it does not refer to all that it can denote. ' Book ' therefore is 
undistributed, but ' this book ' is distributed, in the proposition 
' This book wants rebinding ' ; for ' book ' might be used of other 
books, but ' this book ' is already used of the only book of which, 
so long as I mean the same by ' this ', it can be used. 

2. In speaking of the distribution of terms, we are inevitably 
led to view judgements in extension rather than intension : and 
indeed as referring (ultimately) to so many individual subjects, 
rather than asserting a connexion between universals. Now we 
have seen that a judgement may refer to individuals, but need not ; 
and that in a judgement properly universal, there is no express 
thought of individuals. In saying that a triangle has its angles 
equal to two right angles, I am not thinking of all the particular 
triangles that have ever existed or may exist ; I am thinking of their 

1 The proposition must be taken to refer to European books and movable 
type : the nrst dated examples being of 1454. 



IX] DISTRIBUTION OF TERMS, ETC. 219 

common character as triangles ; this is one and the same in them 
all, and so I use the indefinite singular, a or any triangle. 1 It may 
therefore appear erroneous to say that such a judgement distributes 
its subject, if to distribute a term is to use it with reference to all 
that it can denote ; for of all the individuals which the term triangle 
can denote I am not thinking. But it is true in this sense, that 
whatever particular triangle you choose to take, my judgement holds 
good of that. We must avoid supposing that in every universal 
judgement we are expressly thinking of all the different individuals 
of which the subject-term is predicable ; but we must recognize that 
our judgement holds of them all. 

The distribution of the predicate in a judgement is not generally 
so readily understood as that of the subject ; for the extension of 
the predicate is not naturally before us. The rule is that negative 
propositions distribute their predicate ; affirmative do not : and 
this equally whether they are universal or particular. 

All preachers praise virtue : some practise it. It is easy to see 
here that I refer in one case to all and in the other only to part 
of what the term preacher can denote. The subject therefore is 
distributed in one case, and not in the other. But what of the 
predicate ? That is distributed or undistributed not as it refers to 
all or only some preachers ; for a term is distributed or undistributed 
when it is used in reference to the whole or to a part only of its own 
extension, not of the extension of the subject of which it is pre- 
dicated. Now the extension of the terms ' praiser of virtue ' and 
* practiser of virtue ' includes everything which can be said to praise 
or practise virtue. Preachers may do so, but so may others who 
are not preachers ; these also therefore are included in the extension 
of the predicate ; but what is thus included is not predicated of 
preachers. In the judgement ' X is Y\ I predicate Y of X; but 
I might predicate it also of Z ; X and Z are both included in 
the extension of Y, or in what Y can denote ; but when I 
affirm Y, I do not affirm it in its whole extension ; for then in 
saying ' X is Y ', I should mean that it is X and Z, and in saying 
' Z is Y ', I should mean that it is Z and X. The predicate 
therefore is not used in reference to its whole extension, i. e. is 
undistributed. 

The predicate of an affirmative judgement in fact cannot be 

1 I do not deny that a particular ' representative ' triangle must be con- 
sidered in making the judgement. 



220 AN INTRODUCTION TO LOGIC [chap. 

thought in extension at all. The subject of which it is predicated 
forms part of its extension ; but in the predicate, as opposed to the 
subject, I am thinking of a character or attribute belonging to that 
subject. A great deal of the difficulty which hangs about the 
doctrine of the distribution of terms arises from the fact that a term 
is said to be undistributed both when it is used with explicit refer- 
ence to a part only of its extension, and when it is used without 
explicit reference to its extension at all. The subject of a particular 
judgement is undistributed in the former sense ; when I say that 
Some preachers practise virtue, I am explicitly confining my state- 
ment to a part of the extension of the term preacher. The predicate 
of an affirmative judgement is undistributed in the latter sense. 
When I say that All preachers praise virtue, though it is true that 
preachers, even all of them, are only part of the extension of the 
predicate, yet I am not thinking in the predicate of its extension 
but of its intension. The extension of a term consists of all the 
alternative species, or different individuals, in which its intension is 
manifested. It is impossible to predicate all the alternative species 
of the same subject, or to say of anything that it is so many different 
individuals. ' An ellipse is a conic section.' The extension of the 
predicate conic section is hyperbola, parabola, ellipse, circle ; I cannot 
say that an ellipse is all of these ; I do not want to say that it is 
an ellipse ; I am thinking of the common character in them all, i.e. 
using the predicate in intension. Still, it is onty part of the extension 
of the predicate which is referred to in this judgement, and therefore 
the term is said to be undistributed in the judgement, though 
in the predicate extension is not considered at all. 

In a negative judgement, on the other hand, the predicate is 
necessarily denied in its whole extension. Caesar is not ambitious ; 
there are a thousand varieties of ambition among mankind ; but if 
I deny ambition of Caesar, I deny all these. It is the same whether 
the judgement is universal or particular. No Mussulman fears 
death. Whether we look to the forms which fearing death may take, 
or to the individuals in whom it is exhibited, if I deny the predicate 
of Mussulmans, I deny all forms of it, or deny that they are any of 
those individuals in whom it is exhibited. But again, Some marine 
animals are not vertebrate ; of those animals I do not merely deny 
that they are dogs or cats, plaice or salmon, all of which form part 
of the extension of vertebrate ; vertebration in every form is denied 
of them ; a negative judgement denies its predicate in toto. 



ix] DISTRIBUTION OF TERMS, ETC. 221 

In an affirmative judgement, the subject is necessarily part of 
the extension of the predicate ; in a negative judgement it is as 
necessarily no part thereof. And to say that the subject is no part 
of the extension of the predicate is to say that the predicate is 
denied in its whole extension. 

But here again it is primarily the intension of the predicate 
which is in my mind. When I say that ' Brutus is an honourable 
man ', the only individual referred to is Brutus, though ' they are 
all honourable men that have slain Caesar ' ; when I say ' Caesar 
was not ambitious ', I need not be thinking of any one who was. 
It is an attribute which I affirm in one case and deny in the other. 
Nevertheless, whereas if I do attend in affirmative judgements to 
the extension of the predicate I cannot affirm the whole, and do not 
want to affirm the only part — viz. the subject of the same judgement 
— which is referred to, for that would be mere tautology, in a negative 
judgement, if I attend to the extension of the subject, I can deny 
the whole. ' A cycloid is not a conic section ' ; if I remember that 
conic section includes hyperbola, parabola, ellipse, and circle, I can 
say that a cycloid is neither an hyperbola nor a parabola nor an 
ellipse nor a circle. 

We are not thinking primarily of the extension of the predicate 
in a negative judgement ; but if we do think of it, we must deny 
it in toto, or else our proposition will not mean what we intend it 
to mean ; therefore the predicate is distributed. ' The Tenth don't 
dance ' ; we are not thinking of those who do ; but bears dance, 
and so are part of the extension of the predicate, and if the predicate 
were not denied in its whole extension, it would be compatible 
with the truth of that proposition to say that the Tenth Lancers 
were bears ; or if the predicate were used only in reference to the 
ursine portion of its extension, the proposition would mean no more 
than that the Tenth were not bears. 

[Sometimes the device of circles, representing the extension of 
the subject and the predicate, is used in order to explain the 
distribution of terms. Collect the mammals in one 
circle, and the snakes in another : then if no 
snakes are mammals, snakes will lie outside the 
whole mammal-area : and if some craniates are 
not mammals, some part of the craniate-area will 
lie outside the whole mammal-area ; whereas if 
some craniates are mammals, some part of the 
craniate -area will coincide either with the whole or with a part 




222 AN INTRODUCTION TO LOGIC [chap. 

[only of the mammal-area ; and if all mammals are craniates, the 
mammal -area will fall completely within the craniate-area. But 
all the objections which lie against representing in this figurate 
way the logical relation of a larger to a smaller class within it lie 
equally against so representing the distribution of terms. We may 
say that the negative proposition snakes are not mammals excludes 
snakes from the whole class of mammals, and not merely from 
a portion of it (say men) : but we must not think of the class as 
an area cut up into districts called species, or as a collection of 
which the species are component groups. And if we ask what is 
meant by saying that a larger class craniates is partially coincident 
with the whole of a smaller class mammals, we must answer that 
the relation is not that of one superficies partially coincident with 
another, but of an universal character exhibited in a certain kind 
of subjects ; in fact, the logical relation must explain the diagram, 
and cannot be explained by it.] 

[Any one who realizes that the predicate of a proposition is not 
thought in extension will see that there can be no truth in the 
doctrine of the Quantification of the Predicate. But the doctrine 
has the support of distinguished writers, among others of Sir 
William Hamilton, who invented it, and of Stanley Jevons ; and 
it ought perhaps to be examined here. It may be easily shown to 
be false ; and the conscientious student haply stumbling upon the 
mass of intricate technicalities based upon it may be glad to feel 
excused from the labour of mastering them by the knowledge that 
they are built upon a worthless foundation. 

By quantification of the predicate is meant affixing a mark of 
quantity to the predicate as well as the subject of a judgement. 
Thus instead of the four forms of judgement, A, E, 1, 0, we get 
eight, as follows : — 

V. All X is all Y. All organisms are all mortals. 

A. All X is some Y. All men are some mortals. 

Y. Some X is all Y. Some mortals are all men. 

/. Some X is some Y. Some men are some (things) fleet of 

foot. 
E. No X is any Y. No snakes are any mammals. 
rj. No X is some Y. No men are some mammals [e.g. not 

monkeys] . 
0. Some X is no Y. Some mammals are not any quadrupeds. 
to. Some X is not some Y. Some quadrupeds are not some 

mammals [e.g. not cows]. 

In defence of this mode of stating propositions it is urged that 
as the proposition whose predicate has all before it, and the corre- 
sponding proposition whose predicate has some before it, do not 



ix] DISTRIBUTION OF TERMS, ETC. 223 

[mean the same thing, and we must know which we mean when we 
judge, we ought to express it. It is strange, if that is the case, 
that no language ever has expressed it ; and it may be confidently 
asserted that of these eight forms of proposition only E and express 
anything that we ever really mean when we make a judgement 
(though others express, in ' portmanteau ' fashion, what we mean 
when we make two judgements) ; and that the reason why we 
ought not to express in our proposition whether we mean all or 
some before the predicate, is that we mean neither. 

Let us take an A proposition. It used to be stated ' All X is Y ' ; 
we are told to state it ' All X is some Y '. All men are some 
mortals : which mortals are they ? the horses ? the grass of the 
field ? clearly not, but only the men. Yet it can hardly be meant 
by the proposition, that all men are men ; it is something about 
men that the proposition tells us. What about them ? that they 
die, and not which kind they are among the kinds of things which 
die ; we know that they are men already, and that need not be 
repeated in the predicate. 

But there is a difference between saying that all men are all 
mortals, and saying that all men are some mortals ; the first implies 
that the terms are commensurate, that there are no mortals but 
men : the second that men are mortal, but an undetermined range 
of things (cats and dogs and horses and asses and what not) are 
so besides. Ought not this difference to be expressed ? 

Doubtless, but it requires another proposition ; All men are 
mortals — some mortals are not men. In recognizing that men die, 
we do not judge that things of any other kind die ; and though 
we may be aware of it when we say that men die, it is no part of 
the judgement Men die. All men are some mortals is not one judge- 
ment, but a ' portmanteau ' proposition — two judgements expressed 
in what (in respect of its grammatical form) is one sentence. 

It is true that in some judgements we expressly think the 
predicate and the subject to be commensurate. In a definition, we 
must do this. Momentum is the product of mass into velocity : wealth 
is that which has value in exchange ; in these cases, it is included in 
our thought that the product of mass into velocity is momentum, or 
that which has value in exchange, wealth. But such judgements 
are ill expressed in the form ' All X is all Y '. We do not think of 
all momenta, all samples of wealth, but of wealth and momentum 
each as one thing. Again, the formula ' All X is all Y ' makes us 
think of X and Y as different things : whereas the whole force of 
a definition is to assert that the subject and predicate, the thing 
defined and the definition of it, are the same thing. 

There are propositions whose terms are known to be commen- 
surate, but which are not definitions, such as all equilateral triangles 
are equiangular. These also we are told to represent in the form 



224 AN INTRODUCTION TO LOGIC [chap. 

[' All X is all Y ', and to say that all equilateral are all equiangular 
triangles. But this does not correctly express the true meaning of 
the other proposition. For granted that in enunciating it we are 
aware that the terms are commensurate : what we wish to assert 
is the mutual implication of two attributes in any triangle. It 
follows from this that every triangle exhibiting one exhibits the 
other ; but those which exhibit one are not a different set of 
triangles from those that exhibit the other. By putting a mark 
of quantity before the predicate as well as before the subject, we 
make it appear as if the extension of one term was affirmed of 
the extension of the other, and (if we consider individuals) as if the 
individuals denoted by one term were affirmed of the individuals 
denoted by another. But that is either impossible, if the individuals 
are different, or tautologous, if they are the same. 

1 All ' can be no part of any predicate, except where (as in these 
are all the apostles) the subject is collective. If the universal judge- 
ment ' All living things reproduce their kind ' is true, then it is 
true of any living thing and therefore of peas. I may introduce 
' perfectly ' into the predicate, and then it will be meant that peas 
reproduce their kind perfectly. But I cannot introduce ' all ' into 
the predicate. For then, since all living things are all things that 
reproduce their kind, peas and even a single pea would be said to 
be all things that reproduce their kind ; and that is nonsense. The 
predicate of a judgement is affirmed distributively of each that 
falls under the subject ; the predicate quantified by all could be 
only true of the subject collectively. No equilateral triangle is all 
equiangular triangles ; how then can they all be ? The proposition 
only means that all equilateral triangles are equiangular and vice 
versa. As before, it is a ' portmanteau ' proposition, and not 
a single judgement. 

The U form of proposition has been considered at some length, 
because it is in a way the most plausible member of the series. 
Universal judgements whose terms are commensurate do differ 
from those whose terms are not, and do form a very important 
class of judgements ; and there is no special recognition of them 
in the ordinary fourfold classification of judgements (A, E, I, and 0). 
It has been wrongly alleged that Aristotle ignored such judgements ; 
on the contrary, he recognized their great importance in science. 
To remedy this supposed omission the doctrine of the quantification 
of the predicate offers us an entirely false analysis of them, and one 
which Aristotle himself exposed. 1 The analysis overlooks altogether 

1 De Interp. vii. 17 b 12 eVi Se rov K.aTiiyopovp.ivov KadoXov Kartjyopeiv r6 
KaOoXov oi/K 'itJTiv dXrjdts' ov8epia yap KaTa<pao~ts d\rjdr]s coral, ev rj rov Karrjyo- 
povfievov Ka66Xov to Ka66\ov KaTrjyope'iTai, olov ((tti nds avoptoiros trav (aov. 
(dvdpainos, man, is an universal : when I say ' All men are animals ', I predicate 
of an universal universally ; when I say ' Some men are white ', I predicate of 



DISTRIBUTION OF TERMS, ETC. 225 

[the intension of terms. Professing to complete what is defective 
in the current recognition of different kinds of proposition, itself 
leaves important differences unrecognized. We have seen that 
a proposition of the form ' All I is 7' represents two kinds of 
judgement essentially different in thought, according as it is really 
universal, meaning ' X as such is Y ', or only enumerative, meaning 
' All the X's are Y '. Of this difference, whether in universal judge- 
ments whose terms are commensurate (U) or not (A), this doctrine 
takes no note ; but sets up instead two kinds which misrepresent 
our thought by the sign of quantity prefixed to the predicate. 

The particular affirmative propositions may be dismissed briefly. 
We are told that ' Some X is Y ' should be written either ' Some 
X is some Y ' or ' Some X is all Y '. Take the former, ' Some X is 
some Y ' : we ask immediately, which X are which Y ? ; and the 
only answer is that the X that are Y are the Y that are X. Some 
sowers reap ; if that means some sowers are some reapers, this can 
only mean that the sowers who reap are the reapers who sow. 
Take the latter, ' Some X are all Y ' ; some animals are all the pigs 
(for it does not mean, are all of them pigs : as we might say that 
some families all squint, meaning that all the members of some 
families squint). Which animals are all the pigs ? surely only the 
pigs themselves. If it be said that the proposition means that 
there are more animals than pigs, then the real subject of the 
judgement is the other animals (which are not pigs), and not (as 
this form pretends) the animals which are pigs. If, again, it be 
said to mean that all pigs are animals and some animals are not 
pigs, we have as before two judgements packed into one sentence. 
What is one judgement, and what is the character of a judgement, 
are questions to be determined by considering our thought, and not 
the verbal devices we adopt to express it. To think that all pigs 
are animals, and some animals are not pigs, is to judge not once 
but twice, even though we were to write such a pair of judgements 
in the form some animals are all pigs. 

an universal particularly, or in part. Aristotle goes on to say, in the words 
quoted, that the predicate cannot be similarly taken universally [i.e. not 
' as an universal ', but ' in its whole extension ']. ' But in the case of the 
universal which is predicate, it is not true to predicate universality ; for no 
affirmation is true when universality [in extension] is assigned to the pre- 
dicated universal, e. g. All men are all animals.' Cf. Ammonius in loc. f. 82, 
who points out that then each man would be all animals.) Anal. Pri. 
a. XXvii. 43 b 17 aiiro 8e to inofifvov ov XrjTTTfov o\ov t'jreadai, Xeya 8' oiov dv8pa>n(& 
irav £(5ov fj uovtriicg irdaav eTrtcrTTjfiTju, dWa povov airkcos aKoXovativ, Kaoantp nai 
irpoTeivoptdu' Kai yap a^prjaTou ddrepou Kai dhvvarov, oiov ffdvra av8pa>nov tival 
ndv (aov, fj hiKaioavvr\v airav dyadov. ('But the attribute must not be taken to 
be attributed in toto, I mean for example animal as a whole to man, or 
science as a whole to music, but just simply to follow on the subject, as our 
premiss says ; for the other is both useless and impossible, e. g. that all men 
are all animals, or that justice is all good.') 

1779 Q 



226 AN INTRODUCTION TO LOGIC [chap. 

[To the negative judgement also the quantification of the pre- 
dicate does violence. The universal negative is to appear in the 
two forms ' No X is any Y * (E) and ' No X is some Y ' ( v ). The 
former may stand ; for as we have seen, if X is not Y, it is not 
any case or kind of Y. The latter may well puzzle us. It denies 
of X some part of the extension of Y ; pig, for example, is part of 
the extension of animal, and sheep are not pigs ; hence sheep are 
not some animals ; but this is quite consistent with their being 
animals. ' No X is some Y ' is therefore consistent with ' All X 
are Y ', and what it means is that ' Some Y are not X ' ; whether 
any X are Y or not it leaves doubtful. There remain the particular 
negatives, ' Some X is not any Y ', and ' Some X is not some Y '. 
Again the former will stand ; but what does the latter mean ? It 
does not mean that some X is not Y at all, e.g. that some animals 
are not pigs at all, but are something quite different (say sheep or 
cows) ; for that is expressed by the form ' Some X are not any Y '. 
It can only mean that there are some F's distinct from some X's : 
i. e. that though some X may be Y, they are not every Y. ' Some 
murderers are not caught ' is sense ; but ' Some murderers are not 
some caught ', if different from that, and sense at all, is only true 
because fish and cricket-balls are also caught, and some murderers 
are not these ; so that if the proposition were to be false, they 
would have to be fish and cricket-balls and everything else that is 
ever caught ; it is the contradictory of the impossible judgement 
that those X are every Y. But as we never make that judgement, 
we never want to contradict it ; yet these are forms of judgement 
which those who would quantify the predicate condemn Logic for 
hitherto ignoring. 1 

Thus all the eight forms of proposition with quantified predicate 
have been found vicious, except E and ; and these are so inter- 
preted as to lay undue stress on the aspect of extension in the 
predicate. The truth is that if we prefix to the predicate of a pro- 
position a mark of quantity, all or some, we are bound to think of 
the various individuals (or species) characterized by the predicate, 
not merely of the character, or ' universal ' : we are bound to take 
the predicate in extension, and that we cannot or do not wish to 
do. We cannot affirm of one term the extension of another. If 
a set of individuals, or of species, forms the subject of an affirmative 

1 We might make them a present of certain forms which they appear to 
have overlooked. If the extension of Y be p, q, r, then ' No X is any Y ' 
means ' No X is either p or q or r '. But the parts of the extension are taken 
disjunctively : why should they not be taken together ? Then we should 
have the form ' No X is all Y ' — meaning that no X is both p and q and r. 
So we might have ' Some X are not all Y '. It is true these forms are 
useless ; and in that they resemble the affirmative forms ' All X are all Y ' 
and ' Some X are all Y '. But they have the advantage over those of being 
true. 



ix] DISTRIBUTION OF TERMS, ETC. 227 

[judgement, another set cannot form the predicate. ' All X is some 
F ' is meaningless. ' Some F,' we are told, means ' part of the 
class Y ' ; but which part is X ? Let the class Y be divided into 
two parts, X and Z ; we do not need to say that X is the former 
part ; it is false to say that it is the latter. And in a negative 
judgement, unless the predicate is a proper name, which has no 
extension, what we wish to deny of the subject is having the pre- 
dicate character, not being those individuals which have it. 

Still, it is urged, the judgement compares the extension of two 
classes. ' All X is all Y ' means that the class X and the class Y are 
co-extensive ; ' All X is some Y ' means that the class X is included 
in the class F, which extends beyond it. But if the class X and the 
class Y are co-extensive, how are they two classes ? Taken strictly 
in extension (as the doctrine of the quantification of the predicate 
takes its terms) the class X and the class Y are not the common 
character X and Y realized in many things, but the set of things 
in which this character is realized. If the class X is the things in 
which the common character X is realized, and Y is realized in the 
same things, then there is only one class or set of things, and not 
two co-extensive classes ; so that, after all, we have the class X, 
and predicate the character Y of them, i. e. we do not take Y in 
extension. And if the class X is included in the class Y, what 
does that mean ? Suppose that all F's were collected in one place, 
all X's would be found in the crowd ; then, when we said that all X 
is some Y, we should mean that all X were included in the crowd of 
F's. But now our predicate is no longer Y, and has become ' in- 
cluded in the crowd of F's '. We must quantify that if all predicates 
are to be quantified, and state whether all or part of what is included 
in the crowd of F's be meant. Clearly part ; so that our judgement 
will run ' All X are some things included in the class F (or crowd of 
F's) '. But which things so included are they ? as before, them- 
selves, the X's. If this answer be not accepted, and it be said that 
some means ' included in the class of ', then our new judgement must 
run ' All X are included in the class of things included in the class 
F '. But now the last eleven words become the predicate, and it 
must again be quantified ; we must say ' All X are some things 
included in the class of things included in the class F '. So the 
process goes on ad infinitum. You cannot predicate of one class the 
whole or part of another. You may compare the size of two 
classes : e. g. when we say that male infants are more numerous than 
female ; but then one class is not predicated of another ; female 
infants do not include male infants and extend beyond them. You 
may predicate a genus of a species, and the genus as compared with 
the species has a wider extension ; but it is not the extension of the 
genus which you predicate of the species, nor any part of it. 

It may be thought that in discussing the quantification of the 

Q2 



228 AN INTRODUCTION TO LOGIC [chap. 

[predicate we have been belabouring errors too trivial for notice. No 
one, of course, really supposes that the act of judgement means any 
of these absurdities. But many people have supposed that a judge- 
ment compares the extension of two terms, or includes a subject in 
or excludes it from a class ; and they think of a class as so many 
things or kinds of thing. Such views imply the absurdities that 
have been dragged to light ; and the custom of elucidating the re- 
lation of terms in a judgement by the relative position of circles on 
paper, outside each other, one inside the other, or with a common 
segment, tends, as has been said before, to make us think wrongly 
about a judgement precisely in the direction of these absurdities. 
It is of great importance, in speaking of the distribution of terms 
(as we shall have to do frequently when examining the syllogism), 
not to suppose that the terms of a judgement are all taken in exten- 
sion, and that we are always identifying and distinguishing all or 
part of what our terms denote. The doctrine of the quantification 
of the predicate flourishes upon this mistake, and a thorough 
examination of that doctrine is a good prophylactic measure. 
Moreover, many of the developments of Symbolic Logic J are based 
on the extensional implications of propositions. If I say that all 
mammals are craniates, I imply that there are not fewer craniate 
animals than mammals ; hence I may write, for ' XisY ', ' X =XY\ 
and substitute X Y for X elsewhere in my equations. If all organisms 
are mortal, and every mortal an organism, I may write ' X = Y ', 
and substitute accordingly. When symbols are carefully devised, 
we can represent propositions symbolically, and operate with our 
symbols without realizing their meaning, and so reach results which 
we can retranslate into propositions whose meaning we realize, and 
whose truth follows from that of the premisses which we put into 
symbols at the outset. But the success of such operations does 
not show that we mean by our categorical propositions to assert 
numerical equality between classes, but only that, if what we mean 
is true, then, whether we determine our class by the subject char- 
acter, or by it and the predicate-character together, we shall take 
the same things, and so the same number of things. We are not 
always thinking of classes and their numerical relations when we 
judge. Hence, as it seems to me, the error of representing either all 
thinking as a kind of mathematics, or all thinking as class-thinking, 
and mathematics as merely a special sort of class-thinking. 2 ] 

We may pass now to the opposition of propositions or judge- 
ments. 

Propositions having the same subject and predicate, but differing 
in quantity, or quality, or both, are said to be opposed to one 

1 e. g. Jevons's Equational Logic. 

2 Cf. Mr. Bertrand Russell's Principles of Mathematics. 




ix] DISTRIBUTION OF TERMS, ETC. 229 

another. The four forms of proposition A, E, I, admit four kinds 
of opposition among them. 

1. A — E. Where the propositions differ in quality, and are both 
universal, they are called contrary to each other : everything in 
Aristotle is true, nothing in Aristotle is true are contrary propositions x 

2. / — 0. Where they differ in quality, and both are particular, 
they are called sub-contrary : e. g. some things 

in Aristotle are true, some things in Aristotle 
are not true. 

3. A—O, E—I. Where they differ both in 
quantity and quality, they are called con- 
tradictory : e.g. everything in Aristotle is 
true, some things in Aristotle are not true : no 
Mussulman fears death, some Mussulmans fear death. 

4. A — /, E — 0. Where they differ in quantity but not in quality, 
they are called subaltern : e. g. everything in Aristotle is true, some 
things in Aristotle are true : no Mussulman fears death, some Mussul- 
mans do not fear death. 

Contrary and contradictory are terms in common use, though 
sometimes treated as equivalent ; the origin of the terms subaltern 
and sub-contrary may be seen in the above-given, and ancient, ' dia- 
gram of opposition '. / is placed under A, and under E, for the 
same reason that in setting out a classification we place the species 
under the genus : the wider includes the narrower under it : A and /, 
E and are called subaltern, because in each pair one is subordi- 
nated to the other : / and are called sub-contrary, because they 
are subordinated to the contraries A and E, their respective 
universals. 

It will be observed that in order to overthrow an universal pro- 
position, affirmative or negative, it is only necessary to establish 

1 Contraries are what stand furthest apart upon a scale of some kind — 
to fidXioTa SiHTTTjKOTa (v ra> avrcp yevci : as white and black on the scale of 
illumination, highest and lowest on the scale of elevation, or of pitch, &c. 
Contrary propositions are those which stand furthest apart on the scale of 
quantity : one asserting that to be true of all which the other asserts to be 
true of none. The notion of contradiction belongs properly to judgements 
only, and not to terms, though sometimes transferred to the latter, A and 
not-^1 (blue and not-blue, &c.) being called contradictory terms. (Cf. Ar. 
de Interp. 20 a 31-36.) But we have seen that mere not-^4 is no term at all : 
there must be some positive meaning. (See however Bradley, Principles 
of Logic, p. 119, for the view that all disparate or incompatible terms should 
be treated as contraries : e. g. blue and red. ' In logic the contrary should 
be simply the disparate.') 



230 AN INTRODUCTION TO LOGIC [chap. 

the particular negative or affirmative ; that everything in Aristotle 
is true is refuted by showing something in his writings false ; that 
nothing in Aristotle is true, by showing something true. We con- 
tradict the affirmation ' All men are liars ' by saying ' not all ', not 
by saying ' all not '. But of course the greater includes the less, 
and we refute a proposition by establishing its contrary, as well as 
by establishing its contradictory. In common speech therefore we 
are said to contradict a proposition when we advance another whose 
truth is inconsistent with that of the first, whether it be the con- 
trary or the contradictory ; and since the contrary imputes more 
error than the contradictory (for if a man tells me that all animals 
reason, I impute more error to him by replying that none do, than 
that some don't) it may in a sense be said to contradict more fully. 
It is, however, convenient to have different words to mark the 
relation of A and E to each other, and their relations to and / 
respectively ; and Logic confines the title of contradictory opposi- 
tion to the latter. 

Given the truth or falsity of any proposition, we can see at once 
which of the opposed propositions must be true, which false, and 
which (upon the information given us) remain doubtful. For 
contrary propositions cannot both be true, and therefore if A is 
true, E must be false, and vice versa : but they may both be false 
(for it is not necessary that either all babies should be disagreeable, 
or else none of them), and therefore if one is given as false, the other 
remains doubtful. Contradictory propositions cannot both be true, 
but neither can they both be false ; and therefore if A, E, I, or 
is true, 0, /, E, or A must respectively be false, and vice versa. 
Subaltern propositions may both be true, or both false, or the 
particular may be true while the universal is false ; but the particular 
cannot be false while the universal is true, for the greater includes 
the less ; hence given the truth of A or E, I or is true, and given 
the falsity of / or 0, A or E is false ; but given the falsity of A or E, 
I or remains doubtful, and given the truth of / or 0, A or E 
remains doubtful. Sub-contrary propositions cannot both be false 
(for in that case their respective contradictories; which are contrary 
to one another, would both be true) ; but they may both be true, 
just as contraries may both be false ; hence given the falsity of /, 
is true, and vice versa ; but given the truth of /, remains 
doubtful, and vice versa. 

Of two contrary or of two contradictory propositions one may 



ix] DISTRIBUTION OF TERMS, ETC. 231 

be advanced against the other, i. e. we may deny one, and advance 
the other in its place ; and of two subaltern propositions, the par- 
ticular may be advanced against the universal. If any one said 
' Some animals reason ', we could not answer ' No, but all do ' ; but 
if he said, ' All animals reason ', we could answer, ' No, but some 
do '. Sub-contrary propositions, on the other hand, cannot be ad- 
vanced one against the other. ' Some animals reason ' : we cannot 
retort, ' No, but some don't ' ; ' Some animals don't reason ' : we 
cannot retort, ' No (i. e. that is false), but some do '. We may 
indeed, to the statement that some animals reason, reply, ' Yes, but 
some don't ' ; and to the statement that some animals do not reason, 
' Yes, but some do '. In these cases, however, the particular pro- 
position ' Some don't reason ', or ' Some do reason ', is advanced 
not against its sub-contrary, ' Some do reason ' or ' Some don't 
reason ', but against the universal proposition ' All reason ' or ' None 
reason ' : which it is feared we might otherwise be supposed to 
allow, when we admit that some reason, or that some do not. 
Hence it has been urged that we ought not to speak of sub-contrary 
propositions as opposed, 1 nor include them in a list of the forms of 
opposition ; but if they are not opposed, they are anyhow con- 
trasted, and that may justify their continued inclusion. Given the 
truth or falsity of any proposition, the step by which we pass to 
the perception of the truth, falsity or doubtfulness of its several 
opposites is in the strictest sense formal. It depends in no way 
upon the special content of the proposition, but solely upon the 
necessary relations, according to their quantity and quality, in 
respect of truth and falsity, between propositions having the same 
subject and predicate. And since no other information need be 
given, except whether the one proposition is true or false, in order 
that we may determine the truth, falsity, or doubtfulness of the 
remaining three, the process of inference (if inference it is to be 
called) is immediate. 

1 Aristotle notices this in Anal. Pri. /3. xv. 63 b 27 to yap nvi ra ov nv\ 
Kara tt]v \i^iv dvTineiTai fiovov (Tor some are is only verbally opposed to some 
are not '). 



CHAPTER X 

OF IMMEDIATE INFERENCES 

Inference is a process of thought which, starting with one or 
more judgements, 1 ends in another judgement whose truth is seen 
to be involved in that of the former. This judgement, which, in 
relation to the judgement or judgements from which the process 
starts, is called a conclusion, must, as compared with them, be a new 
judgement ; to repeat in fresh words our original statement is not 
inference, any more than translation is inference. For the most 
part a new judgement is only got by putting together two judge- 
ments, and as it were extracting what they yield. But there are 
a few conclusions which we appear to draw not from any ' putting 
together ' of two judgements, but simply from the relation to one 
another of the terms in one judgement. This is called immediate 
inference, etymologically because (in contrast with syllogism 2 ) it 
proceeds without the use of a middle term : but, to put it more 
generally, because we seem to proceed from a given judgement to 
another, without anything further being required as a means of 
passing to the conclusion. 3 

It was mentioned at the end of the last chapter, that when we 
infer, from the truth or falsity of a given proposition, its various 
opposites to be true, or false, or doubtful, we perform an act of 
immediate inference. We have now to consider other forms ot 
immediate inference, of which the fundamental are Conversion 
and Permutation (or Obversion). 

A proposition is converted, when its subject is made the predicate, 

1 Or, more generally, elements, if we allow (with Bradley, Principles of 
Logic, pp. 370--373) that, e.g., 2 + 2=4 is inference. But the above is not 
intended as a final definition of inference. Cf. infra, p. 244. 

2 For the function of the middle term in syllogism, cf. infra, c. xL 

8 All inference is immediate in the sense that from the premisses we pass 
without the help of anything else to the conclusion ; but this is called 
immediate in the sense that from the given relation of two terms in a single 
proposition we pass without the help of anything else to a different proposi- 
tion. It is doubtful, however, whether, so far as there is any inference in 
it at all, it is really in this sense immediate. Cf. the discussion pp. 240 sq. 



OF IMMEDIATE INFERENCES 233 

and vice versa, its quality (affirmative or negative) remaining 
unchanged : as, for example, when from ' No true Mussulman fears 
death ' we pass to ' No one who fears death is a true Mussulman '. 
The original proposition is called the convertend, and the ne-w 
proposition its converse. 

Whether, and in what way, a proposition can be converted, 
depends on its form, A, E, I, or x : because the process of con- 
version is invalid, unless it conforms to the following rule, that no 
term may be distributed in the converse, which was not distributed in 
the convertend. 2 An A proposition is converted by limitation : an 
E or an / proposition simply : and an proposition not at all 
except through first permuting it. 

A proposition is said to be converted simply, when the quantity 
of the converse is the same with that of the convertend. In an 
universal negative proposition (E) both terms are distributed ; in 
a particular affirmative proposition (/) both are undistributed. 
Therefore their mutual substitution in the process of simple conver- 
sion does not distribute any term that was not distributed before. 
Thus E, ' no X is 7 ', becomes E, ' no Y is X ' : e. g. ' no lawyers 
are parsons ' — ' no parsons are lawyers ' ; 'no true poet admires 
Macaulay's Lays ' — ' no one who admires Macaulay's Lays is 
a true poet 3 ' ; 'no snakes suckle their young ' — ' no mammals are 
snakes 4 ' ; ' Chatham is not the younger Pitt ' — ' the younger Pitt 
is not Chatham \ 

Again, /, ' some X is Y ', becomes I, * some Y is X ' : e. g. c some 
diamonds are black ' — ' some black stones are diamonds ' : ' some 
evergreen shrubs flower brilliantly ' — ' some brilliantly flowering 

1 The matter of some judgements renders their conversion unnatural, even 
where the form allows of it : e. g. ' Civilization spreads by the extermination 
of lower races '. Cf. pp. 235-237, infra. 

2 Another rule for conversion is sometimes given, to the effect that the 
terms (or the subject and predicate) of the converse must be the same as the 
terms (or the predicate and subject) of the convertend. But this is not 
a rule to observe in converting ; it explains the process of conversion itself. 

3 v. M. Arnold, Lectures on Translating Homer, Popular Edition, 1896, 
p. 171 : the question before us is not whether the proposition may be rightly 
contradicted, but how it may be rightly converted. 

4 When the predicate of the convertend is not a substantive or substantival 
term, we must either substitute for it in the converse a substantive, if there 
be one of equivalent meaning (as in this case), or import some substantival 
expression like ' one who ' (as in the previous example) for the original 
predicate, now introduced into the subject, to qualify. We often choose the 
genus of the subject about which we are speaking, as in the first example 
of the conversion of / ; but so far our procedure is not formal. 



234 AN INTRODUCTION TO LOGIC [chap. 

things are evergreen shrubs ' ; ' some victories are more fatal than 
defeat ' — ' some events more fatal than defeat are victories '. 

A proposition is said to be converted by limitation, or per accidens, 
when, it being universal, its converse is particular. In an universal 
affirmative proposition Y is predicated of all X ; but it may attach 
to other subjects equally, P, Q, and R ; therefore what is Y need 
not be X, and we can only say that some Y is X, not that all Y is X. 
To use the language of distribution, the subject is distributed, the 
predicate not : if we merely substituted each for the other, the 
original predicate, become the subject of an universal proposition, 
would be distributed ; for ' all roses are deciduous ' we should have 
' everything deciduous is a rose \ We must therefore limit the 
extent to which we affirm our original subject rose of our original 
predicate deciduous ; and hence such conversion is called ' con- 
version by limitation \ So A, ' all X is Y ', becomes /, ' some 
Y is X ' : 'all men are mortal ' — ' some mortals are men ' ; 'all 
Roman priests are celibate ' — ' some celibates are Roman priests ' ; 
' all isosceles triangles have equal angles at the base ' — ' some 
triangles with equal angles at the base are isosceles '- 1 

In the last example, any one who knows geometry will be tempted 
to convert simpliciter, and say that all triangles with equal angles 
at the base are isosceles. He would not be wrong as a geometrician ; 
but he would need a knowledge of geometry, and not merely of logic, 
to justify him. In conversion, we look solely to what is justified 
by the form of the proposition to be converted, be it A, E, I, or ; 
in this respect ' all isosceles triangles have equal angles at the base ' 
is indistinguishable from ' all isosceles triangles have angles equal 
to two right angles ' ; the geometrician knows that it does not 
follow from the latter, that all triangles having angles equal to two 
right angles are isosceles ; neither therefore does it follow logically 
from the former, that all triangles having equal angles at the base 
are isosceles. The form of proposition ' all X is Y ' only justifies 
a conversion to ' some Y is X ' ; in order to convert to 'all Y is X ' 
we must know that X and Y necessitate each other, or that there 
is nothing accidental in the relation between them ; this is not 
implied merely in the one being predicable of the other, because 
the relation of a predicate to its subject may be either accidental 
or essential. It must at the least be accidental, and therefore 
from its bare form, we are entitled to convert an A proposition as 
1 With this paragraph, cf. supra, pp. 223-224. 



x] OF IMMEDIATE INFERENCES 235 

if Y were an accident of X ; but we are not entitled to do more. 
For this reason, conversion by limitation is called conversion per 
accidens (Kara cry/Ape fir] ko$) ; if Y is an accident of X, i. e. coin- 
cides in the same individual subject with X, then X is predicable 
of a subject which Y characterizes, and we may say that some 
Y is X. 1 

In a particular negative proposition (0), the subject is undistri- 
buted, the predicate distributed ; if here we substituted each for 
the other, the original subject, become the predicate of a negative 
proposition, would be distributed in the converse. And since the 
predicate of a negative judgement cannot, like the subject of a 
judgement, be limited by a sign of ' particular ' quantity, an pro- 
position is not convertible, except by negation : a process which will 
be explained later (p. 238). This is not always realized, when we use 
symbols, and forbid the passage from ' some X is not Y ' to ' some Y 
is not X ' ; for it is quite possible that both of these propositions 
may be true at once : e. g. some freemasons are not freethinkers, 2 
and some freethinkers are not freemasons. But although ' some 
X is not Y ' and ' some Y is not X ' may be true at once, yet we 
are not justified by the form of the one in passing to the other ; 
and this becomes obvious by comparing such an example as the last 
(where both propositions are true) with another, where the converse 
is manifestly false : e. g. ' some men are not monks ' — ' some 
monks are not men '. In form the two propositions (' some free- 
masons are not freethinkers ' and ' some men are not monks ') are 
the same ; and therefore formally the conversion must be invalid in 
the former case, since it is invalid in the latter. 

It is indeed impossible, in converting a proposition, to treat 
the terms quite like symbols, and to proceed solely by the con- 

1 Even when the predicate is known to be of the essence of the subject, 
we must convert per accidens, if the predicate is the genus: e.g. 'all men 
are animals ' — ' some animals are men '. We cannot call animal an accident 
of man, but we may say that it is an accident that an animal should be 
a man, in the sense that an animal may or may not be a man. The term 
accident is not wholly suitable, because, though the conditions necessary for 
the generation of an animal may exist without those necessary for the genera- 
tion of a man, they cannot exist except in a form involving the generation 
of an animal of some species, nor can the conditions necessary for the 
generation of a man exist without those necessary for the generation of an 
animal : there is no coincidence of independent series, as when one series of 
events brings a train to a point whither another series has brought a flood 
and washed away the metals, and the result is a ' railway accident '. But 
the usage is analogous. 

a Though certain persons on the Continent seem to believe otherwise. 



236 AN INTRODUCTION TO LOGIC [chap. 

sideration of the distribution of the terms in the convertend, with- 
out considering what the terms are. In an E proposition, for example, 
if both terms are proper names, the act of conversion is felt to be 
different from what it is where the subject is a general concrete 
term and the predicate attributive : in passing from ' no judge 
has any right to meddle in politics ' to ' no one who has any right 
to meddle in politics is a judge ', the character of the judgement 
alters in a way that it does not, when we pass from ' Chatham is 
not the younger Pitt ' to ' the younger Pitt is not Chatham '. It 
is not natural to say ' no one who has any right to meddle in politics 
is a judge ' ; and though it is natural enough to say ' no one who 
meddles in politics has any right to be a judge ', this is not the 
converse of the proposition with which we started. It is equally 
natural to say ' Chatham is not the younger Pitt ' and ' the younger 
Pitt is not Chatham ', according as we are discoursing about the 
one or the other ; for two individuals stand as it were on the same 
level in thought, and each may indifferently be distinguished from 
either. But our rights depend upon our position, and not vice 
versa ; so that it is natural to deny certain rights to a man filling 
a certain position, but not to deny the position to a man possessed 
of those rights. Other examples of the same thing might be given. 
A proposition both terms of which are singular is called an A pro- 
position, but it cannot be converted per accidens : ' Chatham is the 
elder Pitt ' can only become ' the elder Pitt is Chatham '. If the 
subject is and the predicate is not a singular term, conversion is 
a form without meaning ; ' Chatham was eloquent ' becomes ' an 
eloquent man was Chatham ', and however we may write it, the 
latter means just the same as the former ; we cannot predicate 
Chatham of ' an eloquent man ', for this is a general term, and that a 
singular. 1 Again, 'Demosthenes and Cicero were the greatest orators 
of antiquity ' becomes ' the greatest orators of antiquity were 
Demosthenes and Cicero ' ; we cannot say ' some greatest orators of 
antiquity were Demosthenes and Cicero ' without altering the force 
of the term ' greatest orators ' from comparative to positive. 'Some 
men are Christians ' is a proper, ' some Christians are men ' an im- 
proper mode of speech ; religion can belong only to men, and we 
do not predicate of an attribute partially the subject presupposed by 
it. A difficulty arises again in a proposition not universal where some 

1 We can say ' That eloquent man was Chatham ', but here the subject 
is a singular term. 



x] OF IMMEDIATE INFERENCES 237 

measure is given of the extent to which the predicate characterizes the 
subject, e. g. by using such words as ' many ' or ' few ' ; ' most great 
men have been of obscure origin ' converts to ' some men of obscure 
origin have been most great men ' ; but no one would ever say this, 
for the measure ' most ' applies to ' great men ' as taken in extension, 
and therefore cannot be predicated of ' men of obscure origin '. 

