Ipresenteo to
Xibrarp
of tbe
Tflntversitp of Toronto
bs
professor ffrefcericfe ttrac
JEmeritus [professor of JEtbics
in
College
n\i
JAN INTRODUCTION jr
TO
LOGIC
BY
H. W. B. JOSEPH
FELLOW AND TUTOR OF NKW COLLKfiK
OXFORD
AT THE CLARENDON PRESS
1906
HENRY FJ1OWDE, M.A.
PUBLISHER TO THE UNIVERSITY OF OXFORD
I.OXDOX, EDIXBUHGH
NKW VORK AND TORONTO
TO
J. E. J.
PREFACE
IF an apology that precedes it could mitigate an offence, I should
be inclined to convert my preface into an apology for publishing
this book. Progress, and the hope of progress, in logical investiga
tions, 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 know
ledge 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 pre
tence 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
vi PREFACE
cannot be understood without reference to its history. The termin
ology 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 corruption 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 f 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 need^
less 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 is 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 vii
discussions which a reader need be altogether precluded from fol
lowing 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 Bosanquet,
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 •. 12
III. OF THE CATEGORIES ,35
IV. OF THE PREDICABLES 53
V. OF THE RULES OF DEFINITION AND DIVISION : CLASSI
FICATION AND DICHOTOMY 97
VI. OF THE INTENSION AND EXTENSION OF TERMS . .121
VII. OF THE PROPOSITION OR JUDGEMENT . . .143
VIII. OF THE VARIOUS FORMS OF THE JUDGEMENT . .154
IX. OF THE DISTRIBUTION OF TERMS IN THE JUDGEMENT :
AND OF THE OPPOSITION OF JUDGEMENTS . . 192
X. OF IMMEDIATE INFERENCES ..... 209
XI. OF SYLLOGISM IN GENERAL . - . . . 225
XII. OF THE MOODS AND FIGURES OF SYLLOGISM . . 230
XIII. OF THE REDUCTION OF THE IMPERFECT SYLLOGISTIC
FIGURES ........ 264
XIV. OF THE PRINCIPLES OF SYLLOGISTIC INFERENCE . 272
XV. OF HYPOTHETICAL AND DISJUNCTIVE REASONING . 308
XVI. OF ENTHYMEME, SORITES, AND DILEMMA . . . 323
XVII. OF THE FORM AND MATTER OF INFERENCE . . 338
XVIII. OF INDUCTION . . . . . . . .350
XIX. OF THE PRESUPPOSITIONS OF INDUCTIVE REASONING :
THE LAW OF CAUSATION . . . . . 370
XX. OF THE RULES BY WHICH TO JUDGE OF CAUSES AND
EFFECTS . ,. , .... . . .. 392
XXI. OF OPERATIONS PRELIMINARY TO THE APPLICATION
OF THE FOREGOING RULES ..... 422
XXII. OF NON-RECIPROCATING CAUSAL RELATIONS . .441
XXIII. OF EXPLANATION 466
XXIV. OF INDUCTION BY SIMPLE ENUMERATION AND THE
ARGUMENT FROM ANALOGY ..... 488
XXV. OF MATHEMATICAL REASONING. .... 503
XXVI. OF THE METHODOLOGY OF THE SCIENCES . . . 513
XXVII. APPENDIX ON FALLACIES 525
INDEX .... 559
ERRATA
PAGE 43, notes 1 and 2, for Met. M. read Met. Z.
90, 1. 32, for osprey read egret
140, note 1, 1. 3, for propietas read proprietas
201, note, 1, 5, for fj-ovainrj read povaiKri
215, 1. 20, for converted read permuted
251, 1. 23, for If all is P read If all M is P
255, 1. 20, for affirmative read particular
256, 1. 32, for distributed read undistributed
261, 1. 20, omit reference to note at end of line
261, note 2, insert at end (AO)
272, 1. 16, /or Cread B
282, 1. 25, for B is A read C is A
286, note I, for Dialect, read Dialectic,
291, 11. 9, 11, 18, 23, for Barbara read Celarent
298, 1. 32, for Some B read Some C
325, note 3, 1. 4, for 162a 16 read 158a 16
327, note 2, 1. 13, for 79a 20 read 79a 30
350, 1. 9, for tlie verb read the passive verb
364, last line, for Roman read Greek
365, first line, Jor Greek read Roman
394, 1. 27, for are not related read are related
401, note, 1. 1, insert comma after reasoning
414, 1. 13, for concidence read coincidence
500, 1. 2, for x read y
518, 1. 11, for attributing it to read attributing to it
564, for Zabarella, Cardinal, read Zabarella, Count,
JOSEPH
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 in the case
of 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 any
controversy about its definition 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 bring unity into the different enquiries 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 movements of the heavenly bodies, botany the structure,
growth, history, and habits of plants, geometry the properties of
figures in space; but each attempts to discover the principles
underlying the facts with which it has to deal, and to explain the
great variety of facts 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 Parlia-
ment prescribes rules of conduct to his people. That, however, is
2 AN INTRODUCTION TO LOGIC [CHAP.
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 dis
regarded ; it is a principle illustrated — and existing only in the
necessity of its being illustrated — in the department of fact to which
it belongs. There are therefore no breaches of scientific law, or of a
law of nature * ; 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 tem
perature 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
temperature; and the 'law' is that it should boil only when those
conditions are fulfilled. Such laws, the general principles to which
objects 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 department of
its own, in which it seeks for principles and laws.
That department 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
1 The question of the possibility of a breach of natural law need not
be considered here ; something is said of it in c. xix, infra.
i] GENERAL CHARACTER OF THE ENQUIRY 3
not need to study all subjects ever thought of, we must have before
our minds some subject thought of, in order to realize in it how we
think about it and all possible subjects like it. For example, it is
a general principle of our thought, that we do not conceive of quali
ties except as existing in some subject ; and that nevertheless the
same quality is regarded as existing in many subjects; 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 case of 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 *,
' 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
the case 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 object 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 prin
ciples of voluntary motion, if he was not first accustomed to move
his limbs as he willed. Had God made men barely two-legged
creatures, Aristotle 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, the most careful, clear, and coherent,
f, Bk. IV. c. xvii. § 4.
B 2
4 AN INTRODUCTION TO LOGIC [CHAP.
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.1 What ' the courses of
the stars ' are to astronomy, what figures are to geometry, what
plants are to botany, or the calendar of Newgate to the criminolo-
gist, 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 the best pieces of knowledge that exist, the best
' knowledges ', are the various sciences. But he is not concerned
with the detail of any particular science ; only with those 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 who
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
forms 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
vertebrates, or the identical mode in which the law requires the
different Colleges of the University to publish their accounts.
And all science is formal, in the sense that it deals with what is
common to different individuals. A scientific man has no interest
in a specimen that is exactly similar to one which he has already
examined ; he wants new types, or fresh details, but the mere mul
tiplication of specimens all alike does not affect him.2 So the
logician studies the forms of thinking, such as that involved in
referring a quality to a subject possessing it; but when he has
once grasped the nature of this act of thought, he is quite unin
terested in the thousand different occasions on which it is performed
during the day ; they differ only materially, as to what quality is
1 Joannes Philoponus cites it ad Ar. Anal. Post. a. ix. 76a 15.
2 Unless indeed he is collecting statistics as to the comparative frequency
of different types.