It would be absurd to say that as conversion is a strictly formal 
process, we must therefore convert propositions by its rules, accord- 
ing to their form as A, E, or I. Logic investigates the actual nature 
and procedure of our thought ; and when we find that our thought 
is not governed by the bare form of a judgement irrespective of 
its content, it is no use to pretend otherwise. The conversion of 
propositions may be studied formally, with symbols for terms ; 
but when real terms replace the symbols they must affect the 
judgement, and our treatment of it in conversion ; for example, 
symbols, like X and Y in the proposition ' no X is Y ', are always 
regarded as general terms, but the actual terms need not be general. 
This is said, not in order to discredit the abstract and formal treat- 
ment of conversion, which is sound within its limits ; but in order 
to emphasize the fact that the form and matter (or the form and 
content) of thought are not capable of separate consideration, like 
the mould and the pudding : what from one point of view is form is 
from another matter, and the same form in different kinds of con- 
tent is not altogether the same, any more than is the same genus 
in different species. The importance of this fact must excuse the 
reiteration of it ; meanwhile in a text -book of Logic, as of any 
other science, we must consider typical cases, with a general caveat 
that the subject is thereby artificially simplified. 

In conversion, the subject and predicate were transposed, but 
otherwise unaltered, and the quality of the proposition remained 
the same. In Permutation, or (as it has been also called) Obver- 
Sion, 1 there is no transposition of terms, but the quality of the pro- 
position is changed, and the predicate at the same time replaced 
by its contradictory. It consists in fact of substituting for an 

1 Jevons, in his Elementary Lessons, calls it Immediate Inference by 
Privative Conception. Earlier writers dealt with it under the head of 
Equipollency of Propositions : cf. Sanderson, II. 6 ' Aequipollentia com- 
muniter sumpta est duarum propositionum, verbo tenus, quoquomodo dis- 
crepantium omnimoda in sensu conspiratio '. Aristotle, de Interpr. x. 20 a 
20-26, notices the equivalence of a proposition and its obverse, but gives no 
name to the change. 



238 AN INTRODUCTION TO LOGIC [chap. 

affirmative or negative proposition an equivalent negative or affirma- 
tive of opposite quality, by means of negating the predicate. 
Thus— 

A, All X is F, becomes E, No X is not- Y : All right angles are 
equal, No right angles are unequal ; Barkis is willin', Barkis 
is not unwillin'. 
E, No X is Y, becomes A, All X is not-F: No dogs allowed, All 

dogs forbidden ; Lear is not mad, Lear is not-mad. 
7, Some X is Y, becomes 0, Some X is not not- Y : Some stretches 
of the road are level, Some stretches of the road have no 
gradient. 
O, Some X is not Y, becomes I, Some X is not- Y : Some learned 
theories are not sense, Some learned theories are nonsense ; 
Some swans are not white, Some swans are not-white. 
Further transformation of a given proposition may be effected by 
a combination of Conversion and Permutation. The process of 
permuting and then converting is called Conversion by Negation. 
The conclusion so obtained may be permuted again, and this 
process of permuting, converting, and permuting is called Contra- 
position. 

All forms of proposition except I can be converted by negation ; 
the process is inapplicable to I, because it becomes by permu- 
tation, and a particular negative, as we have seen, cannot be con- 
verted. For the same reason I cannot be contraposed. 
In conversion by negation — 

A becomes E : All X is Y .'. No X is not-F .'. No not-F is X. 
All acids turn blue litmus-paper red .'. No acids do not 
turn blue litmus-paper red .*. Nothing that does not turn 
blue litmus-paper red is an acid. 
E becomes / : No X is F .". All X is not-F .*. Some not-F is X. 
No stimulant nourishes .". All stimulants are innutritious. 
.'. Some things innutritious are stimulants. 
O becomes I : Some X is not F .'. Some X is not-F .*. Some 
not-F is X. Some sea-animals are not vertebrate .'. Some 
sea-animals are invertebrate .". Some invertebrates are 
sea-animals. Some things necessary to life have no market- 
value .*. Some things that have no market-value are neces- 
sary to life. 
This is the only way in which a particular negative can be 
converted. 



x] OF IMMEDIATE INFERENCES 239 

In contraposition 1 — 

A becomes A : All X is 7 .*. No not- 7 is X .'. All not- 7 is 
not-X. All Arabs are hospitable .'. All who are not-hos- 
pitable are not-Arabs. 

E becomes : No X is 7 .'. Some not- 7 is X .'. Some not- 7 is 
not not-X. No unfriendly man is happy .'. Some who are 
not happy are not friendly. 

becomes : Some X is not 7 .'. Some not- 7 is X .'. Some 

not- 7 is not not-X. Some reformers are not radicals .*. 

Some who are not radicals are not not-reformers (are not 

opposed to reform). 
The above processes, when worked in symbols, might be supposed 
to be equally applicable to all judgements. But when we apply 
them to concrete examples, we see at once (as with Conversion) that 
it is not so. It is indeed often convenient in discourse to make 
what was predicated of a subject itself the subject and starting- 
point in our predication, or to lay stress on the affirmative value of 
a negative, or the negative value of an affirmative statement. But 
the use of these processes is limited in part by the idiom and 
vocabulary of the language, in part by the logical character of the 
terms in the judgement. The permutation of / to looks almost 
ridiculous in symbolic form ; but where there exist two terms, the 
affirmation of one of which is equivalent to the denial of the other, 
there the process is in practice perfectly natural. No one would 
pass from ' Steam is invisible ' to ' Steam is not not-invisible ' ; 
but he might naturally pass to ' Steam is not visible '. 

Contraposition, as involving the largest number of steps, and 
employing permutation twice, may seem to lead to the least 
natural modes of expression. For permutation introduces ' infinite ' 
terms, not- 7 and not-X ; and infinite terms do not ordinarily 
figure in speech ; so that unless we can substitute a term that is 
not infinite in form, our result seems fantastic. But we may see 
that the process of thought involved in contraposition is a common 
one (although the mode of expression may be awkward), if we 
look at it under the forms of the hypothetical proposition. Given 
that all lovers are jealous, it is possible to infer that all the not- 

1 What has here been called the converse by negation is by some writers 
called the contrapositive (e.g. J. Wallis, Logic, II. 7) ; and what has here been 
called the contrapositive, the obverted contrapositive. And the converse of 
the obverse of the converse of a proposition has been called its inverse. 



240 AN INTRODUCTION TO LOGIC [chap. 

jealous are not-lovers. No one would, however, express himself 
thus. But the original proposition, if it is a true universal, states 
a necessary connexion between the predicate and the subject ; it 
involves the proposition that if any one is a lover he is jealous. 
Therefore, if any one is not jealous, he is not a lover ; and this is 
an inference quite naturally expressed. ' If anything is X, it is 
Y .*. if it is not Y, it is not X'; we have here precisely the same 
inference as in the contraposition of A, 'All X is Y .'. All not-T 
is not-X '. We may interpret in a corresponding way the contra- 
position of E and 0, if we bear in mind the modal or problematic 
force which may belong to the particular judgement. 'No X is Y * 
will mean, ' If a thing is X, it is not Y ' : from this we cannot, 
however, infer that if it is not Y it is X ; if a man is insufficiently 
fed, he cannot do a proper day's work ; but it does not follow that 
if he cannot do a proper day's work, he is insufficiently fed ; this 
may or may not be so. Hence we can only infer that ' If a thing 
is not Y, it may or may not be X ' : and that is the force of ' Some 
not- Y is not-X ', regarded as a modal particular. Similarly with 
; ' Some X is not Y ' will mean, ' If a thing is X, it may or may 
not be Y ' ; from which it follows that ' If a thing is not Y, it may 
or may not be X '. 

[The operations whose formal character has been considered in 
this chapter are called Immediate Inferences ; but we have seen 
that one of them, Permutation, used to be regarded as belonging 
to the subject of Equipollency of Propositions, and J. S. Mill x is 
not alone in so regarding them all. In his view we have been 
dealing merely with equivalent propositional forms ; the processes 
are ' inferences improperly so called ' ; and indeed they have once 
or twice been called transformations in the course of the text. Thus 
conceived, they would belong rather to a study of language than to 
Logic. We must therefore consider whether there is really any 
inference involved in them or not. 2 

The question is by no means easy, involving as it does that of 
the nature of inference generally. There is no inference where there 
is no movement of thought ; but the movement of thought must 
spring from a perception of connexion in the objects of thought, 
not from subjective conditions in the mind of the thinker ; it must 
involve an advance to the apprehension of a fresh object of thought, 
and be more than a mere playing as it were upon the same object. 
It is not inference, e.g., if the sight of a stormy sea leads one man 

1 System of Logic, II. i. 2. 

* Cf. Bradley's Principles of Logic, Bk. III. PI. I. c. ii. §§ 30-37. 



x] OF IMMEDIATE INFERENCES 241 

[to reflect that steam has reduced the terrors of navigation and 
another that England owed much to the winds in 1588. Nor, if 
a fact involves two terms in a common relation, is it inference to pass 
from a statement that makes one term the subject standing in 
relation to the other to a statement making the second the subject 
standing in relation to the first. For the difference of subject and 
predicate, as Professor Cook Wilson insists, is subjective ; it belongs 
to the order of our approach to the complete act of judgement, in 
which we think the whole fact, and makes no difference to what, 
in that act, we think the fact to be. When Achilles was sought, 
and found playing with the maidens, the seekers were surprised to 
find Achilles their companion, the maidens that their companion 
was Achilles ; but both became aware of the same complex fact. 
I may live by the Atlantic mouth of the Panama Canal, and learn 
one day that it is west of the Pacific mouth, or by the Pacific 
mouth, and learn that it is east of the Atlantic mouth ; but in either 
judgement I should be aware of the same fact, and there is no in- 
ference from one to the other. 1 Again, there is no inference from an 
universal proposition to its subaltern, though they are not the same, 
because what is thought in the latter is only part of what is already 
thought in the former ; there is no advance to the thought of some- 
thing not thought of, though bound up with what was thought of at 
the outset. On the other hand, the obviousness of a transition is no 
ground for denying that it is inference, though lack of obviousness 
might be taken as a sign that inference is present ; for if in thinking 
the premiss we had also thought what is stated in the conclusion, 
it could not come to us as a surprise, that we had committed our- 
selves to the latter. Neither again is the fact that the conclusion is 
implied in the original statement a ground for denying the presence 
of inference ; for all premisses imply their conclusion. 

We must bear in mind also that the same propositional form may 
express different thoughts, and whether there is inference will depend 
on the thought which the words express. It is particularly impor- 
tant to remember this when working with symbols. Symbolic 
notations will often enable us to operate more rapidly than with 
words, and without realizing in the process what is meant ; and 
when we translate into words the result reached, it is sometimes one 
which we should not very readily have seen to be involved in what 
we started from, but sometimes also one not warranted thereby. 
Thus we may argue in symbols, converting and obverting, ' No 
X is Y .-. No Y is X .-. All Y is non-X .-. Some non-X is 7 '. The 
original proposition might be ' Things made of asbestos do not burn ', 
and the final conclusion ' Some things not made of asbestos burn ' ; 
and this arouses no suspicion. But let the original proposition be 

1 Such restatements have nevertheless been sometimes called immediate 
Inferences. 

"779 B 



242 AN INTRODUCTION TO LOGIC [chap. 

[' No man dies twice ', and we can hardly accept the conclusion 
' Some who are not men die twice '. We might hesitate even about 
the simple converse, ' Nothing that dies twice is a man ', as implying 
an admission that dying twice does occur. Such paradoxes arise 
because in working out symbolic sequences we are considering only 
what relations of subject and predicate are excluded and what left 
possible by the information given ; and the inference to ' Some non-X 
is Y ' is intended to mean not that there exist things not X which are 
Y, but that the fact that nothing which is X is Y does not exclude 
their existence. But propositions in significant terms commonly imply 
the existence of instances of their subjects. Not however always ; 
and when we pass from a premiss implying the existence of its subject 
to a conclusion only asserting compatibility of attributes, or such con- 
nexion between them that if there were an instance of one it would 
also be an instance of the other, then, and also vice versa, there 
is inference which would not equally exist if both propositions 
were understood in the same sense. Such inference however may 
involve the use of some other premiss besides the convertend ex- 
pressed ; and mutatis mutandis the same would be true in obversion. 

A categorical proposition commonly implies the existence of 
instances of its subject, and therefore, if it is affirmative, of its pre- 
dicate also. 1 But in making it we may or may not have determinate 
instances in mind. We found that the form ' All X is Y ' is some- 
times used to state a fact about all members of the group or class X, 
sometimes to state a connexion between being X and being Y ; in 
the former case, it might be said to be intended historically (e. g. 
' all the ruminants part the hoof '), in the latter scientifically (e. g. 
1 all rivers run down hill '). But if intended scientifically, the pro- 
position need not be intended to assert the existence of instances 
of the subject ; e. g. ' a perfect fluid is frictionless ' may be intended 
only as a statement of what would be the character of a perfect 
fluid if it existed ; and then, though categorical in form, it is intended 
only hypoihetically. And a particular categorical might be said to 
be intended historically when we make it with instances in mind, 
e. g. if we said that ' some garrison towns are important civilly ', 
thinking of Winchester, York, and Canterbury : and scientifically 
when we wish rather to affirm the compatibility of the subject and 
predicate characters (or, if the proposition be negative, the possi- 
bility of their disjunction). In the latter case, however, we more 
commonly use the modal form ' X may be Y ', than the categorical 
particular ' Some X is Y '. 

Let us now consider the simple conversion of an / proposition. 
Any one starting from the judgement that ' some garrison towns 
are important civilly ', whether he has in mind definite instances 
or not, must know or believe the fact stated in the converse, that 

1 This is sometimes called its existential import. 



x] OF IMMEDIATE INFERENCES 243 

[' some places civilly important are garrison towns '. The fact, of 
which VVmchester, York, and Canterbury are instances, is the same, 
whichever way it is put : whether the logical subject be ' some 
garrison towns ', or ' some places civilly important '. There is there- 
fore here no real inference. There could be inference only if from 
a judgement in which we are thinking definitely of certain towns, 
though not naming them, we passed to one asserting general com- 
patibility. But here in effect we should be passing from the 
proposition that Winchester, York, and Canterbury are important 
civilly, and to the proposition that some towns civilly important 
are garrison towns. This is inference, but syllogistic, not im- 
mediate ; and we should not express it by such verbal variation as 
is symbolized in passing from ' Some X is Y ' to ' Some Y is X \ 
The conversion of I then is not a process of inference. 

The conversion of the universal affirmative A has more show of 
inference, because it proceeds by limitation ; and it might be urged 
that there is inference in seeing that I am not entitled to infer that, 
since all the ruminants part the hoof, all the cloven-footed animals 
ruminate. But surely I know from the outset that in affirming Y 
of X, I do not confine the predicate to that subject ; and to realize 
that Z also may be Y is to realize that what is Y need not be X. 
It can hardly be called inference to realize that information about 
X does not extend beyond X, nor to refrain from asserting what I 
know that I have no right to assert. 1 And I must in the original 
proposition, whether understood historically or scientifically, if I im- 
plied the existence of instances of the subject at all, have meant that 
these were also instances of the predicate ; and therefore I must have 
realized that some things exhibiting the predicate character exhibit 
also the subject character, which is what is stated in the converse. 
So far, therefore, in the conversion of A there is no real inference. 

But the universal affirmative, intended scientifically, does not 
always imply the existence of instances of its subject. Tout savoir 
est tout pardonner ; I might translate this by saying ' Those who 
know all pardon all ', not implying that any of us does know every- 
thing, but only that, if he did, he would pardon everything. Now 
if I convert this and say ' Some who pardon all know all ', I shall 
probably mean that there are persons who both pardon and know 
everything. Here then there will have been inference ; but again, 
it does not lie in the conversion. It lies in combining the thought 
of the general connexion with the thought that there are some who 
know all about some situations ; and so concluding that there are 
some who pardon all in some situations. The inference involves 
a premiss not expressed. To pass from the merely hypothetical sense 
of an universal affirmative to the categorical involves inference, but 

1 Cf. Bradley, loc. cit. 
E2 



244 AN INTRODUCTION TO LOGIC [chap. 

[hypothetical inference \ not conversion. To pass from meaning it 
historically to meaning it scientifically is inference, but it is induc- 
tion. 2 It is more difficult to say whether, if we mean it scientifically, 
but categorically, there is inference in passing to a purely hypothetical 
meaning : suppose, e. g., that I judge that ' all rivers run down hill ', 
meaning that by their nature as running water they must do so, 
is it inference to pass to the thought that any other rivers, if they 
did exist, would also run down hill ? I think not ; in the necessary 
judgement there is really inference from the outset ; it is essentially 
inference to see that if a condition X is realized, Y must be realized 
too ; I advance herein by mere thinking from X to Y. But if I 
have realized this in considering existing instances, there is no further 
inference in seeing that it would hold in others. 

The last point needed notice in relation to the conversion of the 
universal negative, E. ' No X is Y ' converts simply to ' No Y is 
X '. The convertend implies commonly the existence of instances 
of X, but not necessarily of Y ; the converse however does imply the 
existence of instances of Y. Now if in the convertend it be meant 
that there are instances of both X and Y, the thought that the latter 
are not the former hardly seems separable from the thought that 
the former are not the latter ; and there seems to be no inference 
from ' No fish are mammals ' to ' No mammals are fish \ If how- 
ever this be not meant in the convertend, and in the converse it be 
meant that there are instances of Y, then there is inference, but it 
involves another premiss. I might judge that ' nothing inductive 
is self-evident ', while doubtful whether anything is self-evident ; 
if I proceed to judge that ' nothing self-evident is inductive ' 
meaning that there are self-evident propositions, the judgement that 
these are not inductive comes by help of the convertend, but that 
they exist at all is independent of it. Still, I cannot reach the 
universal ' nothing self-evident is inductive ' without realizing that 
if anything were self-evident, it would not be inductive ; and this 
connexion of condition and consequent is not the same as what is 
realized in the universal negative from which I started ; that was, 
that if anything were inductive, it would not be self-evident. From 
' if X, then not Y ' to ' if Y, then not X ' does seem to be infer- 
ence, the condition being different in the two. It is true that it may 
easily be shown that I cannot repudiate this conversion without 
self-contradiction ; if a thing might be Y and still be X, then since, 
if X, it is not Y, it might be Y and not be Y. But though it is im- 
possible to affirm the convertend and deny the converse without 
contradiction, inference is involved in realizing this, and the con- 
verse is not actually thought in thinking the convertend. Only then 
if an E proposition be intended as a statement that two groups of 
instances exclude each other (or that the individuals indicated by 
two singular terms are different), is its conversion not inference. 

1 Cf. infra, o. xv. * Inductive syllogism in Fig. 3. Cf. infra, p. 319. 



x) OF IMMEDIATE INFERENCES 245 

[As the conversion of 0, the particular negative, is impossible 
without first permuting, or obverting, it to /, we must ask next 
whether there is inference in Permutation. The process of Permu- 
tation involves the use of the infinite or negative term not-F in the 
predicate in lieu of F. Now we have seen that an infinite term has 
not any meaning at all unless it has some positive meaning ; not- Y 
must mean something else than Y. 1 We have seen also that the dis- 
junctive judgement 'A is either B or C does not always imply that it 
cannot be both. But Permutation rests upon disjunction ; Y and not- 
Y are alternatives, and it is assumed that if Y is affirmed or denied of 
any subject, not-Y can be denied or affirmed accordingly. Bearing 
in mind these considerations, we shall find that there is a certain 
difference in different cases, in respect of the presence of any real 
inference in permutation, according to the meaning attached to the 
negative term. 

It is unnecessary here to separate universal and particular propo- 
sitions. If we are told that X is not Y, and Y and not-Y are 
alternatives, one of which must attach to it, then since it does not 
exhibit Y, it must exhibit the other, not-Y. We thus reach the 
affirmative, ' X is not- Y ' ; and the question is whether that is any 
way different from the negative with which we started. 

Now we cannot deny that there is any inference in disjunctive 
reasoning at all. When I argue that since A is either B or C, and is 
not B, therefore it is C, there is clearly inference ; and I could not 
argue that, because A is not B, it is C, unless I were given the 
disjunctive premiss, A is either B or C, as well. But in permuta- 
tion, my alternatives are not two different positive terms, like B 
and G, but Y and not-F. Is there any inference in saying that 
because X is not Y, it is not- Y ? 

It will be allowed that the conclusion would not hold unless X 
were either Y or not- Y. But it may be said that this, the ' principle 
of Excluded Middle ', like the Principle of Contradiction, though 
true, is not a premiss of inference. No one knows what he means in 
saying that X is not Y, unless he sees that in that case it is not-F : 
any more than he can know what he means in saying that X is F, 
unless he sees that in that case it is not not-F. If a proposition is 
true, its contradictory is false ; but there is no step from the truth 
of the one to the falsity of the other, no movement of thought ; 
since the truth of the one is not apprehended without apprehending 
the falsity of the other. 

If the infinite term not-Y were purely negative, this view of the 
matter would demand assent. But F and not-Y are in practice 
always alternatives within some definite limits. F may be blue, 
and then not- Y will be of some colour not blue : or F may be English- 
speaking, and not-Y speaking some language not English. And in 

1 Otherwise, the term is Y, and the form not-Y only shows that Y is being 
denied of some subject in a judgement. 



246 AN INTRODUCTION TO LOGIC [chap. 

[passing from one of these predicates to the other, there is inference, 
and we do not rely merely on the law of Excluded Middle. ' Noble 
blood is not blue .*. it is not-blue ' : if this means ' of a colour not- 
blue ', we require the further premiss that it is either blue or of some 
other colour. We thus pass from a determinate positive predicate 
to another predicate less determinate, but still positive. 

If however there is no positive alternative meaning in the 
predicate not-Y, then indeed there is no inference, but only equi- 
pollency. ' Steam is not visible .-. it is in visible ' seems a mere sub- 
stitution of one equivalent expression for another. It follows, that 
we cannot tell by the mere symbolic form whether the permutation 
of a negative proposition contains any real inference or not, but 
must look to the content x ; and if it contains real inference, the 
inference is disjunctive. 

The permutation of an affirmative proposition may, like this last, 
be no real process of inference. We pass here from ' X is Y * 
to ' X is not not-Y'. It is not always possible to find in this 
any other meaning than that from which we started. We cannot 
always interpret not- Y to mean ' possessed of some other of the range 
of alternatives to which Y belongs ' ; if a subject must display some 
one out of a given range of alternatives, and does not display Y, it 
will display one of the others ; but if it does display Y, we cannot 
be sure that it may not display one of the others as well. If a 
man holds office in the Government, and does not hold an office 
that entitles him to Cabinet rank, he must hold an office that does 
not entitle him to Cabinet rank ; but if he does hold an office that 
so entitles him, he may also hold one that does not. Equally, if 
not-Y is quite unlimited in range, and includes everything whatever 
except Y, it will not follow that because X is Y, it is not also not- Y ; 
because we can predicate of a goose that it hisses, we are not pre- 
cluded from applying any predicate but hissing. The only sense, 
therefore, in which it is true to say that X is not not-F, is one in 
which we deny no alternative, but only deny the denial of Y ; 
and that is just equivalent to the affirmation of Y, or at least 
can hardly be said to involve any inference from it. If however 
we have in mind a range of mutually exclusive alternatives among 
which Y is one, then permutation takes us from the affirmation 
of Y to the denial of the rest ; and this is again disjunctive reasoning, 
wherein the conclusion will be more or less definite according to 
the definiteness of our knowledge of the alternatives to Y. But 

1 The reader may be reminded, that among the range of alternatives 
which the denial of a positive term leaves open, the corresponding negative 
term has often come to signify one only. Not-blue may cover all colours but 
blue ; but unfriendly does not cover all tho alternatives to friendly ; it 
implies a definite degree of hostility which may be absent in those who are 
not positively friendly to us. But this is a matter of the interpretation of 
language rather than one of Logic. 



X] OF IMMEDIATE INFERENCES 247 

[so far as there is inference here, there is no use of an infinite term ; 
where not-Y is really infinite or unlimited, the only sense in which 
the permutation of an affirmative proposition is logically justifiable 
is one in which it involves no step of inference. 1 

If this is a just account of the nature of permutation, then any 
inference there may be, apart from disjunctive argument, in con- 
verting by negation, must lie in the converting. And the conversion 
of by negation will no more be inference, if the permutation of it 
is not, than the simple conversion of /. Indeed no one believing 
that there existed things which are not F could judge that ' some 
X are not Y ', without at the same time thinking that some things 
which are not Y are X Similarly the conversion of E by negation — 
1 No X is Y .-. some non- Y is X ' — is like the conversion by limitation 
of A i H there is anything new in the converse, it is the implied 
assertion that there exist instances of what is X, an assertion which 
the convertend, if intended hypothetically, did not contain. ' A 
perfectly wise man does no wrong, .-. some who do no wrong are 
perfectly wise ' ; it is not converting by negation that would justify 
us here in passing from a sense of the convertend in which it does 
not imply that any one is perfectly wise to a converse that does. 
In converting A by negation on the other hand there is inference 
to the extent that there is in simply converting E. ' All X is Y .•. 
No non- Y is X ' involves the transition from ' If X, then Y ' to ' If 
not Y, then not X ', which may be indifferently expressed by 
' No not-Y is X ' or ' All not-F is not-X ' — i. e., the inference is in 
the conversion, not in the second act of permutation, by which 
some distinguish contraposition from conversion by negation.] 

The immediate inferences which we have considered so far have 
all been of a more or less formal character ; as is shown by the 
fact that they have been capable of explanation, up to a point, 
by using symbols and not real terms. There are certain kinds of 
inference, which have been called immediate, that cannot be 
exhibited by symbols at all, but only in concrete. One of these is 
known as Immediate Inference by Added Determinants : in which 
we add the same qualification to both subject and predicate in 
a proposition, and hold the result of our operation to be true, on 
the strength of the truth of the original proposition ; e. g. ' A negro 

1 This is no doubt why Wallis (cf. p. 239, n. 1, supra) did not distinguish 
contraposition from conversion by negation. ' Hanc formulam locum habere 
docent in Particulari negativa. Atque huius potissimum causa videtur fuisse 
introducta : ut quae per neutram reliquarum converti possit. Puta. Aliquod 
animal non est homo : ergo, Aliquod non-homo non est non-animal ; seu 
(quod tantundem est) Aliquod non-homo est animal ; seu, Aliquod quod non 
est homo, est tamen animal.' loc. cit. 



248 AN INTRODUCTION TO LOGIC 

is a fellow creature .'.a negro in suffering is a fellow creature in 
suffering '. x Another is called Immediate Inference by Complex 
Conception : in which the subject and predicate of a given proposi- 
tion are used to qualify in some way the same term, and thus 
complex concepts are formed, that are made subject and predicate 
of a new proposition, e.g. ' Physics is a science .". physical treatises 
are scientific treatises '. The following examples, some of them 
sound and some unsound, but the sound identical in form with the 
unsound, will serve to show that the ground of the soundness of 
these arguments does not lie in the form of them : — 

The horse is an animal .' . the head of a horse is the head of an animal. 

Horses are animals .*. the greater number of horses is the greater 
number of animals. 

A shark is not a mammal .'. the anatomy of a shark is not the 
anatomy of a mammal. 

A shark is not a mammal .'. the food of a shark is not the food 
of a mammal. 

A shark is not a dog . * . the owner of a shark is not the owner of a dog. 

It is not worth while multiplying arguments to show how entirely 
the validity of such inferences as these involves their content. It 
would not be possible to reduce them to a definite number of fixed 
types, though in considering generally which are valid, some of 
Aristotle's observations in the Sophistici Elenchi, especially those 
on what he calls the Fallacy of Accident, would be pertinent. But 
their mention here will serve to illustrate, what it is well to realize 
early, that inference is not a purely formal process ; that argu- 
ments are not all built on the principle of American watches, with 
interchangeable parts, 2 so that terms from one may be transferred 
to another, without interfering with the working of the inference ; 
and that the study of inference, like the study of life, is largely 
a matter of examining types : though there are a certain number of 
common forms, which recur identically in divers contents. One of 
the most famous of these common forms is the Syllogism, to which 
we must now proceed ; it has often been regarded as the form of all 
inference whatever that is not ' immediate ' ; it is indeed highly 
general, and found in all kinds of subject-matter ; though the nature 
even of it cannot be profitably studied altogether in the abstract, but 
is to some extent affected by the concrete character of its terms. 

1 Thomson, Laws of Thought, § 55. 

2 v. Marshall's Principles of Economics, Bk. IV. c. ix. § 4. 



CHAPTER XI 

OF SYLLOGISM IN GENERAL 

Aristotle, who was the first person to work out the theory of 
syllogism, though not, of course (as Locke maliciously suggests 
that his followers claimed), the first to reason syllogistically, defines 
a syllogism as follows : Ao'yos Zv <o reflevraw tlvu>v erepov rt, t6>v 
Kei[A€V(DV i£ avayKrjs <rv/x/3airei tu ravra elvcu * : that is to say, ' dis- 
course in which certain things being posited, something else than 
what is posited necessarily follows merely from them '. 

This definition is too wide. It covers, as the word syllogism in 
its etymological signification itself covers, every argument in which 
from a consideration of two truths we infer a third — every argument 
in which (to use a homely phrase) we ' put two and two together ', 
and find a certain conclusion necessarily following. 2 But neither 
by Aristotle, when he investigated in his Prior Analytics the various 
forms of syllogism, nor by the world, which has followed Aristotle, 
has the term been actually used so comprehensively. A syllogism 
is actually an argument in which, from the given relation of two 
terms, in the way of subject and predicate, to the same third term, 
there follows necessarily a relation, in the way of subject and predicate, 
between those two terms themselves. 3 

Example will best explain what is here meant by the words 
italicized. If A is equal to B, and B is equal to C, then A is equal 
to C. If a bullet travels faster than a horse, and a horse travels 
faster than a man, then a bullet travels faster than a man. Now 
here the terms are A, B, and G : or a bullet, a horse, and a man ; but 
the relations between the terms are in the one case relations of 
quantity, in the other of velocity. A and B are not related as 

1 Anal. Pri. a. i. 24 b 18 : cf. Top. a. i. 100 a 25, where the same definition 
recurs, with the substitution of 8ia rusv Keiyxvoni for rw ravra eivai. 

2 ' Putting two and two together ' is often a process which leads people to 
conclusions of a highly conjectural character. In such cases, their reasoning 
does not come under the Aristotelian definition : for it is expressly stated 
by him that the conclusion must be inevitable — e'| dvayicTjs. 

3 Bradley's Principles of Logic, Bk. II. Pt. I. c. iv. § 10, et alibi. 



250 AN INTRODUCTION TO LOGIC [chap. 

subject and predicate, for I do not say of A that it is B, but only 
that it is equal (in quantity) to B ; a bullet and a horse are not 
related as subject and predicate, for a bullet is not a horse ; its 
asserted relation to a horse is in the way of travelling faster, not in 
the way of being a subject whereof horse is a predicate. No doubt 
it is a predicate of a bullet, that it travels faster than a horse, as it is 
a predicate of A to be equal to B ; but then what I proceed in my 
argument to compare with C is B itself, and not that which is equal 
to it ; what I say travels faster than a man is a horse, and not what 
travels faster than a horse. A, B, and C, a bullet, a horse, and a 
man, are the terms which I compare, the former in respect of quan- 
tity, the latter of velocity ; and from the given relations of A and G 
to the common term B, in the way of quantity, I deduce a relation 
between A and C themselves in that respect ; or from the given 
relations of a bullet and a man to a horse in the way of velocity, 
I deduce a relation in the way of velocity between a bullet and a man. 
Now the relations between the terms of an argument may be in 
the way of subject and predicate ; and then the argument is a syllo- 
gism. Let us for the present use the symbols X, Y, and Z to 
represent terms related in this way. Suppose that X is predicated 
of Y, and Y of Z ; then X must be predicable of Z. For example, 
silver prints fade in the sun ; and the photographs which I have 
bought are silver prints ; therefore they fade in the sun. Here the 
term common to the two premisses (for such the given propositions 
are called, from which the conclusion is deduced) is silver prints ( Y) : 
that is predicable of the photographs which I have bought (Z), and of 
that is predicable to fade in the sun (X) ; hence to fade in the sun (X) is 
predicable of the photographs which I have bought (Z). Or again, 

Y may be a predicate affirmed or denied both of X and Z ; in the 
Dreyfus affair, the French War Office frequently argued that the 
man who wrote the famous ' bordereau ' was on the General Staff : 
Esterhazy was not on the General Staff, and therefore did not write 
it ; here Y (being on the General Staff) is affirmed of X (the man who 
wrote the ' bordereau ') and denied of Z (Esterhazy) ; and hence X is 
denied of Z — Esterhazy did not write the ' bordereau '. Yet again, 

Y may be a subject of which both X and Z are predicates affirmed or 
denied ; then X may be predicable of Z, or vice versa. The horse 
is strong, and is an animal that lives exclusively upon a vegetable 
diet ; therefore an animal that fives exclusively upon a vegetable 
diet may be strong. Here we have two terms, strong (X) and being 



xi] OF SYLLOGISM IN GENERAL 251 

an animal that lives exclusively upon a vegetable diet (Z), affirmed as 
predicates of the same term (Y), the horse ; and we hence deduce 
that X, strong, is predicable of Z, an animal that lives exclusively upon 
a vegetable diet, not indeed necessarily and universally, but as a 
possibility in certain cases. 

These examples may perhaps explain what is meant by terms 
being related in the way of subject and predicate, and how the 
relation of two terms in that way to a common third term may 
necessitate their relation in the way of subject and predicate to one 
another. 

What is here called a relation in the way of subject and predicate 
may be also called a relation in the way of subject and attribute ; 
as it is called, for example, by Mr. Bradley in his Logic, Bk. II. 
Pt. I. c. iv. § 10, and elsewhere. If the word attribute is used, it 
must be understood generally of anything predicated x ; it is an 
attribute of Baal to be a god, to be talking, to pursue his enemies, 
to be on a journey, to be asleep, to need awakening, to have 450 
prophets in Israel, to be worshipped by the Phoenicians ; whatever 
can be affirmed or denied of him is an attribute affirmed or denied ; 
the attribute may be in any category, of substance (as when we say 
that he is a god), of quality, time, place, state, relation, &c. ; the 
only thing necessary is that it should be related to him as what can 
be predicated of it to a subject, not (for example) as an uncle to 
a nephew, as yesterday to to-day, as cause to effect, as here to there, 
as means to end, as more to less, &c. ; all of these are relations in 
which terms may stand to one another, if we mean by terms distinct 
subjects of thought, and not merely the subject and predicate into 
which the judgement which affirms their relation is resoluble. Thus 
when I say that the Old Pretender was nephew to Charles II, he and 
Charles II may be called the terms placed (in this judgement) in 
a relation of consanguinity ; he and ' nephew to Charles II ' are the 
terms placed in a relation of subject and attribute. When I say 
that Edinburgh is west of Liverpool, Edinburgh and Liverpool are 
the terms placed in a space-relation ; but Edinburgh and ' west of 
Liverpool ' the terms placed in a relation of subject and attribute. 
Understanding the word in this comprehensive sense, we may say 
that the theory of syllogism is the theory of inference in the domain 2 

1 i. e. in a wider sense than it is used in when the attributes of anything 
are distinguished from its substance or kind, and its relations. 

2 By a domain here is meant a certain order or system of relations, of 



252 AN INTRODUCTION TO LOGIC [chap. 

of subject and attribute, just as well as in the domain of subject and 
predicate. But it is important to remember that ' attribute ' is 
being used in a wider sense than it usually bears ; we should not 
ordinarily call it an attribute of Mr. Pickwick to have been once 
impounded ; or of Becky Sharp to have thrown Dr. Johnson's 
Dictionary out of the carriage window ; the word is not ordinarily 
understood to include actions, or the casual relations of one thing to 
another ; but in its present use, it includes every predicate. The 
advantage of using it is this, that inference depends on perceiving 
relations in what is thought of, and in taking the word attribute 
instead of predicate, we take a word expressing a real for one express- 
ing a logical relation. Blue is an attribute of the star-gentian 
really and always : a predicate, only when one judges that the 
star-gentian is blue. It is true that in the theory of syllogism we 
have to do with attributes only so far as they are predicated ; but 
we think of our predicates as attributes. 

It has often been held that the syllogism is the type of all reasoning, 
except the inferences called immediate. 1 No one has done more 
to dispel this illusion than Mr. Bradley, in his Principles of Logic ; 
though perhaps the zeal of an iconoclast has prevented him from 
dwelling enough on the fact that the syllogism formulates reasoning 
which is very frequent in occurrence. But our present business is 
to become familiar with the theory of syllogism on its formal side. 
There is a precision and completeness about this theory, which have 

a single kind : as we might call space a domain in which all material things 
are related, and time a domain in which all events are related. The domain 
of subject and attribute is far less unified than that of space and time. 
A thing related to one other thing in space, or an event related to one other 
event in time, is necessarily related in those ways to all others. But a term 
related to a second term in the domain of subject and attribute is thereby 
necessarily related in that way only to those further terms, if any, to which 
the second is related in that manner (and not necessarily to all of them). 
The domain of subject and attribute is, as it were, a system of relations 
embracing group after group of terms, but not necessarily connecting any 
of the terms of separate groups ; whereas time and space, which connect 
group after group of events or bodies, necessarily connect also any two 
members of any two groups. The word category might have been employed 
instead of domain, in the Kantian sense of a principle of synthesis or relation. 
But it was employed on the last page in the Aristotelian sense of a kind 
of predicate (determined indeed, on Kant's view, by the principle, or principles, 
of synthesis employed), and has been generally employed in the text in that 
sense ; and it would have introduced confusion either to employ it without 
notice in a different sense, or to interrupt the present subject in order to 
point out the distinction between them. 

1 e.g. Hobbes, Art of Rhetoric, Bk. I. c. i, ' all inferences being syllogisms ' : 
v. Molesworth's ed., English Works, vi. 423. 



xi] OF SYLLOGISM IN GENERAL 253 

made logicians dwell on it with something of an artist's concen- 
tration ; and the truth of science has sometimes been sacrificed to 
neatness of exposition. 

The business of syllogism is to establish a relation in the way of 
subject and predicate between two terms, by means of their relations 
in that way to the same third term. But the proposition which 
relates two terms as subject and predicate may be universal or 
particular, affirmative or negative. 1 Moreover, we have seen that 
there are various ways in which the two terms that are to be brought 
together in the conclusion may be related to a common third term ; 
both may be predicated of it, or it of both, or one of it and it of the 
other. Therefore the following general problem presents itself to us, 
— Writing S for any subject, P for the predicate which is to be 
brought into relation to it, and M for the third or middle term whose 
relations with 8 and P are to bring them into relation with each 
other, we may ask — What must be the quantity and quality of the 
propositions (or premisses) connecting S and P respectively with M , 
and in which relation, viz. subject or predicate, must M stand to S 
and P in these premisses, in order to establish in the conclusion 
a proposition whose terms are S and P, of the several forms A, E, I, 
and ? In other words, what forms of premisses will prove that all 
8 is P, no S is P, some S is P, or some S is not P, by means of the 
relations, in the way of subject and predicate, of S and P respectively 
to M ? Or, yet again, what relations in the way of subject and predicate 
between two terms S and P respectively and a common third term M will 
establish what relations in the way of subject and predicate between 
those two terms themselves ? This is the question, put in its most 
abstract form, to which the formal part of the theory of syllogism is 
an answer. 

1 When it said that a judgement, or proposition, 'relates' terms, 'places' 
them in a relation, and so forth, it must not be understood that the terms of 
thought come to stand in such relations through that act of judgement. My 
judgement is my apprehending, or coming to believe, that they stand in 
such relations, and the proposition expresses this apprehension or belief, or 
asserts what is apprehended or believed. 



CHAPTER XII 

OF THE MOODS AND FIGURES OF SYLLOGISM 

A. Nomenclature. 1. In any syllogism, there are two proposi- 
tions taken as true, and another inferred or following from them. 
The latter is called the conclusion (Lat. quaestio or conclusio, Gk. 
7rpd/3Ar;jua or avjx-nlpaaixa) : the former the premisses (Lat. praemissa, 
Gk. irpoTcicre is). 

It was said, that the premisses are taken as true : whether they are 
true or false, the conclusion which they yield is the same ; only 
that if they are true, it is true, and if they are false, it is probably 
false. 1 We are not concerned, therefore, in the formal theory of 
syllogism, with the truth or falsehood of our premisses or our con- 
clusion, but only with the validity of our reasoning : we wish to 
know, if the premisses are granted, what must be granted as follow- 
ing from them. If our reasoning be correct, a man cannot con- 
sistently admit the premisses, and deny the conclusion. Suppose 
that a man admits that every restriction upon freedom of contract is 
mischievous, and admits that the marriage laws restrict freedom of 
contract, then he must admit the marriage laws to be mischievous. 

It has been made a reproach to the theory of syllogism, that it 
looks only to the cogency of the inference, and not to the truth of 
the premisses. We need rules, it is said, by which to determine 
whether a proposition is actually true, and not merely whether it 
is true, upon the hypothesis that certain other propositions are so. 
The theory of syllogism is decried as a Logic of Consistency ; for 
the most that it can do is to furnish rules by which to judge whether 
different assertions are consistent with one another. In rivalry 
with the Logic of Consistency, some writers have projected a Logic 
of Truth, and offered it to the world under the name of Induction. 2 

1 Not necessarily, because a true conclusion may follow from false 
premisses (cf. infra, p. 334). But a conclusion correctly drawn from false 
premisses implies ignorance in the reasoner, though not ignorance of 
reasoning. 

■ Cf . Mill, System of Logic, III. iii. 9. 



MOODS AND FIGURES OF SYLLOGISM 255 

But it has been unfortunately discovered that the ' Inductive 
Methods ' that were to test the truth of the premisses, from which 
the doctrine of syllogism enquires what may be inferred, suffered 
from the same defect as the syllogism itself ; for they also were 
processes of inference, in which conclusions were drawn from 
premisses ; their conclusions were only true, if the premisses were 
true ; they showed themselves quite unable to determine whether 
their premisses were true or not, though it was generally just on 
that point that disputes were most pronounced. 

The fact is, that so far as reasoning can be reduced to fixed 
forms at all, and these forms studied in the abstract — whether 
or not the forms are syllogistic — we must disregard the truth 
of the premisses ; for in expounding an abstract form of reasoning 
we may even use symbols for terms, 1 i. e. we do not trouble our- 
selves to ask what in particular the terms are at all ; and hence 
we cannot be asking whether the judgement which connects them 
is true. 2 

Given then the premisses, the conclusion follows necessarily ; 
but it may nevertheless be false, if the premisses are false. The 
premisses, however, need not in the first place be given, they may be 
wanted. 

Supposing a man to have admitted that whatever discourages 
thrift and independence is evil ; and to have admitted that an 
universal system of pensions in old age at the cost of the state 
discourages thrift and independence : then he must admit as a con- 
clusion that such a system is evil. Here, and to such a man, the 
conclusion presents itself in the first place as a consequence of 
what is already granted or ' given '. But supposing a man to 
be in doubt whether an universal system of pensions in old age 
at the cost of the state is evil or not, and to be wanting some 
proof, one way or the other ; and that a friend offers him the 
above ' premisses ', as showing that it is evil : then, and to him, 
the ' conclusion ' presents itself in the first place as a question or 
problem, about which he wants to know whether he is to affirm 
or deny it ; and syllogism is a process of finding proof, rather than 
of drawing consequences. 

1 As J. S. Mill does in expounding his Inductive Methods : but his symbols 
are very inadequate. 

2 Yet inference is at bottom a perception of connexion among facts, and 
how can we perceive any in premisses that are not true ? On this difficulty 
cf. infra, pp. 331-334. 



256 AN INTRODUCTION TO LOGIC [chap. 

It makes of course no difference to the form of premisses which 
will establish a particular form of conclusion, whether the premisses 
be first known, and the conclusion discovered as a consequence : or 
the conclusion raised as a problem, and the premisses discovered to 
settle it. And in either case alike, the premisses are ' given ' in the 
sense of being admitted and not proved in the argument. But they 
are not always ' given ' in the sense of being that with which a man 
begins : our thought is as often occupied in looking for premisses 
to establish what we believe or suspect, as in looking at premisses 
to see what follows from them. And that is why Aristotle used 
the expressions -np6jiXr]p.a and 7rpora<rei9. For him, the conclusion 
was generally regarded as something to be proved x ; the premisses, 
as something proffered in proof of it ; and so he asked rather, 
1 What kinds of premisses are required to prove various kinds of 
conclusion (A, E, I, and 0) ? ' than ' What kinds of conclusion 
follow from various combinations of premisses ? ' But so soon as 
he had answered his question, and said ' These kinds of premisses 
prove the various kinds of conclusion ', then other people could look 
at the matter from the side of the premisses first. To them, the 
premisses were something which, if given, necessitated a certain 
form of conclusion : rather than something which, if a certain form 
of conclusion were to be established, must be given. 

2. The premisses are called respectively the major and minor 
premiss. This nomenclature is adjusted to that of the terms in the 
argument. There are, as we have seen, three terms in a syllogism : 
two, which form the subject and predicate of the conclusion, and 
one with which each of the former is brought into relation (in the 
way of subject and predicate) in one of the premisses. The subject 
and predicate of the conclusion are called respectively the minor 
and the major terms : the term common to the two premisses 
is called the middle term. 2 The major premiss is the premiss in 

1 Or rather, to be proved or disproved : it was a thesis, which might form 
the subject of debate between two parties ; one of them, the oppugner, ' held 
out ' to the other, the upholder, various propositions, which he asked him to 
admit, in hope to obtain admissions wherefrom there followed syllogistically 
a conclusion contradictory of the thesis of the upholder. 

2 These expressions are based upon what occurs in the first figure, where 
the major term is commonly of greater extension than the middle, and the 
middle than the minor : and the major premiss, as compared with the minor, 
is a more general proposition. But being transferred to the other figures, 
in which they cannot any longer be so interpreted, they must be explained 
generally as in the text : cf. infra, pp. 259 sq., where this is explained at 
length. 



xii) MOODS AND FIGURES OF SYLLOGISM 257 

which the major term occurs, and the minor premiss that in which 
the minor term occurs. Thus in the syllogism 

All organisms are mortal 
Man is an organism 
.'. Man is mortal 

the major term is mortal, and the major premiss all organisms are 
mortal ; the minor term man, and the minor premiss man is an 
organism ; the middle term, organism. 

It will be noticed that each term in a syllogism appears twice : 
the major and minor terms each in its respective premiss and in the 
conclusion, the middle in both premisses but not in the conclusion. 

In giving examples of syllogism, it is usual to write down the 
major premiss first ; but in ordinary life and conversation, no 
particular order is observed ; nor is it necessarily the major premiss 
that is written first in a logical example. 1 The only mode of deter- 
mining the major premiss is to look for the premiss which contains 
the predicate of the conclusion. 2 

3. Syllogisms are said to differ in figure (o-x^a) according to 
the position of the middle term in the premisses. 3 (i) The middle 
term may be subject of the major premiss, and predicate of the 
minor : in this case Aristotle called the syllogism of the first (or 
perfect) figure. The example just given belongs to the first figure, 
as also does the following : — 

No insects have eight legs 
Wasps are insects 
.*. Wasps have not eight legs. 

It is convenient to have a conventional symbolism, in which to 
represent syllogisms according to their form ; we shall use the 
letters P, M, and 8. 8 ( = subject, of the conclusion) will always 
indicate the minor term, P ( = predicate, of the conclusion) the 
major term, and M the middle. Thus the figure of both these 
examples (i. e. their form, so far as it depends merely on the position 
of the terms in the premisses) may be written 

M P 
S M 

:. 8 P 

1 Of. Locke, Essay, IV. xvii. 8 (fourth or later edition). 

2 Except in the ' indirect moods ' of Fig. 1. Cf. infra, pp. 262, 268-269. 
■ Cf. c. xi, supra, pp. 250-251. 

1779 8 



258 AN INTRODUCTION TO LOGIC [chap. 

If we wished to indicate in our symbols the character of the pro- 
positions which compose the syllogism (i. e. whether universal or 
particular, affirmative or negative), we should have to write our two 
examples differently. The former is of the type 

All M is P 
All 8 is M 
:. All S is P 



the latter of the type 



No M is P 

All 8 is M 

:. No 8 is P. 



(ii) The middle term may be predicate in both premisses, the 
figure of the syllogism being indicated as follows : — 

P M 

8 M 
.'. S P 

e.g. No insects have eight legs 

Spiders have eight legs 
.*. Spiders are not insects. 

Syllogisms in which the middle term is thus placed were called 
by Aristotle of the second figure. 

(iii) The middle term may be subject in both premisses, the figure 
of the syllogism being indicated as follows : — 

M P 
M S 
.'. S P 

e.g. The Veddahs of Ceylon show great conjugal fidelity 
The Veddahs of Ceylon are savages 
.*. Some savages show great conjugal fidelity. 

Syllogisms in which the middle term is subject in both premisses 
were called by Aristotle of the third figure. 

(iv) Aristotle recognized only these three figures. But he pointed 
out 1 that the premisses of a syllogism in the first figure would some- 
times justify you in concluding to a particular proposition in which 
the minor term was predicated of the major, even though no 

1 Anal. PH. a. vii. 29 a 19-27 (cf. p. 281, n. 2, infra). 



xnl MOODS AND FIGURES OF SYLLOGISM 259 

conclusion was possible that predicated the major of the minor. 
For example, from the premisses 

Some parliamentary voters are freeholders 
No women are parliamentary voters 

it is impossible to determine whether any women are freeholders or 
not (for a reason which will be explained later) ; but we can con- 
clude that some freeholders are not women. 
Again, from the premisses 

All persons who have the franchise are eligible to Parliament l 
No woman has the franchise 

we cannot conclude that women are not eligible to Parliament (for 
others might be eligible besides those who have the franchise) ; but 
we can conclude that some persons who are eligible are not women. 
The famous physician Galen is said by Averroes to have referred 
arguments of this kind to a separate and fourth figure (sometimes 
called after him the Galenian figure), in which the middle term is 
predicate of the major premiss and subject of the minor : the figure 
being accordingly symbolized 

P M 

M 8 
:. 8 P. 

The theory of syllogism has been much darkened by this addition. 3 
For in erecting these arguments into a separate figure it is implied 
that the distinction between major and minor term depends merely 
on their position in the conclusion, and is in no way intrinsic to the 
terms themselves. The meaning of that distinction must be con- 
sidered next. 

4. We have said that the major term is the predicate of the 
conclusion, and the minor the subject. But why are they called 
major and minor ? Did Aristotle merely want shorter names, to 
avoid the constant repetition of such cumbrous expressions as 
* subject of the conclusion ' and ' predicate of the conclusion ' ? Are 
tne names chosen arbitrary ? And would it have been equally appro- 
priate to call the subject of the conclusion the major, and the 

1 If the premiss had to be true, the clergy must be excepted. 

2 In the second and third figures, where the middle term occupies the 
same position in both premisses, either premiss may be regarded as major, 
without affecting the situation of the middle term : and hence there is no 
possibility of erecting a separate figure bearing the same relation to them 
as the fourth does to the first. 

32 



260 AN INTRODUCTION TO LOGIC [chap. 

predicate the minor term ? Or, on the contrary, does the choice of 
names indicate a real feature of the relation between subject and 
predicate in a judgement ? Is there a reason why the predicate 
should be called the major term, and the subject the minor? 

Aristotle conceived that there was such a reason, not indeed in 
all judgements, but in most and especially in scientific judgements 
(i. e. judgements which really express knowledge). We shall do 
best to look first at judgements in which the distinction of major and 
minor term is arbitrary. ' Some scholars are statesmen ' might be 
as well expressed by saying ' Some statesmen are scholars ' ; for 
here the two terms or concepts have no necessary relation : it is only 
as coincident in the same individual that statesman can be predi- 
cated of scholar, or vice versa ; and there is no more reason for 
making one term subject than the other. ' Some poulterers are not 
fishmongers ' is a judgement of the same kind : the two trades are 
frequently conjoined, but merely conjoined, and as there would be 
no more reason for making the sale of fish an attribute of a poulterer, 
than the sale of poultry an attribute of a fishmonger, so in the 
negative judgement, each term is with equal propriety denied of 
the other. But where the subject of a judgement is a concrete 
thing or person, and the predicate an attribute : or where, though 
the subject is an abstract term, yet the predicate belongs to it, 
and is not merely coincident with it in the same thing ; there the 
two terms cannot equally well be predicated of each other. We 
say that Caesar was a great general ; if we said ' a great general 
was Caesar ', we should still be understood to make Caesar the 
subject, and to have merely inverted the usual order of words in 
the sentence. We say that diamonds glitter, rather than that some 
glittering things are diamonds ; that blue is a colour, rather than 
that a colour is blue. 1 To say that a colour may be blue is natural 
enough ; just as it is to say that a stone may be a diamond ; but 
still we predicate the genus of the species or individual, and not the 
species or individual of the genus : it is not the genus colour, but 
colour in some particular case, not the genus stone, but some parti- 
cular mineral that is blue or that is diamond. Commonly, except 
where they are merely coincident attributes, 2 the predicate is 

1 Unless a definite instance is meant. 

2 Terms, though they be general concrete terms, like statesman or fish' 
monger, may yet express only a special or ' abstract ' aspect Df the nature 
of the thing they denote, if they are not in the category of substance : 
cf. tvpta, p. 37, n. 1. 



xii] MOODS AND FIGURES OF SYLLOGISM 261 

a wider term, or more generic, than the subject in judgement ; it is 
something which belongs to this and may belong to other subjects, 
not a part of the extension of the subject itself. It is natural to 
predicate the genus of the species, the attribute of the concrete 
thing. In science especially, whose judgements should be necessary 
and universal, the predicate, if not commensurate with the subject, 
must be the wider term. We cannot predicate universally of any 
term what is only part of its extension. If stone is a wider or more 
comprehensive term than diamond, other things besides diamonds 
are stones, and therefore that proposition must be particular in 
which diamond is predicated of stone. A diamond is a stone, 
a stone may be a diamond ; blue is a colour, a colour may be 
blue. 

In calling the predicate of the conclusion in a syllogism the 
major term, then, Aristotle chose a name which was appropriate, 
both when the predicate is related to the subject as attribute to 
concrete thing, and when it is related to the subject as the more 
to the less generic. By the name major he wished to indicate 
that the predicate is the more comprehensive term : that it signified 
something characterizing the subject, but characterizing, or capable 
of characterizing, other subjects also — something therefore which 
might be regarded as an attribute of the subject (in a wide sense of 
the word attribute), but not as a subject characterized by it. 1 

1 Cf. infra, pp. 379-380. In Anal. Post. j3. xvii. Aristotle uses the word 
iraptKTeivftv, to extend beyond, of the relation of major to middle term. He forgets 
however there, and ignores in the Prior Analytics when he adopts the expres- 
sions major, middle, and minor terms, what in the Posterior Analytics he 
rightly recognizes as characteristic of science (though not of all reasoning), 
that it aims at demonstrating commensurate judgements. Still, there are 
many scientific judgements which have not that character, and even in 
those that have it, the predicate, considered apart from the demonstration, 
is conceived as what does belong to this subject, and might belong to others. 
It is only in the demonstration by which it is shown to belong to one subject, 
that we come to realize it can belong to that subject alone. If we see, for 
example, in proving that the angle in a semicircle is a right angle, that the 
proof hinges upon a feature which cannot belong to the angle in another 
segment (viz. that the subtending chord passes through the centre of the 
circle), then we see that the predicate is commensurate with the subject ; 
and then also the predicate (if I may so express myself) sinks into the con- 
crete nature of the subject, and is conceived as a necessary part thereof. 
While a demonstration is still wanted by us, to show us that the angle in 
a semicircle is a right angle, we have no ground for supposing that that is 
not a property of angles in some other segments as well : so soon as we 
realize that it can be the property of none other, we have incorporated the 
demonstration with the subject-concept (of the angle in a semicircle) and 
major, minor, and middle terms have for us lost their isolation. Demonstration, 



262 AN INTRODUCTION TO LOGIC [chap. 

The middle term takes its name not simply from being a point 
of connexion between the other two, but from being really inter- 
mediate in comprehensiveness. This it is, however, only in the first 
figure. It is only there that the middle term is predicated of the 
minor, and the major predicated of it. In the second, it is predicate 
in each premiss ; in the third, the subject, of which both major and 
minor terms are predicated. But that which in the first figure is 
really a middle term between the major and minor serves equally 
in the others to be the means of establishing that relation between 
the major and minor which we prove ; and the nomenclature that 
is fixed by the first figure is extended to them all. 

It follows that Galen was wrong in assigning to a fourth and 
separate figure syllogisms in whose conclusion the most compre- 
hensive term is subject, and the least comprehensive predicate, as 
in the example 

What breeds rapidly has a short life 
Flies breed rapidly 
.*. Some short-lived things are flies. 

It is true that in them the middle term is predicate of the premiss 
containing the predicate of the conclusion, and subject of the premiss 
containing the subject of the conclusion ; but in respect of compre- 
hensiveness the predicate of the conclusion is minor, its subject 
major ; and therefore such syllogisms are better treated as belonging 
to the first figure, but having an inverted or indirect conclusion. 
The distinction of major and minor between terms is primarily that 
of greater and less comprehensiveness, and this is not altered by 
making the more comprehensive the subject, and the less the 
predicate, in the conclusion. 

But the fourth figure has been taught for so many centuries 
among the ' moods and figures ' of the syllogism, that for the sake 
of the history of Logic we cannot altogether ignore it, even while 
we recognize the error in which it had its birth. 1 

5. The last paragraph spoke of moods and figures of the syllogism. 
The difference of figures has already been explained to depend on 
the position of the middle term in the premisses. The difference 
of mood depends on the quantity and quality of the propositions 

when complete and while completely realized by the mind, may be said to 
collapse into a judgement whose terms are interfused. Cf. p. 311, infra. 
1 Cf. infra, pp. 280-285. 



xii] MOODS AND FIGURES OF SYLLOGISM 263 

composing the syllogism. This may be the same in different figures, 
or different in the same figure : e. g. in the syllogisms 

All organisms are mortal 
Man is an organism 
.*. Man is mortal : 

and No unlicensed body may sell liquor to strangers 

A college is unlicensed 
.'. A college may not sell liquor to strangers : 

the figure is the same (the first), but the component propositions 
are in one case of the form A, A, A, and in the other of the form 
E, A, E. If the second syllogism be now compared with the 
following 

No good comrade avoids pleasure 
All ascetics avoid pleasure 
.*. No ascetic is a good comrade : 

it will be seen that the component propositions are of the same 
form in both, E, A, E : but the figure is different. 

The different moods have received distinct names in the various 
figures wherein they occur ; and hence what are called the ' mood- 
names ' of the various forms of syllogism indicate both figure and 
mood. What moods are possible in what figures — i.e. what com- 
binations of premisses, as determined by their quantity and quality, 
will yield what form of conclusion (A, E, I, and 0) with each position 
of the middle term — is the general problem to which the formal 
part of the theory of syllogism has to find an answer. We are now 
familiar with the technical terms employed in solving the problem. 
We must next consider the solution. 

B. The only method of originally determining what combina- 
tions of premisses will yield what conclusion is to try them all, 
with each position of the middle term, and see. This is what 
Aristotle did, in the Prior Analytics. But when it has been done, 
it is possible to review the result, and there recognize the nature 
of the faults committed in those which are invalid, and the rules 
which therefore must be observed (whether in all syllogisms, or in 
those of a particular figure) in order to validity. These rules may 
then be placed in the forefront of our exposition ; it may be shown, 
by the help of an example, that the breach of them brings invalidity ; 
and in each figure, out of the whole number of ways in which it is 



264 AN INTRODUCTION TO LOGIC [chap. 

mathematically possible to combine two premisses, when either 
may have any one of four forms, we can show which are conform- 
able to the rules that we have found necessary to be observed in 
that figure. 

The syllogism is now generally taught in the latter manner, 
which is the more formal and systematic. But the other is the 
more natural, and we shall therefore begin, for the first figure, 
with that. Indeed the ' rules of syllogism * could not have been 
known first, and then the valid moods determined thence ; their 
formulation is the result of an investigation of the valid mooda 
conducted without them. 

A valid mood of syllogism is immediately seen to be valid by 
any one who considers it in a particular example, and though the 
example is particular, the form of inference is seen to be valid 
universally. The best way, on the other hand, to show that a mood 
is invalid, is to produce examples in which the premisses and 
conclusion are of the quality and quantity which that mood requires, 
and show by them that while the premisses are true, the conclusion 
may be indifferently true or false. For if you cannot rely on a form 
of argument to produce a true conclusion from true premisses, it 
certainly is not a valid form. 

Now in the first figure the middle term is subject of the major 
premiss and predicate of the minor. Let us take the possibilities 
in order. 

1. Both premisses universal. 

a. both affirmative ; the mood is valid, and the conclusion A : 

All organisms are mortal All M is P 

Man is an organism All 8 is M 

.'. Man is mortal l .*. All S is P 

6. both negative ; no conclusion follows : 

Sounds have no scent No M is P 

Colours are not sounds No S is M 

.". Colours have no scent .*, 

Sounds are not visible 
Colours are not sounds 
.*. Colours are not visible * 

1 With actual terms, an universal proposition is often more naturally 
expressed without the use of the mark of quantity, All men or No colours. 
Where this is so, and the content makes it plain that the proposition is 



xii] MOODS AND FIGURES OF SYLLOGISM 265 

c. one affirmative and the other negative : 

i. the major negative ; the mood is valid, and the con- 
clusion E : 
No Protestant acknowledges the Pope No M is P 

Lutherans are Protestants All S is M 

.'. No Lutheran acknowledges the Pope .*. No 8 is P 
ii. the minor negative ; no conclusion follows : 

Lutherans are Protestants All M is P 

Calvinists are not Lutherans No 8 is M 

.'. Calvinists are not Protestants ,\ 

Lutherans are Protestants 
Romanists are not Lutherans 
.'. Romanists are not Protestants 
2. One premiss universal, and one 'particular, 
a. both affirmative : 

i. major universal, minor particular ; the mood is valid 
and the conclusion / : 
What raises prices injures the consumer All If is P 
Some import -duties raise prices Some 8 is M 

.'. Some import-duties injure the consumer .'. Some 8 is P 
ii. major particular, minor universal ; no conclusion 
follows : 
Some taxes are levied at death Some M is P 

Excise-duties (or Legacy-duties) are taxes All 8 is M 

.'. Excise-duties (or Legacy-duties) are levied at death .*. 

6. both negative : 

i. major universal, minor particular ; no conclusion 
follows : 
Starches contain no nitrogen No M is P 

Some foods (or flesh-foods) are not starches x Some S is not M 
.*. Some foods (or flesh-foods) contain no .'. 
nitrogen 

universal, it has not been thought necessary to mark the quantity in that 
way. But with symbols, because there is then no content to guide us, this 
is necessary. 

1 It is true that no flesh-foods are starches. But if with premisses true 
and of the above form the conclusion is to be false, it is impossible to find an 
example where it would not be equally true to enunciate the minor premiss 
universally. For suppose that only some S is not M : then some 8 is 31, 
and with the help of the major premiss, no M is P, it will follow that some 
S is not P. But this conclusion was to be false ; therefore no S can be M 



266 AN INTRODUCTION TO LOGIC [chap. 

ii. major particular, minor universal ; no conclusion 
follows : 
Some quadrilaterals contain no right angles Some M is not P 
The triangle in a semicircle (or The pentagon) No S is M 
is not a quadrilateral 
.*. The triangle in a semicircle (or The pentagon) 
contains no right angle 

c. one affirmative, and the other negative : 

i. major affirmative and universal, minor negative and 
particular ; no conclusion follows : 
All living things change (or contain carbon) All M is P 
Some compounds are not living Some 8 is not M 

.". Some compounds do not change (or do not /. 
contain carbon) 

ii. major negative and universal, minor affirmative and 
particular ; the mood is valid, and the con- 
clusion : 

No political offence is extraditable No M is P 

Some murders are political offences Some S is M 

.*. Some murders are not extraditable ,\ Some S is not P 

ill. major affirmative and particular, minor negative and 
universal ; no conclusion follows : 

Some traders are freeholders (or are members 

of Parliament) Some M is P 

No parson trades No 8 is M 

.*. No parson is a freeholder (or is a member of 

Parliament) 

iv. major negative and particular, minor affirmative and 
universal ; no conclusion follows : 

Some plants are not edible Some M is not P 

Beans (or Monkshoods) are plants All S is M 

.'. Beans (or Monkshoods) are not edible 

3. Both premisses particular. 

a. both affirmative ; no conclusion follows : 
Some Germans are Protestants Some M is P 

Some Calvinists (or Romanists) are Germans Some S is M 
.'. Some Calvinists (or Romanists) are Protestants .*. 



xii] MOODS AND FIGURES OF SYLLOGISM 267 

b. both negative ; no conclusion follows : 

Some things profitable are not pleasant Some M is not P 

Some things popular (or pleasant) are not Some 8 is not M 

profitable 
,*. Some things popular (or pleasant) are not 

pleasant 

c. major affirmative, minor negative : 

Some luxuries are taxed Some M is P 

Brandy (or A cart) for some purposes is Some S is not M 

not a luxury .'. Some 8 is not P 

.*. Brandy (or A cart) for some purposes is 

not taxed 

d. major negative, minor affirmative : 

Some men of science do not study philosophy Some M is not P 
Some rich men (or philosophers) are men of Some S is M 

science /. Some 8 is not P 

,\ Some rich men (or philosophers) do not 
study philosophy 

This exhausts the possible varieties in form of premisses, so far as 
the first figure is concerned ; and we have found only four which 
give any conclusion, namely (to represent them by the accepted 
symbols, and add the symbol for the conclusion) AAA All 

EAE EIO 

Since the thirteenth century, logicians have given to each of 
these moods, as well as to those in the remaining figures, a separate 
name, in which the vowels in order indicate the quality and quantity 
of the major and minor premisses and the conclusion. The names 
of these moods of the first figure are Barbara, Celarent, Darii 
Ferio : and syllogisms of those types are called syllogisms in 
Barbara, Celarent, &C 1 

1 The earliest known work in which these mood-names are found is by 
William Shyreswood (born in Durham, student in Oxford, taught at Paris, 
died as Chancellor of Lincoln, 1249 ; v. Prantl, iii. 10, Absch. xvii. Anm. 29) : 
' Modi autem et eorum reductiones retinentur his versibus — Barbara, &c.' 
(ib. Anm. 52). They passed into general currency through the Summula* 
Logicales of Petrus Hispanus, afterwards Pope John XXI, who was long 
believed to be the author of them (c. 1226-1277), until Prantl found them 
in the unpublished MS. of William Shyreswood in the Library of Paris 
(vol. ii. p. 264). A somewhat similar memoria technica, but less ingenious, 
because it embodies only the form of the moods, and not the rules for the 



268 AN INTRODUCTION TO LOGIC [chap. 

But an addition has to be made. If the minor premiss is an 
universal negative proposition, and the major is affirmative, whether 
universal or particular, then though no conclusion can be drawn 
in which the major term is denied (or affirmed) of the minor, it is 
possible to draw a particular conclusion in which the minor term is 
denied of the major. Thus in 1. c. ii. from the premisses 

Lutherans are Protestants 

Calvinists (or Romanists) are not Lutherans 

it was impossible to infer whether Calvinists or Romanists were 
Protestants : the former in fact being so, and not the latter. But 
it is possible to infer that some Protestants are not Calvinists (or 
Romanists). And in 2. c. iii. from the premisses 

, (freeholders 

Some traders arei , , _, .. 

(members of Parliament 

No parson trades 

it was impossible to infer whether any parson was a freeholder, or 
a member of Parliament : none of them, in fact, being eligible to 
Parliament, while a rector or vicar is legally a freeholder. But it is 
possible again to infer that 

„ (freeholders ) 

Somei , , t. i- ^ r are not parsons, 

(members of Parliament) 

Doubtless no member of Parliament is a parson, as no Romanist is 

reduction of the moods in the second and third figures to the first (v. next 
chapter) is found in the margin of the treatise attributed to Michael Psellus 
(1018—? 1079), Swo^if cis tt]v 'ApicTTorAotif \oyi<i)v €TTi<TTi']fir]i> (Synopsis of 
Aristotle's Logic) (according to Prantl, in the same hand as the text, ii. 275, 
Absch. xv. Anm. 46). Prantl believes the work of William Shyreswood to 
be borrowed from, and that of Petrus Hispanus to be a mere translation of, 
the Synopsis of Psellus. In an article, however, by R. Stapper (Die Sum- 
mulae Logicales des Petrus Hispanus und ihr Verhaltniss zu Michael Psellus, 
published in the Festschrift zum elfhundertjdhrigen Jubilaum des deutschen 
Campo Santo in Rom, Freiburg im Breisgau, 1897, pp. 130 sq. ; cf. also his 
Papst Johannes XXI. pp. 16-19, Miinster i. W., 1898), reason is shown for 
thinking that the ascription of the Synopsis to Michael Psellus is erroneous, 
and that it is really a translation of the Summulae : the Augsburg MS. of 
the Synopsis in which the ascription occurs contains also chapters lacking in 
the Summulae, and partly identical with other works of Psellus ; these may 
have led to his name being placed in the title, which Stapper conceives to 
be in a hand fifty years later than the bulk of the MS. No other MS. of 
the Synopsis ascribes it to Psellus ; all the rest profess to be translations 
from the Latin ; seven give the name of Petrus Hispanus as author, and 
four that of Georgius Scholarius (Gennadius) as translator. Cf. also Sir 
William Hamilton's Discussions, 2nd ed., pp. 128, 671 sq. : who, however, 
wrote before Prantl's work appeared. 



xii] MOODS AND FIGURES OF SYLLOGISM 269 

a Protestant ; and those who know this would not trouble to 
enunciate the subaltern, or particular, propositions ; but our 
premisses do not inform us of the universal ; what they do tell us is 
the truth, even if not the whole truth. 

We have thus two further and indirect moods, i.e. moods in 
which the minor term is concluded of the major, not the major of 
the minor, viz. 

AEO All } ._ . _ 

IEO Some] 

No 8 is M 
.'. Some P is not S 

And there are other indirect moods also. For in Barbara, 
Celarent, and Darii, it is possible, instead of drawing the direct and 
natural conclusion, to draw the converse, wherein the major term 
will be subject and the minor predicate. Thus in 1. a. we might 
have concluded ' Some mortals are men ', in 1. c. i. ' No one who 
acknowledges the Pope is a Lutheran ', in 2. a. i. ' Some things that 
injure the consumer are import-duties '. There are thus five indirect 
moods in all : and the whole nine are given in the first two lines 
of the following hexameters (it is to be noted that the extra syllables 
after the third, in the fifth and ninth names, are inserted metri gratia, 
and have no significance) : — 

Barbara Celarent Darii Ferio, Baralipton 
Celantes Dabitis Fapesmo Frisesomorum 1 : 
Cesare Camestres Festino Baroco : Darapti 
Felapton Disamis Datisi Bocardo Ferison. 

The first four names in the third line belong to the valid moods in 
the second figure : the remainder to those in the third. It would 
be possible to show what moods are valid in these figures by experi- 
menting with all the combinations of premiss possible in respect 
of quality and quantity when the middle term was respectively 
predicate or subject in each premiss. But any one who has followed 
the process for the first figure can work it out for himself in the 
others ; and we may proceed now to the enunciation of the rules 
of syllogism, and the briefer deduction of the valid moods from 
them. 

1 The indirect moods of the first are the same as the moods of the fourth 
figure : cf. pp. 280-285, infra. 



270 AN INTRODUCTION TO LOGIC [chap. 

C. The Syllogistic Rules are eight in number, viz. 

1. A syllogism must contain three, and only three terms. The 
necessity of this rule is manifest ; for we have seen that a syllogism 
is an argument in which a relation (in the way of subject and predi- 
cate) is established between two terms, in virtue of their common 
relation (in that respect) to a third term. Hence, without a third 
term there is no syllogism : and if the terms of the conclusion were 
not related to the same third term, there would be no relation estab- 
lished between themselves, and so again, no syllogism. 

For example, we can draw no conclusion barely from the premisses 
What breathes needs oxygen and Fish have gills. Any one who knew 
that what has gills breathes might infer that fish need oxygen : but 
the inference requires the premiss What has gills breathes no less than 
the other two ; and falls really into two syllogisms, each containing 
three terms : though four terms occur in the whole argument, viz. : 

(i) What breathes needs oxygen 

What has gills breathes 
.". What has gills needs oxygen 

(ii) What has gills needs oxygen 

Fish have gills 
.*. Fish need oxygen 

If the middle term is used equivocally — i.e. in different senses in 
the two premisses — there will in reality be four terms, and no con- 
clusion is possible ; e. g. it is true that no vegetable has a heart : it 
is also true that a good lettuce has a heart : but to have a heart 
means something different in these two propositions, and it would 
be fallacious to conclude that a good lettuce is not a vegetable. 1 

A breach of this first rule is technically known as the fallacy of 
Quaternio Terminorum or of Four Terms ; and where it arises through 
the equivocal use of the middle term, as the fallacy of ambiguous 
middle. 

2. The middle term must be distributed in one premiss at least. 
It will be remembered that a term is distributed, when used in 

reference to its whole extension ; and undistributed, when not so 
used. Thus in the proposition All jealous men are suspicious, the 
term jealous man is distributed (for I expressly refer to all that falls 

1 Conversely, the middle term may be really the same, though verbally 
different, in the two premisses ; and then there is a syllogism, e.g. Branchiate* 
need oxygen, &nd fish have gills .'. Fish need oxygen. 



xii] MOODS AND FIGURES OF SYLLOGISM 271 

within the range of it) ; but the term suspicious is undistributed, 
for I consider it only as characterizing the jealous, and it may very 
well have a wider range than that. If again I say that Some jealous 
men have killed their wives, in this proposition neither term is dis- 
tributed. 

Now when the middle term is undistributed in both premisses, it 
may refer in each to a different part of its extension ; and then the 
major and minor terms are not brought into relation with the same 
term in the premisses at all : hence no conclusion can be drawn. 1 

Examples from the three figures will make plain what is perhaps 
hard at first to grasp in an abstract statement. If a Presbyterian is 
a Christian, and some Christians think that the order of bishops was 
instituted by Christ, it does not follow that a Presbyterian thinks 
this. Christian is a term that includes more than Presbyterian ; if 
all Christians thought that the order of bishops was instituted by 
Christ, then it would follow that Presbyterians thought so ; but if 
only some Christians think it, how am I to tell that the Presbyterians 
are among these ? Again, in the second figure, from the premisses 
Birds fly and Eagles fly, I cannot infer that an eagle is a bird ; for 
though birds fly, many creatures may fly which are not birds, and 
an eagle might be one of these. If in either premiss the middle 
term were used with reference to its whole extension : if nothing flew 
but birds, or nothing flew but eagle3, and if my premiss informed 
me of this : then I could conclude that all eagles were birds, or 
that all birds were eagles ; but as it is, I can make no inference. 
Inference is as obviously impossible in the third figure, with the 
middle term undistributed. Granted that some working-men are 
Tories, and some working-men are tailors : I cannot hence determine 
whether or not some tailors are Tories : for the working-men that are 
tailors may not be the same working-men as are Tories, and then 
the inference would be false. But if in either premiss the middle 

1 This is sometimes expressed as follows : though the expression is apt to 
be misleading (cf. pp. 272, 273). It is said that the premisses assert agree- 
ment (or disagreement, if negative) between the major or minor, and the 
middle, terms ; that if the middle term be undistributed in both premisses, 
the major and minor may respectively agree (or agree and disagree) with 
a different part of its extension ; and therefore we cannot tell that they 
agree (or disagree) with one another. The vogue of such language is perhaps 
to be traced to Locke : cf . e. g. Essay, IV. xvii. 4 : ' It is by virtue of the 
perceived agreement of the intermediate idea with the extremes, that the 
extremes are concluded to agree ' ; cf. also Bacon, Nov. Org., Distrib. Operis, 
1 tametsi enim nemini dubium esse possit quin, quae in medio termino 
oonveniunt, ea et inter se conveniant,' &c. 



272 AN INTRODUCTION TO LOGIC [chap. 

term were distributed : if working-men were referred to in the whole 
extension of the term, and all working-men were spoken of : then a 
conclusion would follow. For whether all working-men were tailors, 
and some Tories, or vice versa, in either case the some of whom the 
one term was predicable would be included among the all of whom the 
other term was predicable, and then these two terms (tailor and 
Tory) would be predicable — not universally, but in part — one of 
the other. 

A breach of this rule is technically known as the fallacy of un- 
distributed middle. 

[It is in the third figure, where the middle term is subject in both 
premisses, that the necessity of distributing it once at least is most 
obvious. Plainly, there, to say that it is used with reference to 
a part of its extension only is to say that only part of what it denotes 
is spoken of ; and if this is a different part in the two premisses, there 
is not really any middle term. Some animals fly, and some are rodents : 
but they are not the same animals ; swallows e. g. fly, and rats are 
rodents ; and it is obvious that our premisses do not justify the 
inference that the same thing flies and is a rodent. But where the 
middle term is not subject, there is a certain awkwardness in talking 
of its distribution. This has already been noticed in discussing the 
'quantification of the predicate'. 1 It was then shown that the 
predicate of a proposition is never really thought of in extension. 
And yet in explaining the present rule of syllogism, one is tempted 
to speak as if it were so thought of. A general demonstration of the 
rule is wanted, applicable equally to any figure ; and it is easy to 
say that if the middle term is undistributed in both premisses, the 
major and minor may be brought into relation only with different 
parts of its extension, and therefore not with the same term at all. 
Or if we speak of agreement between them and the middle term, 
we have a more seductive formula : we can illustrate with circles, 
thus : 

Fig.1. Fig.2.^- — \ Fig.3. 






The inclusion of one area, wholly or partially, within another 
symbolizes an affirmative judgement, universal or particular : it is 
plain that the area 8 may fall wholly within M, and M partially 

1 Cf. c. ix. pp. 222 sq., supra. 



xn] MOODS AND FIGURES OF SYLLOGISM 273 

[within P, and yet S may lie wholly outside P. This is supposed 
to show for Fig. 1, that with an undistributed middle we can draw 
no conclusion ; and the other diagrams are as readily interpreted. 

Yet a syllogism does not really compare the extension of three 
terms, and Euler's diagrams put us upon a wrong train of thought. 
It is true, that unless the middle term be distributed once at least, 
there is no point of identity in the premisses ; and all mediate in- 
ference proceeds in some way by help of an identity. It is not true 
that the point of identity need consist in the same subjects being 
denoted — in the reference to the same part of the extension of the 
middle term in both premisses (for which referring to the whole 
extension in one of them would be an obvious security). In the 
third figure the inference may no doubt hinge on this ; but not in 
the second, or the first. On the contrary, the inconclusiveness 
of an argument in the second figure with undistributed middle is 
best expressed by saying that it does not follow, because the same 
predicate attaches to two subjects, that these can be predicated one 
of the other : and in the first figure, that unless P is connected 
necessarily and universally with M , it is clear that what is M need 
not be P. 1 

If this discussion of the Undistributed Middle should seem too 
lengthy, it must be remembered (1) that for working purposes, in 
order to determine the correctness of a syllogism, the main thing to 
look to is the distribution of terms : and hence (2) that it is of 
great importance, in the theory of syllogistic inference, not to 
misunderstand this reference to distribution. In a later chapter 
(c. xiv) it will be necessary to consider whether the different figures 
of syllogism are really different types of reasoning, or the same ; 
and the present discussion will throw light on that enquiry.] 

3. From two negative premisses nothing can be inferred. A 

negative proposition denies between its terms the relation of 
subject and predicate. It is clear that if the major and minor 
terms are both denied to stand in that relation to the middle term, 
we cannot tell whether or not they are related as subject and 
predicate to one another. Ruminant may not be predicable of 
rodent, or vice versa : neither carnivorous of ruminant, or vice versa : 
we cannot from this infer anything as to the relation of carnivorous 
and rodent. 

4. If either premiss is negative, the conclusion must be nega- 
tive. The same kind of reflection will justify this rule, as the last. 
Two terms stand in the relation of subject and predicate ; between 

1 The fourth figure has not been considered in this note, but in this matter 
it raises no question that is different from those that arise on the other 
figures. 

1778 T 



274 AN INTRODUCTION TO LOGIC [chap. 

one of them and a third term the same relation is denied ; if any 
inference is possible, 1 it can only be to deny the relation also 
between the other and the third term. 

5. The conclusion cannot be negative, unless one premiss is 
negative. This rule is the converse of the last, and equally obvious. 
If both premisses are affirmative, and if they justify a conclusion at 
all, they must establish and not refute our right to predicate the 
major of the minor. 

6. No term may be distributed in the conclusion, which was 
not distributed in its premiss. For if a term is undistributed in 
the premisses, it is there not used with reference to its whole exten- 
sion ; and this does not justify us in a conclusion which uses it with 
reference to its whole extension. 

A breach of this rule is called an illicit process of the major, or 
minor, term, as the case may be. 

[With an illicit process of the minor term, if (as in the first and 
second figures) the minor term is subject in its own premiss, it is 
obvious that we are treating information about a part of the ex- 
tension of the term as if it were information about the whole. If 
all M is P, and some S is M , we can only infer that some 8, and not 
all S, is P. Where the minor term is predicate in its own premiss, 
or with an illicit process of the major term, the matter requires 
a little more reflection. The predicate of a judgement (and the 
major term is always predicate in the conclusion, unless the mood 
is indirect) not being thought in extension, there is some danger 
here again lest we should misunderstand a reference to its distri- 
bution. Take the following example of illicit process of the minor 
term, where the minor term is predicate in the minor premiss : 

To make a corner in wheat produces great misery 

To make a corner in wheat is gambling 
.-. All gambling produces great misery. 
My premisses do not primarily give me information about gambling ; 
nevertheless, if there were no gambling except a corner in wheat, 
the minor term would be commensurate with the middle, and what 

1 It may happen, where the premisses justify no inference, that an affir- 
mative conclusion would in fact be true ; e. g. if some M is not P, and all 
8 is M, it may be true that all S is P. Here of course the middle term is 
undistributed, and therefore there is no real point of identity in the argument. 
However, it is worth while noticing that the proof of this rule also is difficult 
to express in a quite abstract way. The notion of agreement is employed 
here again, but merits the same protest as before : if one term agrees with 
a second, and that disagrees with a third, the first will disagree with the 
third ; but the relation between subject and predicate is too loosely described 
as one of agreement or disagreement. 



xn] MOODS AND FIGURES OF SYLLOGISM 275 

[is predicated universally of the latter could be predicated universally 
of the former. As it is, however, for all the information that is 
given me, the minor term may be (and in fact it is) of wider exten- 
sion than the middle ; for there are many other modes of gambling 
besides making a corner in wheat. It is used therefore with refer- 
ence to a part of its extension only, in the minor premiss ; and 
it is that part which I am told in the major produces great misery; 
I have no right to extend that information to the whole extension 
of the term, and say that all gambling produces great misery ; my 
only proper conclusion is that some gambling does so. Again, with 
regard to the major term : if I argue that productive expenditure 
benefits the country, and expenditure on art is not productive ; and 
that consequently expenditure on art is of no benefit to the country : 
I am guilty of an illicit process of the major term. It may not at 
first sight appear that I have treated information given me about 
a part of what benefits the country as if it were information about 
everything that does so. And indeed expenditure which benefits 
the country is not directly the subject of my thought. Yet it is 
plain that though productive expenditure may benefit the country, 
it need not be the only form of expenditure to do so ; and hence 
expenditure on art, though not productive, may be of benefit to 
the country for some other reason. Yet my conclusion would only 
be justified if I knew every reason why expenditure could benefit 
the country, and knew that none of them applied to expenditure 
on art : whereas my major premiss mentions one ground, and not 
the sole ground, on which expenditure is beneficial. It is therefore 
true in effect to say that in the conclusion I treat as referring to 
its whole extension information which was confined to a part of the 
extension of the major term ; though none the less the extension of 
the major term is not the proper subject of my thought. 1 ] 

There remain two rules which are corollaries of those already 
given, viz. 

7. From two particular premisses nothing can be inferred, and 

8. If either premiss is particular, the conclusion must be particular. 
The truth of these rules is not evident at first sight ; and they 

can only be established generally — i. e. without reference to mood 
and figure — by considering what combinations of premisses there are, 

1 Beginners imagine sometimes that the fallacy of illicit process is com- 
mitted, if a term which is distributed in the premiss is undistributed in the 
conclusion. This is not so. I must not presume on more information than 
is given me, but there is no reason why I should not use less. 

It will be noticed, therefore, that no particular conclusion can be vitiated 
by an illicit process of the minor term : and no affirmative conclusion by an 
illicit process of the major. 

T2 



276 AN INTRODUCTION TO LOGIC [chap. 

both of which, or one of them, is particular ; and it will then be 
seen either that there are not enough terms distributed in these 
premisses to warrant a conclusion at all ; or not enough to warrant 
an universal conclusion, i. e. one that distributes the minor term. 

If both premisses are particular, they must either be both affirma- 
tive (7 and 7), or both negative (0 and 0), or one affirmative and the 
other negative (7 and 0). But in a particular affirmative propo- 
sition neither subject nor predicate is distributed ; so that the 
combination of premisses 77 contains no distributed term, and 
therefore — since the middle term must be distributed if any infer- 
ence is to be drawn — will yield no conclusion. From 00, two 
negative propositions, a conclusion is impossible. From I and 0, if 
there were any conclusion, it would be negative ; but as the predi- 
cate of a negative proposition is distributed, the major term (the 
predicate of the conclusion) would be distributed in the conclusion ; 
therefore the major term should be distributed in its premiss ; and 
since the middle term must be distributed in the premisses also, we 
require premisses with two terms distributed in them, to obtain 
a conclusion ; now the combination of a particular affirmative with 
a particular negative provides only one distributed term, viz. the 
predicate of the latter (0) ; and therefore from them also a conclu- 
sion is impossible. 