i] GENERAL CHARACTER OF THE ENQUIRY
referred to what subject ; formally, so far as the notion of a quality
as existing in a subject 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
meant that Logic is in this like other sciences, which all deal with
what is formal or universal in their subject-matter. 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
different kinds of subjects, and therefore we must, if we wish to
study the principles that regulate our thinking, consider to some
extent the differences in the matter about which we think. The
distinction between form and matter may as it were be taken at
different levels. This is plain in the case of 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
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 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
formed the conception of animal, as something exemplified equally
in kinds of animal so different, it is clear that we can only under-
6 AN INTRODUCTION TO LOGIC [CHAP.
stand what animal nature means by seeing it as it exists in all the
different orders of animals ; whereas we can understand fairly the
nature of a vertebrate animal without seeing it as it exists in every
genus of vertebrates ; still more can we understand the nature 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 ; no
example taken from one order of animals, say the starfish, will enable
us to realize what animal means. It is the same in studying the
forms of thought. The most general forms of thought exist
diversely modified in thinking about different matters ; 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 proposition there is a sub
ject 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 pro
positions there is formally the same distinction of subject and
predicate, take symbols which shall stand for subject and predicate,
whatever they are, and say that all 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. 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 ' 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 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. The meaning of the
formula 8 is P cannot possibly be fully known merely by under
standing that £and P are some subject and predicate ; it is necessary
to understand what kind of subject and predicate they are, and
also the relation 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
i] GENERAL CHARACTER OF THE ENQUIRY 7
thorough study of the form of thought involves the consideration
of material differences in the subjects of thought. 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 matter of thought ; an impracticable task,
because the form itself (as in the above instance of the form of
thought which we call a proposition) is modified according to the
matter in which it appears. On the other hand, and even although
the forms of our thought cannot be studied apart from the par
ticular sort of matter about which we may think, yet Logic is not
interested in the variety of the matters that we think about 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 connexion with the special forms in which it is
manifested ; 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
material objects, like medals from a common die, is not so easily
seen in immaterial objects, 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.
8 AN INTRODUCTION TO LOGIC [CHAP.
[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
objects; and these are its first intentions; 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 a species, and the
members of the several kinds together 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 may
indeed be something in the animals themselves ; and so our names
of second intention will signify something real in things. The
distinction therefore presents difficulties.]
If now we ask for a definition of Logic, to keep before our
minds in the following chapters, perhaps it is simplest and least
objectionable 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.
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 under
stands 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 it should be done. In the
latter sense, art presupposes science; the rules of navigation are
based upon a knowledge of the motions of the heavens, the laws of
hydrostatics, and the build of ships. It is in this sense that Logic
is called an art; and hence it is clear that if there is an art of
i] GENERAL CHARACTER OF THE ENQUIRY 9
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 different 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 our own ideal of what knowledge
about any subject must be, and certain canons of reasoning which
no sound argument can violate. But though we may thus pre
scribe to ourselves the conditions which should be fulfilled in
science or in common thought, we are not thereby enabled to
fulfil them; for art, as a theoretical knowledge of what is to be
done, does not always bring the art or practical skill of doing it.
An art of Logic would therefore be no infallible means of coming to
know about all subjects ; it is against that sort of pretension that
a protest like Locke's, quoted above, may well be made ; and yet
the rules and the ideals which the study of Logic suggests are not
without value in keeping our thoughts about things straight.
We have said that Logic studies the way in which we already
think about things. But a good deal of our so-called thinking is
incoherent, and breaks down when we criticize it. That we can
discover for ourselves without learning Logic; an economist can
correct his own or his predecessors' errors in political economy,
a mathematician in mathematics; 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 con
struction 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
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.
10 AN INTRODUCTION TO LOGIC [CHAP.
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 means : 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 1.
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 its practical value can lie
solely in its furnishing 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 other 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 into clearer
consciousness, as aforesaid, our ideal of what knowing is, and so far
furnishes us with a sort of negative standard ; it makes us more
alive to shortcomings in our ordinary opinions. But its chief value
lies in its bearing upon those ultimate problems, concerning the
1 if* ?USi n°5 however be supposed either that Ethics can determine what
Dught to be done in every difficult case of conscience, or that Lome
letermmes exhaustively the forms of reasoning which the sciences must
employ. Cf. Bradley, Logic, pp. 247-249. The phrase normative science, which
some writers have of late applied to Logic, Ethics and Aesthetics, has
£efeap8 fcefn suggested by the character in them to which this paragraph
refers. But it is liable to create misunderstanding, as if it were the buSness
these enquiries to prescribe rather than to ascertain the principles which
r rational thinking, or action or appreciation of beauty exhibits
i] GENERAL CHARACTER OF THE ENQUIRY 11
nature of reality, and man's place and destiny in the world, from
which at first sight it might seem far remote. ' Logic,' says
J. S. Mill, in the Introduction to his famous work 1) f 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 it thinks : 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 such controversies, however, it is not the aim of
this book to enter. It would be absurd to pretend that the treat
ment of many topics in it does not rest upon a metaphysic which
some would reject, and of which the rejection would mean the
restatement of what is written here. But he would essay a vain
task, who should attempt to expound the rudiments of Logic with
no metaphysical presuppositions ; therefore it is better not to
conceal them ; but though the points at which they are most
important will be indicated, they will not be discussed as they
deserve.
'§7.
CHAPTER II
OF TERMS, AND THEIR PRINCIPAL DISTINCTIONS
WE have to study the principles which regulate our thinking
about any subject ; and these can only be discovered by examining
our various particular thoughts. Now the true unit of thought,
the simplest complete act of thought or piece of thinking, is the
Judgement, or Proposition : between which, if a distinction is ever
intended, it is that the proposition is the expression in words of
a judgement, and unless a judgement were expressed in words, we
could not study it. This does not mean that it need be uttered
aloud, or written down, though these may be helps to us in fixing
our attention ; but we must express it mentally to ourselves in
words or in a proposition, if it is not to evade us. The judgement
being thus the unit of thought, it might be expected that Logic
should begin with a discussion of judgement ; but it is more usual to
begin with the elements of judgement, viz. terms. It is, however,
only through its place in a judgement that we can understand what
is meant by a term. When that has been explained, it may then
be convenient to discuss the doctrine of Terms, before passing to
a fuller consideration of Judgement.
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. It is easy,
however, to see the connexion between the two uses of the word ; for
when I judge, in the logical sense, I decide with myself what is,
or is happening. 'Vengeance belongeth unto the Lord/ ' Sweet
are the uses of adversity,' yaXeita ra /caAa, Balbus aedificat, are .all
judgements. In each I recognize a matter of fact, and what
I recognize in each is different.1 But in the matter of fact there
is a distinction seen when I judge, between the subject and the
1 Of course judgements with the same subject may have different predi
cates, and those with different subjects may have the same predicate.
' Vengeance is sweet.'
TERMS, AND THEIR PRINCIPAL DISTINCTIONS 13
predicate ; for I recognize something1 in particular as characterizing
the object of thought already before me.1 Subject and predicate
unite with one another in the object, and we are aware that because
distinguished they are not separate, as the words that indicate them
are in our proposition. Nevertheless, the judgement admits of
analysis into those two factors, as has been already said. Subject »,
and predicate (Gr. viroKei^vov and Kar^yopov^vov), as the parts
into which it is analysed, are called the terms of the judgement.2
From this it will be clear that a term is not the same as a word ;
a proposition may contain any number of words ; but one judge
ment never contains more than two terms. Subject and predicate
may be expressed each in a single word, as in the proposition
' Tastes differ ' ; more commonly each requires several words, as in
c Dead men tell no tales ' ; while sometimes, on the other hand,
a single word expresses both, Caesar's famous message of three
words, ' Veni, vidi, vici/ containing as many distinct propositions,
each of which may be broken up into the subject-term ' I ', the
same in each, and a predicate-term which is different. Again,
some words are not normally capable of signifying the terms of
a judgement 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 conjunctions and pre
positions, to indicate a relation between different parts of a com-
1 This statement needs modifying in the case of judgements which define
their subject ; but in these also there is a distinction between the subject as
an unity, and the elements composing it.
2 "Opov Ka\5> fit ov SiaAuerm 17 Trporao-ir, Ar. Anal. Pri. a. i. 24b 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 propo
sition ' (Jevons) is clearly wrong ; for that is an accident of language, and
of the proposition bos locutus est it is not true. It is possible that Aristotle
symbolized the proposition in the form ' B — A ' (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, 530a 21) thinks it a metaphor from
mathematics, where if the ratio of two quantities was considered, these
were called opoi, 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 6'poi too. The word is, however, also
used like 6pi(rp.6s, 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.