A similiar line of reasoning will establish rule 8 ; no combina- 
tion of premisses, whereof one is particular, contains enough dis- 
tributed terms to allow of an universal conclusion. For again, 
either both are affirmative (A and 7), or both negative (E and 0), or 
one affirmative and the other negative (A and : E and 7). The 
two negative premisses may be struck out as before. The combina- 
tion of A with 7 contains only one distributed term, the subject of 
the universal affirmative (.4) ; and as the middle term must be 
distributed if the reasoning is to be valid, the subject of A must be 
the middle term ; hence the minor term will be one of those that 
are undistributed in the premisses, and therefore also in the conclu- 
sion (of which it is the subject) it must be undistributed — i. e. the 
conclusion must be particular. The combinations A and 0, E and 7 
both contain two distributed terms ; viz. in the former the subject 
of the universal affirmative and the predicate of the particular 
negative, in the latter the subject and predicate of the universal 
negative ; but both of them require negative conclusions, in which 
the major term is distributed ; in both therefore the terms distri- 



xii] MOODS AND FIGURES OF SYLLOGISM 277 

buted in the premisses must be the major and middle, and the 
minor term be one of those that are undistributed, so that the 
conclusion again will be particular. 
The above rules are all contained in four rude hexameter lines : 

Distribuas medium, nee quartus terminus adsit ; 
Utraque nee praemissa negans, nee particularis ; 
Sectetur partem conclusio deteriorem ; 
Et non distribuat, nisi cum praemissa, negetve. 

The third line (that the conclusion must conform to the inferior 
part of the premisses) covers both the fourth and eighth rules ; a 
negative being considered inferior to an affirmative, and a par- 
ticular to an universal judgement. The fourth line (that the 
conclusion must not distribute any term, unless the premiss does 
so, nor be negative unless a premiss is so) gives the sixth rule, 
and the fifth. 

D. Determination of the moods valid in the several figures. 

We have seen that syllogisms are distinguished in mood accord- 
ing to the quantity and quality of the propositions composing 
them ; and in figure according to the position of the middle term 
in the premisses. The validity of a syllogism, and the character of 
the conclusion that can be drawn, depend very largely on the dis- 
tribution of the several terms — middle, major, and minor — in the 
premisses ; and this again on the question whether the middle term 
is subject, and one of the others predicate, in a premiss, or vice 
versa. Hence a combination of premisses which yields a conclusion 
in one figure, may yield none in another : e.g. All M is P, All S is 
M yields the conclusion All S is P ; but All P is M, All S is M 
yields no conclusion, though the quantity and quality of the pre- 
misses are unchanged. We shall therefore have to take the possible 
combinations of premisses in each figure in turn, strike out those 
which yield no conclusion in that figure, and ask what kind of 
conclusion — i. e. whether universal or particular l — the others yield 
in it. 

Now as there are four kinds of proposition, so far as quantity 

1 For this depends on the distribution of terms in the premisses, which 
varies according to the figure : whether the conclusion is affirmative or 
negative depends on whether both premisses are affirmative or not, a point 
which can be determined without asking where the middle term stands, i. e. 
what the figure is. 



278 AN INTRODUCTION TO LOGIC [chap. 

and quality are concerned — A, E, I, and — and our premisses must 
be two in number, there are sixteen combinations of premisses 
mathematically possible. 

These combinations are as follows, the premisses being indicated 
by the conventional vowels, and the major premiss in all cases by 
the vowel which stands first. 



AA 


EA 


IA 


OA 


AE 


EE 


IE 


OE 


AI 


EI 


II 


01 


AO 


EO 


10 


00 



It is not however necessary to try the validity of all these sixteen 
combinations in each figure in turn ; for four can be seen to yield 
no conclusion on a ground holding in all figures alike, without 
reference to the position of the middle term, viz. those wherein both 
premisses are negative, EE, EO, OE, 00. Four more are excluded 
by the rules just given, viz. (i) II, 10, 01 (as well as 00 again) on 
the ground that both premisses are particular, and (ii) IE, on the 
ground that it involves illicit process of the major term ; for since 
one premiss is negative, the conclusion would be negative, and so 
distribute the major term, while the major premiss, being a particular 
affirmative, would not distribute that term, whether it were subject 
in the premiss or predicate. But the inconclusiveness of these four 
combinations cannot be rightly understood, as that of combinations 
of two negative premisses can be, without taking examples in the 
several figures : the rules from whose truth it follows being them- 
selves a generalization of what we discover in so doing. 

There remain eight combinations of premisses, not excluded by 
any general rule, on whose validity we cannot pronounce without 
reference to the figure and the position of the middle term, viz. 

AA AE AI AO EA EI IA OA 

It will be found that four of them are valid in the first figure, 
four in the second, and six in the third ; there are also five indirect 
moods of the first, or moods of the fourth, figure : making in all 
nineteen moods. 

In the first figure, the middle term is subject of the major premiss 
and predicate of the minor : hence in this figure M P 

1 . The minor premiss must be affirmative : for if it were S M 

negative, the conclusion would be negative, and so distri- 8 P 



xnj MOODS AND FIGURES OF SYLLOGISM 279 

bute the major term P ; the major term must therefore be distri- 
buted in the major premiss ; but as it is there predicate, it cannot 
be distributed unless the major premiss is also negative (since 
no affirmative proposition distributes its predicate) : we should 
thus have two negative premisses, or else an illicit process of the 
major term. 

2. The major premiss must be universal : for since the minor is 
affirmative, its predicate M, the middle term, will be undistributed ; 
therefore M must be distributed in the major premiss ; and for this 
purpose the major premiss, of which it is the subject, must be 
universal. These rules however do not hold for the indirect 
moods. 

In this figure, therefore, the premisses AE, AO are invalid, by 
rule 1 : I A, OA by rule 2 x ; A A, EA, AI, EI are valid. The 
conclusions which they yield will be respectively A (universal 
affirmative), E (universal negative), / (particular affirmative), and 
(particular negative) ; and the moods — in which the quantity 
and quality of the conclusion are indicated, as well as of the pre- 
misses — are AAA, EAE, AH, ElO. Their names are Barbara, 
Celarent, Darii, Ferio. But in the first three of these moods, as we 
have seen, the converse conclusions can also be drawn ; and with 
the premisses AE, IE, a particular conclusion follows denying 8 of 
P ; and so we get also the indirect moods AAI, EAE, AH, AEO, 
IEO, whose names are Baralipton, Celantes, Dabitis, Fapesmo, 
Frisesomorum. 

In the second figure the middle term is predicate in both P M 
premisses : hence in it 8 M 

1. One premiss must be negative, for otherwise the middle 8 P 
term would be undistributed. 

2. The major premiss must be universal : for since one premiss is 
negative, the conclusion will be negative, and so distribute the major 
term P : P must therefore be distributed in the major premiss ; 
i. e. as it is here the subject thereof, the major premiss must be 
universal. 

Hence the premisses AA, AI, IA are invalid, by rule 1 : the 

1 e. g. from the premisses Contemporary evidence is of great historical value, 
Tradition is not (or Some inscriptions are not) contemporary evidence, it cannot 
be inferred that Tradition is not (or Some inscriptions are not) of great historical 
value (AE, AO) : from the premisses Some pointed arches are (or are not) four- 
centred, All Gothic arches are pointed, it cannot be inferred that All Gothic 
arches are (or are not) four-centred (I A, OA). 



280 AN INTRODUCTION TO LOGIC [chap. 

premisses OA (and I A again) by rule 2 x ; EA, AE, EI, AO are valid. 
The moods are therefore EAE, AEE, EIO, AOO ; their mood-names 
are Cesare, Camestres, Festino, and Baroco. 

In the third figure the middle term is subject in both M P 
premisses : hence in it MS 

1 . The minor premiss must be affirmative, for the same reason 8 P 
as in Fig. 1 (the major term, in both figures, being similarly placed 
in its premiss). 

This rule excludes the premisses AE, AO 2 : the remaining com- 
binations, A A, AI, EA, EI, I A, OA, are valid. But because the 
minor term in this figure is predicate of the minor premiss, and the 
latter is affirmative, the minor term will not be distributed in it ; 
hence it must not be distributed in the conclusion ; and therefore in 
all cases 

2. The conclusion will be particular. 

The moods are consequently AAI, All, EAO, EIO, IAI, OAO : 
their mood-names are Darapti, Datisi, Felapton, Ferison, Disamis, 
Bocardo. 

[It is impossible at this point to pass over the so-called fourth 
figure. We have seen above (pp. 268-269, 279) that in the first 
figure, besides the four direct moods, there are five ' indirect ' 
moods, i. e. moods in which the conclusion affirms or denies the minor 
term of the major. In so describing these moods, we base the dis- 
tinction of major and minor terms on their meaning ; the major 
term is the more comprehensive ; it signifies the general nature of, 
or some element in, the being of that real subject which the minor 
term stands for. If we consider ' terms of thought ' we may say 
that the minor is characterized by the major, not vice versa. This 
relation is natural between two terms, when (as in Fig. 1) we can find 
a middle term predicable of one of them, and the other of it. But 
two terms of which the same predicate may be respectively affirmed 
and denied (as in Fig. 2), or which may be affirmed, or respectively 
affirmed and denied, of the same subject (as in Fig. 3), need stand in 
no such relation. And if this relation is ignored, and being major 
or minor term is made to consist barely in being predicate or subject 
of the conclusion, then we cannot describe any mood as affirming or 

1 e.g. from Some (or All) daisies have a great number of flowers within 
a single calyx, All (or Some) compositae have a great number of flowers within 
a single calyx it cannot be inferred that Some, or All, compositae are daisies 
{A A, AI, I A) : nor from Some annuals are not (or are) hardy, All poppies are 
hardy, that Some poppies are not (or are) annuals {OA, IA). 

2 e. g. from the premisses All ostriches have wings, No ostriches can (or 
Some ostriches cannot) fly, it cannot be inferred that No creatures that can fly 
have wings or that Some creatures that can fly have no wings {AE, OA). 



xn] MOODS AND FIGURES OF SYLLOGISM 281 

[denying in its conclusion the minor of the major. Instead therefore 
of the scheme J 

(1) M P What is sensible is in the mind 
S M Material things are sensible 

.•. P S .'. Some things in the mind are material thinga 

we must have the scheme 

(2) P M Material things are sensible 

M S What is sensible is in the mind 
••. S P .*. Some things in the mind are material things. 

Aristotle, as already remarked, did not recognize a fourth figure, 
but he recognized the possibility of concluding indirectly in the first 
figure, though not as a thing peculiar to the first. In one place he 
says 2 : ' It is clear that in all the figures, when there is no [direct] 
syllogism, if both premisses are affirmative or both negative nothing 
at all necessarily follows, but if one is affirmative and one negative, 
and the negative is universal, a syllogism always arises with the 
minor as predicate to the major : e. g. if all or some B is A, and no 
C is B : for, the premisses being converted, it is necessary that some 
A is not C. And similarly in the other figures ; for by means of 
conversion a syllogism always arises.' This covers the moods 
Fapesmo and Frisesomorum in Fig. 1. Elsewhere he points out 
that ' whereas some syllogisms are universal [in their conclusion] 
and some particular, those which are universal always have more 
conclusions than one ; of those which are particular, the affirma- 
tive have more conclusions than one, but the negative have 
only the [direct] conclusion. For the other propositions convert, 
but the particular [negative] does not ' 3 . He means that any syllo- 
gism concluding to E, No $ is P t gives also, by conversion of that, 

1 It will be noted that the real terms indicated by 8 and P respectively 
in (1) are indicated by P and 8 in (2), because in (1) S and P symbolize 
minor and major in the sense of less and more comprehensive, in (2) minor 
and major in the sense of subject and predicate of the conclusion, and what 
is minor in the former sense is major in the latter, and vice versa. 

Anal. Pri. a. vii. 29 a 19 ArjXov 8( na\ on iv anao~i to'is o~X'IH- a<riv > orap pi) yiprjTai 
ovWoyiapos, KaTT]yopiKa>v p.ev r} o~T(pr]Tiica>v dp<portpo>v ovru>v tg>v opcav ovbev o\ws 
yiverai avayKalnv, KaTrjyopacov 8e kcl\ are prjriKoii, KadoKov \Tj<pdevros tov o-TfprjriKou 
aei yivfrat avWoyiafios tov fXarrovos anpov npos to /uetfov, olov d to pei> A navri 
Ta B t] Tivi, to be B fir/oevi tw r* dvTicrrptfpofj.fi'av yap tu>v irpoTa.o~i<&v avaynq to T 
Ttvl to) A p.rj vnapx*iv. Sfioicos Be Kan\ Tutv ertpo&v o~xrnjniT<x>v' a*\ yap yiftrat 8ia 
rfj? dvTio-Tpo<f)r]i o-v\Xoyio-p.6s. It is plain that otuv pt} yivr)Tai avWoyio-pos 
means ' when there is no direct syllogism '. 

3 Anal. Pri. j3. i. 53 a 3 eVe l 8' ol piv Ka66\ov ratv avWoyio-pcov tlo~\v ol &e Kara 
pepos, ol pev KadoXov Tvavra del irXelto o-v\\oyl£ovTai, to>v d' iv pepti ol ptv Karrj- 
yoptKol nkfitOf ol 8 djrocpaTiKol to avpnepaapu povov. al pev yap aWai Trpordafis 
di/Tio~rpf<j)ovo-iv, rj 8e o-TfptjTiK?) ov< avTio-rpe'cpei. What Aristotle says here 
would cover the Subaltern Moods (cf. p. 285, infra) ; but he had not got 
them in his mind ; he would not have regarded them as drawing a different, 
but part of the same, conclusion. 



282 AN INTRODUCTION TO LOGIC [chap. 

[the conclusion No P is S, and any concluding to A or I, All S is P 
or Some S is P, gives also the conclusion Some P is S. We have 
therefore here a recognition of the possibility of the other three 
indirect moods of Fig. 1, Baralipton, Celantes, and Dabitis : whose 
conclusions are merely the converse of those which follow directly 
from the same premisses in Barbara, Celarent, and Darii. 

These observations are applied to all three figures, because 
Aristotle thought that in the second and third also the major and 
minor terms, though not distinguishable, as in the first, by having 
different positions in the premisses, could yet be distinguished by 
their meaning, so that we could tell whether a syllogism concluded 
directly or indirectly, and distinguish, e. g., between concluding 
directly in Camestres and indirectly in Cesare, or directly and 
indirectly in Darapti. And sometimes this may be done. To 
be rock is of the being of all granite, to be granite is not of the 
being of all rock ; hence ' rock ' and ' granite ' are by their meaning 
relatively major and minor. Now from the premisses 

Some rocks are sedimentary 
Granites are not sedimentary 

I cannot conclude that Granites are not rocks ; but I can conclude, 
indirectly, that Some rocks are not granites. Again, in gases 
lighter than air, to be lighter than air is a character of the gas, not 
vice versa ; hence from the premisses 

Steam and hydrogen are lighter than air 
Steam and hydrogen are gases 

the natural conclusion is that Some gases are lighter than air, 
though the converse, that Some things lighter than air are gases, 
also follows. But often enough in the second and third figures 
there is nothing in their meaning to make us regard one of two 
terms as major and the other as minor, rather than vice versa, and 
then their position in the conclusion must be taken to decide it. And 
if we make that decide it always, there is still no syllogism in Figs. 2 
and 3 which cannot formally be referred to one of the direct moods. 
The above example in Fig. 2 may be treated as in Festino, thus : 

Granites are not sedimentary 
Some rocks are sedimentary 
.*. Some rocks are not granite 

and with premisses A and E in Fig. 2, according as the subject of 
A or of E is predicate in the conclusion, the syllogism may be referred 
to Camestres or to Cesare ; for each mood yields the converse of the 
conclusion of the other. From the premisses 

Spiders have eight legs 
Insects have not eight legs 



xn] MOODS AND FIGURES OF SYLLOGISM 283 

[it is more natural to conclude in Cesare that Spiders are not insects 
than in Camestres that Insects are not spiders, because ' insect ' is 
a more generic term than ' spider '. But whichever conclusion is 
drawn, the syllogism can be referred to a mood whose form covers it. 
So with Fig. 3, which has no universal conclusions ; an indirect 
syllogism with premisses A A still has the form of Darapti, an indirect 
syllogism with Al or I A the form of Datisi or Disamis. But in 
Fig. 1 it is otherwise. Here, if we draw the indirect, or converse of 
the direct, conclusion in Barbara, Celarent, or Darii, we cannot by 
transposing the premisses make the premiss containing the predicate 
of the indirect conclusion the major premiss, and yet preserve the 
scheme of the figure, because in this figure the middle term has not 
the same position in both premisses, and their transposition alters 
the position of it, and so, if the figure of a syllogism is determined 
by the position of the middle term, alters the figure also. And if from 
the premisses AE or IE, which have no direct conclusion in this 
figure, we draw the indirect conclusion, and therefore treat E as 
major premiss because containing the predicate of the indirect 
conclusion, again the middle term becomes predicate and the minor 
subject of its premiss, and the scheme of the figure is altered. Thus 
it is easy to see why the indirect moods of Fig. 1 came to be regarded 
as belonging not to Fig. 1 at all, but to a separate fourth figure. 
For in many syllogisms of Figs. 2 and 3 there is nothing to settle 
which shall be called the major and which the minor term but their 
position as predicate or subject of the conclusion. And settling it 
thus, we do not need to admit indirect moods in these figures. Only 
those syllogisms then remain outstanding which in Fig. 1 from pre- 
misses that admit of no direct conclusion draw indirect conclusions, 
or from premisses that yield direct conclusions draw the converse 
of those. These syllogisms, if the distinction of major and minor 
terms is still made to depend on their position in the conclusion, do 
not belong to the scheme of Fig. 1, and a fourth figure is therefore 
instituted, in which the middle term is predicate in the major 
premiss and subject in the minor. 

That what Aristotle notices about the three figures generally, in 
the passages quoted above, works out rather differently in the 
first and in the other two was very early noticed ; and an explicit 
recognition of the five indirect moods as supplementary moods of 
Fig. 1 is attributed to his pupil and successor in the Lyceum, Theo- 
phrastus. 1 If Averroes is right in saying that Galen was the first to 
regard them as belonging to a distinct figure, 2 the view of Theo- 
phrastus held the field for some five centuries. Averroes himself 

1 v. Prantl, i. 365, Abschn. v. Anm. 46, where the passages from 
Alexander, who ascribes the addition of these moods to Theophrastus, are 
quoted. 

a Prantl, i. 570-574. 



284 AN INTRODUCTION TO LOGIC [chap. 

[disagreed with Galen, and in this he was followed by Zabarella, 1 
one of the best of the scholastic commentators on Aristotle, whose 
De Quarta Figura Syllogismi Liber is still worth reading on the sub- 
ject ; though in the reason he gives for not regarding the Galenian 
as really a fourth and independent figure he relies in part upon the 
questionable analysis which regards all syllogism as an application 
of the principle called the Dictum de omni et nullo (cf . infra, p. 296). 
The real objection to Galen's view is that it implies a defective 
insight into the character of the thinking in these forms of argument, 
and treats the syllogism too much as a matter of verbal manipulation. 
In the fourteenth chapter an endeavour is made to explain the 
grounds on which this verdict rests. The external and mechanical 
way of regarding syllogism, which underlies the reference of these 
moods to a fourth and separate figure, finds what is hardly more 
than its logical issue in some of the later scholastic writers, who 
erect separate moods on no better ground than the order in which 
the premisses are enunciated, without there being any actual 
difference in the premisses or conclusion. 2 

Granted, however, that we are to acknowledge a fourth figure, 
the following will be the special rules of it : it must be remembered 
that as referred to this figure we call that premiss the major which as 
referred to the first figure we should call the minor, and vice versa. 

1. 7/ either premiss is negative, the major must be universal : for if 
either premiss is negative, the conclusion must be negative, and 
will distribute the major term ; which in this figure is subject of 
the major premiss ; and if it is to be distributed there, the premiss 
must be universal (cf. Fig. 2). 

2. If the major premiss is affirmative, the minor must be universal : 
for the middle term, as predicate of an affirmative proposition, will 
not be distributed in the major premiss ; it must therefore be dis- 
tributed in the minor premiss, where it is subject ; and therefore 
the minor premiss must be universal. 

3. If the minor premiss is affirmative, the conclusion will be par- 
ticular : for the minor term, as predicate of an affirmative proposi- 

1 And by others, e.g. Lambert of Auxerre, thirteenth century med., quoted 
Prantl, iii. 30, Abschn. xvii. Anm. 121. 

2 e.g. Petrus Mantuanus, quoted Prantl, iv. 178. Petrus, in the edition 
of his Logica dated 1492, gives as an example of a syllogism in Cesare, 
' Nullus homo est lapis, omne marmor est lapis, igitur nullum marmor est 
homo '. If the conclusion drawn from the premisses enunciated in this order 
is ' Nullus homo est marmor ', he calls the mood Cesares ; but were they 
enunciated in the opposite order, and the latter conclusion drawn, he would 
call it Camestres. By such and other even more questionable methods, 
Petrus compiles fifteen moods in Fig. 1, sixteen in Fig. 2, eighteen in Fig. 3, 
and eleven in Fig. 4. Cf . also Crackenthorpe, Logicae Libri Quinque, Oxoniae, 
1670, p. 197, who appears to treat the moods of Fig. 4 and the indirect 
moods of Fig. 1 as two different things. 



xh] MOODS AND FIGURES OF SYLLOGISM 285 

[tion, will not be distributed in the premiss, and so must not be 
distributed in the conclusion, which will therefore be particular. 

Hence the premisses OA are invalid by the first rule : A I and AO 
by the second x ; A A, AE, EA, EI, I A are valid ; but A A will afford 
only a particular, instead of an universal, conclusion. The moods 
are thus AAI, AEE, EAO, EIO, IAI ; and their mood-names, aa 
moods of the fourth figure, are Bramantip, Camenes, Fesapo, 
Fresison, Dimaris. 

The complete memoria technica, with the fourth figure replacing 
the indirect moods of the first, is commonly given in English text- 
books nowadays as follows 2 : — 

Barbara Celarent Darii Ferioque prioris ; 
Cesare Camestres Festino Baroco secundae ; 
Tertia Darapti Disamis Datisi Felapton 
Bocardo Ferison habet ; quarta insuper addit 
Bramantip Camenes Dimaris Fesapo Fresison. 
Quinque subalterni, totidem generalibus orti, 
No men habent nullum, nee, si bene colligis, usum. 

The meaning of the last two lines is explained in the next 
paragraph.] 

It will be noticed that in five out of these nineteen moods the 
conclusion is universal, viz. in Barbara and Celarent in Fig. 1, Cesare 
and Camestres in Fig. 2, and Celantes in Fig. 1 ( = Camenes in Fig. 4). 
It is, of course, possible a fortiori to draw the particular, or subal- 
tern, conclusion in any of these cases ; and the syllogism is then 
said to have a weakened conclusion, or to be in a subaltern mood. 
Subaltern moods would be used by no one who was asking what 
could be inferred from given premisses ; for it is as easy to see that 
the universal conclusion, as that the particular, can be drawn from 

1 e.g. from the premisses Some change is not motion, All motion is change, 
it cannot be inferred that Some cha?ige is not change {OA) : nor from All 
great critics are scholars, Some scholars are pedants, that Some pedants are 
great critics (AI) : nor from All members of the Government belong to the party 
in power, Some of the party in power are not in the Cabinet, that Some of the 
Cabinet are not members of the Government (AO). 

2 I have not been able to trace this form of the mnemonic verses any 
further back than to Aldrich's Artis Logicae Eudimenta. A good many 
writers have tried their ingenuity in devising variations upon the original 
lines. Watts has a version recognizing only fourteen moods, the indirect 
moods of Fig. 1 appearing neither in that capacity nor as moods of Fig. 4. 
Sir William Hamilton (Discussions, p. 666) also offers ' an improvement of 
the many various casts of the common mnemonic verses '. But the reader 
will probably wish for no more. In various modern textbooks, Baroco and 
Bocardo are spelt with a k, in order that c medial may not occur with 
a different meaning from c initial. 



286 AN INTRODUCTION TO LOGIC 

them. But in seeking for the proof of some particular proposition, 
we might very likely find premisses that would really prove the 
universal ; yet, since we are only using them to prove the particular, 
our reasoning would fall into one of the subaltern moods. Still, we 
should see that our premisses proved more than we had set out to 
establish, and substitute at once the wider thesis ; the subaltern 
moods are therefore of little importance, and are not included in the 
enumeration of valid moods of syllogism. 

[It would have been possible to determine what moods are possible 
in each figure, without enunciating the special rules (as they are 
called) of the different figures. It might merely have been pointed 
out, e. g., that in the first figure AA would yield an A conclusion, 
AE involve an illicit process of the major term, AI yield an I 
conclusion, AO again involve an illicit process of the major, EA 
yield an E, and EI an conclusion, I A and OA involve an undistri- 
buted middle. And if it were asked why the mood IAI is invalid 
in this figure, the proper answer is not because in the first figure 
the major premiss must be universal (though that is the second rule 
of this figure), but because such a combination of premisses in it 
involves an undistributed middle ; the rule being directed to 
avoiding this fallacy, and not the fallacy condemned because it 
breaks the rule. The rules, however, if the grounds on which they 
rest are understood, give in a general form the principles which must 
be observed in each particular figure. Therefore the knowledge of 
these rules helps us to master the theory of syllogism ; but only if 
their grounds are understood. It is better to know what moods are 
invalid in each figure, and what fallacy they severally commit, than 
to know the special rules and apply them in a mechanical manner, 
without being able to justify them.) 



CHAPTER XIII 

OF THE REDUCTION OF THE IMPERFECT 
SYLLOGISTIC FIGURES 

Aristotle distinguished between syllogisms which were only 
valid (bwaToc) and syllogisms which were perfect (re'Aetot). In the 
latter, the necessity of the inference appeared sufficiently from the 
premisses as they stand ; in the former, they required to be supple- 
mented, in order that it might be seen. The second and third 
figures, in his view, were in this plight. Their validity, though 
real, needed proving, by means of the first figure. By converting 
one of the premisses in the two imperfect figures, he showed that we 
might obtain a syllogism in the first or perfect figure, either with 
the same conclusion or with one from which that could be recovered 
by conversion ; where this direct method of validating an imper- 
fect mood fails, we can still validate it indirectly, by proving, in 
a syllogism of the first and perfect figure, that the falsity of its 
conclusion is inconsistent with the truth of its premisses. 1 

The process of exhibiting by the help of the first figure the validity 
of syllogisms in the other two (or three) is called Reduction. A 
knowledge of the method of reducing the imperfect moods to moods 
of the first figure belongs to the traditional part of the theory of 
syllogism. The present chapter will explain this ; in the next we 
must ask whether the process of Reduction, sanctified by the tra- 
dition of many centuries, is really necessary, in order to validate 
the imperfect figures. 

Directions for Reduction are concealed in the mood -names of 
4 Barbara Celarent '. Those who have thoroughly mastered the 
theory of syllogism will see at a glance how a given imperfect mood 
may be reduced ; but the mood-name enables one to do it, as it were, 
with a mechanical correctness. 

1 This method of establishing the validity of a syllogism per impossibile is 
applicable to all the imperfect moods ; but the direct method was preferred 
where it is available. 



288 AN INTRODUCTION TO LOGIC [chap. 

Reduction, as already stated, is either direct or indirect. Direct 
Reduction of an imperfect mood to the first figure consists in 
showing that from premisses either the same as in the original 
syllogism, or inferred immediately by conversion from these, the 
original conclusion, or one from which it can be immediately inferred, 
follows in the first figure. 

As the figures are distinguished from one another by the position 
of the middle term in the premisses, it is plain that, to reduce a 
figure from one of the imperfect figures to the first, we must alter the 
position of the middle term. In the second and third figures, it 
occupies the same position in both premisses, being predicate in the 
second, and subject in the third, whereas in the first figure it is 
subject of the major premiss and predicate of the minor. We must, 
therefore, convert one premiss of a syllogism in the second or third, 
in order to reduce it to the form of the first. In the second we should 
naturally convert the major, for there it is in the major premiss that 
the middle term is out of place ; in the third, the minor. But it 
may happen that this would give us a combination of premisses 
which, in respect of quality and quantity, cannot stand ; e. g. in a 
syllogism in Disamis (Fig. 3), by converting the minor premiss A, we 
should get the combination II, which yields no conclusion. We 
therefore have sometimes to transpose the premisses, making our 
original minor premiss the major, and vice versa, and converting in 
the second figure that which becomes the major, in the third that 
which becomes the minor. Where the premisses are transposed 
to make a syllogism in the first figure, they will give a conclusion 
in which the terms of the original conclusion have been transposed 
likewise ; and it will be necessary to convert this conclusion in order 
to recover that of the original ' imperfect ' syllogism. 

By way of illustration, we may take the following example in 

Camestres, the form of which, as indicated by the vowels of the 

mood-name, is 

All P is M 

No S is M 

.'. No S is P 

If we were to argue that a spider is not an insect because it has not 
six legs, our argument would fall quite naturally into the above form : 

Insects have six legs 

The spider has not six legs 
.*. The spider is not an insect. 



xin] REDUCTION OF THE IMPERFECT FIGURES 289 

Now if we want to get the same conclusion in the first figure, we 
cannot convert the major premiss ; for that would give us a parti- 
cular major 

Some animals with six legs are insects 

and no conclusion as to whether a spider is an insect or not would 
follow. 1 We must therefore convert the minor premiss, which 
being E can be converted without change of quantity : and trans- 
posing at the same time, form the syllogism in Celarent : 

No animal with six legs is a spider 

Insects have six legs 
.*. No insect is a spider 
From this conclusion we can recover by conversion the original 
conclusion 

The spider is not an insect 

Had our argument run slightly differently, to the effect that the 
spider is not an insect because it has eight legs, it would have fallen 
into a syllogism in Cesare : 

No insect has eight legs No P is M 

The spider has eight legs All S is M 

.'. The spider is not an insect .'. No 8 is P 

Here the major premiss can be converted simply, being E :' ana 
transposition is not required. The premisses 

No animal with eight legs is an insect 
The spider has eight legs 
conform to Celarent, and yield at once the original conclusion. 

The indirect moods of the first figure (the moods, as others regard 
them, of the fourth figure) fall into two groups, when we wish to 
show that their conclusions (or others yielding them by conversion) 
can be obtained directly in the first figure from the same premisses 
(or from premisses which these yield by conversion). Three, 
Baralipton, Celantes, and Dabitis, simply draw the converse of the 
conclusion which the same premisses yield directly in the first 
figure ; all we have to do therefore is to draw the direct conclusion 
and convert it. But Fapesmo and Frisesomorum yield no direct 
conclusion. From the premisses 

Every soldier serves his country 
Women are not soldiers 

1 Though it would follow by an ' indirect conclusion ' in Frisesomorum 
that some insects are not spiders. 

1779 U 



290 AN INTRODUCTION TO LOGIC [chap 

I cannot infer that Women do not serve their country. The only 
conclusion is that Some who serve their country are not women. 
Now if this is to have the form of a direct syllogism in the first 
figure, women must be the major term, soldiers the minor : but if 
' Women are not soldiers ' were the major, and ' Every soldier serves 
his country ' the minor premiss, the terms would occupy the wrong 
positions in the premisses. To obviate this, I must convert both 
premisses ; then indeed I shall get the syllogism 

No soldier is a woman 
Some who serve their country are soldiers 
.*. Some who serve their country are not women 

which does prove my original conclusion in a direct mood of the 
first figure, Ferio ; though whether it is the most natural way of 
removing any doubts I may have had about the validity of the 
indirect inference in Fapesmo must be considered in the next chapter. 

[If these moods, instead of being regarded as belonging to the 
first figure, are placed in a fourth, their reduction will be formally 
a little different. To reduce the first three, we shall simply have 
to draw the conclusion which naturally follows from the same 
premisses in the first figure, and then convert it ; but this will now 
be said to involve transposition of the premisses ; for what is major 
regarded as in the fourth figure is minor regarded as in the first, 
and vice versa : thus 

Fig. 4. Bramantip. Fig. 1. Baralipton. 

Men of stout heart are free The free are happy 

The free are happy x Men of stout heart are free 

.•. Some who are happy are of stout heart 

The premisses in Baralipton are premisses in Barbara ; those in 
Bramantip are not so, till they are transposed. 

On the other hand, in the last two moods only conversion and not 
transposition will now be necessary ; for the fourth figure already 
regards the universal negative premiss in Fesapo or Fresison 
(= Fapesmo or Frisesomorum) as the major, because it contains 
the term which is predicate in the conclusion, though it is subject 
in the premiss ; conversion will bring it to the position which the 
major term should hold in its premiss in the first figure ; and so 
with the minor ; and our original conclusion then follows in Ferio.] 

Whether, in reducing a syllogism of any imperfect mood, the 
premisses need transposing ; which, if any of them, must be con- 

1 to (v8ai{iop to iXtiidepov, to $' theiiOtpov to ev\j/v\ep KpLvavTfs, Thuc. ii. 43. 



xm] REDUCTION OF THE IMPERFECT FIGURES 291 

verted ; whether we have to convert the conclusion obtained in the 
syllogism of reduction, in order to recover the original conclusion ; 
and in which mood of the first figure the validating syllogism will 
be — all these matters are indicated by the consonants of the mood- 
names. The significant consonants 1 are : 

1. the initial, always the same as that of the mood in Fig. 1 to 
which the imperfect mood must be reduced. 

2. m (= muta), which indicates that the premisses must be 
transposed. 

3. s (= simpliciter), which indicates that the premiss, or con- 
clusion 2 , signified by the preceding vowel must be converted simply. 

4. p ( = per accidens), which indicates that the same must be 
converted by limitation. 

5. c ( = conversio syllogismi), which, occurring medially, indicates 
that we must employ the process of Indirect Reduction, to be 
explained immediately. 

In order to illustrate the mechanical use of these instructions, 
it will be enough to work out in symbols the reduction of a single 
mood, Disamis. That, as the mnemonic tells us, is in Fig. 3 ; the 
middle term is therefore subject in both premisses. The major, 
being indicated by /, is a particular affirmative, and the minor, 
being indicated by A, an universal affirmative ; the conclusion 
similarly a particular affirmative. Our syllogism is therefore to be 
of the type : — 

Some M is P / 

All M is 8 A 

.'. Some 8 is P I 

In reducing it, the m of the mood-name indicates that we must 
transpose the premisses, and the s that we must convert simply the 
premiss indicated by the vowel after which it stands ; the D that 
we shall so obtain a syllogism in Darii, thus : — 

All M is S 
Some P is M 
:. Some P is 8 

1 Except the initials, these are explained in the old lines — 

Simpliciter verti vult 8, P verti per acci, 
M vult transponi, C per impossibile duci. 

If any one is horrified at the doggerel, he may be assured that much worse 
things could have been quoted in earlier chapters. 

2 i. e. not the conclusion of the original syllogism (which has to be obtained 
again as it stood), but the conclusion of the validating syllogism. 

U2 



292 AN INTRODUCTION TO LOGIC [chap. 

The simple conversion of this conclusion, enjoined by the s after 
the third vowel in Disamis, gives us 

Some 8 is P 

This process of Direct Reduction cannot be applied to the two 
moods, Baroco and Bocardo. The reason is obvious. In order that 
the middle term may occupy a different position in the two pre- 
misses, as the first figure requires, one of the premisses in the second 
and third figures must be converted. In these moods, the premisses 
are an universal affirmative and a particular negative proposition. 
The latter, 0, cannot be converted either simply or per accidens ; 
the converse of A is J ; and so by converting that we should obtain 
two particular premisses. These syllogisms can, however, be 
validated by the process of Indirect Reduction. 

Indirect Reduction, or Reduction per impossible, consists in 
showing, by a syllogism in the first figure, against which no objection 
can be taken, that the falsity of the conclusion in the original 
syllogism is inconsistent with the truth of its premisses. This w 
done as follows : — 

Baroco is of the form 

All P is M All negroes have curly hair 

Some S is not M Some natives of Africa have not curly 

hair 
.*. Some S is not P .'. Some natives of Africa are not negroes 

Now if this conclusion is false, its contradictory will be true, i. e. 
that All natives of Africa are negroes. We can then combine this 
with our original major premiss to form a syllogism in Barbara, 
thus : — 

All P is M All negroes have curly hair 

All S is P All natives of Africa are negroes 

.*. All S is M .*. All natives of Africa have curly hair 

But the conclusion thus obtained contradicts the original minor 
premiss ; hence if the original premisses are true, the conclusion we 
drew from them cannot be false, and our original syllogism is there- 
fore valid. 

The method of reducing a syllogism in Bocardo is the same : 
except that here by combining the contradictory of the conclusion 
with the original minor we reach a result inconsistent with the 
original major premiss ; while in the former case, by combining 



xiii] REDUCTION OF THE IMPERFECT FIGURES 293 

it with the major, we deduced a conclusion contradictory of the 
minor. The medial c in the mood -name directs us to substitute for 
the premiss indicated by the vowel after which the c is placed the 
contradictory of the conclusion. 1 

[All the imperfect moods could be validated in this indirect 
manner 2 : take, e.g., Darapti — All M is P, All M is S .-. Some S is 
P; if this is false, then No 8 is P ; and All M is S ; .-. No M is P ; 
which is inconsistent with the truth of the original major premiss. 
The first figure, on the other hand, cannot be appealed to in order 
to confirm itself ; if we suppose its conclusion to be false, and com- 
bine the contradictory thereof with one of the premisses, it is only 
by a syllogism in the second or third figure that we can deduce 
a conclusion inconsistent with the other premiss ; e. g. in Barbara 
(All M is P, All 8 is M .-. All 8 is P) ; if the conclusion is false, then 
Some 8 is not P ; and All M is P ; .-. Some 8 is not M — which 
contradicts the original minor ; and again, Some 8 is not P, and 
All S is M .-. Some M is not P — which contradicts the original 
major ; but the arguments are in the second and third figures.] 

1 It is possible to validate the moods Baroco and Bocardo by the direct 
method, if we employ the processes of permutation, and conversion by 
negation. From Baroco we obtain a syllogism in Ferio, thus : Baroco, All 
P is M, Some 8 is not M .*. Some S is not P : Ferio, No not-M is P, Some S 
is not-Jf .". Some S is not P ; from Bocardo we obtain a syllogism in Darii : 
Bocardo, Some M is not P, All M is 8 .'. Some S is not P : Darii, All M is 
S, Some not-P is M .'. Some not-P is S .'. Some S is not P. Names have 
been given to the two moods in place of Baroco and Bocardo, by logicians 
who considered these methods of reduction to be preferable, in which the 
processes to be followed are indicated. These processes have been relegated 
to a note, and the names suppressed, because there is no purpose in burdening 
what may be called the mechanical part of the theory of syllogism with any 
fresh refinements. ' Barbara Celarent ' may be retained and explained, on 
historical grounds ; we need not add to it. On the other hand, the question 
as to whether the imperfect moods need validating, and if so, what is the 
most proper way of doing it, will be discussed in the next chapter. 

2 Though for Fig. 4 the syllogism which employs the contradictory of the 
original conclusion as one of its premisses will yield a conclusion contradicting 
the converse of one of the original premisses. 



CHAPTER XIV 

OF THE PRINCIPLES OF SYLLOGISTIC 
INFERENCE 

When I argue that because A=B and B = C, therefore A=C t 
my reasoning proceeds upon the same principle as when I argue 
that because X=Y and Y = Z, therefore X = Z. This principle is 
expressed in the familiar axiom that things which are equal to the 
same thing are equal to one another. In the particular inference, 
A=B, B = G .'. A=C, I do not deduce any conclusion from that 
axiom, as from a major premiss. It has indeed sometimes been 
contended that the argument is really syllogistic ; that it should 
be written 

Things equal to the same thing are equal to one another 
A and C are things equal to the same thing 
.'.A and C are equal to one another. 1 

But the following considerations will show that this is not the case. 
Firstly, we may appeal to an analogous argument, in which a quan- 
titative relation is established between A and C on the ground of 
the quantitative relations of both to B, although the quantities are 
none of them equal. If A is greater than B, and B is greater than 
C, A is greater than C. Are we to maintain that this inference 
should properly be written 

Things of which one is greater and the other less than the same 

thing are greater the one than the other 
A and C are things of which one is greater and the other less 
than the same thing 
.'. A and G are greater the one than the other ? 

The cumbrousness of this would be no reason for refusing to recog- 
nize it, if it were correct ; and if the other is correct, this must be. 
Yet where, as in this case, it requires some violence and ingenuity 
to give a quantitative inference the appearance of a syllogism, it is 

1 Euclid, for example, wrote under the impression that this is the right 
way of stating such an argument. 



PRINCIPLES OF SYLLOGISTIC INFERENCE 295 

not habitually done ; and since men have been content not to force 
into the form of syllogism the inference ' A>B, B>G .'. A>G ', 
it may be surmised that they would not have so dealt with the 
inference ' A = B, B = G .'. A = G ', if it had not been for the apparent 
ease of the transformation. But appearances may be deceptive ; 
and it must be noticed secondly, that in the syllogism which is 
supposed to represent the latter inference, viz. 

Things equal to the same thing are equal to one another 
A and C are things equal to the same thing 
.*. A and G are equal to one another, 

our minor premiss and our minor term are both faulty. The minor 
premiss is not a correct statement of the grounds of our inference ; 
these are, that A and G are both equal to B, and therefore the 
major required is ' Things equal to B are equal to one another \ 
And the minor term ' A and G ' is not really a subject of which we 
demonstrate an attribute ; it is two subjects, which are shown to 
stand in a certain relation to each other. Thirdly, and chiefly, the 
so-called major premiss is itself established through the so-called 
minor and its conclusion. It is because I see that if A and C are 
both equal to B, they are equal to one another, that I recognize the 
truth of the general principle or axiom. If I were incapable of 
recognizing the validity of the inference in the case of the three 
quantities A, B, and C, or X, Y, and Z, I should not be able to 
recognize the truth of the axiom. The axiom, therefore, is not one 
of the premisses from which we reason, when we argue that ' A=B 
and B = C .'. A = C ' : it is the principle in accordance with which we 
reason. If it were denied, the validity of any particular inference 
that conforms to it would be denied also ; its truth is therefore 
involved in that of the particular inferences. But a man may see 
the validity of the particular inference, without formulating the 
axiom. This would not be so, if it were really a suppressed major 
premiss, and ' A and G ' a true minor term. In the argument that 
' Silver is a good conductor because it is a metal ', every one recog- 
nizes that it is implied that ' All metals are good conductors ' ; and 
without this premiss, the grounds of the inference are not apparent. 
But no one requires any further grounds for inferring ' A = G ', 
than are contained in the premisses ' A=B and B = G '. 

We may therefore dismiss the attempt to reduce this argument 
to syllogistic form, and recognize in the axiom not a premiss but 



296 AN INTRODUCTION TO LOGIC [chap. 

the principle or canon of the argument. But the question then 
arises, whether there is similarly a principle or canon of syllogistic 
inference. Let us recall what was shown in Chapter XI, of which 
what has just been said is only a corollary. We there distinguished 
between an argument in which a relation of quantity was estab- 
lished between two terms, through their relation in quantity to 
a common third term : and an argument in which a relation was 
established between two terms in the way of subject and predicate, 
through their relation in that respect to a common third term ; the 
latter being syllogism. Now the axiom ' Things that are equal to 
the same thing are equal to one another ' is a principle of inference 
in the domain of quantity. It specifies no particular quantities, 
but states that two quantities will stand in a certain relation (of 
equality) to one another, if they stand in certain relations (of 
equality) to a third. May there not be a corresponding principle 
in syllogistic inference — one which specifies no particular terms, but 
states that two terms will be related to each other as subject and 
predicate in a certain way, if they are so related in certain ways to 
a third term ? 

Such a principle has been supposed to be furnished in the Dictum 
de omni et nullo ; and a consideration of this, and of other canons 
which have been proposed in its place, will throw a good deal of 
light on the nature of syllogistic inference, and the difference 
between its different types or figures. 

The phrase ' Dictum de omni et nullo ' is really a short title by 
which to refer to a principle too long to enunciate always in full ; 
just as we refer to statutes or papal bulls by their first word or two. 
The principle may be expressed thus — Quod de aliquo omni praedi- 
catur [dicitur, s. negatur], praedicatur [dicitur, s. negatur] etiam 
de qualibet eius parte : What is predicated [stated, or denied] about 
any whole is predicated [stated, or denied] about any part of that 
whole. 1 

1 I have quoted Zabarella's formulation of the Dictum de Omni, de Quarto 
Figura Syllogismi Liber, Opera Logica, Coloniae, 1597, p. 115 A. The words 
in square brackets are not his. There are numerous variants of no particular 
importance. Crackenthorpe (III. 16, p. 202 in ed. of 1670) gives ' Quidquid 
amrmatur (s. negatur) universaliter de aliquo, idem affirmatur (s. negatur) 
etiam de omni de quo illud praedicatur'. This form Beems (as Mansel 
remarks of Aldrich's) to be more nearly a translation of the passage in 
the Categories than of that in the Analytics. The formula 'quod valet 
de omnibus valet etiam de singulis ' (the reference for which I cannot now 
find) treats the major premiss nakedly as an enumerative judgement ; the 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 297 

If we take syllogisms in the first figure — and it is enough to 
consider Barbara and Celarent — the meaning of the principle will 

same view is implied in speaking of the middle term as a class, as e.g. 
Whately and Bain do. 

The passage in Aristotle from which the Dictum de Omni was primarily 
derived is Anal. Pri. a. i. 24 b 26-30 to 8e iv 5\a> tlvai trtpov ereptp ku\ to Kara 
navroi KaTT)yope't(T@ai darepov Bar tpov raiirov ttrriv. Xeyopev §« to Kara navrbs 
Karqyopela&ai, orav prjtiep jj Xaffelv ra>v mv vnoKfiptvov, Ka6 ov Bartpov ov 

\fxdt]<reTai' ko\ to Kara p.T]8ev6s ixravToos (' That one term should be contained 
in another as in a whole is the same as for one to be predicated of all 
another. And it is said to be predicated of all anything, when no part 
[ = logical part] of the subject can be found, of which the other term [the 
predicate] will not be true ; and to be predicated of none, similarly '). 
Aristotle is here explaining the meaning of expressions which he is about 
to use in the Analytics ; if mortal is predicated of animal or man Kara rrai>T6s, 
it means that there is no animal (e.g. man) or man (e.g. Socrates) who is 
not mortal. And no doubt that is involved in the truth of the universal 
proposition ; but it does not follow that Aristotle thought of the universal 
proposition as no more than an enumerative judgement about every species 
(or individual) of which the subject-term can be predicated. He uses the 
formula to pio-ov itrriv iv oXa> t<u irpcorco (' the middle is contained in the 
major as its whole ') as well as to Trpanov KaTrjyopdrcu koto, navrot tov pto-ov 
(' the major is predicated of all the middle ') to indicate the relation of the 
major to the middle term in Fig. 1 (and similarly with the relation of the 
middle to the minor) ; and SXov means a logical whole or universal, not an 
aggregate of individuals. Elsewhere he says of that figure, d yap to A koto 
ttclvtos tov B nai to B Kara ttovtos tov T, dfdy<Tj to A Kara iravTos tov T kott)- 
yope'io'dat' rrportpov yap elprjrai n&s to koto namros \eyopev (' For if A is predicated 
of all B, and B of all C, A must be predicated of all C : for we have already 
stated what we mean by predicating of all ') (Anal. Pri. a. iv. 25 b 33-4, 37-40). 
Doubtless if it is involved in saying ' All B is A ', that every B is A, and in 
saying ' All C is B ', that every C is B, then it is involved that every C is A ; 
but the universal proposition need still not be viewed as a statement about indi- 
viduals. Indeed if it were, each particular C must be already known to be A in 
making the judgement ' All C is A \ and therefore the inference that all C is A 
would be unnecessary. Aristotle himself points this out in Anal. Post. a. i, and 
makes it plain that in his view the universal proposition was not an enumera- 
tive judgement about known individuals ; and he hardly ever uses a singular 
term to illustrate the minor of a syllogism. And although we must admit 
that in regarding Fig. 1 as the only perfect figure, and in exhibiting the 
necessity of the inference in Fig. 1 as he does in the words last quoted, 
Aristotle lays too much stress on the aspect of extension, and not enough 
on that of necessary connexion of characters within the subject, yet he 
largely corrects this himself in his account of demonstration, and he did not 
think that the essential meaning of the universal proposition, and what 
constituted the nerve of the reasoning, lay in the fact that it made an assertion 
about every individual falling under it. 

There is another passage sometimes quoted as the source of the Dictum, 
viz. Cat. iii. l b 10 (e. g. Mansel's Aldrich, p. 85, note a : Baldwin's Dictionary 
of Philosophy and Psychology, s. voc. Aristotle's Dictum). The section runs 
as follows : orav tTfpov KaO' erepov K(iTT]yoprjTai a>s <a6' liroKfipevov, Saa Kara tov 
Karrryopovpfvov XeyeTtu, rrdvTa ko\ Kara tov vnoKciptvov pt]drjo~tTai, otov avdpanos 
Kara tov Tivbs dvdpdmov KaTTjyopt'iTai, to 8e (atov Kara tov dvOpdoirov' ovkovv nai 
koto, tov tivos dvdpcitnov KaTr)yopr)8rjo~eTai to fojof" 6 yap tis avdpanros kcli ai>6pu>ir6s 

tart koA (uov (' When one thing is predicated of another as of a subject de 



298 AN INTRODUCTION TO LOGIC [chap 

be plain. All (or No) B is A, All C is B .'. AU (or No) C is A. Here 
it matters not for what real terms A, B, and C stand, any more than 

quo, all that is asserted of the predicate will be asserted of the subject as 
well ; e. g. man is predicated of a particular man [as subject de quo], and 
animal of man, and therefore animal will be predicated also of the particular 
man ; for the particular man is man and animal '). But its context dispels 
any presumption that this passage is an enunciation of the Dictum. There 
is nothing about syllogism in the Categories at all. In the previous chapter 
a distinction was made between different kinds of ovto. — beings, or entities. 
Some KuB vTroKeipivnv rivos Xeyerai, iv vnoKeijiivu) he ovbev'i iirnv : they 
are said, or predicated, of a subject, but do not inhere in a subject ; man, 
e. g., is predicated of Caesar, but not inherent in him. Others iv vnoKeipeva) 
fari, nati' 1 imoKeifj.evov de ov8ev6s Xtyercu, they inhere in a subject, but are 
not predicated of a subject ; as Priscian's grammatical knowledge inhered 
in the soul of Priscian, but is not predicable of any subject which could be 
said to be Priscian's grammatical knowledge. Others again nad" 1 vnoKeip.evov 
re heyerai kcu iv vTroKei.jj.evu> eariv, they both are predicated of a subject 
and inhere in a subject ; as knowledge is predicated of Priscian's grammatical 
knowledge, and inhered in the soul of Priscian. Others, lastly, ovt iv vnoicei- 
fxevto iarrlv, ovre Ka8' vrroKeifjievov Xeyerai, they neither inhere in a subject 
nor are predicated of any ; such are concrete individuals, like Caesar and 
Priscian. Here the opposition between <a6" vnoKeifxevov \eyeo~8m, being 
predicated of a subject, and iv vnoKeip.eva> elvm, inhering in a subject, is 
parallel to that between essential and accidental predication. If I say of 
Caesar that he is a man, of grammar that it is a science, of colour that it is 
a quality, those predicates give the general being of their subjects, the sub- 
jects are essentially those, or (as it may be put) are their subjects de quo. 
But if I say of Priscian that he is a grammarian, or of a map that it is 
coloured, grammar and colour are not what the soul of Priscian, and the 
map, essentially are ; they inhere in them, and the soul of Priscian and the 
map are their subjects in quo. In the language of the Categories, that is in 
a subject, which being in anything not as a part of it cannot exist apart 
from that wherein it is ; iv inroKeipiva) \eya>, 6 'iv tivi fif] a>? pepos vnap\ov 
ahvvarov x a P ls 6 " /al T °v 6 " <? iarlv (ii. l a 24-25). Colour cannot exist except 
in a body, but is not a part of the body : nor grammar except in a soul, 
but it is not part of a soul. 

Upon these distinctions succeeds immediately the sentence quoted at the 
head of the last paragraph ; and it must clearly be interpreted with reference 
to them. The connexion seems to be as follows. There exist (1) individual 
substances, like Caesar, which are subjects de quo, and subjects in quo, but 
neither predicable of nor inherent in anything else ; (2) universal substances, 
like man, predicable of individual substances, and not inherent in anything ; 
(3) individual attributes (or accidents), like Priscian's grammatical knowledge, 
which is a subject de quo, because the universal attribute is predicable of it, 
and it of no attribute else, but is not a subject in quo, being itself inherent 
in an individual substance, not that wherein anything inheres ; (4) universal 
attributes, like knowledge, predicable of individual attributes and inherent 
in individual substances. Man then is not an bnoKeipevov or subject, but 
is predicated of a subject ; nevertheless we find terms predicated of man, 
in such a proposition as ' Man is an animal '. What then is animal ? for it 
is not a subject, and apparently not predicated of a subject, for man is not 
really a subject. The answer is, that animal is really predicated of the 
subject whereof man is predicated, and therefore, like man, falls into the 
Becond of the above classes. 

If we consider this doctrine on its own account, it is open to considerable 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 299 

in the axiom of equals it mattered what real quantities were intended. 
Whatever they are, suppose that A can be affirmed or denied of all B, 

criticism. There is the same failure to distinguish different senses of imoK*L- 
ficvov, subject, as in Mill's discussion of connotative terms (cf. quotation 
supra, p. 148). As subject de quo, it is the individual, whether substance 
or attribute, the instance of an universal ; as subject in quo, it is the individual 
substance. Thus in relation to knowledge, the grammatical knowledge of 
Priscian is a subject de quo, as in relation to man, Priscian is ; and language 
allows me to say that the former is a knowledge, and the latter is a man. 
But again in relation to knowledge, Priscian, or the soul of Priscian, is the 
subject in quo ; and language allows me to say not that Priscian is a know- 
ledge, but that he is knowing, though both man and knowledge are sometimes 
6aid to be ' predicated of ' Priscian : clearly not in the same sense. When the 
subject of a predicate is its subject de quo, then if the predicate is in the 
category of substance, the subject is a substance ; if the predicate is in some 
other category, the subject is in that category ; but when the subject of 
a predicate is its subject in quo, the subject is a substance, the predicate in 
some other category than substance. Now the language of the Greek, 
when it distinguishes <ca#' vnoKeifj.<ii><w XeyeaOm and iv inroKt ineva> tlvm, being 
predicated of a subject and inhering in it, does not suggest that the word 
inroKfipevov, subject, has any but one sense ; the difference is put as if lying 
in the relation of the predicate to it ; but really to be a subject of inherence, 
or substance, is not the same as to be a subject de quo, or individual, though 
some individuals are individual substances. 

There is a further difficulty in the passage. It professes to distinguish 
kinds of 6Wa, things or entities. Now when we say that an attribute inheres 
in a substance, we mean, according to the teaching of the passage, that an 
individual attribute inheres in an individual substance ; and these are rightly 
distinguished as things of different kinds. But when we predicate something, 
whether substance or attribute, of its subject de quo, we do not mean that 
an individual is the universal of which it is an instance. ' His grammatical 
knowledge inheres in Priscian ' ; here the words His grammatical knowledge 
denote an individual attribute, and Priscian denotes an individual substance. 
But when I say that Priscian is a man, or that attribute of his a knowledge, 
man does not denote an universal substance, nor knowledge an universal 
attribute. Yet these are what are said to be predicated of their subjects 
de quo. We have seen (supra, pp. 33-35) that the same abstract term is 
commonly used as a general name of attributes, and as name of the universal 
whereof they are instances. But here the general concrete term is treated 
as the name of the universal whereof individual substances are instances, 
and man is said not to be, but to be predicable of, a subject. The word ' man ' 
is doubtless so predicable ; but what it denotes is some individual subject. 
Aristotle however treats general concrete names as names of universals. 
In de Interpr. vii. 17 a 38- b l we are told that some things are universal, some 
individual ; universal, what can be predicated of more than one, individual, 
what cannot ; man e. g. is an universal, Callias an individual (enel 8' £<rr\ 
Ta fieu KadoXov tg>v irpay^iaruiv ra he ko.8' eKaarov' Xeycu de KnOoXov \xev o enl 
nXeiovcov nefpvKe Kar-qyopeiaPai, icad' eKacnov de 6 jxrj, olov av&pconos fiev rcov 
KadoXov, KaXXlas $e rcov Kciff 1 eKaarov' ktX.). 

But whatever the scruples which the whole passage raises, the words in 
question are far from enunciating the Dictum de ornni et nullo. In the 
syllogism ' All men are animals, Socrates is a man .*. Socrates is an animal ' — 
if indeed Aristotle would have called that a syllogism (cf. infra, p. 321) — 
man is predicated of Socrates cos ku6' imoKemivov, as its subject de quo, and 
animal kclt avBpconov Xeyerm, not iv av6pu>n(p e'arip, it is predicable of, not 



300 AN INTRODUCTION TO LOGIC [chap. 

it can be affirmed or denied of each particular subject, C or any other, 
included in B. Here, according to a tradition which has been 
strong, is the fundamental principle of syllogistic inference. In 
this Dictum is nakedly displayed what is the nerve of our reasoning, 
whenever we syllogize in the concrete. It is the assurance that A 
is true of all B, which satisfies us that it is true of this B, viz. of 
C ; the business of reduction is to bring imperfect syllogisms into 
a form, in which we can see at once that the principle applies to 
them ; and the title of the first to be the perfect figure lies in its 
conforming to the formula of the Dictum de omni et nullo. 

There are several objections urged against the claims of this 
formula. In the first place, it suggests the ' nominalist ' doctrine 
expressed by Hobbes, when he said that reasoning is but the right 
ordering of names in our affirmations. It suggests that our ground 
for affirming or denying that C is A lies in the fact that A is said of 
all, or no, B, and B is said of G. Clearly it is because we believe 
that B is A, and G is B — not because B is called A, and G is called 
B — that we assert the conclusion. However, this nominalist inter- 
pretation of the Dictum is not necessary ; it is not as thus inter- 
preted that it will be here discussed ; and therefore this objection 
may be dismissed. 

It may be said secondly, that if the reduction of the other figures 

inherent in man, being in the same category, and its general being ; animal 
therefore is predicated of Socrates as its subject de quo, i.e. Socrates is an 
animal. The conclusion is justified by the rule in the Categories. But to 
most syllogisms it has no application. ' All organisms are mortal, Man is an 
organism .*. Man is mortal.' Here the minor term is not an vnoKeifievov, 
or subject de quo, in the sense of the passage in the Categories, but some- 
thing predicated of a subject ; and though the middle is predicable of the 
minor, the major is inherent in the middle. Again if Priscian was a gram- 
marian, and a grammarian is scientific, Priscian was scientific ; but here 
though the minor term is an hnoKe'ipc-vov, an individual substance, the middle 
is predicated of it not as its subject de quo, but as its subject in quo ; it is 
not therefore a case orav erc-pov K.a.6' (Ttpov KarrjyoprjTdi cos Kad vTioKcipevov, 
where one thing is predicated of another as of a subject de quo, and so does 
not fall within the scope of the rule. Once more, if all men are jealous, 
and Priscian was a man, Priscian was jealous ; here the middle is predicated 
of the minor term as of a subject de quo ; but as in the proposition ' All 
organisms are mortal ', so it is in this major premiss ; jealousy is not some- 
thing which Kara tov Karriyopovpevov XiytTai ; man is to jealousy not sub- 
ject de quo, but subject in quo ; we cannot, according to the language of 
the context, say that jealousy kot avdpionov Xiytrai, is predicated of man, 
but that it ev iiv$pu>na> toriv, inheres in a man. There is therefore no justifica- 
tion for finding in this rule a statement of the Dictum. Whether Aristotle 
would have accepted the Dictum as a correct expression of the principle of 
syllogistic inference is another question, to which the answer depends very 
much on how we interpret the Dictum. 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 301 

to the first is not necessary, i. e. if the true character of our reason- 
ing in them is not more clearly displayed in the first figure, the 
Dictum is not the principle of all syllogistic inference. In claiming 
to be that, it denies any essential difference between the different 
figures ; and those who think them essentially different are so far 
bound to question the analysis of syllogistic inference which the 
Dictum implies. This is quite true ; but we can hardly discuss 
the relation of the different figures, until we have settled whether the 
Dictum expresses correctly the nature of our reasoning in the first. 
We come therefore to what is the main criticism which has been 
urged against the Dictum, and against all syllogistic inference, if 
it be supposed that the Dictum is a true analysis of its nature. It 
is said that a syllogism would, on this showing, be a petitio principii. 
By petitio principii, or begging the question, as it is called in English, 
is meant assuming in one of your premisses what you have to prove. 
Of course, the premisses must implicitly contain the conclusion ; 
otherwise you would have no right to draw it from them, and could 
deny it, while admitting them : this much is true of every kind of 
cogent inference, whether syllogistic or not, though it has been 
sometimes treated as a peculiarity of syllogism by persons who 
thought they could find other kinds of inference not obnoxious to it. 
But you do not beg the conclusion in the premisses, except where 
the conclusion is necessary to establish one or other of the premisses. 
For example, I may know that treason is a capital offence ; and the 
law might make it treasonable to publish libels against the sovereign ; 
and in that case, from the premisses, All treason is a capital offence, 
To libel the sovereign is treason, I could infer that To libel the sovereign 
is a capital offence. In this argument, there is no petitio principii ; 
I can learn the truth of both premisses by consulting the statute- 
book, and do not need to be aware that it is a capital offence to libel 
the sovereign, in order to know either of the premisses from which 
that conclusion is deduced. But the case is different in such a syllo- 
gism as that All ruminants part the hoof, and The deer is a ruminant 
.'. The deer parts the hoof. I have no means here of ascertaining 
the truth of the major premiss, except by an inspection of the various 
species of ruminant animals ; and until I know that the deer parts 
the hoof, I do not know that all ruminants do so. My belief in the 
constancy of structural types in nature may lead me to expect that 
a rule of that kind, found to hold good in all the species which I have 
examined, holds good universally ; but this presumption, so long 



302 AN INTRODUCTION TO LOGIC [chap. 

as it rests merely on the examination of instances, is not conclusive ; 
I should not accept the conclusion merely on the strength of the 
premisses, but should seek to confirm it by an examination of the 
hoof of the deer ; the case of the deer therefore is necessary to 
establish the rule. 

Now it has been alleged that all syllogism is a petitio principii * ; 
and the allegation has gained colour from the Dictum de omni et 
nullo. * That which is affirmed or denied of any whole may be 
affirmed or denied of anything contained within that whole.' What 
do we mean by a whole here ? If it is a class or collection, if the 
major premiss is to be understood in extension, then it can hardly 
be denied that it presupposes a knowledge of the conclusion. If in 
the proposition All B is A, 1 mean not that B as such is A, but that 
all the B's are A, I must certainly have examined C (if that is one of 
them) before making the assertion ; and therefore the major pre- 
miss, All B is A, rests {inter alia) on the present conclusion, G is A. 
According to this view, the major premiss of a syllogism is (at least 
in most cases 2 ) a statement of fact about the whole of a number of 
particulars ; it is really an enumerative, and not a true universal, 
judgement. 3 We make it, not because of any insight that we have 
into the nature of B and A, and into the necessity of their connexion : 
but simply because we have examined everything in which B is 
found, and satisfied ourselves that A is equally present in all of them. 

There is indeed another sense in which the major premiss may be 
enunciated without our having insight into the necessary connexion 
of characters in things, and in which it no longer makes a collective 
assertion about every one of a number of particulars. If I say that 
all gold is yellow, I need not mean to assert that every piece of metal, 
which by other qualities I should identify as gold, is also yellow 
— a statement for which I certainly cannot claim the warrant of 
direct experience. I may mean that a yellow colour is one of the 
qualities on the ground of which I call a substance gold ; or, in 

1 Cf., e.g., Mill, System of Logic, II. c. iii. Mill's own way of avoiding 
the charge is not very successful. 

2 Where general rules are made by men, as in the case of laws, we can of 
course know them, in advance of any knowledge about the particular acts 
or events to which they refer. Such syllogisms, therefore, as that about 
libelling the sovereign, given in the last paragraph, can in no case be alleged 
to beg the question. If any other authority (such as revelation) acquaints us 
with general rules, they will serve as major premisses of equally unexcep- 
tionable syllogisms. All other general propositions have, by the extremer 
cmtics, been interpreted in the way mentioned in the text. 

3 For this distinction, cf. supra, p. 177. 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 303 

Locke's language, that it is included in the nominal essence of gold. 
By a nominal essence, Locke means what J. S. Mill called the 
connotation of a name — those attributes which, in using a general 
name, we imply to belong to the subjects called by it. We may 
collect together in our thought any set of attributes we like and 
give a name to the assemblage of them ; and then it will, of course, 
be true to say that anything called by the name, if rightly called by 
it, possesses any of the attributes included in the signification of 
the name. The general proposition ceases, in that case, to be 
enumerative ; but it does not become really universal. It becomes 
a verbal proposition. Gold is yellow, because we do not choose to 
call anything gold which is not yellow ; but we are not asserting 
that there is any necessary connexion between the other attributes 
for which a parcel of matter is judged to be gold, and this of yellow- 
ness. Given such and such attributes, we call it gold ; and there- 
fore gold has all these. Let any one of them be wanting, and we 
should not call it gold ; therefore that is not gold which is not 
yellow ; but there may be a parcel of matter, for all that we mean 
to affirm, which has all the other qualities of gold, but is of the 
colour of silver. 1 

Locke did not suppose that the ordinary man, who says that 
gold is yellow, means only to assert that yellowness is one of the 
attributes included by him and others in the nominal essence (or 
connotation) of the word gold : but rather that he means, that with 
certain other qualities collected in the ' complex idea ' to which the 
name gold is attached the quality yellow is constantly conjoined. 
This however, on Locke's view, we cannot know ; for knowing is 
perceiving a necessary agreement or disagreement between our 
1 ideas ' (it would be better to say, connexion or disconnexion 
between the characters of things) ; and this in regard to our ' ideas 
of substances ' we do not perceive. 2 It is not our present business 
to discuss this ; we have not to ask how many of the general pro- 
positions of the sciences state connexions known to be necessary 
(though, if we did, we should find Locke not very far in that matter 
from the truth), nor what means there are (if any) of proving uni- 
versal propositions about such matters of fact. We are concerned 

1 Cf. Locke's Essay, III. vi. §§ 6, 19, and also pp. 92 sq., supra, on Definition. 

2 Cf. Locke, Essay, IV. vi, esp. §§ 8, 9. Miss Augusta Klein has justly 
objected to me that in the first edition of this book I represented Locke as 
holding propositions about ' nominal essences ' to be more verbal than he 
really does 



304 AN INTRODUCTION TO LOGIC [chap. 

with the theory of syllogism, and the allegation that it begs the 
question. We found that if the major premiss be interpreted in 
extension as an enumerative judgement, the charge is true ; and 
that the Dictum de omni et nullo at least lends colour to such an 
interpretation. We have now seen that there is another interpreta- 
tion, according to which the major premiss may be known to be true 
without examination of every individual instance included under the 
subject of it, but only by becoming a verbal proposition. On this 
interpretation the syllogism will still be a petitio principii, though 
not in the way which the Dictum de omni et nullo suggests. For 
though the major premiss will no longer presuppose a knowledge of 
the conclusion, the minor will do so. If nothing is to be called gold 
unless it is yellow, I cannot tell that a parcel of matter is gold, in 
which I have found the other qualities which the name implies, unless 
I have first seen that it is yellow. Of course, colour being the most 
obvious of the properties of a substance, I am not likely ever to be in 
the position of inferring the colour of a substance from its name ; 
but the argument is the same if I took some unobvious quality, 
like solubility in aqua regia. If that is part of the nominal essence 
of gold, then I cannot tell that a particular parcel of matter with 
the familiar weight and colour of gold is gold, until I know that it is 
soluble in aqua regia. I do not therefore infer its solubility from the 
knowledge that it is gold, but I call it gold because I know it to be 
thus soluble. 1 

We need not dwell longer on the view that a general proposition 
is only warranted by agreement as to the meaning of a name, nor on 
the consequences, fatal enough, which this view would entail on the 
syllogism. Reasoning is not a mere process of interpreting names ; 
and it is not the principle of syllogistic inference, that whatever 
a name means may be affirmed of the subjects called by it. In 
considering the charge that the syllogism is a petitio principii, it was 
necessary to notice the view which makes the petitio lie in the 
minor premiss, as well as that which makes it lie in the major. We 
must now return to the latter, and to the Dictum which is supposed 
to countenance it. 

We saw that the crucial question here concerned the nature of 
the major premiss ; is it universal, or merely enumerative ? is it 

1 It will now be seen why a syllogism was explained to beg the question, 
if it presupposed the conclusion not in the premisses together, but in either 
of them singly ; all syllogisms in a sense presuppose it in the premisses 
taken together (though they do not presuppose a knowledge of it). 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 305 

based on an enumeration of particulars, or on the connexion of 
universals ? If it is enumerative, and rests on a previous review 
of all the particulars included in the middle term, the charge of 
petitio is sustained. We should then accept the Dictum, de omni et 
nullo as the general principle of syllogism, the ' whole ' of which it 
speaks being understood as a whole of extension, a collection or 
class ; but we should scarcely be able to speak of syllogistic inference. 

Now Aristotle, who thought syllogism to be the type of all demon- 
stration, could not possibly have understood the major premiss in 
this way. 1 He thought that, although we might know as a fact 
that C is A, yet we did not understand it, without seeing that it 
must be so ; and to see that it must be so is to see that in it which 
makes it so — to see that it is A in virtue of B. B is a middle term, 
because it really mediates between G and A ; it performs for G the 
office of making it A, and is the reason why G is A, not merely the 
reason why we know G to be A. 

We have already, in discussing the modality of judgements, met 
with this distinction between the reason for a thing being so and so, 
and the reason for our knowing it to be so — between the ratio essendi 
and the ratio cognoscendi. 2 When I say that wheat is nourishing, 
because it contains nitrogen and carbon in certain proportions, I give 
the reason for its being nourishing : it is this constitution which 
makes it so. When I say that Mellin's Food is nourishing because 
Baby grows fat on it, I do not give the reason for its being nourish- 
ing, but only the reason for my thinking it to be so : it is not Baby's 
condition which makes it nourishing, but its nourishing properties 
which produce Baby's condition. The physical sciences always look 
for rationes essendi, so far as possible ; though it may be noted that 
in what is, in many ways, the most perfect of the sciences, viz. 
Mathematics, we reason very largely from rationes cognoscendi. 2 If 
A =B, and B = C, then A = G ; but it is not because A and G are 
both equal to B, that they are equal to one another, though that is 
how I may come to know of their equality. The reason why they 
are equal is that they contain the same number of identical units. 3 

The middle term does not in all syllogisms give the reason why 
the major belongs to the minor. It does so only in the first figure, 

1 The doctrine of the Posterior Analytics must in this respect be taken as 
overriding the more formal and external treatment of syllogism in the Prior. 

2 v. supra, pp. 205-206. 

5 But we cannot give this reason for the equality of the units. 

1779 X 



306 AN INTRODUCTION TO LOGIC [chap. 

and not always there. Because, whenever the middle term really is 
a ratio essendi, the syllogism falls into the first figure, Aristotle called 
it the scientific figure, o-xw a ^icrr^jxoviKov. 1 Why are modest men 
grateful ? Because they think lightly of their own deserts. This 
implies a syllogism in Barbara. All who think lightly of their own 
deserts are grateful, and modest men think lightly of their own 
deserts. But if I try to establish the conclusion by an appeal to 
instances, pointing out that Simon Lee and Tom Pinch, John Doe 
and Richard Roe, were modest, and were grateful, I am giving not 
a reason why the modest are grateful, but reasons which lead me to 
judge them to be so ; and my syllogism falls into the third figure, 
not the first : These men were grateful, and these men were modest, 
therefore modest men are (or at least they may be) grateful. 

The first figure then is scientific, because a syllogism which makes 
you know why G is A falls into that figure ; but the middle term in 
the first figure need not be a ratio essendi. ' Parallel rays of light 
proceed from objects at a vast distance ; the sun's rays are parallel ; 
therefore they proceed from an object at a vast distance.' Here 
my syllogism is again in Barbara ; but the distance of the sun is 
not due to its rays (at the earth) being (so far as we can detect) 
parallel : their being parallel is due to the distance of the sun from 
the earth. Nevertheless, the syllogisms in which the middle term 
does account for the conclusion are enough to show that syllogism 
is not essentially a process of inferring about a particular member 
of a class what we have found to be true of every member of it. The 
importance of the scientific, or demonstrative, syllogism in this 
connexion is, that it most effectually disposes of this analysis of 
syllogistic inference. It shows that there are syllogisms which 
cannot possibly be brought under the Dictum de omni et nullo, thus 
interpreted. We shall, however, find that even where the middle 
term is not the cause of the conclusion, in the sense of being a ratio 
essendi, the Dictum thus interpreted does not give a true account of 
the nerve of our reasoning. 

For syllogism really works through the connexion of concepts, or 
universals. The major premiss, ' B is A ', is not a collective state- 
ment about every B, C included ; if it were, there would certainly 
be nothing new in the conclusion ' C is A '. When Jacob lamented 
' Me have ye bereaved of my children : Joseph is not, and Simeon 

1 Anal. Post. a. xiv. 79 a 17. The rest of the chapter is by no means all of 
it true. On ' scientific ' and ' dialectical ' syllogisms cf. infra, pp. 398-399. 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 307 

is not, and ye will take Benjamin away ', he added, speaking 
collectively of the loss of two sons, and the threatened loss of a third, 
' all these things are against me '.* It would have been no inference 
to proceed ' Therefore the loss of Simeon is against me ', because that 
was definitely included by the demonstrative these. To be ' one of 
these ' is not a common character in each of them, with which a 
further character is connected ; it is not therefore a middle term. 
Where B is a middle term, the major premiss connects being A with 
being B. 2 We must not be misled by our use of symbols. In 
a syllogism of the form ' All B is A, C is B .'. C is A ', we say that 
B is the middle term. The following is a syllogism of that form : 

Those who can find things out for themselves are little depen- 
dent on education 
Men of genius can find things out for themselves 
.*. Men of genius are little dependent on education. 

Now if we symbolize the major premiss by the formula ' All B is A ', 
B represents the words ' those who can find things out for them- 
selves '. But if we say that B is the middle term, B really repre- 
sents the words ' being able to find things out for oneself \ It is 
that which, in men of genius, is either the ground or the sign of 
being little dependent on education. The middle term therefore 
is not the collection of things called by a general name ; it is the 
common nature intended by the name, a ez> eirl ttoW&v, something 
one in many subjects. And the same is of course true of the major 
term. The minor may indeed be an individual, or a number of 
individuals, though it need not be so. 

The perception that the middle term is not a class but a character, 
universal and not a sum of particulars, has led to the formulation 
of a principle intended to express this more satisfactorily than the 
Dictum de omni el nullo does ; of which it has already been said 
that it at least lends itself to an erroneous view of the major premiss, 
as an enumerative proposition, though it was by no means always 
so intended. The principle is this — Nota notae est nota rei ipsius 
(and for the negative, Repugnans notae repugnat rei ipsi) : i. e. what 
qualifies an attribute qualifies the thing possessing it. Certain 
objections may be made to this formula also. It suggests that the 
minor term is always a concrete individual, and that the syllogism 

1 Genesis xlii. 36. 

2 Or, if negative, asserts that being B excludes being A. It will be remem- 
bered that we are discussing the first figure. 

X2 



308 AN INTRODUCTION TO LOGIC [chap. 

re fere to this (res ipsa) what in the major premiss is stated to char- 
acterize its predicates. It speaks also as if one attribute were 
conceived to qualify another in the same way as an attribute qualifies 
a concrete subject. And the conception of a mark or nota is no 
improvement on that of attribute. 1 We need not interpret it as 
a purely external sign, related to what it signifies as a word to its 
meaning or a letter to a sound. The ' notes ' of a thing are its 
characteristics, as Cardinal Newman spoke of the notes of the 
Church ; they are not the mere indications by which we judge what 
thing is present, but themselves contribute to make it the thing 
that it is. Yet the nature of a thing is no less ill conceived as an 
assemblage of marks than as a bundle of attributes. The notes of 
the Church would not exhaust the notion of the Church ; the marks 
of a disease, though elements and features of it, would not give a 
complete conception of what the disease is. There are predicates 
of a thing which include too much of its nature to be called marks 
of it. Nevertheless this formula has the great advantage that it 
does prevent our regarding the middle term as a class which includes 
the minor in its extension. 2 

But a better formula may be found. Kant said of the syllogism 
that it subsumed a cognition (i.e. a subject of knowledge) under the 
condition of a rule, and thus determined it by the predicate of the 
rule. 3 The rule is given in the major premiss, which connects 

1 Cf. Hegel's Logic, § 165, E. T. (Wallace), p. 296 : ' There is no more 
striking mark of the formalism and decay of Logic than the favourite category 
of the " mark ".' 

8 J. S. Mill (System of Logic, II. ii. 4 and note) strangely misinterprets 
the maxim Nota notae est nota rei ipsius. He understands by res ipsa the 
major term, and by nota the minor ; so that the whole, instead of meaning 
that what qualifies an attribute qualifies the subject of it, comes to mean 
that what indicates the presence of an attribute indicates what the latter 
indicates. He naturally gets into great difficulties where the minor term is 
singular. We may treat the attributes of man as a mark or indication of 
mortality (though this is rather like saying that a Bank of England note 
is a mark of the presence of the chief cashier's signature) ; but we cannot 
treat Socrates as a mark or indication of the attributes of man. Therefore 
in the syllogisms All men are mortal, All kings are men (or Socrates is a man) 
.'. All kings are (or Socrates is) mortal, while the minor premiss of the former 
is paraphrased The attributes of a king are a mark of the attributes of man, 
that of the latter runs Socrates has the attributes of man. This is a rather 
desperate shift. But res ipsa never meant the major term, the most general 
or abstract term in the syllogism ; and the whole interpretation, which neces- 
sitates a measure so violent, is impossible. The formula is really an abridged 
equivalent of the passage in Ar. Cat. l b 10-12, quoted p. 297, n., supra. 

3 Krit. d. r. Vern., Transcendental Dialectic, Introd. II. B (p. 215, Meikle- 
john's Translation). 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 309 

a predicate (the major) with a condition (the middle term) : the 
minor premiss asserts the fulfilment of this condition in its subject ; 
and in the conclusion we determine the subject by the predicate 
which the rule, in the major premiss, connected with this condition. 
This analysis brings out the essential nature of the major premiss, 
as a rule connecting a predicate with a condition universally, not an 
assertion that the predicate is found in every member of a class. 
It also applies equally where the middle term is, and where it is not, 
the ratio essendi of the major. And it is free from the objections 
just urged against Nota notae. 1 If we were to frame from it a ' canon ' 
parallel to this and to the Dictum de omni et nullo, it would run 
somewhat thus : Whatever satisfies the condition of a rule falls under 
the rule. In the rule ' Whatever is B, is A ', being B is the condition, 
the fulfilment of which involves being A ; and to a given subject C 
fulfilling the condition the rule will apply, and it will be A. We 
may perhaps accept this as a statement of the nature of the reasoning 
employed in syllogisms of the first figure. We need not deny that 
the Dictum de omni et nullo, if rightly interpreted, is free from the 
offences charged against it. If the omne be understood as an unity 
present in many instances — a logical whole or whole of intension, 
not an aggregate of individuals — then the principle will serve. But 
the other puts more clearly the nerve of the inference. And it 
applies to all syllogisms in the first figure, whatever the nature of 
the middle term : whether it be a mere sign of the major term, as if 
we said that ' All men with large hands and small eyes are choleric ' 
— where the connexion of the predicate with its condition, though 
accepted de facto, is one for which we can see no necessity : or 
whether it give, wholly or in part, the reason and the explanation of 
the major, e.g. in such premisses as that 'All trees fertilized by the 
wind blossom before their leaves are out ', or that, ' Men successful 
in a work that gives full play to all their faculties are happy '. 
Whatever our particular syllogism is, we shall find it true to say 
of it, that it brings a subject under a rule, on the ground that it 
satisfies the condition of that rule : that it affirms (or denies) a 
predicate of a subject, on the ground that this subject fulfils the 

1 Kant himself applied this analysis to hypothetical and disjunctive argu- 
ments also. In a later chapter, these are more strongly distinguished from 
' categorical ' syllogisms than he allows. But this need not prevent the 
acceptance of his analysis. A statement may correctly express the nature 
of syllogistic inference, even when some arguments, which are not strictly 
syllogistic, are also alleged to fall under it. 



310 AN INTRODUCTION TO LOGIC [chap. 

condition with which the predicate (or its absence) is universally 
conjoined or connected. 

This canon is exemplified even where the major premiss rests on 
an examination of all the instances included under the middle term ; 
so that there is inference there, though not proof of the conclusion. 
The major premiss is indeed in such a case a sort of memorandum, 
as Mill says of it, 1 to which we subsequently refer in order to save 
the trouble of repeating our observations ; but a memorandum in 
general terms requires inference to make use of it. Suppose a man 
intending to dispose of part of his library ; he might look through 
his books and put a mark in all those which were not worth keeping ; 
if he then forgot what a certain book contained, but finding his mark 
in it said that it was not worth keeping, he would be syllogizing. 
He would argue ' Books thus and thus marked are not worth keeping, 
this book is thus and thus marked, .'. it is not worth keeping'. 
There is no real proof here that it is not worth keeping ; that could 
only be determined by reading the book ; and his mental note that 
no book thus and thus marked is worth keeping requires that he 
have read this book and ascertained that it was not worth keeping 
before marking it. But he may have forgotten all about it ; and he 
now asserts that it is not worth keeping because by containing the 
mark it satisfies the condition on which the ascription of that predicate 
rests. In applying his rule he trusts of course to his past care in 
reading and marking ; and so he may be said to take the major 
premiss on trust. But that is common enough. Even when an 
universal proposition is capable of proof, many reason from it 
syllogistically who never knew the proof, or if they knew it, have 
forgotten it. We may go further. Subsumption, or bringing 
a subject under the condition of a rule, which is the nature of syllo- 
gism in the first figure, always implies that in a measure the rule is 
taken on trust. To this extent the major premiss is always a sort 
of memorandum. For if we understood at the moment the neces- 
sary connexion between the middle term and the major, we should 
appeal to no rule, but in considering C, the minor term, itself, pass 
from the knowledge that it is B to the further knowledge that it is A. 
We should indeed realize herein that the connexion of the character 
A with the character B was not limited to the subject G. But 

1 System of Logic, II. iii. 4. Mill's mistake lies not in saying that the 
major premiss of a syllogism is a memorandum, but in making it a false 
memorandum, which records that all B is A when we have only observed 
that X, Y and Z (which are B) are A. 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 311 

we should rather extract the general rule from consideration of the 
subject before us than bring it in independently and as it were 
ab extra to the consideration of that subject. And that would not 
be syllogism. Syllogism does not belong to the level of complete 
insight into the connexion of facts. In geometry we never syllogize 
except when we rely upon the results of a previous demonstration 
whose steps we do not realize in the case before us. ' The triangle 
in a semicircle has the square on its hypotenuse equal to the squares 
on the other two sides, because it is right-angled ' ; that is a syllo- 
gism ; but if we realized at once the construction of Euclid i. 47 for 
the figure in iii. 31, the proposition that in a right-angled triangle the 
square on the hypotenuse is equal to the squares on the other two 
sides would appear rather as generalized from what we saw to be 
true in the triangle in a semicircle than as a rule applied to that case. 
The subsumption in syllogism belongs therefore to thinking which 
has not complete insight into the necessity of all the facts in its 
premisses at once. When Aristotle taught that syllogism is the 
form of demonstrative thinking, he failed to realize this. Because 
C's being A is seen to be involved in its being B, he thought we used 
a major premiss, ' All B is A\ He was nearer the truth when he 
said that in demonstration our terms are connected per se. The 
putting together of, or the appeal to, premisses already known is 
not necessary to demonstration. Supposing I already understood 
that to be an organism involved being mortal, yet if I discovered 
some thing of strange kind to be an organism, I should know that it 
was mortal, in virtue of my now understanding the connexion, not 
in virtue of having understood it before. But because we have 
constantly to appeal to the conclusion of a previous process of 
demonstration or other reasoning without re-thinking that process 
at the time, we are constantly syllogizing ; and where the premisses 
are such of which we remember to have previously satisfied our- 
selves by reflection or demonstration or inductive argument, or (if 
they concern facts established by authority) by reference to autho- 
rity, there syllogism may deserve the name of proof. It is other- 
wise where, in order to establish a conclusion, we appeal to a premiss 
which itself needs the help of the conclusion to establish it ; this 
is not proof ; yet if the premiss has been so established, and is now 
appealed to as a record, there is syllogistic inference. Our argument 
is one whose general form is given in the canon of syllogism. 
That canon, like the axiom of equals, is not itself a premiss but 



312 AN INTRODUCTION TO LOGIC [chap. 

a principle of reasoning. It is easy to see this. Any one denying it 
would as readily deny the validity of any particular syllogistio 
argument ; but a man may admit the validity of the inference, 
in a particular case, without needing to consider this general prin- 
ciple. And, as no one could see that Things equal to the same 
thing are equal to one another, who was incapable of seeing the truth 
of that principle in a given case, so no one could see the truth of the 
principle that What satisfies the condition of a rule falls under the 
rule, who failed to recognize that if all organisms are mortal, and 
man is an organism, man must be mortal. What then is the use 
of the principle, if it is not a premiss of inference ? It might be 
used to stop the mouth of a disputant who denied the conclusion 
which followed from the premisses he had admitted. We might 
ask such a disputant, whether he denied the truth of this principle, 
and unless he was prepared to do that, require him to admit the 
validity of the syllogism he was disputing. It is true that in con- 
sistency he might decline. A man who denies the validity of a given 
syllogism in Barbara may with equal reason deny the argument 
which attempts to prove its validity. For that argument will 
itself take the form of another syllogism in Barbara : 

All inferences upon this principle (that what satisfies the condition 

of a rule falls under the rule) are valid 
The syllogism in question is an inference upon this principle 
.*. It is valid 

Why should a man admit this reasoning, if he will not admit that 
since 

All organisms are mortal, and 

Man is an organism 
.*. Man is mortal ? 