14 AN INTRODUCTION TO LOGIC [CHAP.
plex object of thought.1 Such words are called syncategorematic
((ruyKaTrjyoprjfjLaTLKa) 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 for terms,
may also enter into a term as one of 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 hearty
of man is deceitful ' : the sea in the proposition ' The sea shall give
up its dead ', but not in the line ' She left lonely for ever the
kings of the sea'. In this line the words italicized are syncategore
matic; but sea is not syncategorematic, because it can stand for
a term, though here it does not do so. Terms composed of words
of both kinds have been called * mixed terms '. It is true that
syncategorematic words, though signifying nothing about which
anything can be asserted, or which can be asserted of anything, can
yet as words be made the subject of linguistic or grammatical
discussion, as when we say ' Of is a preposition ', or ' is the sign
of the genitive case in English '. When words which signify no
complete object of thought are made objects of our thought them
selves as words, it is said to be by a suppositio materialist
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 is, 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 possessing 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 sub
stances, copulatio to verbs and adjectives. Substantiality and adjectivality
were supposed to be characters of the things signified ; the adjective coupled
some adjectival with some substantival thing, the substantive 'put' the
latter 'under' the former (v. Prantl, Geschichte der Logik, vol. II. Abschn.
xv. Anna. 67; vol. III. xvii. 59). So far, the sense of suppositio seems to be
active ; but it is defined as acceptio termini substantivi pro aliquo ; and here
the sense is passive : the ' supposition ' of a term is ' being put ' for some
thing. It was then said itself supponere pro aliquo (cf. Prantl, vol. III. xvii.
61, 201 : Sanderson's Compendium Logicae Artis, Lib. II. c. 2) ; and 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
suppositio naturalis of a common term ; in ' Homo currit ', it stands for some
ndividual, and this is suppositio personalis. Now as a sound having signifi
cation, 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
n] TEEMS, AND THEIR PRINCIPAL DISTINCTIONS 15
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. f 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 \l This definition
admirably expresses the function of a name, though it covers
many expressions that contain more than one word ; but it is not
equally appropriate to define a term. For the name not is but !\
signifies the term. A term is properly one of the elements
into which the object of our thought is analysed when we
break up the judgement ; a name is the mark which serves to
fix and recall these elements in the object of our thought. The
name belongs to the expression of our thought in language ; but
thought itself is not made up of, and is not generally about, names.
We shall therefore commonly speak of terms, and not of names.
Nevertheless, by term will sometimes be meant the name which
signifies the term. For example, when it was said that in the pro
position ' The heart of man is deceitful ' man entered into the
subject-term as one of the words of which it is composed, it would
have been more accurate to say that it entered into the name (or
phrase) which signified the subject-term. But we may consult
brevity by the other expression without serious risk of confusion ;
for the name and the object of thought which it signifies are
obviously different, and it is easy to know in which sense ' term '
is meant in any context. Usage has sanctioned the application
of the word ' term ' both to the object thought of, and to the
verbal expression for it; this usage extends beyond Logic into
common speech ; and more difficulties would probably be caused
by departing from than by acquiescing in it.2
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. 140, infra.
1 Computation, or Logic, c. ii. § 4.
2 We can talk in English of the name of a person, thing, place, river,
&c. ; it is less natural to speak of the name of a quality, or to call a
descriptive phrase, like ' the only man who escaped from the slaughter of
Cavagnari's mission ', a name ; while verbs and adjectives, which can be
16 AN INTRODUCTION TO LOGIC [CHAP.
A term then may most properly be defined as whatever can be
thought as the subject or predicate of a proposition.1 But if we mean
the name or verbal expression signifying what is thus thought, we
may define it as a word or combination of words capable of standing
as the subject or predicate of a proposition. In order to mark the
former sense more unambiguously, logicians where the subject or
predicate is not an individual 2 speak sometimes of concepts
instead of terms, the word ' concept ' signifying always an object
of thought, and never the name of it. What the logician calls
a concept is often in common speech called a conception ; my con
ception of heaven is what I think of when I speak of heaven.
But it is desirable to be able to distinguish between the act of
conceiving of heaven, and what I conceive it to be ; in popular
speech ' conception ' may signify either the act of conceiving
or what is conceived, as ( narration' may signify either the act
of narrating or the story narrated, and ' 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
printer. The Greek language distinguished these two meanings
by different verbal terminations, the act by nouns in -rrts (like
al(T0r)(TLs and wfycris), the object or product by nouns in -pa (like
cuo-0T7//a and ZJO'TJJUCI). It is this distinction which Logic marks, by
using the word concept for the object or product of the act of
conception.3
[It has been said that a concept is an object of thought. But
it may be urged that the objects of our thought are things them
selves ; are things then the same as concepts ? When we make
a judgement, it is possible to distinguish between (i) the object,
reality, or matter of fact which we recognize, and (ii) our thought
in recognizing it. If I say ( Gibraltar belongs to the British
predicates in a proposition, can hardly be called names at all. Nor would
any one speak of the ' middle name ' in a syllogism, though it is words which
are^ ambiguous when we have an ' ambiguous middle '. Hence it seems
desirable to retain the word ' term ' in both the senses mentioned in the next
paragraph.
1 Nothing is a term except when it is so thought ; but when we consider
terms in isolation, the question is not whether anything is a term in a given
judgement -for there is no judgement given— but whether it is a term of
a possible judgement. Hence in our definition we must say ' whatever can
be thought, &c.' and ' capable of standing *.
1 Technically, in the case of concrete general or of abstract terms. Cf.
infra.
3 On the nature of concepts cf. pp. 55-57 infra.
n] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 17
[Crown ', I refer to a rock at the entrance of the Mediterranean,
and a fact in its present history. These form the ' first intention '
of my mind. But my recognition of this fact about Gibraltar is
itself a fact, and the thought in which I recognize it may be con
sidered, and will form the ' second intention ' of the mind. If
I consider this recognition, i. e. my judgement, I find it involves
a recognition of the union with Gibraltar of this relation to the
British Crown. These therefore are the terms of my judgement,
and its terms are objects or realities recognized] for ' belonging to
the British Crown ' is as real as the rock, though not visible
or tangible. But I might have thought Gibraltar to belong to
the Spanish Crown ; and that relation, though real — it is real for
example of Algeciras — is not real of Gibraltar. Again, I might
have spoken about Atlantis, instead of Gibraltar ; and Atlantis
never existed except as an object of Plato's or other men's imagina
tion. Inasmuch then as we may think about that which does not
exist, or think falsely about that which does exist, it is necessary
to distinguish objects of our thought from objects existing. Terms
therefore are always objects of our thought; but they are not
always objects that exist * ; though in any true judgement they are
both. Hence it is possible to say that a term is some reality,
or element in the reality, thought of, and it is possible to say
that it is merely something thought of ; the objects of our thought
need not exist, and even if they do, we need not consider whether
they do or not. When concepts, or — more generally — terms as
the elements into which a judgement is broken up, are taken
in isolation, we do not ask whether, in thinking of them, we are
thinking of an existing object ; it is enough that they should
be objects of thought ; for this purpose, they must not contain
elements which cannot be thought of as combined (as in the term
' square circle ') ; but they may be incapable of being thought
of as combining with what really exists, and yet be objects of
thought just because we are ignoring the question of their com
bination therewith. A concept then is an object of our thought —
or our thought of an object, if that means what we think it to be,
and not the fact of our thinking about it — as opposed to an object
as existing irrespectively of our thinking about it ; though of an
individual, so far as its being goes beyond what thought can
grasp, there is no concept.2 Whether any objects exist altogether
irrespectively of the knowledge of them is a profound meta-
1 £)r have existed or will exist.
8 It would be possible in ordinary speech to talk of a man's ' conception '
of Gibraltar, or his 'idea' of it, in distinction from the rock itself; but
concept in Logic signifies properly something universal. The question
however in this paragraph is a general one concerning the relation of what
are sometimes called ' ideas in the mind ', to things, whether or not these
are ' ideas of individuals '.