The two are of the same form, and this shows that you cannot make 
the principle of syllogistic inference into the premiss of a particular 
syllogism, without begging the question. 1 Yet a man who disputes 

1 Cf. an article on 'What the Tortoise said to Achilles', by ' Lewis Carroll ', 
in Mind, N. S. iv. 278 (April, 1895). It is obvious that the validity of the 
latter of these two syllogisms cannot require to be deduced from the principle 
which stands as major premiss in the former. For if until that is done its 
validity is doubtful, then the principle by which we are to establish its 
validity is equally doubtful. Besides, what proves the validity of the former, 
or validating, syllogism ? The validity of a syllogism cannot be deduced 
from its own major premiss ; else the fact that all organisms are mortal 
would show that the syllogism, of which that is the major premiss, is valid. 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 313 

in a particular case the conclusion that follows from his premisses 
may hesitate to maintain his attitude, if the principle of reasoning 
involved is put nakedly before him, and shown to be one which 
he daily proceeds upon, and cannot disallow without invalidating 
his commonest inferences. For this reason it may cut wrangling 
short, if we can confront a man with the principle of the inference 
he questions. Show him, for example, that the inference ascribes 
to a subject, in which certain conditions are fulfilled, a predicate 
connected universally with those conditions, and he cannot longer 
refuse his assent. For to do what it does is to be a syllogism x : and 
therefore valid. 

And there have been writers 2 who thought that the only object of 
knowing the theory of syllogism was to cut short wrangling. But 
there is another object, connected with a side of logic which the 
same writers for the most part ignore. Logic is not an art. Its 
business is to know and understand the processes of thought, and 
not least the true nature of our processes of inference. To this 
business belongs the question, what is the principle of a certain 
inference which we make, and recognize to be valid ? To find and 
formulate that principle — to extricate it from its concrete setting 
in the matter of a particular argument, and set it out in abstract, 
— this is the logician's task. Now men may misinterpret the 
character of syllogism, and formulate wrongly the principle involved; 
yet if their misinterpretation is generally received for true, the 
wrong principle will serve in practice to stop dispute as well as 
the right principle would have done. Those who are agreed that 
syllogism is conclusive, however they define a syllogism, will accept 
an argument if it can be shown to accord with their definition ; 
and the same misinterpretation which appears in their account of 
the general nature of syllogism will appear in their view of particular 
syllogisms, from which that account is of course derived. There- 
fore, though it be said that a syllogism is an argument which applies 
to some one member of a class what is true of every member, yet 
even this analysis of it, however faulty, will serve to ' stop wrangling' 

If it be said that the validating syllogism needs no proof of its validity, the 
same can be said of the syllogism which it validates. But if it needs a proof, 
the syllogism which validates it will need validating by another, and so 
ad infinitum. No form of inference can have its validity guaranteed by 
another inference of the same form with itself ; for we should be involved 
at once in an infinite process. 

1 Cf. Ar. Post. An. p. vi. 92 a 11-16. 

8 e. g. Locke, Essay, IV. xvii. 4. 



314 AN INTRODUCTION TO LOGIC [chap. 

among persons who accept it. For let a particular argument be 
exhibited as doing this, and it will be accepted as valid. But the 
theoretical objections to this analysis of syllogistic inference are in 
no way lessened by its being practically as useful as any other that 
men could be brought to accept. The paramount question is, 
whether it is true : not whether for any purposes it is useful. And 
the present chapter has been quite disinterested ; it has aimed 
at throwing light on the question, What is a syllogism ? i. e. What 
is the principle of inference which a syllogism exemplifies ? 

We have ignored of late the imperfect figures, in seeking an 
answer to this question. They furnished a possible objection to the 
claims of the Dictum de omni et nullo x ; for if their reduction to the 
first figure is unnecessary, then the Dictum, which only contem- 
plates the first figure, cannot be the principle of all syllogistic 
inference. But this objection was deferred, until the Dictum had 
been examined on its own ground. We must now return to the 
subject of the imperfect figures. 

It may make things clearer, if the view to be taken in the follow- 
ing pages is given summarily at the outset. There are difficulties 
in any view of the matter ; because the same verbal form may be 
used where the thought in the speaker's mind is different. The 
true character of an argument depends not on the verbal form, but 
on the thought behind it. And therefore sometimes the movement 
of a man's thought, though he expresses himself, e. g., in the second 
figure, would be more adequately exhibited in the first. 2 In such 
a case direct reduction may be defensible, though still unnecessary ; 
and yet it may be true that, speaking generally, the direct reduction 
of the imperfect figures distorts them, and purchases a show of 
conformity with the first figure at the expense of concealing the 
genuine movement of thought in them. 

It would seem then that syllogisms in the second and third figures 
do not as a rule merely present under a disguise the reasoning of 
the first ; they are independent types. Their validity is confirmed, 



1 Cf. supra, p. 301. 

2 e. g. in this syllogism in Festino, ' No fragrant flowers are scarlet, Some 
geraniums are scarlet .*. Some geraniums are not fragrant ', I think a man 
would probably substitute in thought for the major its converse, ' No scarlet 
flowers are fragrant', and argue to himself in Ferio. With such a premiss, 
where there is no priority as between the two accidents, fragrant and scarlet, 
that is the more natural way to argue. But this does not show that all 
syllogisms in Festino ought to be thus treated. 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 315 

in the second figure, by the reductio ad absurdum, 1 and in the third, 
by the method which Aristotle called eK0e<ris, or exposition. The 
fourth figure (or indirect conclusion in the first) is not an independent 
type ; its first three moods are merely moods of the first figure, with 
the conclusion converted, as the process of reducing them assumes ; 
its last two moods draw conclusions which are shown to be valid 
most naturally by reduction to the third figure. 

Let us begin with the second figure. Take the syllogism : All 
true roses bloom in summer : A Christmas rose does not bloom in 
summer .'.It is not a true rose. Surely, if a man hesitated for 
a moment about the necessity of this consequence, he would reassure 
himself, not by transposing the premisses, and converting the 
present minor into the statement that No rose which blooms in 
summer is a Christmas rose : but by considering, that a Christmas 
rose, if it were a true rose, would bloom in summer, whereas it does 
not. The same remarks will obviously apply to a syllogism in 
Baroco. Nor is it otherwise with the remaining moods. If No 
fish has lungs, and Whales (or Some aquatic animals) have lungs, then 
Whales (or Some aquatic animals) are not fish. A man sees at once 
that if they were, they w r ould not have lungs : whereas they have. 

It might be said that the last conclusion could be as naturally 
reached in the first figure ; that if a man, confronted with the con- 
clusion that Whales are not fish, and not feeling that he was clear 
about its cogency, were to ask himself ' Why not ? ', he would 
answer ' Because they have lungs ' ; and that this implies a syllo- 
gism in Celarent, with the major premiss What has lungs is not 
a fish. Whether this gives the reason why a whale is not a fish 
(in which case Celarent would be a better way of proving it) we 
need not dispute ; but there certainly are cases where, in what a 
subject is, we can find a reason for its not being something else. 
Notes that produce beats are not harmonious : The fourth and fiftf 
produce beats ; Therefore they are not harmonious. This argument 
might be set forth in the second figure : Harmonious notes do not 
produce beats : The fourth and fifth produce beats ; Therefore they are 
not harmonious : but here undoubtedly the syllogism in Celarent is 
better than the syllogism in Cesare ; and any one who knew that 
concord was dependent on regular coincidence in vibrations and 
discord on the clashing of them, would extricate from the major 
premiss of the latter syllogism the major of the former, and think 

1 Called by Aristotle aTrayayfj eh to abvvaTOv. 



316 AN INTRODUCTION TO LOGIC [chap. 

in Celarent. Nevertheless it is only this knowledge which makes 
him do so ; and without it he might perfectly well validate to 
himself his conclusion by considering that if those notes were har- 
monious, they would not produce the beats they do. If the middle 
term gives a ratio essendi, we naturally put our reasoning into the 
first figure. 1 The Chinese are not admitted into the United States, 
for fear lest they should lower the white labourer's standard of 
living. The likelihood of their doing this is the cause of their 
exclusion. It would be unnatural to express this in Cesare — 

None admitted into the United States are likely to lower the 

white labourer's standard of living 
The Chinese are likely to lower it 
.*. The Chinese are not admitted into the United States. 

But we are not concerned to prove that no arguments expressed 
in the second figure are better expressed in the first ; only that 
there are arguments which are more naturally expressed in the 
second, and which we should not, if challenged, attempt to validate 
by reduction to the first. Thus I may argue that Notes which pro- 
duce beats are not harmonious, and A note and its octave are harmonious, 
.'. They do not produce beats ; and it is as much a distortion to put 
this into the first figure by conversion of the major premiss as to 
put the previous example which used that major premiss into the 
second figure by the same means. Again, if I give, as a reason 
why whales are not fish, that they have not the characteristics of 
fish, such as breathing through gills, laying eggs, &e., my syllogism 
may very well be in Camestres — All fish breathe through gills, and 
Whales do not .'.A whale is not a fish ; if I still ask myself why not, 
I should probably answer, ' Because if it were a fish, it would 
breathe through gills, which it does not do \ The conclusion states 
a fact of difference between two things, which the premisses prove 
but do not account for ; and the proof in the second figure may be 
said to be here the primary form. 2 Moreover, if I were to recur to 
the first figure in order to establish this inference, it would naturally 
be by contraposing the major premiss 

1 It must not be forgotten that most reasoning which explains facts through 
their causes is not syllogistic at all ; but if it is syllogistic, it will be in the 
first figure. Cf. supra, p. 305. 

2 Hence the statement, frequently quoted from Lambert (Neues Organon, 
vol. ii. p. 139 ; Dianoiologie, iv. § 229, Leipzig, 1764), that the second figure 
points us to the differences between things : ' Die zweite Figur fiihrt auf den 
Unterschied der Dinge, und hebt die Verwirrung in den Begriffen auf.' 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 317 

What does not breathe through gills is not a fish 
Whales do not breathe through gills 
.*. Whales are not fish 

for the absence of a feature essential to any fish may be treated as 
explaining why a thing is not a fish. But the syllogism to which 
Camestres is supposed to be reduced is not the above ; it is the 
following — 

What breathes through gills is not a whale 
A fish breathes through gills 
.*. A fish is not a whale 

from which the original conclusion that a whale is not a fish is 
recovered by conversion. Now this argument, instead of relying 
on something in whales (viz. the absence of gills) to show that they 
are not fish, relies on something in fish (viz. the presence of gills) 
to show that they are not whales ; whereas whales are really the 
subject of my thought. The same line of reflection may be applied 
to the argument, Matter containing active bacilli putrefies : Frozen 
meat does not putrefy .'.It contains no active bacilli ; where no one 
could maintain that non-putrefaction was really the cause of matter 
containing no active bacilli. 

Thus the second figure is really different in type from the first ; 
although reasonings which would naturally fall into the first may be 
thrown into the second. And the difference is this, that the second 
is fundamentally indirect, the first direct. In the second, we see 
the validity of the conclusion through the contradiction that would 
be involved in denying it ; in the first (though, of course, it would 
be equally self -contradictory to admit the premisses and deny the 
conclusion) the perception of this is not a ' moment ' in our thought. 
It may fairly be said that the first figure is prior to the second, in 
the sense that it is involved in the perception of the contradiction 
which would result from admitting the premisses and denying the 
conclusion in the second. But that does not justify us in reducing 
the second to the first. For it is an essential part of our thought 
in the second figure, to see that the conclusion must follow on pain 
of contradiction ; and not merely to see the validity of the first- 
figure syllogism, by help of which the contradiction is developed. 
There is therefore a movement of thought in the second figure which 
is absent from the first. This is what makes a new type of it ; 
and this is why its direct reduction, representing second-figure 



318 AN INTRODUCTION TO LOGIO [chap. 

syllogisms as only first-figure syllogisms in disguise, is wrong, and 
therefore superfluous. 

It may be asked, is even indirect reduction necessary ? Is not the 
validity of the argument plain, without our being at pains to show 
that, if it were disputed, we should be involved in a contradiction ? 
Cannot a man appreciate that if No A is B, and C is B, then G is 
not A, without the necessity of pointing out that C would not other- 
wise, as it is, be B1 The answer is that a man may certainly not 
require this to be pointed out, inasmuch as he sees it at once to be 
involved in the premisses. The so-called indirect reduction is really 
a part of the thought grasped in the syllogism ; not something 
further, by which, when a man has already made his inference, and 
realized the act of thought involved in making it, he then proceeds 
to justify his act. It rather brings out what is in the inference, 
than reduces or resolves it into another. Hence a man may feel it 
to be unnecessary, but only because it is a repetition, not because, if 
he did not see it, the syllogism would still be seen to hold without it. 
Yet it must not be supposed that a form of argument is valid only 
because to question it would involve a contradiction. With equal 
reason it might be said that unless the argument were valid, there 
would be no contradiction in rejecting it. Hence, in the second 
figure, the contradiction that would ensue if we denied the con- 
clusion, is not the reason for admitting the conclusion, but the 
perception of it is involved in realizing its validity. An analogy may 

help us. If a straight line, falling on two 
other straight lines, makes the exterior and 
the interior and opposite angles on the 
same side of it equal, the two lines must be 
parallel. Strictly speaking, this cannot be 
proved by reasoning ; we just see, when we 
try to draw the figure otherwise, that it must 
be so. But this necessity may be brought out indirectly by the con- 
sideration, that if B E F were to be greater than BCD, E F and 
C D would cut A B at a different slant, and therefore incline to- 
wards one another ; and the perception of this is really part of seeing 
the necessity of the original proposition. Nevertheless it cannot be 
given as a reason for the truth of that proposition ; for unless the 
lines were parallel when the angles B E F, B C D are equal, they 
would not necessarily tend to meet when each cuts A B at a different 
slant. The confirmation, such as it is, is obtained by looking at the 




xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 319 

tame matter from another side ; and so it is in the second figure of 
syllogism. The truth of one side cannot really be separated from 
the truth of the other, and therefore the one is not dependent on 
the other ; but it is not fully appreciated without it. The develop- 
ment of the contradiction involved in denying the conclusion in the 
second figure is a development of the system of relations between 
the terms alleged in the premisses, or of the consequences involved 
in these. It is not, like a suppressed premiss, something without 
the consideration of which the argument is altogether broken- 
backed ; but it is something involved in the full appreciation of the 
argument. 

If then the second figure is not a mere variation of the first, it 
follows that the principle or canon on which the first proceeds is not 
that of the second. If the above account of the nature of our 
reasoning in the second figure is correct, its principle is this, that no 
subject can possess an attribute which either excludes what it 
possesses or carries what it excludes. 

Of the third figure we must give a different account. Its two most 
noticeable features are that the middle term is subject in both pre- 
misses, and the conclusion always particular. For this reason it 
has been well called the inductive figure ; for induction (whatever 
else besides may be involved in it) is the attempt to establish a con- 
clusion upon the evidence of instances. The terms of the conclusion 
are always general . The conclusion declares two characters to be con- 
joined, or (if negative) disjoined : Sailors are handy, The larger carni- 
vora do not breed in captivity. In the premisses we allege instances of 
which both characters can be affirmed ; or of which one can be affirmed 
and the other denied ; and these instances are our evidence for the 
conclusion. But the conclusion is not general ; we are never justi- 
fied, by a mere citation of instances, in drawing a really universal 
conclusion. If All B is A, and All B is C, we cannot say that All G 
is A ; in traditional phraseology, G is undistributed in the minor 
premiss, and therefore must not be distributed in the conclusion ; 
and the thing is obvious, without any such technicalities, in an 
example ; if all men have two arms, and all men have two legs, it 
does not follow that all animals with two legs have two arms ; for 
birds have two legs, besides men, and have not arms at all, but 
wings. Yet, though our instances will never justify a really universal 
conclusion, they may suggest one ; and they will at any rate over- 
throw one. The instances of Queen Elizabeth or Queen Victoria, 



320 AN INTRODUCTION TO LOGIC [chap. 

of Catherine of Russia or Christina of Sweden, wall disprove the 
proposition that No woman can be a statesman ; and truth is often 
advanced by establishing the contradictory of some universal 
proposition, no less than by establishing universal propositions 
themselves. 

Now what is the true nerve of our reasoning in such arguments ? 
It is the instance, or instances. We prove that some C is A, or some 
C is not A, because we can point to a subject which is at once C and 
A, or C and not A. Unless we are sure that the same subject is 
referred to in both premisses, there can be no inference : Some 
animals are quadrupeds, and Some animals are vertebrates ; but they 
might be different animals, and then there would be no instance of 
a vertebrate that had four legs. But if either premiss is universal — 
if e. g., with mammal as our middle term, we take the premisses Some 
mammals are quadrupeds, and All mammals are vertebrates — then it 
follows that Some vertebrates are quadrupeds ; for the ' some ' 
mammals of the major premiss are included among the ' all ' of the 
minor, and therefore we could pick out, from among the latter, 
instances of animals that were both vertebrate and quadruped. The 
instances, however, instead of being vaguely indicated as ' some ' 
of a whole class or kind, may be specified by name ; and then the 
nature of our reasoning is unambiguous ; we are manifestly arguing 
through instances. In order to show that A woman may be a states- 
man, we can appeal to the four queens mentioned above ; these were 
statesmen, and these were women ; and therefore some women have 
been (or women may be) statesmen. But whether the instances in 
which C and A are united, or G is present without A, be cited by 
name, or only indicated as ' some ' of a whole class, in both cases 
alike it is on them that the reasoning hinges, and it is by producing 
them that a sceptic could be confuted, who refused to admit the 
conclusion. 

Aristotle called this production of the instance by the name 
«?K0eo-is, or Exposition. He conceived that the proper mode of 
validating a syllogism in the third figure was by direct reduction, 1 
but added that it was possible to validate it per impossibile or by 
* exposition ' : ' if all S is both P and R, we may take some 
particular S, say JV ; this will be both P and E, so that there will be 

1 Except, of course, where the major premiss is a particular negative and 
the minor an universal affirmative proposition (Bocardo), in which case we 
can only proceed per impossibile or by exposition. Anal. PH. a. vi. 28 b 15-21. 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 321 

some R which is P ' 1 ; and what is possible where both premisses 
are universal and affirmative is equally possible in any other mood. 
This seems to exhibit the real movement of thought in the third 
figure better than the artificial process of direct reduction. For, in 
the first place, if the middle is a singular term, as in this figure it 
often is (though Aristotle took little note of such cases), the con- 
version of a premiss is forced and unnatural. In words I may say 
that since Queen Elizabeth and Queen Victoria were statesmen, 
and some women were Queen Elizabeth and Queen Victoria, there- 
fore women may be statesmen ; but in thought, Queen Elizabeth 
and Queen Victoria will still be subject in the minor premiss. And 
secondly, even where the middle is a general term, direct reduction 
often conceals, rather than expresses, our thought. No ostrich can 
fly, All ostriches have wings .'. Some winged animals cannot fly : here, 
though it is possible to substitute for the minor premiss Some winged 
animals are ostriches, the other is the form in which we naturally 
think ; the more concrete term stands naturally as the subject of 
our thought. 

It may be admitted that there are cases where direct reduction 
is unobjectionable. No clergyman may sit in Parliament, and Some 
clergymen are electors to Parliament .". Some electors to Parliament 
may not sit in it. Here it would be as natural to say that Some 
electors to Parliament are clergymen ; for the franchise, and the 
clerical office, are each an ' accident ' of a man, and either, elector to 
Parliament or clergyman, can equally well be subject in the pro- 
position, and the other predicate. But the character of the argu- 
ment seems changed by this alteration. Clergymen are no longer the 
instance which shows that a man may be entitled to vote without 
being entitled to sit ; the middle term is now a status in virtue of 
which certain voters cannot sit. The point contended for is not 
that there may not be syllogisms in the third figure, whose conclusion 
could be equally well, or even better, obtained with the same middle 
term in the first : but that the movement of thought characteristic 
of the third figure is not, and cannot be reduced to, that of the first ; 
and that reduction, as a general principle, is thereforesuperfluous and 
misleading : the true confirmation of the validity of the syllogism 
lying in the perception that, if the premisses are true, there actually 
are instances of the fact alleged in the conclusion. 

One objection to this view of the third figure needs consideration. 

1 Anal Pri. a. vi. 28 a 24-26. 

177» Y 



322 AN INTRODUCTION TO LOGIC [chap. 

It may be said that the production of a particular instance in support 
of the conclusion does not do full justice to the grounds on which 
we accept it, in cases where the middle term is general and both 
premisses universal. All horned animals ruminate, and they all 
part the hoof ; this, it may be urged, is better ground for concluding 
that cloven-footed animals may be ruminants, than if I merely 
called attention to the cow in my paddock. To settle this, let 
us look for a moment at the two meanings, which (as we saw before) 
may be intended by a particular proposition. 1 If I say that Some 
C is A, I may either mean to refer to certain unspecified but definite 
members of the class C, and predicate A of them ; or without any 
special thought of any particular case, I may mean to declare the 
compatibility of the two characters, C and A, in one subject. In 
the latter case, I can also express my meaning by the problematic 
judgement C may be A ; which contains no doubt the thought of 
unknown conditions under which it will be so. Now supposing 
I understand the proposition in the latter sense, the cow in my 
paddock is as good a middle term as horned animals generally ; 
supposing I understand it in the former sense, then my conclusion, 
that Some cloven-footed animals ruminate, undoubtedly has more to 
rest on, when the premisses speak of all horned animals, than when 
for middle term I refer only to a cow or two in a neighbouring 
paddock. But it is also really a different conclusion ; the ' some ' 
intended are a larger number of unspecified animals in the one case 
than in the other ; and it is only by the production, or ' exposition ', 
of all the instances to which our ' some ' refers, that the reference 
to them all, in the conclusion, may be justified. 

It may fairly be said that the argument, in this view of it, does 
not really amount to a syllogism : it comes to this, that if all horned 
animals ruminate, and all part the hoof, then all cloven-footed animals 
that are horned ruminate. If the exact sphere of the conclusion is 
thus borne in mind when we say that some cloven-footed animals 
ruminate, and we mean by ' some ' all that are horned, there is not 
really and in thought that elimination of the middle term in the 
conclusion which is characteristic of syllogism. It would not be 
reckoned a syllogism if we argued that since Wolsey was a cardinal 
and Wolsey was chancellor, he was both chancellor and a cardinal 2 ; 
neither is it a syllogism (though it is inference) to argue, from the 

* Cf. supra, pp. 178-180, 199. 

* Cf. Bain's Logic, Deduction, p. 159 (ed. 1870). 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 323 

premisses above, that all horned animals are both ruminant and 
cloven-footed : from which it follows that all cloven-footed animals 
that are horned are ruminant. 

We may admit the view of the last paragraph to be the right one. 
Supposing that when we conclude, in the third figure, that Some 
C is (or is not) A, we refer in thought, though not in words, just to 
those particular instances, and no others, which in the premisses 
were stated to be both B and A (or not A), then we have not got 
a proper syllogism. Still our conclusion rests entirely on the pro- 
duction of those instances, few or many, beyond which our thought 
refuses to travel. The true and characteristic syllogism in the third 
figure, however, intends its conclusion in the other sense : as a 
statement of the proved compatibility or separability of two attri- 
butes. And to establish this too it relies on the production of an 
instance ; nor are many instances really more sufficient than one, 
to establish mere compatibility, except as minimizing the risk of 
mal -observation. The appeal need not indeed be to an individual 
it may be to a kind. If we want to prove that an evergreen may 
have conspicuous flowers, we can cite the rhododendron ; and we 
may mean by that not any particular specimen, but any of the 
species generally. 1 But very often, and mostly where one premiss 
is particular, 2 and of course always where the premisses are singular, 
it is on determinate individual instances that we rely ; and one 
instance or one species is enough. Therefore it is by exposition 
— by a production, not of course in bodily form, but in thought, of 
one instance or species — that we justify the inference to ourselves ; 
we actually make this appeal in our minds, if we realize the ground 
of our conclusion. Persons familiar with a type of reasoning may 
draw conclusions from premisses as it were by precedent, and 
without realizing the evidence on which they act ; but whenever we 
are fully conscious of what we are about, there is, in the third figure, 

1 It may be urged that the appeal is really to specimens, not species : for 
the species does not blossom. The question raised is not peculiar to the 
third figure. If I argue that the rhododendron is popular because it flowers 
brilliantly, it may equally be said that rhododendrons do so, not ' the rhodo- 
dendron '. The relation of an universal truth to its instances is involved 
in the question, which is an important one. But it need not complicate the 
present discussion. 

2 Not always, even there ; I may argue that all breeds of dog are 
domesticated, and some are savage, and therefore some domesticated breeds 
of animal are savage (Disamis). Here I am speaking, and thinking, 
throughout not of individual animals but of their kinds. 

Y2 



324 AN INTRODUCTION TO LOGIC [chap. 

the recognition that the conclusion is proved by its exemplification 
in a case cited, or included in what we cite. 

Of course there is a way in which the number of instances makes 
a real difference to the conclusion which we are inclined to draw. 
The case of Prince Bladud is alone enough to show that a man who 
washes in the waters of Bath may recover of a disease. The two 
events, however, may be accidental and unconnected. But if cases 
were multiplied, we should begin to suspect there was a connexion 
between the use of these waters and the cure of certain ailments ; 
or if the ailments which disappeared after taking the waters were of 
all sorts, we might begin to look on Bath waters as a panacea. For 
establishing a connexion between two attributes the number and 
variety of instances are matters of great importance ; but for estab- 
lishing compatibility one instance is enough. Now the third figure 
does not prove more than a compatibility ; and never can prove 
a connexion, however many the instances are ; and though the 
number of instances may make a connexion highly probable, yet we 
are influenced in reaching such a conclusion by other considerations 
besides the mere number of the instances. For example, a man 
who observed in several cows the combination of the cloven foot 
with the ruminating stomach would be much less inclined to suppose 
that there was any general connexion between these characters in 
nature, than if he had observed the same thing in an equal number 
of beasts belonging to as many different species. For we are 
accustomed to find characters constant throughout one species, and 
failing when we go beyond it ; so that the accumulation of instances 
would be discounted by the fact that they all belonged to the same 
kind. Again, we might meet a Privy Councillor in a light suit, and 
yet not be led to regard the next man we met in a light suit as a Privy 
Councillor ; but if we met a Guardsman in a breastplate, we should 
very likely suppose the next man in a breastplate to be a Guards- 
man. The readiness with which we infer connexion is controlled 
by our general knowledge of the kinds of attributes that are con- 
nected ; such considerations do not appear in our premisses, but 
greatly influence our thought. Hence it is, that those who are 
thoroughly familiar with the facts of a science, or of some historical 
period, can make inferences from isolated facts which to persons 
ignorant of the field of investigation, and the controlling principles 
applicable to it, appear foolhardy. But all this belongs to rather 
a different department of logical theory, the Logic of Induction. It 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 325 

remains true that so far as we bring no extraneous considerations to 
bear, and are guided only by the facts contained in our premisses, 
we can infer no more than the compatibility of two characters (or 
their separability) from any number of instances ; and we can infer 
thus much from a single instance. 

It should be noticed, before leaving the consideration of the third 
figure, that it always argues from a ratio cognoscendi. It is not 
because the rhododendron has brilliant flowers, that this attribute 
can be combined with evergreen foliage ; if it were not that there 
is no incompatibility between them, the rhododendron could not 
exhibit both. Our instance merely teaches us that the two are 
compatible ; it is the ground of our assertion, not the ground of 
the fact asserted. And this in itself is enough to show that there 
is a real difference between the nature of our reasoning in the third 
figure, and in the first — at least when our syllogisms in the first 
figure are scientific ; and that the attempt to reduce all syllogisms 
to one typical form imposes an unreal appearance of conformity 
upon arguments which are essentially disparate. 

[The fourth figure of syllogism remains for consideration. 1 It has 
this peculiarity, that its premisses as they stand, if we transpose 
them, present the arrangement of terms required by the first figure. 
And three of its moods (Bramantip, Camenes, and Dimaris), when 
thus regarded as being in the first figure ( =Baralipton, Celantes, 
Dabitis), afford conclusions of which those drawn in the fourth 
figure are merely the converse ; but the other two moods (Fesapo 
and Fresison) yield no conclusion in the first figure, from which the 
conclusion in the fourth might be obtained. Are we therefore to 
regard this figure as presenting a separate type of inference from the 
first, or was Aristotle right in disregarding it ? 

Let us look first at the moods which are reduced to the first 
figure by a mere transposition, and without any alteration, of the 
premisses. In the premisses All nitrogenous foods are flesh-forming , 
All grains are nitrogenous, if we treat flesh-forming as the major 
term, we have a syllogism in Barbara ; but if we treat grains as 
major term, our syllogism is in Bramantip, and the conclusion 
is that Some flesh-forming foods are grains. It is surely true that 
the cogency of this inference, as compared with the other, is pecu- 
liarly unobvious. The conclusion is not what we should naturally 

1 This note may, of course, be equally well regarded as a discussion of the 
indirect moods of the first figure. But if a new type of inference were 
involved in them, the erection of a fourth figure would be justified. As 
that is the question under discussion, it seems fairer to call them moods of 
the fourth figure at the outset. 



326 AN INTRODUCTION TO LOGIC [chap. 

[draw from the premisses ; and we need to look a little closer, in 
order to convince ourselves that it necessarily follows. And this 
conviction comes to us when we realize either that from the given 
premisses it follows that All grains are flesh-forming, and our other 
conclusion follows by conversion from that : or else that if no flesh- 
forming foods were grains, no nitrogenous foods would be grains ; 
and that in that case grains could not all, or any, of them be nitro- 
genous. The same remarks would apply mutatis mutandis to syllo- 
gisms in Camenes or Dimaris ; and we may therefore conclude that 
these moods are not evidently cogent without a further act of 
thought than their formulation in the fourth figure displays. Are 
we therefore to treat them as belonging to the first figure ? The 
reason for doing this is, that the simplest and directest way of 
justifying the inference which they contain is by drawing a con- 
clusion in the first figure from their premisses, and converting it. 

The two remaining moods, Fesapo and Fresison, are less easily 
disposed of. As the same considerations apply to both, it will 
suffice to take an example of the former. No animals indigenous to 
Australia are mammals, All mammals are vertebrate .•. Some vertebrates 
are not indigenous to Australia ; if we transpose these premisses, 
no direct conclusion follows ; we cannot tell from them whether 
any of the animals indigenous to Australia are vertebrate, or not ; 
so that if our argument requires validating, we must validate it 
either by direct or indirect reduction, or by exposition. That it 
does need validating seems to follow from the fact, that in its 
present form it is no more obvious than the three preceding moods 
of the fourth figure ; no one ever argues in the fourth figure, and 
that shows that it does not adequately exhibit the movement 
of thought in inference. Aristotle exhibited the validity of this 
mood 1 by converting both premisses (i.e. by direct reduction): 
No mammal is indigenous to Australia, and Some vertebrates are 
mammals ; and this is a more natural way of putting the argument. 
But there are cases in which conversion would substitute a less 
natural mode of expression in the premisses ; e.g. from the pre- 
misses No mineral waters are alcoholic and All alcohol is taxed, 2 we 
can infer that Some things taxed are not mineral waters ; it would be 
less natural, although it would yield the same conclusion, and that 
in the first figure, to say that Nothing alcoholic is a mineral water, 
and Some things taxed are alcoholic. Again we may proceed by 
indirect reduction ; we may argue that if all vertebrates were 
indigenous to Australia, then since no animals indigenous there 
are mammals, no vertebrate would be a mammal ; we thus reach a 

1 i.e. of Papesmo and also Fresison = Frisesomorum : v. Anal. PH. a. vii. 
29 a 24-27. 

2 It would complicate the illustration too much to make the exception 
required by methylated spirits. 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 327 

[conclusion inconsistent with the premiss All mammals are vertebrate, 
and that shows that our original argument cannot be disputed ; but 
we should more naturally say that No mammals are vertebrate than 
that No vertebrates are mammals ; and the former contradicts 
more directly the premiss that All mammals are vertebrate. Still 
more do we feel this, if we apply indirect reduction to our other 
example ; there, if Everything that is taxed were a mineral water, 
then since No mineral waters are alcoholic, Nothing taxed is alco- 
holic ; it is clearly more natural to say that No alcohol is taxed, 
and that exhibits better the contradiction with our premiss. If we 
employ the method of eK0ecn? or exposition, we must convert the 
premiss No animals indigenous to Australia are mammals ; then we 
have it given that mammals, in any instance that we like to take, 
are not indigenous to Australia, and are vertebrate ; from which it 
follows that an animal is sometimes vertebrate, and not indigenous 
to Australia. Similarly we may convert No mineral waters are 
alcoholic. 

Thus we have in this mood an argument undoubtedly valid, yet 
lacking something to be obvious ; it is possible to validate it in 
several ways, either bringing it into the first figure by conversion 
of both premisses, or into the third by conversion of one, or leaving 
the premisses and showing, as in the second figure, that the falsity 
of the conclusion is inconsistent with their truth. Which of these 
methods is preferable ? and to what figure should the mood be 
referred ? or is it really of a fourth sort ? That it is not of a fourth 
sort is shown by the fact that without one of these methods of 
validation its conclusiveness is not apparent, that conversion of both 
premisses reduces it to the first figure, and that if reduction ad 
impossibile or exposition is to be used, it may as well, and better 
(as will be explained two pages below), be regarded as a syllogism 
belonging, by the nature of its premisses, to the first figure, but need- 
ing validation by this means. Perhaps the first of the above questions 
will be best answered, if we ask in what way, by the use of the same 
middle term, the conclusion of the given syllogism could most 
naturally be reached. How are we to prove that Some vertebrates 
are not indigenous to Australia, using mammals as our middle term ? 
or that Some things taxed are not mineral waters, using alcohol as 
middle term ? In both cases we should appeal to an instance in 
point ; the mammals may be cited to show the former, and alcohol 
to show the latter. It would seem therefore that exposition is the 
natural way of validating the argument ; or in other words, that we 
realize its cogency most readily if we realize that in the major premiss 
there is involved a converse, from which the conclusion follows at 
once in the third figure. 

Are we then to reckon the mood to the third figure, and not 
(with Aristotle) to the first ? Aristotle would, of course, have said 
that since the third figure itself needed validating through the first, 



328 AN INTRODUCTION TO LOGIC [chap. 

[we had stopped half-way in reducing it to the third ; but if, as 
has been held above, the third figure is really a different type of 
inference, our question cannot be settled thus. Let us recall the 
meaning of the distinction between major and minor terms. The 
distinction is not purely formal and external. A term is not really 
the major term because it is made the predicate, and minor because 
it is made the subject, in a conclusion. It is the meaning of 
the terms themselves which determines which ought to be subject, 
and which predicate, and therefore which is major and which 
minor. Otherwise, Aristotle would have recognized the fourth as 
a separate figure. We may take a syllogism in Darii, and by trans- 
position of the premisses produce one in Dimaris ; e.g. the pre- 
misses White is conspicuous at night, Some flowers are white, whose 
natural conclusion is that Some flowers are conspicuous at night, 
furnish instead, if we transpose the premisses, the conclusion that 
Some things conspicuous at night are flowers. But this is an obvious 
inversion, for it is the flower which is conspicuous, and not the 
conspicuous, as such, which is a flower. It is true that there are 
cases where either conclusion is equally natural, as there are pro- 
positions which may be converted without contortion. Those who 
are friendless are unhappy, Some rich men are friendless .: Some rich 
men are unhappy ; or, in Dimaris, Some unhappy men are rich. Here 
the conclusion in Darii is the natural conclusion to draw, because 
the premisses give the reason why a rich man is sometimes unhappy, 
but not why an unhappy man is sometimes rich ; yet, considered 
apart from the premisses, either conclusion is an equally natural 
form of judgement. But the reason is, that the concrete subject men 
is retained throughout ; in the conversion, the attributes rich and 
unhappy change places, but the subject of which they are attributes 
is retained in its place. Now these are merely coincident attributes, 
and neither is properly the subject of the other ; we feel this in 
making the judgement ; and instinctively convert Some rich men 
are unhappy not into Some unhappy are rich men (where the concrete 
term ' rich men ' could not be predicated of ' unhappy ' as such) 
but into Some unhappy men are rich. When, however, this is not 
the case — when the subject-concept contains the ground of the 
predicate-concept, or is the concrete whole in which the latter inheres 
as one feature — then the former is properly the minor and the 
latter the major term, and no verbal artifice which inverts them can 
alter what the fact is for our thought. 

Hence in the first three moods of the fourth figure, reduction to 
the first does no more than recognize in outward form as major and 
as minor terms what we must acknowledge to be so in our thought. 
But in Fesapo and Fresison, the conclusion is the same as what we 
should draw in Ferio after their reduction, and not its converse ; 
we have therefore no ground so far for giving a preference to the 
expression of the argument in the first figure. But the same con- 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 329 

[siderations which make it not an arbitrary matter, which term is 
major and which is minor in the conclusion, will help us to determine 
the right position of the middle term in the premisses. If then the 
premisses of a syllogism in Fesapo or Fresison were both of them 
inversions of what would naturally be expressed in the converse 
form, we should instinctively think them back into the form required 
by the first figure, in drawing the conclusion. This can hardly 
occur with Fesapo ; for bad logic, as well as verbal contortion, 
is required in order to express a particular affirmative by an uni- 
versal converse ; and therefore the minor premiss A cannot be an 
inverted way of stating J : the original of Fesapo cannot be Ferio. 
With Fresison it is more possible ; that is to say, a syllogism in 
Fresison may be reached by converting both premisses of one in 
Ferio (or Celarent) ; and then it is possible that our thought may 
validate the conclusion by converting them back again. Gold does 
not tarnish, Some ancient ornaments are of gold : we may, however, 
say, if we like, that What tarnishes is not gold, and Some things of 
gold are ancient ornaments, and from these premisses draw the same 
conclusion as from the others, that Some ancient ornaments do not 
tarnish ; yet our thought, justifying to itself an inference made by 
outward rule, may fly to the other forms of premiss. If so, it is 
hard to say that we are not really arguing in the first figure, and in 
such a case the syllogism which wears externally the garb of the 
fourth belongs really, and is rightly forced by direct reduction 
to show that it belongs, to the first. It is however possible even 
here to convert only the minor premiss in thought, and reach the 
conclusion in the second figure : by realizing that ancient ornaments, 
if they tarnished, would not be of gold. But the important cases 
are not such as these, where the premisses are palpably in an un- 
natural form, and would be restored to natural form by conversion. 
They are those in which the position of the middle term, as the pre- 
dicate of the major premiss and subject of the minor, is the natural 
position. For here conversion to the first figure produces a result 
as unnatural as there conversion to the fourth figure produced in the 
premisses of an argument naturally belonging to the first ; No 
mineral waters are alcoholic and All alcohol is taxed are propositions 
put in their natural form ; Nothing alcoholic is a mineral water and 
Some taxed things are alcoholic are not. 

And if that is so, there is only one ground on which we can justify 
Aristotle in reckoning these moods to the first figure. It is, that 
what is properly the major term — that is, the most general and 
comprehensive — does stand as predicate in its premiss, and what is 
properly the minor term — that is, the most concrete and specific 
— as subject. Hence looking to the character of the premisses, we 
may fairly say that our syllogism is of the first figure. And it 
follows that Aristotle is right when he says that we prove the minor, 
not universally but partially, of the major ; for major and minor, 



330 AN INTRODUCTION TO LOGIC [chap. 

[as we have seen, are such intrinsically, and not barely in virtue of 
their position in the conclusion ; so that where the two criteria 
lead to opposite results, it is right to base our nomenclature on the 
former. It was through overlooking this, and taking a purely formal 
and external view of the distinction of major and minor terms, that 
some of his successors were led to add a fourth figure to the three 
of Aristotle. But if we recognize these moods as of the first figure, 
we must no less recognize that they need validating ; and the most 
natural way of realizing their validity is by the process of exposition 
which we found to be the characteristic method for the third figure. 
We need not on this account say that the syllogism belongs to the 
third figure. The occurrence of a syllogism of the first figure in the 
reduction per impossibile by which we validate the second did not 
lead us to resolve the second figure into the first. Exposition too, 
though the most natural, is not the only way in which we can 
realize to ourselves the validity of these arguments ; so that the 
third figure could not receive them unchallenged. We must be 
guided, therefore, by the character of the premisses, and assign them 
to the first : but admit that the conclusion is not really drawn with- 
out a further act of inference than appears upon the face of them.] 

We may now sum up the results of our enquiry. There are three 
figures, each with a distinctive character, and the ' imperfect ' 
figures are misrepresented by reduction to the first. The first is the 
chief, because the demonstrative, but not because the only figure. 
Arguments in it need not be demonstrative, but when they are, our 
thought is moving on a higher level of intelligence, though not of 
cogency, than in the other figures. In realizing the validity of the 
second figure, the inconsistency involved in denying the conclusion is 
a more prominent ' moment ' in our thought than the necessity of 
admitting it. The third figure appeals not to relations of concepts, 
but to experience of the conjunction of attributes (or their dis- 
junction) in the same subject, and from that argues the general 
possibility, under conditions unspecified, of what is exhibited in 
a given case. There is no fourth figure ; but in the first three moods 
of the first figure we may also argue to the converse of their conclu- 
sions ; and two moods may be added, with an universal negative 
minor premiss, in which, while the major term cannot be denied of 
the minor without fallacy, the minor can be denied of the major ; 
though such a conclusion is only particular, and realized by the help 
of conversion or of exposition or of reduction per impossibile. It must 
always be remembered that the character of an argument is deter- 
mined not by the form into which it is thrown in words, but by that 
which it assumes in our thought. This is our justification for 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 331 

recognizing the figures as distinct types. In particular cases, 
a syllogism may not belong to the figure into which it has been 
verbally compelled ; in others, it may be possible with the same 
terms to construct syllogisms in more than one figure ; but then 
there must be a real movement of thought in the process of conver- 
sion by which the change is effected. The theory of syllogism ought 
not to be regarded as a lesson in the manipulation of symbols and 
the application of the formulae. What we have to look to is the 
character of the thinking involved in it, and to that end we need to 
realize our symbols and see how the varying character of our terms, 
and of the relations between them in judgement, affects the inference. 
If our enquiry has done anything to bring this lesson home, its length 
and intricacy will not have been altogether vain. 

[One further question about syllogism must be considered. It 
was said above (p. 311) of syllogism in the first figure that its use 
belongs to the stage of incomplete insight into the nature of facts. 
Yet inference depends on seeing the connexion of facts. 1 How then 
can we infer syllogistically ? The same problem may be reached 
another way. We may see that a syllogism is valid, without 
knowing whether its premisses are true, or even knowing them to be 
false ; or we may follow out syllogistic arguments with symbols, 
not knowing what they stand for. 2 Now to see the validity of an 
argument is a process of inference. How then can inference depend 
on seeing connexions of fact ? Again, it is well known that, although 
a false conclusion cannot be validly drawn from true premisses, 
a true conclusion may be validly drawn from premisses one or both 
of which are false ; here then we reach the truth by inference, yet 
clearly not by tracing out the connexions of fact. 

The problem cannot be solved by distinguishing between the 

1 Cf. supra, p. 240. 

8 Neither this fact, nor the fact that the validity of an argument may 
be considered independently of the truth of the premisses, is confined to 
syllogism. Indeed all symbolic logic is an investigation of validity. Mr. Hugh 
MacColl (Symbolic Logic, § 52) makes the strange statement that ' it ia 
a demonstrable fact that not one syllogism of the traditional logic — neither 
Darapti, nor Barbara, nor any other — is valid in the form in which it is 
usually presented in our text-books, and in which, I believe, it has always 
been presented since the time of Aristotle '. The reason he gives is that it 
asserts the premisses and the conclusion, as well as the implication of the 
latter in the former ; and he thinks Barbara, invalid as commonly formulated, 
is valid in the form ' If every A is B, and every B is C, then every A is G \ 
But that is exactly what is meant by saying that the traditional form is valid. 
To call an argument valid is not to call either its premisses or its conclusion 
true, but to say that if the premisses are true, the conclusion is true. The diffi- 
culty is, how we can know this, without knowing whether the premisses or 
conclusion are true. 