18 AN INTRODUCTION TO LOGIC [CHAP.
[physical question ; holding that they do not, we must still admit
that they exist irrespectively of this or that man's knowledge of
them. And existence is not necessarily material existence ; the
objects of mathematical knowledge exist, though they are not
material, like Gibraltar, and no one could mount a battery on
them. But there are objects thought of which certainly do not
exist except as objects of thought to the individuals who think
of them ; these have their being only in and for thought, and
are concepts which have to be distinguished from t things them
selves '.]
Having considered what a term is in general, and distinguished
a term as an object of thought from a term as the word or words
signifying it, we must now consider 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, and in our way of thinking about things.
Terms as objects of thought are divided first of all into
abstract and concrete : terms verbal l 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 ; so
that the distinction between the thing and its qualities, between
substance and attribute, is the basis of the distinction between con
crete and abstract terms. Attributive terms will be explained later.
Our notion of a thing involves two elements, which furnish
the basis for a further division of concrete terms into those which
are singular and those which are common or general. A thing
is, first, an individual, 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 called sometimes 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.
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
1 i. e. terms as = the word or words signifying an object of thought.
n] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 19
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 predicdble of one individual only in the same sense.
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 defender 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.
We are seldom at a loss for some general term by which a
particular 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
expressions are indeed in a manner singular terms, for they serve
to designate particular objects ; they are not however proper names,
and they have been conveniently christened designations.
But where particulars of a kind are distinguishable, and we
are interested in them singly and wish to be able to refer individu-
C 2
20 AN INTRODUCTION TO LOGIC [CHAP.
ally 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 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 f four-acre ' is a field, the ' Cornishman ' 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
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 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 the same name, except because they have or are believed to
have the ^ same nature ; nor is it conceivable that we could
name an individual by a proper name, without at the same time
recognizing in it, however vaguely, some character that, as
capable of existing equally in other individuals, might be marked
by a general name. General names therefore are not a mere means
of abbreviating discourse, but their existence arises from a necessary
feature in our thought about objects. Aristotle's distinction at the
n] TEEMS, AND THEIR PRINCIPAL DISTINCTIONS 21
[beginning1 of his ' Categories ' between o^ww^a, or things called by
the same name having only the name in common, and vvv&vvpa, or
things called by the same name having also what is meant by the
name in common, may be mentioned here : the distinction is nowa
days embodied from the side of names instead of things in that
between equivocal and univocal terms (v. infra, p. 34).]
There are thus two kinds of concrete terms, viz. singular terms, \l
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 seems inconsistent with calling
them concrete : for the common character of many individuals,
regarded by itself, seems like a quality — something considered in jj
abstraction from the things possessing it.
The importance and difficulty of this problem can only be appre
ciated in a more advanced study of thought than this volume
contains. Here the following solution must suffice ; but we shall
come upon the same issue again in other connexions.
A general .tejgn , being predicable of any number of individuals
in t£e same sense, implies that though they are individually different
they have something in common; in other words, that there is
something the same in different individuals. This common charac
ter is only found realized along with the special differences that
distinguish one individual from another ; the common character of
man is found in you and me concrete with all that distinguishes one
of us from the other ; and man is a concrete term. When on the
ground of that common character we are called by the same name,
the name is concrete ; but when the common character is considered
by itself, and a name is given to that, without regard to or in
abstraction from the individuals who manifest it, that name is
abstract. Thus humanity1 is an abstract term, though it is what
1 The term humanity has of course other meanings, viz. mankind collec
tively, and also kindliness ; in the text it means the human nature common
to all men.
22 AN INTRODUCTION TO LOGIC [CHAP.
makes «ach of us a man. The term gold, again, is concrete ; we
may say ' this gold ' and ' that gold ', and ' the gold in the cellars
of the Bank of England5; but if we regard the common character
of all these, in abstraction from any particular parcel of gold, we
should call it ' goldness ', which would be an abstract term. The
readiest test whether a term is concrete is furnished by asking —
' Do I mean by it some person or thing (or some assemblage
of persons or things), or only a quality or attribute of such ? '
Thus animal is a concrete term, t>ut colour is not ; society, when we
talk about ' a society ', is concrete ; when we say men live together
f in society ', it is abstract, for then we mean by the word not men
living together in a certain way, but only the way in which they
live together.
[It was stated above (p. 18) that the distinction between concrete
and abstract terms rested on the distinction between substance and
attribute ; and in the last paragraph it might have been said with
more precision that the test whether a term is concrete was fur
nished by asking whether it could be used of a substance or assem
blage of substances. And the difficulties often felt in determining
whether a term is concrete or abstract spring from the difficulties
lurking in the distinction of substance and attribute. If by sub
stance we mean the fully determinate individual, then what we
call the attributes of a substance are elements in its being, and it is
not something to which they can be attributed as addenda, like an
article of clothing ; the individual is not substance -f attributes, the
attributes are rather factors in the substance. Any of these attri
butes, however, can be considered separately or in abstraction from
the rest of the nature of the concrete substance, and so considered
can be as it were replaced in thought in the concrete whole from
which it has been abstracted, or be attributed to it. But while
sometimes what we thus consider separately is only some compara
tively simple feature of a thing, as its colour, or size, or price, at
other times we consider in one notion or concept indefinitely numerous
features, on the strength of which the thing is grouped with others
in a ' natural kind ' (cf. pp. 41-43 inf.). If we gave a name to
these features considered in abstraction from what else characterizes
the substance, such name would be abstract ; but just because they
constitute so much of its being, we give a name only to it as
constituted by them, and such a name, like man or gold, is concrete ;
they are not abstracted from and attributed to the remainder ; and
therefore we have no name for them considered separately, unless
special reasons prompt us, as in the case of ' humanity'; but as
a rule, where occasion demands abstraction, we use a periphrasis
n] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 23
[like * the nature of gold ', and have not abstract terms like goldness.
It is perfectly justifiable to say one abstract term is less abstract
— more concrete — than another, in the sense that though we are
considering not any substance, but some part of the full and deter
minate nature of a substance, yet the part we are considering is
more, and more determinate, in one case than in another. Thus the
properties of figure and number, which can pre-eminently be studied
in isolation from all else about things, are pre-eminently abstract.
Language, unfortunately, is apt to mislead us in this matter.
Many abstract terms are not commonly used in the plural ; and
when we find a term used in the plural, we are apt to think it con
crete, as predicated of divers individuals. But this is not neces
sarily the case. Triangle is not really a concrete term because we
can talk of triangles ; ' triangles ' is indeed concrete if it refers to
things of wood or steel, and so is the singular in like case; but
' triangle ' often means the triangularity of every individual
triangle, and ' triangles ' different modes of such triangularity. And
fblour is not concrete because we can speak of colours. ' Colours '
is concrete if I mean certain slabs of pigment ; but if I mean blue,
green, and yellow, as qualities, it is abstract.
The distinction of concrete and abstract terms is therefore only
really intelligible if we ask ourselves what we are thinking of. If
we look alone to terms verbal, it is impossible to tell whether
a name is abstract or concrete ; for many names are equivocal,
being sometimes one and sometimes the other.]
Abstract terms then are the names of qualities or attributes ;
but we must understand this definition rather widely. It is not
only single sensible qualities, like flavours or odours, whose names
are abstract terms ; all that goes to make the nature of an object,
when it is considered merely as qualifying such object, is abstract,
and its name (where it has any) an abstract term. Moreover, the
object 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 object 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 animality, discipline, civilization, paternity,
are all abstract terms, though it is only by adoubtful extension of
language that we could call any of them a quality, like fragrance
or sweetness.
24 AN INTRODUCTION TO LOGIC [CHAP.
[The distinction of singular and general is not applicable to
abstract terms. The calling a concrete term general rests upon a
consideration of the many different individuals who being of the
same kind claim the same name. But an abstract term is the name
of that which is common to many individuals, considered without
reference to its repetition in them all. It may be thought that
abstract terms ought therefore to be called singular; but neither
would that be correct. A singular term denotes an individual ;
but an abstract term denotes something common to many individuals,
something therefore which is ' universal '.
It is indeed true that whereas general terms are applied to many
distinguishable individuals, certain abstract terms are predicated of
many distinguishable attributes. Colour is used equally of blue and
red j*nd all the other colours of the spectrum ; disease, of measles,
whooping-cough, bronchitis, and many other ills that flesh is heir to ;
whereas we do not distinguish different examples of blue by
different names x, nor different cases of bronchitis. But ' blue 3 and
' bronchitis y are not for this reason singular terms ; the true
analogy of the relation of the terms ' blue ' and ' colour ' is the
relation of the terms ' man' and ' animal ', and not that of ' Socrates '
and ' man \ Just as no one would say that ' man ' is a singular term
because it is one species of animal, so we ought not to say that
( blue ' is a singular term because it is one species of colour, nor
' bronchitis ' because it is one species of disease ; for that would be
to confuse the distinction of species and genus with the distinction of
individual 2 and universal. * Socrates ' is a singular term because
it is the name of an individual having attributes ; ( blue ' is not a
singular term because it is not the name of an individual at all, but
of an attribute that may belong to many individuals.]
Besides abstract and concrete terms, a kind of terms has been
recognized which cannot well be classed with either — viz. adjec
tives 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, and 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
1 We may of course distinguish varieties of any one colour by special
names, like sky-blue and peacock-blue. But this does not affect the argu
ment in the text : it would only require us to treat, not blue, but sky-blue
or peacock-blue as the abstract term that is applicable only to one attribute.
The individuals of one kind are sometimes also called particulars (cf.
p. 18), in contrast with the universal or kind that characterizes them all.
n] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 25
so may a company, but to explain what 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; 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 thought ; if terms
are objects thought of, attributives are not terms at all ; we may
attribute a quality to a subject, but that is an act of judgement ;
thing and quality, substance and attribute differ as objects thought
of ; thing or substance is concrete, quality or attribute abstract,
and everything abstract is attributable; but there is no third kind
of object thought of to correspond to the attiibutive term. 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 erected for adjectives
a third class, along with abstract and concrete, in the division of
terms verbal. For terms are the parts into which a judgement 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 meaning of the verb this life
lingers, even if a verb be taken without its subject. Hence
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 com
pany could be insolvent unless capable of having debts. Cf. p. 98, n. 1, inf
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 substan
tives, and are predicated of concrete things, they do not primarily signify
the concrete things of which they are predicated. Cf. pp. 140.-142, infra.
2 Logic, I. ii. 4.
26 AN INTRODUCTION TO LOGIC [CHAP.
logicians, anxious to effect the resolution of a judgement 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 doctor1, 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 names are either substantival or adjectival, and concrete
and abstract names are both substantival, some place is wanted for
names 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 the 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
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 certain specific individuals
* King Lear, Act iv. 7. 1. 13.
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
the article is generally necessary in order to make an adjective do duty as
a substantive.
n] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 27
(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 all collective
terms are concrete, for they are the names of the individuals taken
together, and not of the mode of organization among them. A
general collective term is said to be used distributive ly 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 Guards, the 6oth Rifles, the
Sutherland Highlanders, &c., and collectively of the men in each
several regiment.
We may sum up what has been so far said of the kinds of terms
as follows : — Terms as objects of thought are either concrete or
abstract ; as names or terms verbal, concrete abstract or attributive :
concrete terms are either singular, and then either proper names
or designations, or else general : abstract terms, having no reference
to individuals, are not conveniently considered as either singular or
general, but always signify something universal ; and some of them
are not names of one recognized attribute (or state or quality or
relation) only, but include under themselves divers species thereof.
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 objects taken
together, which would apply to none of them by itself, so we may
give to an object or quality, when we regard it in its relation to some
other object or quality, a name which would not apply to it con
sidered in itself. Such terms, attributing to one object or quality
some definite relation to another, are called relative terms : and in
contrast with them, terms that indicate an object or quality con
sidered in itself are called absolute. It is clear that if one object or
quality stands in relation to another, the latter must also stand in
relation to the first ; and the name applied to it 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 correlatives
equal, less, ruler, child • apple, sound, man are absolute terms.
Relative terms are necessarily general *, like attributive terms ;
* Except so far as they are combined into a term whose whole meaning is
singular : e. g. first is general, but the first Pharaoh is singular.
28 AN INTRODUCTION TO LOGIC [CHAP.
for the same relation may be exemplified in many particular
instances, and therefore many objects 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 ; they are not however themselves neces
sarily attributive — thus 'contemporary' is relative and attributive,
but ' a contemporary ' is relative and concrete. 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, and nothing can be absolute except the totality of
existence, 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 indi
cate 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, unjitness : a privative term to
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
n] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 29
meant. A term must have some positive meaning or content, 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 look not-book, to square not-square^ to colour not-colour ; not-
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-
cable; 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 ;
and 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-J.' x
Such negative terms as these do not really figure in our thought ;
they are ' mere figments of logic ' 2 ; Aristotle long ago pointed
out that ovK-avOpiaiTos was not properly a name at all ; and he
1 This formula, ' Everything is either A or not-^4,' is sometimes given as
the ' Law of Excluded Middle '. The ' Law of Excluded Middle ' means 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 con
tradiction 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 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-A ' 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, Logic, I. v. §§ 23, 24. 2 Stock, Deductive Logic, § 133.
30 AN INTRODUCTION TO LOGIC [CHAP.
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^.a aopio-Tov) because, being the name of nothing positive
and in particular, it had a purely indeterminate signification ; it
was applicable equally to things existent and non-existent.1
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 ' may be resolved into the terms flesh (the
subject) and grass (the predicate affirmed of it) ; but the negative
judgement ' Man is not a fly ' 2 into the terms man (the subject)
and^y (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 very
reason that the negative term not a fly has no meaning ; and 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 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 affirma
tive can only be understood by restoration to the negative. But it
is out of such attempts that purely negative terms like 'not-fly'
have arisen ; and it is only by understanding that the term A has
been the predicate of a negative judgement, that we can understand
how the term noW should ever have been formed.
There are however certain negative terms which are not such
mere figments of logic as the ' infinite terms ' which have been just
considered. Where the positive is not a general concrete term but
1 de Interpr. ii. 16a 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.
Why hath not man a microscopic eye?
For this plain reason, man is not a fly.
—POPE, Essay on Man, i. 193.
n] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 31
is attributive, there the corresponding negative may be quite
legitimate ; indeed the distinctions of positive, negative, and priva
tive most properly apply not to all, but only to attributive terms,
or to abstract terms founded upon these.1 For all attributive
terms imply by their very form 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, in the absence of the attribute which
the negative term excludes, is positively conceived as having some
other character instead. And here we have a basis of positive
meaning to the negative term ; for let A be a positive term ; then
not- A will signify what a subject, ivhich might be A, will be if it is
not A. Thus intemperate 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 surface of a road, will be if it is not even ;
not-blue suggests what a thing which might be blue (that is, an
object which must have 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, according 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 in
temperance, yet they have more affinity with one another as
contrasted with temperance than the different colours which remain
when we exclude blue ; unruffled has a more definite meaning still,
for a surface which is not in any way ruffled can only be smooth.2
It has been alleged that f 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
hiust convey a notion of what the subject consequently is without
that attribute, so negative terms (at any rate when they are not
1 Cf. next page.
2 The old Greek proverb will illustrate the point here— co-0\o\ fieV yap
tos Se K«K<H.
32 AN INTRODUCTION TO LOGIC [CHAP.
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 in
the genus ; 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
negative 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.1
The statement that the distinction of terms into positive, nega
tive, and privative is only applicable properly to attributive or
relative terms may seem to be contradicted by the fact that many
negative terms, such as injustice, inequality, non-intervention, are
not relative or attributive. But it will be found that all such
terms are abstracts that presuppose the relative or attributive
negative term ; and 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 not-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
1 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 which constitutes the
genus 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. de Interp. iii. 16b 22.