332 AN INTRODUCTION TO LOGIC [chap. 

[logic of consistency and the logic of truth. Doubtless in the theory 
of syllogism we have no more than an account of what conclusions 
we must admit, if we are to be consistent, when we have admitted 
certain premisses. That indeed is all we have in any attempt to 
formulate by the help of symbols types of argument that are found 
recurring with various real terms. But what is meant by the con- 
dition ' if we are to be consistent ' ? Consistency is not a matter of 
arbitrary convention ; it is determined by what is possible in the 
nature of things. Inconsistency may be a disregard of the ' laws of 
thought ' ; but these, as we know 1 , are laws of things. That con- 
sistency requires us to admit a certain conclusion if we have admitted 
certain premisses means then that the nature of things requires it. 
Yet if the premisses and conclusion are false, and if we are working 
with symbols, how have we the nature of things before us ? 2 

The problem is partly one that arises in regard to all hypothetical 
thinking. In the inductive sciences, for example, we are constantly 
forming hypotheses, whose consequences we proceed to deduce, only 
to reject the hypotheses if their consequences differ from observed 
facts. Now here the premisses and the conclusion are both false, 
yet the inference from those to this is or should be sound, and 
clearly rests on perceiving connexions of fact. What is seen to 
involve certain consequences is something in the nature of the facts 
supposed. 3 Thus in support of the view that so-called acquired 
characters are not inherited it has been argued 4 that, if the 
conditions of town -life which injure the growth and health of the 
individual disposed the individual to produce correspondingly 
feebler offspring, and again this offspring to produce a yet feebler, 
and so continuously, the later generations of town-dwellers would 
be less resistent to the injurious influences of towns than the earlier, 
the stock, so far as not replenished from country districts, would 
die out, and infants with a long town ancestry, transferred to healthy 
surroundings and reared there, would grow up markedly feebler 
than infants of country ancestry reared with them. But these 

1 Cf. supra, p. 13. 

2 In Mind, vol. xix. N. S. 76, pp. 544-546, I drew a distinction between 
the (ivdyKr) tlvat, the necessity for certain facts to be thus and thus, which ia 
apprehended in demonstrative thinking, and the dvdyicr] Xeyfir, the necessity 
to say one thing if we have said another, which was alone considered in the 
formal treatment of syllogism. Professor J. A. Smith pointed out to me 
the futility of this distinction. What is meant by my being compelled to 
say anything ? As far as talking goes, I can say what I please. But the 
compulsion here is a logical compulsion, not a moral or physical ; and so 
I have not got away from apprehending connexions of fact. By admitting 
the premisses I am compelled to admit the conclusion only because, if what 
the premisses express exists, what the conclusion expresses exists also. But 
how can I see this connexion unless I am considering existents ? 

3 I have learnt from Professor Cook Wilson the importance of this. 
« By Dr. Archdall Reid, The Principles of Heredity, pp. 335-337. 



xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 333 

[things do not happen ; the Jews e.g. have lived mainly in towns 
for many centuries, and often under worse conditions than most 
town-dwellers ; yet they thrive better, not worse, in towns than 
men of other stocks. In this argument, it is because, or so far as, 
we understand what are injury, transmission, identity of relation be- 
tween every two members in a series of terms, &c, that we can 
follow the deduction. 1 Whether in the facts of town-life prolonged 
over a succession of generations we have an example of all these is 
another question, and is the question that has to be settled. So in 
syllogism ; we so understand what an universal relation is between 
one character M and another P, as to see that it involves the 
presence of P in any subject S exhibiting M . The man who sees 
that if the premisses of a given syllogism are true, the conclusion is 
true, moves by insight into relations which are displayed in some 
facts, even if not in the terms of his syllogism. And syllogistic 
reasoning can be used in ' indirect reduction ' just as hypothetical 
reasoning is used in refuting theories in the inductive sciences. 

We may get some further light from our procedure in geometry. 
When we wish to follow a geometrical demonstration about a triangle 
ot circle, we draw a triangle or circle ; but our power to follow the 
demonstration is not dependent on our figure being really triangular 
or circular. We are thinking, as Plato says, 2 not about the figure 
we draw, but about what it represents. So it is when we use 
symbols in working out syllogisms, and equally when we use pre- 
misses with real terms, that we know to be false. ' Whoever knows 
Greek is a compound householder, and all snapdragons know Greek 
.•. All snapdragons are compound householders ' is a syllogism whose 
validity we can only grasp if we think about relations no more 
exemplified in the terms before us than is equality of radii in a badly 
drawn circle, but yet understood because exemplified in some real 
terms. It is still therefore on insight into connexions of fact that 
reasoning rests. 

1 If any one likes to say that the consequence depends on the fact that 
the relation of parent to offspring is an asymmetrical transitive relation, we 
can agree. But if we could think of no example of such relations, we could 
not think out their implications. Oar reasoning therefore rests on our 
perceiving real connexions. This is so even in non-Euclidean geometries. 
We do not really know what would happen if straight lines making equal 
angles with the same straight line could meet ; but when it is said that in 
consequence a triangle might contain more than two right angles, that ia 
because we see that, where x is a positive quantity, l + l + £>2. In other 
words, we are guided by our insight into real connexions whenever we follow 
out the implications of a false hypothesis, whether the falsity of the hypo- 
thesis is only revealed by the discrepancy between its consequences and 
observed fact, or is self-evident. From an unintelligible hypothesis we 
cannot reason. We must reason therefore from what is intelligible in the 
hypotheses of meta-geometry ; and this is relations and analogies exemplified 
in fact. Implication is connexion of fact, not of mere thought, or statement. 

* Rep. vi. 510 d, e. 



334 AN INTRODUCTION TO LOGIC 

[As to drawing a true conclusion from false premisses (e. g., if in 
the syllogism in the last paragraph we put, for the term compound 
householder, the term labiate), if it is simply a question of seeing its 
validity, what has been said already applies here equally, and the 
truth of the conclusion is irrelevant. But if a man is led by arguing 
correctly from false premisses believed true to entertain a true 
belief, he has not been thereby enabled to understand the real con- 
nexion between the terms in his conclusion. All that he understands 
there at all is the subject-attribute relation, which he rightly sup- 
poses to be exemplified between the terms of the conclusion, without 
seeing the connexion there : as a man might rightly suppose, on 
others' testimony, that a portrait was like its original, because he 
knows from other examples what likeness is, though he had never 
seen the original of this portrait. He does not reach an under- 
standing of the connexion which the conclusion states between its 
terms. That is impossible apart from the apprehension of the 
connexion of its terms with the middle term, and therefore impos- 
sible if its terms are not really connected with the middle term 
taken. Consequently in drawing a true conclusion from false 
premisses, not by way of logical exercise, but in actual life, when we 
express in premisses and conclusion what we do think, the inference 
does not really make use of the special (or material) nature of the 
terms, any more than the inference of the geometer makes any 
use of the irregularities or length or thickness or other special 
characters of the lines he draws ; and the connexion alleged in the 
conclusion between just this nature, say being a snapdragon, and 
just that, say being a labiate, is not made manifest, and so, in 
strictness, not concluded, but we come to believe it for a reason 
independent of the nature of those terms. That reason is, that it 
happened to be by help of those terms and the middle term 
that we contemplated a certain connexion of relations displayed 
frequently in what is real, though not in those terms. We 
believe the conclusion, therefore, as Aristotle said, accidentally 
(Kara av\xQ(fir)Kos). Only by studying the structure of snapdragons 
and other flowers, and detecting in them a common character 
variously modified, should we understand that they are labiates. ] 



CHAPTER XV 
OF HYPOTHETICAL AND DISJUNCTIVE REASONING 

The form of argument which we have been examining under the 
name of Syllogism has for its premisses only categorical propositions ; 
but there are forms of argument to which the name has been 
extended, in which this is not so. In what have been called 
Hypothetical and Disjunctive Syllogisms, hypothetical and dis- 
junctive propositions figure in the premisses. For reasons, how- 
ever, to be considered later, it appears better not to call them 
syllogisms, but to speak rather of hypothetical and disjunctive 
arguments. They are processes of argument that recur with great 
frequency both in ordinary thought and in the reasonings of science. 

In a hypothetical argument, one premiss is a hypothetical pro- 
position, connecting a consequent with a condition or antecedent : 
the other is a categorical proposition, 1 either affirming the ante- 
cedent or denying the consequent. From these follows as con- 
clusion a categorical proposition, either affirming the consequent or 
denying the antecedent. In the former case, the argument is 
said to be in the modus ponens or constructive : in the latter 
case, in the modus tollens or destructive. Examples will make 
this clear. 

1. The modus ponens is of the form : — 

If A is B, it is C or If ^ is 5, CisZ> or If A is C, B is G 
AisB AisB AisO 

.'.AisC :.CisD /.BisC 

e. g If the soul is uncreated, it is indestructible 

The soul is uncreated 
.*. It is indestructible 

or If all men are born equal, slavery is unjust 

All men are born equal 
.*. Slavery is unjust 

1 But cf. infra, p 337, iii 



336 AN INTRODUCTION TO LOGIC [chap. 

or If men have obligations towards their friends, they have 

them towards their enemies 
Men have obligations towards their friends 
.*. They have them towards their enemies. 

The following points should be noted further : — 
i. The subject of the minor premiss may either, as in the fore- 
going examples, be the same as the subject of the antecedent in the 
major premiss (if we may retain the name of major for the hypo- 
thetical and of minor for the categorical premisses in this form of 
argument), or it may be a term that we recognize as included 
therein, falling under it. Thus we may argue that 

If a beautiful thing is rare, it is costly 
Diamonds are rare 
.'. They are costly. 

Here it is implied and recognized that diamonds are beautiful things. 
The argument might of course be expressed 

If anything is at once beautiful and rare, it is costly 
Diamonds are at once beautiful and rare 
.". They are costly. 

But diamonds are still ' subsumed ' as a special case under a rule 
that applies beyond them ; the condition in the major premiss does 
not concern them in particular. 

ii. We saw in a previous chapter that the distinction of affirmative 
and negative has no application to hypothetical judgements — for 
every hypothetical judgement connects a consequent with a condition, 
whether that consequent itself be expressed in the form of an 
affirmative or of a negative statement : it would be no hypothetical 
judgement to say that ' If the weather changes at full moon, it 
does not follow that the change will last '} Hence the character 
of the modus ponens is unaltered, whether the antecedent or the 
consequent (and therefore the conclusion) be affirmative or negative. 
I may argue 

If the North American colonies were unrepresented in Parlia- 
ment, they ought not to have been taxed by Parliament 
They were unrepresented in Parliament 
.*. They ought not to have been taxed by Parliament. 

1 This is the denial of a hypothetical judgement, but not itself hypothetical: 
being equivalent to saying ' It is not true that if ', &c. 



xv] HYPOTHETICAL REASONING, ETC. 337 

Here my conclusion is negative ; but the argument is still in the 
modus ponens : for by that is meant not the mood which is affirma- 
tive in its conclusion, but the mood which establishes the consequent 
set down in the major premiss. The reader will easily see that if 
the antecedent were of the form ' If A is not B ', it would still 
make no difference to the character of the argument. 

iii. It is possible to argue with both premisses and the conclusion 
hypothetical, in the form : — 

If .4 is C, it is D or If C is D, E is F or H .4 is D, -B is Z) 

If A is B, it is C If A is B, G is D If B is D,CisD 

.'. li A is B, itisD .' . If A is B, E is F .'. UA is D, GisD 

e. g. If the price of an imported article rises, those who manufacture 
the same article at home will charge more for it 
If a tax is imposed upon the importation of an article, the price 
of the imported article rises 
.*. If a tax is imposed upon the importation of an article, those who 
manufacture the same article at home will charge more for it. 

The remarks made in the last paragraph apply, mutatis mutandis, 
to this form of the modus ponens also ; and the subject of the 
antecedent may be in one premiss the same with that of the con- 
sequent, and in the other different. It is unnecessary to illustrate 
all these variations. 

2. The modus tollens is of the form : — 

If A is B, it is G or If ^ is 5, C is D or If^isC,£isC7 
A is not G Cis not D £ is not G 

:. It is not B .'. A is not B .'. A is not G 

e. g. If matter is indestructible, it is uncreated 
Matter is not uncreated 
.*. It is not indestructible 

or If the earth did not rotate, the winds that blow from the poles 
to the equator would not be deflected westward 
But they are deflected westward 
.*. The earth does rotate. 

or If any one has a natural right to a vote, every one has 
Not every one has 
.". No one has. 
It is plain that the observations made above with regard to the 

1779 z 



338 AN INTRODUCTION TO LOGIC [chap. 

modus ponens are equally applicable, mutatis mutandis, to the modus 
tollens. 

Thus, given a hypothetical proposition, we can proceed to draw 
an inference whenever we have a further premiss given us, either 
affirming the antecedent or denying the consequent. But from the 
affirmation of the consequent, or the denial of the antecedent, no 
conclusion follows. Arguments of the form 

If A is B, it is C 
AisC 
:. It is B 

or A is not B 

.' . It is not G 

are invalid. It is true that if a member of the Commons House of 
Parliament is declared a bankrupt, he loses his seat ; but it is not 
true that if he loses his seat, it must be because he has been declared 
a bankrupt, or that if he is not declared a bankrupt, he may not 
still lose his seat. For the connexion of a consequent with a con- 
dition does not preclude the possibility, that there are other conditions 
upon which the same consequent may follow ; so that the fact of 
the consequent having occurred is no proof of this particular con- 
dition ; nor is the fact that this particular condition is not fulfilled 
any proof that the consequent has not occurred in virtue of the 
fulfilment of some other condition with which it is connected. 
Obvious as these considerations are, yet these are among the com- 
monest errors to occur in men's reasonings. We are all of us apt 
to conclude, that by disproving the allegations advanced in support 
of a proposition, we have disproved the proposition itself ; or that 
by showing that facts agree with the consequences of some hypothesis 
which we have formed, we have established the truth of that hypo- 
thesis. We do not realize that it would be necessary to show, not 
only that the facts agree with the consequences of our hypothesis, 
but that they do not agree with the consequences of any other. 
The Teutonic races have during the last three centuries increased 
and expanded faster than those which speak languages of Latin 
stock ; and some may be inclined to attribute this to the fact that 
the former in the main embraced, while the latter rejected, the 
principles of the Reformation. Grant that the facts are consistent 
with the hypothesis that this difference of growth is due to a differ- 
ence of religion ; yet if there are other ways of explaining it, what 



xv] HYPOTHETICAL REASONING, ETC. 339 

ground has yet been shown for accepting that way ? When facts 
are equally consistent with the truth and with the falsity of our 
hypothesis, we have so far no reason for believing it true. 

It is then fallacious to draw any inference from the affirmation 
of the consequent, or the denial of the antecedent, in a hypothetical 
argument. It is sometimes said that to do the former is to commit 
the fallacy of undistributed middle ; and to do the latter, to commit 
the fallacy of illicit process of the major term : for that the argument 

If A is B, it is C 
AisC 
.'. A is B 



may 


be 


exhibited in 


the form 

ABisO 
AisG 
.'. AisAB 


and the 


argument 










If A is B, it is G 








A is not B 








.'. A is not G 


may 


be exhibited in 


the form 








ABisG 








A is not A B 








.'. A is not G 



And valid hypothetical arguments, it is said, may be similarly 
' reduced ' to categorical syllogisms ; when it will be found, that 
the modus ponens is really a syllogism in Barbara, and the modus 
tollens one in Camestres. 1 

It seems to be an error thus to identify hypothetical reasoning 
with syllogism. In syllogism, as we have seen, a relation is estab- 
lished between two terms in the way of subject and predicate, by 
means of their common relation in the way of subject and predicate 
to a third or middle term. Hypothetical reasoning rests upon 
another relation than that of subject and predicate — the relation 
of condition and consequent ; and there is not necessarily any 
middle term. Where antecedent and consequent, in the hypothetical 

1 A number of modern text-books teach this doctrine. For an older 
authority cf. Zabarella, In Lib. Prior. Anal. Tabulae, p. 158, ' syllogismus 
hypotheticus an valeat necne cognoscitur per eius reductionem ad categori- 
cum.' — Opera Logica, Coloniae, 1597. 

Z2 



340 AN INTRODUCTION TO LOGIC [chap. 

premiss, have the same subject — where that proposition is of the 
iorm ' If A is B, it is G ' — a middle term may at times be found, 
and the reduction effected ; but where that is not so — where it is of 
the form ' If A is B, C is D ' or ' If A is C, B is C '—there a middle 
term is wanting, and the violent nature of this process of reduction 
becomes manifest. 

' If the value of gold is affected by the amount of labour needed 
to obtain it, improvements in mining machinery must raise prices. 
The value of gold is affected by the amount of labour needed to 
obtain it. Therefore improvements in mining machinery raise 
prices.' We are not concerned here with the truth of this hypo- 
thetical proposition. So many circumstances, many of them varying 
independently of one another, combine at any time to affect the 
course of prices, that it would be hard to rest on observation the 
effect which it is here asserted that improvements in mining 
machinery ought to have. Our concern, however, is with the 
character of the argument ; it is clearly difficult to reduce it to 
a syllogism. There is nothing asserted of improvements in mining 
machinery, which in turn is asserted universally to raise prices ; 
the connexion between the value of gold and the amount of labour 
needed to obtain it is not a predicate of improvements in mining 
machinery, nor is raising prices a predicate of that connexion. It 
is a consequence of it ; but that is another matter. Attempts have 
indeed been made to get round this difficulty. It is said that the 
major premiss may be expressed in the form ' The case r of the value 
of gold being affected by the amount of labour needed to obtain it 
is the case of improvements in mining machinery raising prices. 
The existing case is the case of the value of gold being affected by 
the amount of labour needed to obtain it. Therefore the existing 
case is the case of improvements in mining machinery raising 
prices.' But such linguistic tours de force do not alter the nature 
of the argument which they conceal. What does that major premiss 
mean ? Interpreted literally, it is undoubtedly false. Modification 
in the value of gold, because gold has become easier or harder 
to obtain, is not a rise in prices due to improvements in mining 
machinery. The one fact may be dependent on the other, but the 
one is not the other. It is not therefore until we mentally substi- 
tute for this premiss the hypothetical proposition it attempts to 

1 Had I written, for the case, all cases, the proposition would have been 
still more absurd. But the contention should be examined in its strongest form. 



xv] HYPOTHETICAL REASONING, ETC. 341 

supersede, that we assent to it at all ; the ' reduction ' is purely 
verbal ; our meaning remains unchanged, and cannot be put into 
the categorical form. Nor does the minor premiss stand criticism 
any better. What case is ' the case of the value of gold being 
affected by the amount of labour needed to obtain it ' ? To say ' the 
existing case ' is useless, unless we are told what the existing case 
is a case of. If it is a case of the value of gold being affected by the 
amount of labour needed to obtain it, the proposition becomes 
tautological, and the conclusion will only repeat the major premiss 1 : 
if it is a case of something else, we ought in the first place to have 
that something stated, in order that we may know what the pro- 
position means ; and in the second place, when it was stated, we 
should find the proposition had become false, in the same way as 
the major premiss, literally interpreted, was false. It is clear then 
that this syllogism is far from exhibiting more correctly the true 
character of the hypothetical argument in question ; on the contrary, 
the hypothetical form exhibits the true nature of the argument thus 
violently forced into a syllogism. 

Had we indeed taken an example in which the subject of the 
antecedent was the same with the subject of the consequent in 
the major premiss — in which, to put it otherwise, the major premiss 
was of the form ' If A is B, it is C ' : then the process of reduction 
to syllogism would not have appeared to be so difficult or violent. 
For then the condition on which it depends that A is G is a condition 
fulfilled in A. ' If the moon rotates in the same period as it revolves, 
it must present always the same face to the earth. It does rotate 
in the same period as it revolves. Therefore it does present always 
the same face to the earth.' ' If Christian nations had the spirit of 
Christ they would avoid war. They do not avoid war. Therefore 
they have not the spirit of Christ.' There is little change made, if 
we substitute for these arguments the following syllogisms : 

A body rotating in the same period wherein it revolves round 

another body presents always the same face to the other 
The moon is a body rotating in the same period wherein 
it revolves round the earth 2 
.'. The moon presents always the same face to the earth 

1 The case of A is the case of B : the existing case of A is the case of A : 
therefore the existing case of A is the case of B. 

2 It will be seen that in this minor premiss not only is the moon ' subsumed ' 
under the more general notion of a body rotating, &c. : but the earth is also 



342 AN INTRODUCTION TO LOGIC [chap. 

and Those who have the spirit of Christ avoid war 

Christian nations do not avoid war 
.*. Christian nations have not the spirit of Christ. 

Indeed, if it be granted that the hypothetical premiss is unaltered, 
otherwise than in verbal form, by reduction to the form of a cate- 
gorical proposition, we must grant that the argument is unaltered 
by reduction. And there are logicians who have contended that 
all universal judgements are really hypothetical 1 ; from which it 
would follow that there is no real difference between a syllogism 
in Barbara or Camestres, when it has a genuinely universal (i. e. not 
a merely enumerative) major premiss, and a hypothetical argument 
in the modus ponens or the modus fattens — though the former rather 
than the latter would demand reduction. Yet there do seem to be 
some judgements which, in their context, intend to affirm the 
existence of the subject about which assertion is made, and not 
merely to assert that something would be true about it if it existed. 
To say that, if Christian nations had the spirit of Christ, they 
would avoid war, leaves it an open question whether any have that 
spirit ; to say that those who have the spirit of Christ avoid it, 
naturally implies that there are such. The reduction of a hypothe- 
tical argument to a syllogism is no merely verbal change, if it 
substitutes one of these forms of statement for the other. 

Attention ought to be called to one other change incidental to this 
reduction in the last two examples. Our hypothetical major con- 
cerned the moon and the earth, or Christian nations ; in the syllogism, 
the major concerned any two bodies in which certain conditions are 
fulfilled, or any in whom the spirit of Christ is found. Thus in 
the syllogism, a principle is stated in more general form than in the 
hypothetical proposition. Here again, more than a merely formal 
change is involved. It is true that no one could assent to the 
proposition, that if the moon rotates in the same period wherein it 
revolves, it must present always the same face to the earth, without 
seeing that its truth has nothing to do with the fact that the bodies 

subsumed under the more general notion of the other body. Hence it is 
difficult to express the argument completely in symbols. Suppose that we 
write ' Any X is Y, the moon is X .". the moon is Y ' : now here, in the 
major premiss, X='body rotating in the same period wherein it revolves 
round another body ' ; in the minor premiss, X = i body rotating in the same 
period wherein it revolves round the earth ' ; and similarly with Y. The 
argument is none the less a syllogism ; the difficulty is linguistic ; but we 
are really bringing the moon in its relation to the earth under the condition 
of a rule. Aristotle recognizes this : cf. Post. An. 0. xi. 94 a 36- b 7. 
1 Cf. pp. 183, 185, n. 1, supra. 



xv] HYPOTHETICAL REASONING, ETC. 343 

in question are the moon and the earth, but holds equally for any 
two bodies ; so that the more general form of the universal cate- 
gorical proposition given above is obviously justified. Yet it is 
not the mere form of the hypothetical judgement which enables us 
to see this ; and it might be contended in the other case that the 
more general form of the categorical judgement is not justified, and 
that we ought not to have said more than that ' Nations which have 
the spirit of Christ avoid war '. It might be said that if a Christian 
nation had the spirit of Christ, it would avoid war ; but that an 
individual may be morally bound to take part in warfare, though 
he has that spirit, when the nation to which he belongs has it not. 
Now there is, doubtless, in every true hypothetical judgement of 
the form ' If A is B, it is G ', some general principle involved : we 
may express this as ' a /3 is y '. But if A is some determinate 
individual, or case of a particular kind, and if the condition B is 
similarly determinate, we may know that if A is B, it is G, without 
knowing generally what conditions /3, occurring in what kind of 
subject a, will involve the predicate y. Where this is the case 
the hypothetical form is more natural to the expression of our 
argument than the syllogistic. 1 

We find, then, that even when antecedent and consequent have 
the same subject in a hypothetical major, reduction of the hypo- 
thetical argument to syllogism may mean a real change in the 
nature of the argument used ; and that where they have different 
subjects, such reduction can only be effected to outward appearance, 
and by violent means ; for here the condition on which it depends 
that G is D is not a condition asserted to be realized in the nature 
of G itself ; in other words, there is no middle term. 2 No doubt 

1 If the subject of the antecedent in the hypothetical premiss be a singular 
term, and we know of no general term under which it falls which can be 
substituted as subject in its stead, the impossibility of reducing a hypo- 
thetical argument to syllogism is specially obvious ; for we cannot replace 
such a hypothetical proposition by any categorical proposition. ' If he 
marries her, he will be happy ; he will marry her .\ He will be happy ' — is 
an example in point. 

2 The inference in a hypothetical argument might hence be called 
immediate; but such an expression would readily give rise to misunder- 
standing. It is immediate in the sense of having no true middle term : and 
in this it differs from syllogism ; it is also immediate in the sense, that given 
the premisses, nothing more is needed in order that we may see the necessity 
of the conclusion: and in this sense, syllogism, and indeed every step of 
valid argument when fully stated, is immediate. But it was in yet another 
sense that the processes of conversion, &c, were called immediate, and 
distinguished from syllogism : viz. that in them we passed from a single 



344 AN INTRODUCTION TO LOGIC [chap. 

there is an unity embracing both condition and consequent ; they 
belong to a system, of which it might be said that, when affected 
by the condition, it exhibits the consequence. Sometimes this 
admits of ready expression. ' If the rainfall is deficient, the hay- 
crop is light ' : we may express this by saying that ' Grass which is 
insufficiently supplied with moisture makes only a small growth 
that can be used for hay '. In other cases, the interconnexion 
of facts within a whole does not admit of being stated except in 
hypothetical form. And anyhow, it must be contended that 
hypothetical reasoning is not identical in character with syllogism, 
and that we ought not to pretend to validate it by reducing it to 
syllogism, nor to identify the fallacies involved in argument from 
the denial of the antecedent or the affirmation of the consequent 
with the syllogistic fallacies of illicit process of the major term or 
undistributed middle. 

In a disjunctive argument, one premiss is a disjunctive proposi- 
tion ; the other is a categorical proposition, affirming or denying 
one of the alternatives in the former. From these follows as con- 
clusion a categorical proposition, denying or affirming the other 
alternative. In the former case, the argument is said to be in the 

proposition to another inferred therefrom, without anything further being 
required as a means of reaching the conclusion. (Cf. supra, p. 232, n. 3). 
Hypothetical arguments are not immediate in this sense. Given that ' If 
A is JB, it is C , I cannot conclude that A is C, unless I also know that 
A is B : nor could I conclude that A is C, from the fact that A is B, without 
the hypothetical premiss. I can, however, conclude from ' If A is B, it is C 
to ' If A is not C, it is not B ', without any further knowledge : and to this 
we saw that some forms of so-called immediate inference amounted. 

The conditions of valid hypothetical reasoning are of course recognized 
by Aristotle (cf. e. g. Top. /3. iv. lll b 17-23 et al.) ; but he does not speak of 
hypothetical syllogisms. The term ovWnyta-fxos «£ inroBiaeuis has a different 
meaning — viz. a syllogism proving the antecedent of a hypothetical pro- 
position, and therefore, by virtue of the acceptance of that hypothesis, proving 
the conclusion. Let it be granted that if A is B, C is D : then any syllogism 
which proves that A is B will by virtue of this agreement establish also 
that is D : but without such agreement, it would not have been shown at 
all that G is D : that is therefore said to be proved only ex hypothesi. In 
a case between University College, Oxford, and the City of Oxford (v. Times 
of July 5, 1904) arising out of a claim by the College to put a bridge between 
two blocks of buildings on either side of a narrow street called Logic Lane 
without payment of any acknowledgement to the City, it was agreed that 
if the soil of Logic Lane were vested in the College, the College was entitled 
to do this (subject to any building regulations which the City had power to 
make) ; the arguments advanced on behalf of the College (which established 
its case) were directed to show that it was owner of the soil ; but, e'| woft'trfs)?, 
the College showed by the same arguments that it was entitled to erect the 
bridge without acknowledgement. 



xv] HYPOTHETICAL REASONING, ETC. 345 

modus ponendo tollens : in the latter case, in the modus tollendo 
ponens. Examples and observations follow. 

1. The modus ponendo tollens is of the form 

A is either B or G Either A is B or G is D Either A or B is G 
A is B or A is B or A is G 

.'. It is not G ,\ G is not D .'. B is not G 

e. g. ' Possession by devils ' is either a form of mental derangement, 
or supernatural 
It is a form of mental derangement 
/. It is not supernatural 

or Either the interests of religion require the maintenance of the 
Temporal Power, or the Popes are actuated by worldly 
motives in continuing to claim it 
The interests of religion do require its maintenance 
.*. The Popes are not actuated by worldly motives in continuing 
to claim it 

or Either Newton or Leibniz invented the calculus 
Newton invented it 
.*. Leibniz did not 

2. The modus tollendo ponens is of the form 

A is either B or G Either A is B or C is D Either A or B is G 
A is not B or A is not B or A is not G 

.'. ItisC .'. GisD .'.BisG 

e. g. The belief in a golden age rests either on history or on hope 
It does not rest on history 
.'. It rests on hope 

or Either God is unjust, or no man is eternally punished 
God is not unjust 
.*. No man is eternally punished 

or Either Aristotle or Eudemus wrote Bks. v, vi, vii of the Nico- 
machean Ethics 
Eudemus did not write them 
.*. Aristotle did write them. 

The following points should be noted : — 

i. It is sometimes contended that the modus ponendo tollens is 



346 AN INTRODUCTION TO LOGIC [chap. 

invalid : that the affirmation of one alternative does not justify the 
denial of the other. This will depend on the interpretation given 
to the disjunctive proposition. If the alternatives therein stated are 
mutually exclusive, the argument is valid : if otherwise, it is not. 
Whether they are so intended can only be determined in a given 
case by reference to the context and the matter of the judgement ; 
but mutually exclusive alternatives may exist, and therefore a valid 
argument in this mood is possible. Of the examples given above, 
the third is clearly the most open to objection ; for Newton and 
Leibniz may well have invented the calculus independently, as 
they are now believed to have done. In the first, it is implied that 
if we can otherwise account for the phenomena of demoniacal 
possession, we shall not attribute them to supernatural agency ; and 
the argument may be considered valid, provided that we are justified 
in that view. 1 The second is more doubtful ; men may do from 
bad motives what ought anyhow to be done, and the motives of the 
Popes in maintaining their claim to temporal power might be 
worldly, even though their possession of it were required in the 
interests of religion. The premisses do not really prove the un- 
worldliness of their motives ; but they show that we need not 
assume the contrary, in default of further evidence. The validity 
of the present mood of disjunctive argument will, in fact, depend 
on what hypothetic als are implied in its disjunctive premiss ; for 
we have seen (p. 187, supra) that the disjunctive judgement 'A is 
either B or G ' may imply, though it is not reducible to, the hypo- 
thetical judgements ' If A is B, it is not G \ ' If A is G, it is not B ', 
' If A is not B, it is G ', and ' If A is not G, it is B '. If the alter- 
natives are mutually exclusive, all four will be implied, and the 
modus ponendo fattens will be valid. If not, we cannot get, out of 
the proposition ' A is either B or C ', the propositions ' If A is B, 
it is not G '—' If A is G, it is not B '. To say that ' Either the 
interests of religion require the maintenance of the Temporal Power, 
or the Popes are actuated by worldly motives in continuing to claim 
it ' will mean that if the interests of religion do not require it, they 
must be so actuated ; but not that if the interests of religion do 
require it, they cannot be so actuated ; and therefore to argue 
from the premiss that the interests of religion do require it is to 
argue from the denial of the antecedent in a hypothetical argument. 

1 The argument may be valid even though the conclusion be false : the 
truth of the conclusion further presupposes that of the minor premiss. 



xv] HYPOTHETICAL REASONING, ETC. 347 

Here we might leave this matter, with this as our result — that 
the validity of the modus ponendo tollens depends on the alternatives 
in the disjunctive premiss being mutually exclusive, and that there 
is no way of determining on merely formal considerations whether 
they are so * ; that the form of argument is not universally invalid, 
because they may be so ; but not universally valid, because they 
may not. It is, however, worth noticing that quite independently 
of this doubt about the validity of the modus ponendo tollens in 
any given case, the modus tollendo ponens is of more impor- 
tance on other grounds. We are more often interested in proving 
one alternative by disproof of others, than vice versa. A prisoner 
indicted on a charge of murder may indeed be content to show that, 
whoever committed the crime, he did not ; and his ends may be 
satisfied by proving an alibi. But the ends of justice are not satis- 
fied except by discovering the murderer. And so it is with disjunc- 
tive argument generally ; its use lies more in what it can establish 
than in what it can overthrow. 

ii. As in hypothetical, so also in disjunctive argument, the major 
premiss may make a more general assertion, which in the conclusion 
is applied to some special case. Thus a man might argue 

Every man at forty is either a fool or a physician 
My son at forty is not a physician 
.*. He is a fool 

or from the premiss ' Either God is unjust, or no man is eternally 
punished ', I might have concluded that I shall not be eternally 
punished. 2 

iii. The mood of a disjunctive argument is not affected, any 
more than the mood of a hypothetical argument, by the quality — 

1 It might be said that we could give an unambiguous form to the 
argument by writing it thus : ' A is either B only, or C only, or both B and 
C : it is B only .\ it is neither C only, nor both B and C' But here there 
seems to be no inference ; for if we already know that it is B only, we must 
already know that it is not C. The inference rests upon the knowledge 
that A is B, and that B and C are mutually exclusive : if we are doubtful 
of the latter point, and only know that A is B, we cannot tell whether it is 
C or not : and this information is all that we have ; we must not substitute 
for the minor premiss ' A is B ' a different one, ' A is B only '. 

a The subsumption involved may be expressed if we like in a separate 
and syllogistic argument : thus 

Every man at forty is either a fool or a physician 
I am forty 
.*. I am either a fool or a physician : but I am not a physician, &c. 



348 AN INTRODUCTION TO LOGIC [chap. 

affirmative or negative — of the minor premiss or the conclusion. 
Arguments of the type 

A is either B or C 
A is not B 
.'. It is C 

are in the same mood as those of the type 

A is either not B or not C 
AisB 
.'. It is not C 

I establish one alternative by way of rejecting the other, equally 
whether from the premisses 

A diplomatist must either be insincere or fail 
Bismarck did not fail 

I conclude that he was insincere, or whether I conclude that he was 
not honest from the premisses 

A diplomatist is either not honest, or not successful 
Bismarck was successful 

Attempts have been made to reduce disjunctive arguments also 
to syllogistic form. We have seen that a disjunctive proposition 
implies two or perhaps four hypotheticals ; and every disjunctive 
argument can be exhibited as a hypothetical argument using for 
major premiss one of these. But as hypothetical argument is not 
syllogism, we do not thereby make disjunctive argument into 
syllogism ; nor do we really identify it with hypothetical argument ; 
for the hypothetical major premiss expresses only a part of the 
meaning of the disjunctive proposition, from a perception of the 
relations involved in which a disjunctive argument proceeds to 
draw its conclusion. 1 

and having reached the conclusion ' No man is eternally punished ', I can 
with the minor premiss ' I am a man ' draw the conclusion that I shall not 
be eternally punished. This act of subsumption is a different act of inference 
from the disjunctive argument. 

1 The term hypothetical was long used (following Boetius) sensu latiore, 
to cover both what have in this chapter been called hypothetical and what 
have been called disjunctive arguments ; and for hypothetical, in the nar- 
rower sense employed above, the term conjunctive. Conditional — originally 
equivalent to hypothetical in the wider sense — has by some who retained the 
wider sense for the latter been used as equivalent to conjunctive (cf. Sir W. 
Hamilton's Discussions, p. 150). A few points may be noted here which did 
not seem worth a place in the text. 

1. The order in which the alternatives in the disjunction are mentioned 



xv] HYPOTHETICAL REASONING, ETC. 349 

being irrelevant, it makes no difference to the nature of the argument whether 
we proceed from the affirmation of the first to the denial of the second, or 
from the affirmation of the second to the denial of the first. 

2. A disjunction may contain more than two members : e.g. it may be of 
the form A is either B or G or D. In this case, if the minor is categorical, 
the conclusion will be disjunctive ; and in the modus ponendo tollens, a dis- 
junctive minor will give a categorical conclusion — A is either B or C .'. it 
is not D. But the minor ' A is neither B nor C ', which is needed in order 
to get a categorical conclusion in the modus tollendo ponens, is not a dis- 
junctive proposition. But such details involve no fresh principle of reasoning, 
and need not be pursued, any more than it is necessary to work out all the 
variations that are possible according as the disjunction is between two 
predicates of the same subject, or two subjects of the same predicate, or 
two assertions differing both in subject and predicate, when either or both 
assertions in each of these cases are affirmative or negative. 

3. An argument of the form ' A is either B or C : C is either D or E .". A 
is either B or D or E ' is not a disjunctive argument, but the application of 
syllogism to one limb of a disjunctive proposition. 



CHAPTER XVI 

OF ENTHYMEME, SORITES, AND DILEMMA 

This chapter deals with certain forms or modes of stating an 
argument which introduce no new principle of reasoning beyond 
those now already discussed, but for one reason or another deserve 
a special name and mention. 

An enthymeme indeed is not a particular form of argument, but 
a particular way of stating an argument. The name is given to 
a syllogism with one premiss — or, it may be, the conclusion — 
suppressed. 1 Nearly all syllogisms are, as a matter of fact, stated 

1 By Aristotle the term ivQv^yLa is defined as avWoyicrpos e£ (Ikotuv f) 
a-r)fj.(ia)v, Anal. Pri. i3. xxvii. 70 a 10. Its nature is discussed in that chapter 
and in various passages of the Rhetoric. Roughly speaking, etKos is a general 
proposition true only for the most part, such as that Raw foods are unwhole- 
some ; in applying this to prove the unwholesomeness of some particular 
article of diet, we are open to the objection that the article in question may 
form an exception to the rule ; but in practice we are often compelled to 
argue from such probable premisses. A ar)p.iiov is either a particular fact, 
to which one can appeal in support of a general proposition, because if the 
proposition were true, the fact would follow as a consequence of it : thus 
we may argue that ' The wise are just, for Socrates was wise and just ' : 
where Socrates is the arj^flov (Rhet. a. i. 1357 b 11) ; or it is a particular fact 
appealed to as evidence of another particular fact, because the existence of 
one such fact implies the previous or subsequent or concurrent existence of 
the other : thus ' Pittacus is liberal, because ambitious men are liberal, and 
Pittacus is ambitious ' : here his ambition is the orr^xtlov of his liberality 
{Anal. Pri. 0. xxvii. 70 a 26). In this case, the appeal to a <tt)ph'lov implies 
a general principle which, if it is irrefragable, gives to the a-^pdov the nature 
of an evidence, or Tenpi'ipiov (Rhet. a. ii. 1357 b 3) ; to argue from a TtKp.i)ptov 
is not, however, to argue from the true cause of the effect ; for this would 
be scientific syllogism, and not iv8vprip.a. It may be added that, where the 
general principle implied is not irrefragable, but true for the most part, it 
is hard to distinguish the auXXoyio-juoy 4k arjfieiov from a avWoyicrnos ef 
flxoTos. It should be noted that Aristotle includes under arjpelov that which, 
as a consequence of something else, is assumed, where it exists or occurs, 
to presuppose it, whether it could exist or occur without the existence or 
occurrence of that other thing or not ; where it could not, we have a reKprjpiov ; 
and of this character are what doctors call the symptoms of a disease (and 
such reasoning from effect to cause is not 'scientific ') ; where it could, the 
argument — as Aristotle recognizes — is not really valid ; it may be true that 
persons in a fever breathe rapidly, but I cannot safely infer that a person 
who breathes rapidly has fever (ib. 1357 b 19) ; there are, of course, symptoms 
of disease that are of doubtful interpretation. The evBipqiia is said to be 
a rhetorical demonstration, or rhetorical syllogism (Rhet. a. i. 1355 a 6, ii. 



ENTHYMEME, SORITES, AND DILEMMA 351 

as enthyinemes, except in the examples of a logical treatise, or 
the conduct of a formal disputation. It must not be supposed, 
however, that we are the less arguing in syllogism, because we use 
one member of the argument without its being explicitly stated. 
Syllogism is an act of thought, and if, in order to perform this act, 
we need to recognize in thought all three propositions, we are 
arguing syllogistically, whether we enunciate the whole syllogism 
or not. That we do recognize a suppressed premiss may be shown 
by the fact that, if any one were to deny it, we should feel that 
he was attacking our argument, though we had not expressly 
asserted it. 

The suppressed member may be the major premiss, or the minor, 
or — less frequently — the conclusion. Medea, in Ovid's play of that 

1356 b 4), because public speakers make use of the appeal to such probable 
premisses or signs, and do not expect or provide more strictly demonstrative 
or scientific arguments. But they also commonly present their thought 
without enunciating all three propositions of a syllogism, whereas in a set 
debate one endeavours to get both premisses explicitly admitted, and so 
establish a conclusion. And Aristotle, in distinguishing the arguments of 
the platform from those of such debate, probably had in mind both the 
sort of premisses to which orators appeal, and the mode in which they 
present their arguments. The chapter (Rhet. ft. xxi) on yv&fiai, sententiae, 
or apophthegms, describes a yvu>p.rj as part of an enthymeme, because, when 
it is justified by another proposition, we have an enthymeme ; e. g. ' There 
is no man free ' is a yva>p,r], but when we add ' For each is a slave to money 
or to fortune ', there is an enthymeme (1394 b 4-6). So a ypo)p.t) which includes 
the ground of its own statement is called enthymematic.e. g. dOdvarov opyfjv p.f) 
4>v\aTTe 6vj]t6s a>v (' Nurse not immortal anger, being mortal'). Both the 
character of the premisses and its incomplete statement seem then to dis- 
tinguish the enthymeme from other syllogisms, according to Aristotle. That, 
in spite of the definition quoted from Anal. Pri. ft. xxvii, above, the latter 
feature has come to determine the use of the term, may perhaps be due to 
a later passage in the same chapter, 70 a 24-28 idv fiev ovv 17 pla Xexdfj 
TrpoTcuris, arjp.flov ylverai p.6vov, iav be nai 17 iripa Trpoa\ij(f)6rj, <ruXXoyicr/LtoV, oiov 
on UtTTaKos e'Xevdepios' 01 yap $tXoVt/xoi (Xtvflepioi, Ulttokos 8e (fyikoriiios 
('If the one premiss be stated, there is a sign only, but if the other be 
taken also, a syllogism: e.g. Pittacus is generous; for the ambitious are 
generous, and Pittacus is ambitious '). This, however, seems merely to mean 
that, if I say ' Pittacus is generous, because he is ambitious ', I only state the 
sign ; whereas, if I add that the ambitious are generous, I make a syllogism ; 
but this syllogism was implied all along, and is an fvdvp.r}p.a, whether I state 
it in full or not, because of the character of the premisses. A demonstrative 
syllogism could not be so called by Aristotle, even though incompletely 
expressed : e. g. ' The moon is liable to eclipse, because it may be hidden 
by the earth from the sun '. Cf. on the question Cope, Introduction to 
Aristotle's Rhetoric, p. 103, n. The term enthymeme has more commonly been 
applied to a syllogism omitting one of the premisses, than to one omitting 
the conclusion. Sir W. Hamilton (Discussions on Philosophy, dsC, pp. 153-158) 
traces the antiquity of the non- Aristotelian use of the term. It goes back to 
the oldest of the commentators. 