Such a ' limited universe ' is sometimes called an ' universe of discourse '.
n] TERMS, AND THEIR PRINCIPAL DISTINCTIONS 33
privative) have a positive meaning, what is the use of the dis
tinction 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 desic
cated, 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 attribute within a genus except one ; the latter is compara
tively indeterminate and uninstructive ; e. g. vertebrate signifies a
definite anatomical structure ; invertebrate signifies a structure
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 im
portant, 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 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 £) we may ' permute ' it
to the form A is not-J5 (in which the terms are A and not-J?) ; and
we may formally regard A} JS and not-.Z? all equally as terms.
But whether the proposition A is not-j5, and the ' negative term '
1 These two examples are not quite parallel. The notion of deafness can
be formed by any one who knows what hearing is. The notion of ' desic
cated ' cannot be formed 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 way we think about things.
JOSEPH £)
34 AN INTRODUCTION TO LOGIC
, have any meaning or none will depend upon the matter of
the proposition — upon what kind of a term B was. Looking at
the form, B has a corresponding negative not-i? ; but whether such
a form of thought, or notion, as not-.Z? is possible cannot be told
by considering the form alone.]
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 the object stands. We ought in strictness to regard
this distinction as one not in terms but in the use of terms; for
fab- 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. 20) between a-vv^w^a and o^vv^a was one of things.
Univocum and equivocum are merely translations of (rvvtovvpov
and ofjitovviJLov, 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. fUnivoca 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. If we remember that terms are not primarily names, but
the objects of thought intended by the names, 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 retain both, like the Latin, when
it was said that ' aequivoca ' were either ( aequivocantia, ipsae voces
aequivocae ', or f aequivocata, res ipsae per illam vocem significatae '.]
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 distinction in
chemistry between names in -um, which signify metals, and names
in -gen, which signify gases. They belong to all sciences, and are
based on certain features that reveal themselves to reflection about
any subject whatever; and that is why they are logical. But
these differences of form in our thought about things correspond
to and involve differences in the manner of being of these things
themselves. 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.
The word category, /carr/yo/ata, means predicate l ; and the
categories may be described as a list of predicates, one or other of
which defines the mode of being belonging to everything that
exists. In the complete list there are ten, viz.
ova-Co. substantia substance
TTOO-OV quantitas quantity
TTOWV qualitas quality
Tfpos rt relatio relation
TTOV ubi place
Trore quando time
situs situation
habitus state
actio activity
passio passivity (being acted on)
f * Or predication : but the difference IB here unimportant, and Aristotle some
times uses KaTT)y6pr)iw. instead of KarTjyopia in the present sense : v. Bonitz,
Index Aristot., s. v. KaTrjyoprj^a. The Latin equivalent is Praedicamentum.
D 2,
36 AN INTRODUCTION TO LOGIC [CHAP.
These Aristotle calls both ' kinds of predicate ', ytvrj T&V KdTTjyoptwi;,
and 'kinds of being ', ytvt] rS>v ovrav. We must examine the
latter phrase first, if we wish to understand his doctrine.
We have seen that propositions may be expressed generally in
the form A is B. But the predicate 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 breaking 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 ' What
is Tray ? ' ; and that the fifth is a fuller answer than the sixth
to the question ' What is a musician ? '. Now Aristotle would have
said that the first, third, and fifth of them declared what their
respective subjects were naO' auro, or per se : the second, fourth, and
sixth what they were Kara o-v/x/3e/3r]Koy, or per accidens. In other
words, the predicate is in the one case of the essence of the subject,
and the subject could not exist at all without it being predicable of
him ; in the other case it is an accident of the subject. What is
predicated of a subject xad' avrd tells you what it is necessarily,
and permanently1; what is predicated of it Kara o-vju/3e/3?]Kos tells
you indeed something about it, but something less necessary, and
perhaps unnecessary, to its being — something of which it could be
divested, and still remain the thing it is.
The ultimate subject of predication is the concrete individual
thing — you, Socrates, Bucephalus, or the stone in your signet-
ring2 ; and if you ask of this what it is, you will have to specify
in your answer, some kind of substance i3; you are a man, Buce
phalus is a horse, the stone in your signet-ring is an agate. All
1 This is not a complete statement of the meanings in which, according
to Aristotle, a predicate may be said to belong to a subject K.O.& aurd ; but
it is, I think, a sufficient account of the sense in which the expression is
used in this connexion.
2^ This is the true meaning of the statement in Cat. iii. lb 10 orav Zrepov
KaB" fTcpov KarrjyopfiTai CDS Kad* vnoK(tp.€Vov, o&a Kara rov Karrjyopovpevov Aeyerm,
iravra KOI Kara TOV vTroKfipfvov prjdrja-frai — a statement sometimes erroneously
quoted as equivalent to the Dictum de Omni et Nullo. Cf. infra, c. xiv. p. 275 n.
3 But there are concrete things denominated from 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 dp that, I should
have to say that it was a stone. It is a threshold because it is a stone in
a certain situation.
m] OF THE CATEGORIES 37
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. But
if I ask what is a substance, I cannot find any more general signi
ficant notion under which to bring that, as I bring Bucephalus,
in declaring what he is, under the notion horse, and horse, in
declaring what a horse is, under the notion 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 were substances. Large, loud, blue, heavier, here, yesterday,
fever, horizontal, fighting, running, defeat, virtue — all these are
something, or they could not enter into true predication : but what
are they ? Directly or indirectly they all presuppose substances ;
if there were no animals, there would be no fever : if no one fought,
no one could be defeated. But they are something incident to
substances, attributes and not things. To say that they are
attributes, however, only declares their relation to something else,
their dependence ; it does not declare what they are in themselves.
If we ask that, we shall find ourselves ultimately giving as an
answer some one of the other categories.
Thus I may say that c 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 ; fighting and running are activities y
defeat a being acted on.
38 AN INTRODUCTION TO LOGIC [CHAP.
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 the
things 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 ; but 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 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. The conception of a state, therefore, is more
complex than that of quality ; and so it is with situation 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
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., all involve essentially different kinds of relation ; and
mere relation, which is not any definite kind of relation, is almost as barren
a conception as mere being. Aristotle probably erected relational predicates
into a separate class because they appear to tell us less than others what a
subject is. ' Six feet high ' would be in the category of noa-ov : ' taller than
his neighbour ' in that of npos n ; it gives more information about what
a man is feo 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 can only change by a change in the man himself. The former
involves relation also ; but the latter is more plainly and purely relational.
in] OF THE CATEGORIES 39
ask what in itself it is. They are yei>rj ro>y KarTjyo/nwy, kinds of
predicate, and equally yevrj T&V OVTMV — the kinds of being- which
we recognize, the kinds (if we may put it so) of what things
are.1 In saying things here, however, we do not mean things as
opposed to their attributes ; we mean anything real, and attri
butes are as real as the substances to which they belong. Never
theless, the distinction between substance and attribute is promi
nent in Aristotle's doctrine ; for all the other categories are called
by him incidental to substance. And terms in the other categories,
while they may be subjects of predication (as when we say that
blue is a colour, or that the wise are few), are not metaphysically
subjects — are not independently existing, but exist in concrete indi
viduals. There is no blue except the blue of the sea or the sky, of
a larkspur or a gentian, &c. ; no wise, except wise men or women.
In the category of substance come all concrete individual things, and
these are substances in the strict and fullest sense. Of these in the
last resort everything is predicated. But what is predicated of
them is partly itself in the category of substance, and 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.
First substances are individuals like Socrates or Cicero ; second
substances are predicates like man, horse, peppermint, parsley, which
tell what kind of thing an individual is. The former are never
properly predicates at all ; Socrates or Cicero is a subject of predi
cation, but not predicable of anything else ; for what is predicable
is universal, i. e. might be predicable of any number of subjects ;
but these are individuals, and singular. The latter are predicates
of the former, and are universal ; but they tell what an individual
essentially is, and so are predicates in the category of substance,
1 Cf. Ar. Met. A. vii, and Apelt, Beitrdge zur Geschichte der griechischen
Philosophic, III. Die Kategorieenlehre des Aristoteles. In the expression y^vrj
TO>I> KdTTjyopivv, ' kinds of predicate,' Karrjyopia 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. Some inter
preters have therefore held that the concrete individual is not in any
category, since it is never properly a predicate (cf. Cat. v. 3a36 dn-o p.(V
yap rfis irp<i)TT)s oixrias oufie/it'a cirri KtiTTjyopia). But Met., I.e., seems to show,
what the whole doctrine of that treatise implies, that the concrete indivi
dual is in the category of substance ; it is certainly one of the ' kinds of
being'. The account in the text accordingly follows the implications of
the expression yei/q r&v OVTUV in this point of discrepancy between the two.
40 AN INTRODUCTION TO LOGIC [CHAP.
while 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 sought gratuitously ;
they arise naturally in our reflection upon the nature of things.
We naturally incline to think, in considering an 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.
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 predicates in other categories are. And some have
held that these < second substances ' are real, whether there be any
concrete individual of their kind or not : while others have held
that, though only realized in individuals, yet each is one and the
same in all individuals of its kind — man in all men, iron in all
iron — and so may be called one substance, in a different way from
m] OF THE CATEGORIES 41
this or that man or lump of iron, but just as truly. Each of these
doctrines was called by the schoolmen realism 1) as opposed to the
nominalism which denied the real identity of anything1 in different
individuals bearing1 the same kind-name.
But secondly, because the kind is universal, it is predicated of
the concrete individual, as predicates in other categories are. 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 particular 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, we are yet quite unable to say what
the individual is, to which they all belong. 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.
This gives rise to a new way of considering the subject of predica
tion. Originally it was the concrete individual, Socrates or Plato ;
but of what he is, one part was distinguished as what he is essen
tially, 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
ef 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 predi
cates, which cannot in itself be described as specifically of this kind or
of that, Aristotle called matter? We only know matter in con
junction 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 — that which is found in various forms, but has no
1 The former was said to maintain the existence of universalia ante rem,
the latter of universalia in re : where the res is a concrete individual.
2 Cf. Ar. Phys. a. vii. 191a 8-12.
42 AN INTRODUCTION TO LOGIC [CHAP.
form of its own — is unknowable.1 It may be questioned whether
Aristotle was justified in his use of the conception of matter. The
material of anything is always something- of a quite determinate
character. 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 car
penter, 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 lumber or pig iron. In the one
relation, 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 ; in the other, 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 different subjects of the
same form in different individuals, I may not at first sight
seem to rely upon 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, and different houses, however closely other
wise alike, are distinguished by being built of different material.
But if we ask what distinguishes the material used in building one
house from that used in building another, and do not find it in the
kind of material, we shall have either to say that the materials
are themselves made out of different material or that they just are
different; in the former case we shall be assuming, in order to
account for the difference between determinate materials that are
the same in kind, other determinate materials the same in kind
but individually different ; in the latter, any further analysis into
matter and form brings us to an indeterminate matter that furnishes
different subjects for the same form in different individuals. The
1 T) uXrj ayvata-Tos <ad* avrrjv, Met. Z. X. 1036a 8.
2 In the foregoing criticism I am particularly indebted to lectures of
Professor Cook Wilson.
m] OF THE CATEGORIES 43
proper outcome of this line of reflection would seem to be that what
makes possible different individuals of the same kind is the matter
of which what they are is predicated ; and this at times Aristotle
says l, 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 reconcile 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 his substance ; and it is neither merely the specific
\ form of man, nor does it include all that can be predicated of him ;
/ but we are not told how to distinguish it from predicates in the
I 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 may
start with the concrete individual, and draw a distinction, among
all the things that can be predicated of him, between that which
declares what he is essentially, and is his substance, or belongs to
the category of substance, and that which declares about him some
thing not essential, and belonging to one of the other categories.
But predicates in the category of substance seem universal, as in
any other ; and predicates in the other categories are not essential ;
hence the tendency to say that what individualizes is material
substance, not universal, nor capable of figuring as predicate. If,
to avoid this, we suppose that there is something about Socrates
which makes him Socrates, less than the sum total of all his
predicates, we shall find it impossible to say what this is. The
attempt to distinguish what is from what is not essential to the
individual leads us to distinguish the individual both from his
essence and from his non-essential attributes ; the ' first substance '
is alternately regarded as the whole concrete individual and as
what is essential in him; while the fact that the possibility of
distinguishing the essential seems first possible when we look for
the character which belongs to him as of his kind leads to the con-
2,
1 Cf. Met. *M* viii. 1034a 5-8; and v. Bonitz, Index Arist. s.v. vAn, 786a
52-58. ^
2 Cf. Met. -Ml x. 1035^ 27-1036a 9, xiii, 1038b 8-15 ; H. i. 1042a 28-9. But
one cannot really support any statement on the point except by reference
to his whole discussion.
44 AN INTRODUCTION TO LOGIC [CHAP.
ception of an universal essence possessed of a sort of substantiality
of its own, a sort of ' second substance '.
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 features
that 'characterize our thought about things in general, without
asking how things can be conceived to exist ; for our most general
thoughts about them are just our conception of their manner of
existence. And it may readily be shown, with regard to the
different categories in particular, that we could not use predicates
in them, except so far as we conceived objects 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 ^^iip^iinlllfflgjtrnt/"' ^T ^ 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
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
OF THE CATEGORIES 45
therefore the category of situation, would not exist. Again, there
are predicates in TTOICUJ and itacryjeiv 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 iroitiv or
T7CL(TX€iv, €X€tz; or KflaOai *, presuppose that things exist in time ;
otherwise, how could we distinguish the meanings of vyiatVet and
vyCavtv, vapulat, and vapulabit, vivit and vixitt sits and salt 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 objects
existed in certain ways — as substances, with qualities, extended in
space, persisting in time, &c. — so we cannot predicate about objects
except in one or other category ; in other words, not only are they
contained in, but they are necessary to our thought of any object.2
That which was not conceived as a substance, 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 they characterize 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 an object, in order to be an object, 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 an object must have some quality or other : in the category of
relation, or in noticing that it must stand in relations to other
objects : and so on.
The idea 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
1 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.
46 AN INTRODUCTION TO LOGIC [CHAP.
whatsoever. His classification may exhibit defects, but the impor-
tancTTF'his undertaking1 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 manner in which we conceive things to exist. The distinction
between singular and general concrete terms corresponds in the
main to that between Trp^rrj and Seure/oa ovcria 1 ; for the most notice
able of general concrete terms are in the category of substance,
as man, stone, or beast, though some (which might be called sub
stantives of an attributive kind) are in other categories, as, for
instance, officer and organist. The distinction between concrete and
abstract terms corresponds roughly to the distinction between ovaia
and the other categories ; for abstract terms formed from kind -names
are, as we saw, scarce and unnatural. That relative terms are predi
cates in the category of relation is plain. The attention paid to
collective terms reminds us that we can consider not only objects
severally, but what they are in certain groupings or combinations ;
and the distinction between quality and state involves the same
fact.2 The logical divisions of terms rest on differences in the
being of things, as we apprehend them ; 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 throughouffit 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 in 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.3 Moreover a conception of
categories not very far removed from that of Aristotle has, through
1 = first and second substance.
! It is not meant that collective terms are in the category of State.
3 Except as terms in a derivative category involve terms in those from
which it is derived.
in] OF THE CATEGORIES 47
[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, Tjhe different categories are
not all equally distiiuj.t or ultimate. Thus the distinction between
TTOV and irorl is fur more Tundnmontal than that between noielv and
Ti&vytw. 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 /avrjo-ts.1 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, thafftneT 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 €\€i.v J?
A>--«hd K€i(r0<H are derivative : state presupposes the distinction of
whole and part, which, in material objects at least, implies the
category of TTOOW, and it presupposes also the categories of noitlv
and irda")(€iv, and of TTOLOV ; 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 and irpos n ; 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 derivative
categories Aristotle lays least stress; they are only twice 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
1 Met. Z. iv. 1029b 25.
48 AN INTRODUCTION TO LOGIC [CHAP.
[criticism, that he had not taken account of all the derivative
conceptions which call for recognition.