352 AN INTRODUCTION TO LOGIC [chap. 

name, asks Jason — Servare potui, perdere an possim rogas ? here the 
major premiss ,Qui servare possunt, perdere possunt, is understood : 
Medea supplies only the minor, and — in the form of a rhetorical 
question — the conclusion. 1 If I argue that ' those cultivate the 
land best who have a personal interest in its improvement, and 
therefore peasant proprietors are the best cultivators ', I omit — yet 
I clearly use, for to deny it would destroy the argument — the minor 
premiss, that ' peasant proprietors have a personal interest in the 
improvement of the land \ 2 The conclusion may be omitted from 
motives of delicacy, or sometimes for purposes of effect, as in the 
Greek couplet 

kcu ro'oe <Pa>KvX.Cbov' Aipioi kclkoi, ovx o [iiv, OS o' ov, 
ttclvtcs, Tr\r]V Uponkiovs' /cat YlpoKXerjs Aepios. 8 

It is, of course, possible that an enthymeme may be contained in 
what grammatically is only a single sentence ; as in Goneril's address 
to King Lear : 

You, as you are old and reverend, should be wise, 

or in Regan's, later in the play : 

I pray you, father, being weak, seem so. 

A syllogism, whether expressed in full or as an enthymeme, is 
a single act of inference ; it may be analysed into premisses and 
conclusion, but not into parts which are themselves acts of infer- 
ence. The premisses may, however, be themselves in turn conclu- 
sions reached by other acts of inference ; and the conclusion may 
itself serve as premiss to a further act of inference. A syllogism 
proving one of the premisses of another syllogism is called, in 
relation to that, a prosyllogism : and a syllogism using as a premiss 
the conclusion of another is called, in relation to it, an episyllogism ; 
where the prosyllogism is expressed in the form of an enthymeme, 
the whole argument is sometimes called an epieheirema. 4 The 

1 This example is used in the Port Royal Logic, Pt. III. c. xiv. 

8 I am inclined to think it would be found that the major premiss is more 
frequently suppressed when the conclusion of the enthymeme is put in the 
forefront, the minor when we begin with a reason. If we begin with a reason, 
we like to lay down a general principle. 

3 ' This too is from Phocylides : The Lerians are bad men, not this one 
only and not that, but all of them except Proclees ; and he is a Lerian.' 

* v. Mansel's Aldrich, p. 97, note t : and Trendelenburg's Elementa Logices 
Aristotelicae, note to § 33, cited by Mansel. The term einx^PW - was differently 
defined by Aristotle (who called it, as well as the epOiprjpa, a dialectical 
syllogism, (rvWoyitrnos 8ui\eKTiK6s, Top. 6. xi. 162 a 16) : it was an assault 
upon a position maintained in disputation by the respondent. 



xvi] ENTHYMEME, SORITES, AND DILEMMA 353 

following argument contains both a prosyllogism and an episyllo- 
gism, and as the former is expressed in abbreviated form, it is also 
an epicheirema. ' Those who have no occupation have nothing to 
interest themselves in, and therefore are unhappy ; for men with 
nothing in which to interest themselves are always unhappy, since 
happiness depends on the success with which we advance the objects 
in which we are interested ; and so wealth is no guarantee of happi- 
ness.' Here the central syllogism is 

All who have nothing in which to interest themselves are 

unhappy 
Those who have no occupation have nothing in which to 

interest themselves 
.'. Those who have no occupation are unhappy. 

The major premiss is proved by a prosyllogism to this effect : 

Happy men are those who succeed in advancing objects in 

which they are interested 
Men who have nothing in which to interest themselves do 

not succeed in advancing any object in which they are 

interested 
.'. Men who have nothing in which to interest themselves are 

not happy. 

And an episyllogism is added thus : 

Those who have no occupation are unhappy 
Rich men may have no occupation 
.'. Rich men may be unhappy. 1 

We have in such a case a train of argument, of which the several 
steps are not each set out in full, though the premisses necessary to 
complete the sequence of thought are readily supplied, as in an 
enthymeme. Trains of argument may, of course, be of any length, 
and vary indefinitely in composition, according to the nature of the 
separate steps into which they can be broken up ; and it would be 
useless as well as impracticable to invent names for every variety. 
But there is one well-marked variety to which the name of Sorites 
has been given by logicians. 

1 The schoolmen gave the name of syllogismus crypticus to a syllogism 
which lay so concealed in the wording of an argument, that some process 
like conversion, or other substitution of equivalent propositions, was necessary 
in order to show clearly the terms of the syllogism, and their relation : as, 
here, * rich men may be unhappy ' is taken as equivalent to ' wealth is no 
guarantee of happiness '. 

1779 A a 



354 AN INTRODUCTION TO LOGIC |chap. 

A Sorites 1 may perhaps be defined as a syllogism in the first figure 
with many middle terms ; or if it be thought that nothing should be 
called a syllogism that contains more than one act of inference, as 
a polysyllogism 2 in the first figure with the intermediate conclusions 
suppressed. Schematically, it is of the form 

A is B 
BisC 
CisD 
DisE 
EisF 
.'. AisF 

where it will be observed that we start with the minor premiss, and 
each subsequent premiss is, in relation to that enunciated before it, 
a major. 3 

There must be, at least, two steps, and therefore three premisses, 
in a sorites, else we should have no series or chain of syllogisms ; 
and there may be any number of steps more than two ; the premisses 
will always be more numerous by one than the steps into which the 
argument can be resolved. 4 Short sorites are of common occur- 
rence. A well-known example occurs in Romans viii. 29, 30, ' For 
whom he did foreknow, he also did predestinate to be conformed to 

1 The name is derived from o-topoy = heap. 

2 A series of syllogisms, one proving a premiss of another, is called a 
polysyllogism : while each single step of syllogistic reasoning is called 
a monosyllogism. 

8 Where the order in which the premisses are enunciated is reversed, 
starting with the major and proceeding always to one which in relation to 
the preceding is a minor premiss, the sorites is called a Ooclenian Sorites, 
after Rodolphus Goclenius, Professor at Marburg at the end of the sixteenth 
century, who first called attention to this form of presenting the argument. 
But though it is important to notice that the order in which the premisses 
are commonly placed in a sorites is the opposite of that which is customary 
in a simple syllogism, it must not be supposed that the character of the 
argument is affected by reversing the order, or that the Goclenian sorites 
is a thing, as such, of any importance. The Goclenian is known also as 
a regressive, and the other, or ' Aristotelian ', as a progressive sorites. 
Aristotle, however, does not discuss the sorites (though clearly believing it to 
occur in science, cf. An. Post. a. xiv. 79 a 30, xx-xxiii),so that the progressive 
is not entitled to be called Aristotelian. Sir W. Hamilton states that he 
could not trace the term back beyond the Dialectica of Laurentius Valla, 
published in the middle of the fifteenth century. From the sixteenth century 
onward it found a regular place in logical treatises. Cf. his Lectures on Logic, 
xix. p. 377. 

* ' Sorites est syllogismus multiplex . . . Est enim sorites progressio enthy- 
mematica, syllogismos continens propositionibus [ = praemissis] uno tantum 
pauciores.' Downam's Commentarii in Petri Rami Dialecticam, 1510, p. 653. 



xvi] ENTHYMEME, SORITES, AND DILEMMA 355 

the image of his Son. . . Moreover whom he did predestinate, 
them he also called : and whom he called, them he also justified : 
and whom he justified, them he also glorified.' 

But long specimens are less common, not because long trains of 
reasoning are rare, but because the successive steps do not generally 
continue for long together to be of the same form. Leibniz, in 
the second part of his Confessio Naturae contra Atheistas, written in 
1668 (and containing doctrines as to the nature of matter which he 
subsequently abandoned), offers a proof of the immortality of 
the human soul in the form of a continuous sorites ; but even 
so, many of the propositions are supported by reasons that do not 
enter into the series of premisses constituting his sorites. 1 In the 
following transcription the premisses that do not belong to the 
sorites are placed out of line to the right ; and some of them are 
omitted. 

The human soul is a thing whose 
activity is thinking. 

A thing whose activity is thinking 
is one whose activity is imme- 
diately apprehended, and with- 
out any representation of parts 
therein. 

A thing whose activity is appre- 
hended immediately without 
any representation of parts 
therein is a thing whose activity 
does not contain parts. 

A thing whose activity does not for all motion is divisible 
contain parts is one whose acti- into parts, 
vity is not motion : 

A thing whose activity is not for the activity of a body is 
motion is not a body : always a motion. 

What is not a body is not in space : for the definition of body is 

to be extended. 

What is not in space is insus- 
ceptible of motion. 

What is insusceptible of motion for dissolution is a movement 
is indissoluble : of parts. 

1 v. Erdmann's ed., p. 47. 
A a 2 



356 AN INTRODUCTION TO LOGIC [chap. 

What is indissoluble is incorrup- for corruption is dissolution 

tible : of the inmost parts. 

What is incorruptible is immortal. 
.*. The human soul is immortal. 

We may pass from examples to a consideration of the form of 
the argument, and the rules of its validity. It will be observed 
that the predicate of each premiss is the subject of the next, while 
the subject and predicate of the first and last premiss are the subject 
and predicate respectively of the conclusion. For each premiss is 
minor to that which follows, and major to that which precedes it ; 
and as we start from the minor premiss of the whole argument, each 
middle term is predicate of one premiss and subject of the next. 
It follows, that (i) no premiss except the first may be particular, 
and (ii) none except the last negative ; for in the first figure, the 
major premiss must be universal, and the minor affirmative ; now 
each premiss except the last is a minor, in relation to a premiss 
following it, and must therefore be affirmative ; and each premiss 
except the first is a major, in relation to one preceding it, and there- 
fore must be universal. This will be easily seen if we resolve the 
sorites into its constituent syllogisms : 



1. beginning from the minor 




Ai&B 


AiaB (i) 


BiaC 


B is C (ii) 


CisD 


.*. A is G 


DisE 


CisD(iii) 


EisF 


.\ A is D 


.'. AiaF 


DiaE (iv) 




.'. A is E 




EisF{v) 




.'. AisF 



It is clear that if the first premiss were particular, the conclusion 
of the first syllogism would be particular ; this stands as minor to 
the third premiss in the second syllogism, whose conclusion would 
therefore again be particular, and so ultimately would the conclusion 
of the whole sorites be ; but if any other premiss were particular, 
there would be an undistributed middle in the syllogism into whioh 
it entered. 



xvi] ENTHYMEME, SORITES, AND DILEMMA 357 

2. beginning from the major 

EisF (v) 

DisE (iv) 
.*. D is F 

CisD (iii) 
.*. C is F 

BisC (ii) 
.*. B is F 

AisB (i) 
.'. A is F 

Here, if the last premiss (E is .F) were negative, the conclusion of 
the syllogism in which it stands as major would be negative : this 
as major to the premiss C is D would make the next conclusion 
negative, and so ultimately the conclusion of the whole sorites ; but 
if any other premiss were negative, there would be an illicit process 
of the major term in the syllogism into which it entered. The 
rules of a sorites are thus nothing but the special rules of the first 
figure. 1 

A sorites is distinguished from other chains of syllogistic 
reasoning by the fact that not only is one of the premisses sup- 
pressed, at every step of the argument except one, but the inter- 
mediate conclusions, by which the final conclusion is reached, are 
all suppressed ; for the conclusion of one argument is the sup- 
pressed premiss of the next. This is, perhaps, what has led 
logicians to give special attention to it. 2 

The Dilemma combines into one argument hypothetical and 
disjunctive reasoning. Generally it is an argument in which one 
premiss is a disjunctive proposition, and the other consists of hypo- 
thetical propositions connecting with either alternative in the 

1 Either an E or an I proposition may be converted simply. With an 
7 premiss for the first, if it be converted, the sorites may be broken up into 
a series of syllogisms in the third figure ; with an E premiss for the last, 
if it be converted, the sorites may be broken up into a series of syllogisms 
in the second figure. Yet, except for the premiss thus converted, the middle 
terms stand throughout in the premisses as in the first figure. A series of 
premisses in the second or in the third figure will not form a sorites : because 
there would be no series of middle terms, but only one middle term through- 
out ; hence as soon as we come to combine the conclusion of two premisses 
with the next premiss, we should be involved in quaternio terminorum. The 
sorites is therefore essentially confined to the first figure, though its resolution 
may involve the second or third. 

2 It is however only one example of what mathematical logicians like 
Mr. Bertrand Russell call a system of asymmetrical transitive relations. 



358 AN INTRODUCTION TO LOGIC [chap. 

disjunction an unpalatable conclusion. In one form, however, of the 
simple destructive dilemma ' the disjunction may be in the conse- 
quent of the hypothetical premiss, and the other premiss be cate- 
gorical, denying both alternatives in the disjunction. 2 We may 
therefore define a dilemma, to cover this case, as a hypothetical 
argument offering alternatives and proving something against an 
opponent in either case. The conclusion may be either the same, 
whichever alternative is accepted, or different ; in the former case 
the dilemma is called simple, in the latter complex. It is called 
constructive, if it proceeds from affirmation of antecedent in the 
hypothetical premiss to affirmation of consequent ; destructive, if 
it proceeds from denial of consequent to denial of antecedent. 

1. Simple Constructive. 

If A is B, E is F ; and if C is D, E is F 
But either A is B or C is D 
.*. EisF 3 

Troops with a river behind them have sometimes been placed in 
a dilemma none the less painful because it is simple. If they 
stand their ground they die — by the sword of the enemy : if they 
retreat they die — by the flood ; but they must either stand or 
retreat ; therefore they must die. 

2. Complex Constructive. 

HAisB,EisF; and if C is D, G is E 

But either A is B or C is D 
.'. Either E is F or G is H 

Thus we might argue — and this too is unfortunately a dilemma 
from which it is not easy to see an escape : 

11 there is censorship of the press, abuses which should be 
exposed will be hushed up ; and if there is no censorship, 
truth will be sacrificed to sensation 
But there must either be censorship or not 

1 See below, pp. 360-361. 

2 The hypothetical premiss is sometimes called the major, in accordance 
with the nomenclature used also of hypothetical reasoning : and the other 
premiss the minor. 

3 Antecedent and consequent may, of course, all have the same subject (if 
A is B, it is D ; and if it is C, it is D) : or the same subject in one case and 
different subjects in the other ; and the minor premiss will vary accordingly. 
It would be tedious to give each time all these varieties, which involve no 
difference of principle. 



xvi] ENTHYMEME, SORITES, AND DILEMMA 359 

.*. Either abuses which should be exposed must be hushed up, 
or truth be sacrificed to sensation. 

3. Simple Destructive. 

If A is B, G is D and E is F 
But either C is not D or E is not F 
.*. A is not B 

Plato, in the Republic, 1 urges that children should not learn the 

poems of Homer, from which they will derive very false beliefs about 

the nature of the gods. One of his arguments might be put thus : 

If Homer speaks truth about things divine, the heroes were 

sons of gods, and did many wicked deeds 
But either they were not sons of gods, or they did not do 
wicked deeds 
.*. Homer does not speak truth about things divine. 

Again, If A is B, either C is D or E is F 
But neither is G D, nor is E F 

: . A is not B 

Of this character was one of the arguments used by Zeno to 
disprove the possibility (or perhaps we might say, the intelligibility) 
of motion : 

If a body moves, it must either move in the place where 

it is, or in the place where it is not 
But it can neither move in the place where it is, nor in the 
place where it is not 
.*. It cannot move. 

4. Complex Destructive. 

ttAisB,EisF; and if Cis D, Gia H 
But either E is not F, or G is not H 
.'. Either A is not B, or G is not D 

A nation having colonies like those of Great Britain might fairly 
urge : 

If we give our colonies self-government, we shall make 
them powerful ; and if we attempt to control their use of 
it, we shall make them hostile 
But either we ought not to make them powerful, or we 
ought not to make them hostile 

1 III. 391 G-E. 



360 AN INTRODUCTION TO LOGIC [chap. 

.'. Either we ought not to give them self-government, or we 
ought not to attempt to control their use of it. 

[It is sometimes said that a destructive dilemma is always com- 
plex, and such arguments as those given under (3) above would not 
be allowed to be dilemmas. Mansel's definition (which follows 
Whately, and has been adopted by others since) definitely excludes 
the simple destructive ; according to him (v. his Aldrich, p. 108, 
n. i) a dilemma is ' a syllogism having a conditional major premiss 
with more than one antecedent, and a disjunctive minor ' ; as the 
destructive dilemma proceeds from denial of consequent to denial 
of antecedent, if there is more than one antecedent its conclusion 
must be necessarily complex. A number of writers, however, have 
admitted the simple destructive dilemma ; and it seems very difficult 
to exclude examples of the first form above given, at any rate. 
The simple constructive (If A is B, E is F ; and if G is D, E is F) 
may be written 

If A is B or C is D, E is F 

But either A is B or C is D 
.-. E is F 

The simple destructive runs 

If A is B, C is D and E is F 
But either G is not D or E is not F 
.♦. A is not B 

It may be said that there is a disjunction in the hypothetical premiss 
of the former, and not of the latter ; but this does not seem to 
constitute an essential difference, such as would render one a dilemma 
and the other not. In the former, one or other of two alternatives 
must be affirmed, and whichever be affirmed, the same conclusion 
follows, because it is logically a consequent of affirming either 
alternative ; in the latter, one or other of two alternatives must be 
denied, and whichever be denied, the same conclusion follows, 
because it is logically a consequent of denying either alternative. 
The essence of the dilemma seems to lie in the fact of confronting 
a man with alternatives at once ineluctable and unpleasant : cf . the 
definition quoted by Mansel from Cassiodorus, loc. cit. : Dilemma, 
quod fit ex duabus propositionibus pluribusve, ex quibus quidquid 
electumfuit, contrarium esse non dubium est. And therefore the other 
example given above — Zeno's argument about motion — seems also 
to be fairly called a dilemma. 1 It is true that its second premiss is 
not disjunctive at all, but denies a disjunctive proposition ; it does 
not assert the truth of one of two alternatives, but the falsity of both. 
But the whole argument is a combination of the hypothetical and 

1 So Minto takes it, Logic, Inductive and Deductive, p. 224. 



xvi] ENTHYMEME, SORITES, AND DILEMMA 361 

[the disjunctive, and drives a man into a corner by way of alterna- 
tives between which his choice is alleged to be confined. If we are 
to maintain that a body moves, we have to assert one or other of 
two propositions which are both self -contradictory ; and that seems 
a good example of being placed between the devil and the deep sea. 
The simple constructive dilemma is a hypothetical argument in 
the modus ponens ; its hypothetical premiss has a disjunctive 
antecedent and a simple consequent, and therefore the other premiss 
must be disjunctive and the conclusion simple. The simple destruc- 
tive dilemma of the second form given above is a hypothetical 
argument in the modus tollens ; its hypothetical premiss has a simple 
antecedent and a disjunctive consequent ; the other premiss must 
therefore be the denial of a disjunctive proposition, and the con- 
clusion the denial of a simple one. But the denial of a disjunctive 
proposition is a categorical, whereas the affirmation of it is of course 
a disjunctive proposition. Hence the difference which has led to 
refusing the name of dilemma to this form of argument ; yet its 
parallelism with the simple constructive seems correct and clear. 
It may be asked why there are two types of simple destructive 
dilemma, against one type of simple constructive. The answer 
feeems to be this. In the destructive dilemma, I may overthrow 
the antecedent, either if its truth involves two consequents, one or 
other of which I can deny, or if its truth involves one or other of 
two consequents, both of which I can deny ; and each case involves 
a disjunction. In the constructive dilemma, I can establish the 
consequent, either if two antecedents involve its truth, both of 
which I can affirm, or if either of two antecedents involve its truth, 
one or other of which I can affirm. But here the former case 
does not constitute a dilemma, because no disjunction is involved 
anywhere : If A and B are true, C is true ; but A and B are true 
.-. C is true. It would appear therefore that so far from there being 
no such thing as a simple destructive dilemma, there are two forms 
of it, against only one form of simple constructive dilemma.] 

A dilemma is sometimes spoken of as if it were a peculiarly 
unsound form of argument. It shares with all inference the pro- 
perty that it is of no material value unless its premisses are true ; 
but formally it is quite sound, and if there is about it any special 
weakness, it must lie in some special difficulty in getting true pre- 
misses for it. Now it is generally difficult, except where one alter- 
native is the bare negation of the other, to get an exhaustive 
disjunction ; it is here that any one ' in a dilemma ' would look 
for a way out ; and it is this difficulty which inspires mistrust of 
the dilemma as a form of argument. 

To show that there is some other alternative besides those, on 



362 AN INTRODUCTION TO LOGIC [chap. 

one or other of which your opponent attempts to drive you, is called 
escaping between the horns of a dilemma : the alternatives being the 
' horns ' on which you are to be ' impaled '. In reply to Zeno's dilemma 
to show the impossibility of motion, it is often said that a body 
need not move either in the place where it is or in the place where 
it is not ; since it may move between these places. It may be 
questioned whether this is a very satisfactory solution of the para- 
dox ; for those who offer it might find it hard to say where the body 
is when it is between these places ; if it is not in some other place, 
the continuity of space seems to suffer disruption. But however 
that may be, we have here an attempt to escape between the horns 
of Zeno's dilemma. 

The other two ways of meeting a dilemma also bear somewhat 
picturesque names ; we may rebut it, or we may take it by the horns. 
To rebut it is to produce another dilemma with a contradictory 
conclusion. The old story of Protagoras and Euathlus, without 
which a discussion of Dilemma would hardly be complete, furnishes 
a good example of rebutting. Protagoras had agreed with Euathlus 
to teach him rhetoric for a fee, of which half was to be paid at the 
conclusion of the instruction, and the remainder when Euathlus won 
his first suit in court. Observing that the latter delayed to practise, 
Protagoras thought he was endeavouring to evade payment, and 
therefore himself brought a suit for the recovery of the second half 
of his fee. He then argued with the jury that Euathlus ought to 
pay him, in the following way : 

If, he said, he loses this case, he ought to pay, by the judge- 
ment of the court ; and if he wins it, he ought to pay, 
by his own agreement 

But he must either lose it or win it 
.*. He ought to pay. 

Euathlus, however, rebutted this dilemma with the following : 

If I win this case, I ought not to pay, by the judgement of 
the court ; and if I lose it, I ought not to pay, by my own 
agreement 

But I must either win it or lose it 
.*. I ought not to pay. 

It will be seen that the rebutting dilemma is produced in this 
case by connecting in the hypothetical premiss, with either ante- 



xvi] ENTHYMEME, SORITES, AND DILEMMA 363 

cedent, the contradictory of the consequent originally connected 
with the other. With a destructive dilemma the parallel procedure 
would be to comiect with the contradictory of either antecedent 
the consequent originally connected with the other. But this is not 
the only way of rebutting ; you rebut whenever you produce 
a dilemma with contradictory conclusion, even though you do it with 
quite different premisses. Nor can every dilemma be rebutted in 
this way or in any other way : not in this, for the alternative con- 
ditions are not always such with which you can connect the contra- 
dictory of each other's consequents. And if a dilemma can be 
rebutted, it must be for one of three reasons. Either (1) there must 
(as in the last example) be some impossible assumption in the 
supposed situation ; and some of the ancients spent much ingenuity 
in imagining situations of this kind, in which our reason was 
entangled by finding that two contradictory solutions of a problem 
could apparently be maintained with equal force. 1 Or (2) the 
premisses are unsound, and premisses equally or more plausible 
can be found for another dilemma proving a contradictory con- 
clusion ; in this case, it would be possible to attack the original 
dilemma directly, either by showing that you can escape between 
the horns of it, if the disjunction is not complete, or in the third of 
the ways mentioned above, by ' taking it by the horns '. Or else 
(3) as happens, unless there is an impossible assumption in the situa- 
tion supposed, when we rebut by transposing and denying the conse- 
quents or the antecedents, the conclusions of the two dilemmas are 
perfectly consistent, and the second merely shows that you will escape 
one or other of the alternatives, of which the first showed that one 
or other would be incurred. In a complex dilemma whose alterna- 
tives are mutually exclusive this is obviously necessary ; but it is 

1 Of this nature are the well-known sophisms of the 'Liar' and the 
'Crocodile' ; Epimenides the Cretan said that all Cretans were liars; if they 
were, was he lying, or was he speaking the truth ? — a crocodile had stolen 
a child, and promised the mother he would restore it, if she could guess 
rightly whether he intended to do so or not ; if she said he would not restore 
it, she could not claim the child by his promise, because her taking it would 
make her guess wrong ; if she said he would restore it, she could not claim 
it, for she guessed wrongly ; what was she to say ? (cf . Lucian, Vit. Auct. 
§ 22, cited Mansel's Aldrich, p. 151). The solution of the first is easy unless 
we suppose that no Cretan ever spoke the truth ; in which case the truth 
of the statement attributed to Epimenides is incompatible with his making 
it. It may be said generally of both these sophisms, and of the story of 
Protagoras and Euathlus, that the difficulty arises from supposing that a 
statement or agreement about certain matters can itself be within the scope of 
such statement or agreement. 



3G4 AN INTRODUCTION TO LOGIC [chap. 

small consolation to any one on the horns of a dilemma, to point it 
out. When Henry VIII desired to force upon Sir Thomas More the 
oath of supremacy, More was asked whether he thought the statute 
' giving to the King the title of Supreme Head of the Church under 
Christ ' had been ' lawfully made or not. He replied that the act 
was like a two-edged sword, for " if he said that it were good, he 
would imperil his soul ; and if he said contrary to the statute, it 
were death to the body ".' * If a man is threatened with death or 
damnation, the threat is not proved empty by showing that he will 
escape damnation or death. Sir Thomas More indeed ' declined to 
swear at all '. But that also was death to the body. 

To take a dilemma by the horns (or by one of them) is to accept 
an alternative offered you, but to deny that the consequence, which 
the opponent attaches to its acceptance, follows. Perhaps the 
following will serve for an example. It is held by many naturalists, 
that species are modified in the course of descent only by the accu- 
mulation of many slight variations, and not per saltum : variations 
not being directly adaptive, but being distributed, in respect of 
frequency and degree, in proportions that follow the well-known 
' curve of error ', on either side of the standard represented in the 
parents. Against this it has been argued, that though the cumula- 
tive effect of many slight variations might be useful, it will often 
happen that in the incipient stages, while the distance traversed in 
the direction of some new peculiarity is still very slight, the variation 
would be valueless, and therefore not tend to be perpetuated ; 
so that the basis for accumulation would not exist. This line of 
objection has been applied to the particular case of protective 
colouring in insects in the following argument. 2 If, it is said, the 
slight variations, with which the process of mimicry in insects must, 
as alleged, begin, are of no use in leading birds to mistake the 
individuals exhibiting them for members of some protected species, 
then they will not be preserved by natural selection, and no accumu- 
lation can take place ; while if they are of use, any further and 
more exact resemblance to the protected species is unnecessary, and 
could not, if it occurred, be preserved by natural selection. Now 
against this dilemma we may answer that it does not follow that, 
because a slight degree of resemblance is useful, any further degree 

1 Political History of England, vol. v, by H. A. L. Fisher, p. 350. 
* See an article on The Age of the Inhabited Earth, by Sir Edward Fry, in 
the Monthly Review for January, 1903. 



xvi] ENTHYMEME, SORITES, AND DILEMMA 365 

would be superfluous. On a particular occasion a particular insect 
no doubt needs no greater resemblance than what has actually 
enabled it to escape ; but with a large number of insects over a long 
series of occasions, it may well be that the percentage of escapes 
would be higher with those in whom the resemblance was closer. 
Thus the dilemma is ' taken by the horns ' ; but that does not settle 
the important question at issue as to whether variation ever does 
proceed per saltum or not. We saw before that a thesis is not 
disproved by the refutation of any particular argument brought 
forward in support of it. 



CHAPTER XVII 

OF THE FORM AND MATTER OF INFERENCE 

So far we have considered and examined some of the commonest 
forms of inference — syllogism, hypothetical and disjunctive reason- 
ing, and certain complications of these. We have not pretended 
— what has nevertheless sometimes been maintained — either that 
the last two can be reduced to syllogism, or that syllogism, even if the 
term be taken to include the three, is the type to which all valid 
inference must conform ; though we have maintained, and it will 
appear more fully in the sequel, that all are forms of great fre- 
quency and importance in our thought. Were Logic a purely formal 
science, the analysis of these forms would be, to those who thought 
that all reasoning really moved in one or other of them, the end of 
the task imposed upon that science ; to those who did not think 
them the only forms in which men's reasoning moves, no other task 
would be left than to offer a similar analysis of the remainder. 
But if it is impossible to understand fully the form of thinking 
without reference to differences in it springing from the nature of 
that about which we think, then the task of Logic is obviously 
harder. It will not suffice to work with symbols. We cannot 
make abstraction of the special character of our terms. Already 
we have found this to be the case. We saw that what is called 
demonstrative syllogism in the first figure rests upon a perception 
of the necessary relation between certain notions, or universals ; 
while in the third figure such a perception of necessary relation 
neither need be given in the premisses of a syllogism, nor can 
be reached in the conclusion. We saw too how hypothetical reason- 
ing, where it differs most from syllogistic, differs because it establishes 
a connexion between subject and predicate in the conclusion by 
means of a condition which is apparently extraneous to the nature 
of the subject ; and yet how our thought recognizes that there 
must be some wider system to which the subject and that condition 
both belong, and through which it comes about that the fulfilment 
of the latter should affect the predicates of the former. None of 
these things could be explained or understood merely through 



THE FORM AND MATTER OF INFERENCE 367 

symbols : examples were needed not only to show that the argu- 
ments symbolized were such as we do actually often use, but because 
only in suitable examples could those facts of our thought with 
which we were concerned be realized. The symbols, e.g., are the 
same, but do not symbolize the same thing, when some terms in our 
syllogism are singular, and stand for individual concrete subjects, 
whose attributes are set down as we find them, and when they are 
all general, and signify universal characters of things, between 
which we perceive connexion. 

It will be said that if the form of thought be thus bound up with 
the matter, and if the matter be different according as we think 
about different things, an understanding of the form must wait upon 
a knowledge of these, and the task of Logic will not be complete 
until we have finished the investigation of what is to be known. 
In a sense this is true. It may be illustrated by mathematics ; 
no one can understand the nature of mathematical reasoning 
except in reflection upon his thinking about number or space or 
quantity ; it cannot be seen in application to heterogeneous sub- 
jects. And it consists with the position which we have taken up 
from the outset, that Logic is the science which brings to clear 
consciousness the nature of the processes which our thought per- 
forms when we are thinking about other things than Logic. Never- 
theless we must bear in mind one or two facts, which may make the 
task of Logic seem a little less hopeless than it would appear to be, 
if it had to wait altogether upon the completion of knowledge. 

In the first place, the dependence of the form of thought upon 
the matter is consistent with some degree of independence. It may 
be impossible to grasp the nature of mathematical proof except in 
application to mathematical subjects ; but an analysis of one or two 
examples of geometrical reasoning may serve to show us the nature 
of geometrical reasoning in general, and after that the form of it will 
not be any better understood for tracking it through all our reason- 
ings about every figure and space-relation. So also it may be 
impossible except in examples of the relation of subject and predicate 
to grasp the distinctive character of syllogistic reasoning ; but we 
may grasp it there universally, and realize that it will be the same 
for all terms that stand in those relations. If this were not so, 
science would be impossible ; for science seeks to reduce a multi- 
plicity of facts to unity of principles. Thus our apprehension of 
the forms of thought has not to wait upon the completion of our 



368 AN INTRODUCTION TO LOGIC [chap. 

knowledge so far as that completion means only its extension to fresh 
subjects of the same kind. If some branch of our knowledge is 
defective in point of extent — as it would appear, for example, that 
the science of number must ever continue to be, because the numeri- 
cal series is by its nature inexhaustible — yet its further extension 
may involve no change in its character ; and so soon as all the main 
branches of possible knowledge have been discovered — that is, 
knowledge about all the main departments of fact — the forms which 
thought assumes in them can be studied even while our knowledge 
is incomplete in its extent. The main departments of fact must, 
of course, be taken to include not merely those which form the sub- 
jects of the physical sciences, but equally those of which philosophy 
treats, and not least the relation of the world to the mind that 
knows it. It would be rash to assert that this stage has been 
reached in the progress of knowledge. The completion of our 
knowledge may yet require not only its extension, but in large 
degree its transformation. Yet we may assert that a great deal of 
our ignorance forms no bar to the completion of the investigations 
of Logic. 

And in the second place, though Logic is in the main a reflection 
upon the nature of knowledge already gained, there is this paradox 
about knowledge, that we seem to some extent to know what know- 
ledge ought to be, before we know anything as we ought. We 
have an ideal, of which we are sufficiently conscious to realize the 
imperfections of the actual, though not sufficiently conscious to be 
able to put it clearly and fully into words. This paradox is not 
confined to knowledge ; it occurs in art and in morality also. 1 We 
may recognize defect in an aesthetic whole without being able to 
rectify it, and yet we may be able to say in what direction its per- 
fection must lie ; we may know that ' we have all sinned ', without 
having seen ' the glory of God ', and still be able to prescribe some 
of the conditions which that must realize. So also we may know 
that the form of our thought, even when we think best and most 
patiently, often falls short of the full measure of knowledge : that 
our way of thinking — our way of looking at things, if one may put 
it so — is wrong because it fails to escape contradictions and satisfy 
all doubts ; and that there must be some way of thinking (if the 
world is as a whole intelligible at all) in which contradiction and 
uncertainty will vanish. We may know all this, and know that we 

1 Cf. supra, p. 10, n. 2. 



xvii] THE FORM AND MATTER OF INFERENCE 369 

have not found that better way (for if we had, we should certainly 
not remain in the worse) : and still we may be able to say something 
about it though we have not found it : to lay down conditions 
which our knowledge of any subject must satisfy because it is 
knowledge — i. e. to prescribe to some extent the form of knowledge, 
not only as a result of reflection upon instances of subjects being 
perfectly known or by abstraction from the activity of knowing 
perfectly in the concrete, but by way of anticipation, out of reflection 
upon instances in which we know subjects less than perfectly, and 
know the imperfection of our knowing. The extent to which we can 
thus anticipate is not unlimited ; a man must get some way in 
science, before he will realize what science should be, and that it is 
not what it should be ; just as a man must get some way in virtue 
before he will realize how much more it requires of him than he has 
achieved. Yet it remains true that thought can in some degree 
anticipate a form of knowing a subject which it has not exercised 
therein ; and it is the business of Logic to set this form forth. 
So far again Logic has not to wait, in order to complete its task, 
until our investigation of what is to be known has been completed. 

If this is true, we may say on the one hand, that no study of the 
nature of inference can be adequate which treats it as an operation 
performed with symbols, or one intelligible at any rate when we work 
merely with symbols. On the other hand, we may recognize that 
there are recurrent forms of inference, whose nature is the same in 
their different occurrences, 1 and that they occur commonly and are 
displayed in regard to subjects in many respects very diverse ; we 
may also recognize an ideal of what inference should be if it is to 
convey knowledge : if we are to realize in making it not merely that 
the conclusion follows from the premisses, but that we are getting 
at indubitable truth. 

Our discussion of inference up to this point must therefore be 
incomplete, in so far as (a) we have failed to deal with all those 
distinguishable recurrent forms of inference whose universal nature 
can be realized in an example ; (b) we have failed to make plain the 
conditions of knowledge as well as the conditions of cogency. 

As to the first count, there are certainly forms which have not 

1 Some might maintain that it is never quite the same when the matter is 
different, any more than the nature of man is quite the same in any two 
individuals. I do not wish to subscribe to this view ; but even its upholders 
would admit that such differences may be negligible. 

1779 B b 



370 AN INTRODUCTION TO LOGIC [chap. 

been examined. For example, there is the a fortiori argument. 'He 
that loveth not his brother whom he hath seen ', asks St. John, 
' how can he love God whom he hath not seen ? ' And there is 
mathematical reasoning, of which we have only said that it is not 
syllogistic ; this from its importance may claim rather fuller con- 
sideration. But perhaps more remains to be done in the way of 
showing how far inference of these different forms enters into the 
building up of our knowledge, and what other operations of thought 
enter into it. 

As to the second count : it is a charge brought against the analysis 
of syllogism, and the other inferential forms considered above, that 
such analysis only shows us the conditions of consistency in reason- 
ing, and not the conditions of truth. To reason consistently is very 
different from discovering truth ; for the consistent reasoner will 
reproduce in his conclusion the error there may be in his premisses. 1 
Those who have brought this charge have sometimes supposed that 
what is wanted is other and better forms of inference. It would 
be much truer to say that what we want is to realize how much 
besides formal validity of inference must be present in an argument 
which is to convey knowledge. To realize what is needed is not 
indeed the same thing as to supply it ; but Logic cannot help us to 
more. The critics of the Logic which was content to analyse the 
conditions of validity in some of the common inferential forms (and 
which often supposed — it must be admitted — that there were no 
other forms of inference) have not always believed this. Many of 
them, as has been said in the first chapter, still looked on Logic 
mainly as an instrument for the discovery of truth about any 
matter on which we might propose to reason, and hoped to find 
a new and better instrument than what the Logic which confined 
itself to such analysis afforded. This was the object with which 
Bacon wrote his ' New Instrument ' or Novum Organum ; and 
J. S. Mill, though he calls Logic a science, wrote his famous treatise 
in the hope that familiarity with the methods of reasoning used 
successfully in the physical sciences would enable men to prosecute 
the study of the moral and political sciences with more success. 2 
Logic is not a short cut to all other branches of knowledge. But 
this we may say, that men who know the difference between con- 

1 Though formally a true conclusion may be got from false premisses, the 
error still infects the mind, and will lead to a false conclusion somewhere. 

2 Cf. System of Logic, VI. i., and Autobiography, p. 226. 



xvii] THE FORM AND MATTER OF INFERENCE 371 

sistency and demonstration, who know what is required before it 
can be said that they have knowledge about things, in the full and 
proper sense of that term, are less likely to remain content with the 
substitutes that commonly pass muster in men's minds for know- 
ledge. By a study of the conditions of demonstration we may be 
led to see how far from being demonstrated are many of the beliefs 
we hold most confidently. To know what we do know, and what 
we do not — what, out of the things we suppose ourselves to know, 
we really know and are rationally justified in believing : this, as 
Plato long ago insisted, 1 is neither a small thing, nor an easy ; and 
until we understand what knowing a thing means and requires, 
we are not likely to achieve it. This is why Logic should do more 
than present us with a study of the forms of consistent reasoning, 
and should attempt to exhibit the nature of knowledge and demon- 
stration : not because such an exposition of the form of knowledge 
is itself an instrument for bringing our thoughts upon any subject 
into that form, but because it stimulates us to use such powers as we 
have, and to appraise the results which we have so far attained. 

Now the most obvious criticism that can be made upon a Logic 
which confines itself to setting forth the formal conditions of valid 
inference is that it ignores the question of the truth of the premisses ; 
the validity of the reasoning affords no guarantee that these are 
true. It is no doubt possible to direct men's attention so exclusively 
to the form of argumentation that they will bestow little upon the 
truth of the premisses from which they argue. It has often been 
complained that the study of Logic did this — or, as its critics would 
say, the study of Deductive Logic. 2 The epithet, however, implies 
a misunderstanding ; it is a disproportionate attention to validity 
of form in general which the critics ought to deprecate. Validity 
of form is a thing worth studying, not only for its own sake, but in 
some degree lest we infringe it ; yet it is psychologically possible, 
by studying it too much and too exclusively, to become distracted 
from due care about truth of fact. It is, however, probable that 

1 Charmides 171 D. 

2 The popular antithesis between Deductive and Inductive Logic has been 
so far avoided, and that deliberately ; we shall have to consider presently 
what the nature of the difference between deductive and inductive reasoning 
is ; but it may be said at once that it does not lie in using the forms of infer- 
ence that are commonly expounded under the titles of Deductive and of 
Inductive Logic respectively. For inductive reasoning uses forms of inference 
with which treatises that would be called Deductive always deal ; and treatises 
called Inductive discuss forms of inference which are certainly deductive. 

B b 2 



372 AN INTRODUCTION TO LOGIC [chap. 

in the times when men have been most remiss in the examination 
of their premisses, the state of the study of Logic has been as much 
a symptom as a cause of this ; and however that may be, so far as 
it lies with Logic to provide a corrective, it is very important for 
the logician to be clear as to the nature of the corrective he is to 
provide. And for that purpose he must distinguish two questions ; 
he may try to show what kind of premisses knowledge requires, or 
by what process of thought we may hope to get them. In modern 
times, the former of these questions has been too much neglected. 

These last remarks may be a little expanded. And first as to 
the causes which for many centuries made men remiss in the 
examination of their premisses ; one sometimes finds the blame for 
this thrown upon the futility and misdirection of the scholastic 
Logic, which absorbed during the Middle Ages, and even later, so 
large a part of the energy of men's minds. It would be hard to 
deny that much of it was futile, and that much energy was mis- 
directed ; but it is as likely that energy went into this channel 
because others were temporarily closed to it, as that others were 
robbed of it because it ran in this ; though no doubt there is action 
and reaction in such a case, and a habit which certain influences 
tend to form may in turn strengthen those influences. 

It has been said that the mandate issued to the age of Plato and 
Aristotle was Bring your beliefs into harmony with one another ; that 
the mandate of the Mediaeval Spirit was Bring your beliefs into 
harmony with dogma ; and that the mandate of the new spirit which 
rebelled against the authority of the Church was Bring your beliefs 
into harmony with fact. 1 Such a mode of putting things may suggest 
some errors. It is impossible to bring one's beliefs into harmony 
with fact, except so far as facts are known to us ; our knowledge of 
facts is expressed in propositions which we believe ; and therefore 
to bring our beliefs into harmony with fact is to bring them into 
harmony with one another (though not conversely). It would be 
wrong to suppose that Plato and Aristotle forgot that among the 
beliefs they had to harmonize with one another were the beliefs they 
held about matters of daily experience, or that they were indifferent 
to the necessity of correcting and enlarging those beliefs by more or 
less systematic observation ; Aristotle in particular added largely 
to men's knowledge of facts. Again, it is clear that to bring one's 
beliefs into harmony with dogma is to bring them into harmony 
1 Minto, Logic, Inductive and Deductive, p. 243. 



xvii] THE FORM AND MATTER OF INFERENCE 373 

with other beliefs ; and that those who rated highest the importance 
of that task would least have doubted that they were bringing them 
into harmony with facts. Propositions do not cease to state facts 
because they are presented as dogmas. But it is true, as Minto 
wishes to bring out in the passage quoted, that dogma and the spirit 
which accepts dogma did during the Dark and the Middle Ages play 
a part in the history of thought far greater either than they played 
in classical antiquity or than they have come to play since the revival 
of learning. And such dogma was not necessarily ecclesiastical 
dogma ; it came from the scientific works of Aristotle, or other great 
men of old whose works were known, as well as from the Bible and 
the Church ; just as to-day there is orthodoxy in science, against 
which new scientific doctrines find it at times a little difficult to 
battle, as well as in theology. 

The schoolmen knew, as well as Bacon or any other of their critic