A word may perhaps 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 were ; Kant was interested rather
in the question how there come to be for us objects 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 on the part of the mind the relating to one
another in various ways of 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 consciousness. 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 for us, of objects. He
noted 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. There could be no permanent objects for me, unless
I somehow held together past and future in an unity with the present ;
I should not be aware of my own existence as persisting through
time, unless I realized myself as the same in moments which
I distinguished as different ; and I could not do this, unless I had
an object which combined manifold successive states into the unity
of one and the same thing ; here then we have one function of
synthesis. 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 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 : (i) 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 given temperature and blue must be of a given
in] OF THE CATEGORIES 49
[shade and saturation : (2) its having quantity, or being a whole
composed of parts : (3) that it should be ^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 material
diversity of concrete objects as we know them, these categories or
forms of synthesis 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 using in a specific way that conception of
quality which is one of the notions by which I relate together what
different 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 recognizing 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 and 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 guide
us consciously in our apprehension and description of 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 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 uncon
sciously made of them ; just as we become aware in the abstract of
using certain forms of inference, by reflecting upon the concrete
inferences we have drawn in divers subjects. But as there would
be no men if there were no animals, and no circles if there were no
figures, so we should recognize no colours if we could not conceive
qualities ; 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
50 AN INTRODUCTION TO LOGIC [CHAP.
[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 : we are effecting a synthesis in what would otherwise be
a mere chaos or confusion of manifold sensations.
/^ Now it will have been seen that Aristotle also noted that what
/ we lecognized as existing were sometimes substances with attri
butes, 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 relations and positions iu place
and time ; of what things do and have done to them ; of their
states and situations. But Aristotle approached the matter from
the side of the object ; he asked what modes of being we can dis
tinguish in what 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 thought, through which objects were
apprehensible by us as being 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 prin
ciples their manifold differences, then we should expect that when
we reflect upon the manner of being which what we recognize to be
exhibits, we should find those modes of being which the mind by its
synthetic or relating activity makes possible for itself. And if, while
this in the main is true, there are certain differences between the
two lists of categories, yet they 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,
and Interaction (which last really involves the other two) ; the dis
tinction of substance and attribute is present in Aristotle's doctrine,
and in Tioitlv l and TTCLO-^LV 2 we have the recognition of the rela
tion of cause and effect ; but there is nothing in Kant correspond
ing to the Aristotelian category of Trpoy n 3. The reason of this is
that all predicates in the category of Ttpcs n 3 really involve some
other category as well ; larger involves TTOCTOV 4, earlier Trore' 5, slave
Tiaa-y^tiv 2, farthest TTOV 6, and loudest iroiov 7 ; reciprocally, all cate
gories involve relation, and Kant's whole point is that they are
different relational functions. To Kant, who was interested in
distinguishing these functions specifically, it would have been
absurd to treat the function of relating genericaily as one of its
1 Action. 2 Passion. 3 Relation. 4 Quantity.
6 Time. « Place. 7 Quality.
m] OF THE CATEGORIES 51
[own species J; or to suppose that there was any other kind of
relation involved when I say that Socrates was more scrupulous
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 terms which
relate it particularly to some definite other object; and these
Aristotle placed under the category of irpos TI 2. It might
perhaps be objected to him that all terms in the category of irpds
n 2 were also in TTOV 3 orTrore4, Troto'j;5 or e^eiv6, Troieiv7 or nav-
Xeii;8, TTOO-OV^ or iccurflai 10 ; but he would have replied that they
were referred to the category of relation not because they in
volved qualitative or quantitative, spatial, temporal, or causal
relations, but because they determined a thing as standing in some
special relation (of any one of these kinds) to some other thing,
and had their being not so much in themselves as in relation to
something else n. Again, terms in -noo-ov, 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 conceptual synthesis of whole and
part ; hence also he objected to the presence of nov and Trore 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 here 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 €\€LV an(^ K€io-6ai with the rest, because
they certainly are different modes of being ; Kant, who thought
them to involve only the co-operation of functions of synthesis
already recognized, gave no place to them. The most considerable
difference between the two doctrines is the absence from Aristotle's
1 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.
2 Relation. 3 Place. * Time. 6 Quality. c State.
7 Action. 8 Passion. 9 Quantity. 10 Situation.
11 Ta Trpof TI are defined first in Cat. vii. 6a 36 as 'what are called what
they are of another ' — on-a aira arrep enriv irtp&v flvat Xe'yerat, and more closety
later in 8a 32 as that ' for which to be is the same as to be related in some
way to another' — ols TO dvai TCLVTOV fo~n roiTrpor TI trws e\fiv. The implication
of Trpo? it with some other category is recognized by Aristotle in particular
cases, but not stated generally; cf. vn. 6b 11, ix. lla 20-38, and esp. 37-38,
(TI ft Tvyxiivoi TO avro irpos TI *<n iroiov ov, ovftev UTOTTOV ev afj.(f>OT€fjoisTols yfveaiv
(IVTO KaTapi0fjL('i(T0ai (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).
E 2,
52 AN INTRODUCTION TO LOGIC
[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 essen
tially 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
differ one from another, are all alike objects of knowledge and so
far formally the same. Merely to be, said Aristotle, is not possible :
nv is not a significant predicate l ; what is must be in a particular
way,, and thereby fall under one or other of the yeV?} r&v Karr/yo/nw^
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
knowledge, and therefore for us cannot exist, 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 involved (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 f categories of the understanding *.2]
1 Unless indeed it is equivalent to oicria or Substance ; but that is one of
the categories.
2 If Kant was wrong in supposing that the formal characters in an object,
whose presence there he ascribed to the synthetic activity of the mind,
are not merely recognized in it, but are there to be recognized through the
mind's activity, yet what has been said will still express the relation which,
from his point of view, subsists between Aristotle's doctrine and his own.
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 Aristotelian treatise called the Categories
indicates this when it puts forward the list of ten categories as
a division of terms out of syntax.1
In the present chapter we have to consider another division of
terms, based upon the relation Jn 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 (ye'yoj), the differentia (biatyopa),
a property (Ibiov), or an accident (<n>|Li/3e/3r7/cos) of the subject. The
later list 2, losing sight of the principle on which the division was
1 T£>v Kara fjujSe p.iav (TVfJLTrXoKrjv \cyop.€i>a)V tKacrrov fjroi oixriav (T^finivfi 77 TTOCTOV
T! TTOIOV f) irpOS Tt j) TTOO T/ 7TOT6 ff Kflffddl ff e\tiV T) TTOlflv fj ira<T\flV, C(tt. iv. lb 25.
2 The Aristotelian list is given in the Topics, a. iv. 101b 17-25 : the later
list passed into modern Europe through the medium of a little work by
Porphyry, the EtVayoxyq or Introduction to Logic, in the Latin version made
by Boethius. diafopd is ranked by Aristotle with -yeVos-, as being a modifica
tion of that ; and as the surplus in opos over yeW , it is known in knowing
them. Cf. infra, p. 60.
54 AN INTRODUCTION TO LOGIC [CHAP.
made, omits definition, and includes instead species (flbos), 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
constitution; 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 features in our thought about all kinds of
subject.
A predicable is merely that which can be predicated : viz. that
which is universal, not an individual; all kinds, qualities, states,
relations, &c., are predicable, and they are universal, as was
explained in Chapter II, because they may be exemplified in and
belong to more than one individual subject. All names, therefore,
except proper names are classified under these five heads of pre-
dicables; but proper names are not included here, though they
would come in the division of categories as denoting a substance.
The Parthenon, for example, is not the name of 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 — a temple, Doric, of Pentelic marble, beautiful by the
simplicity of its proportions and the magnificence of its sculptures,
the work of Pheidias and his assistants, the glory of Athens. All
these things are predicable 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 *.
1 To use a phrase of Mr. F. H. Bradley's, it is the ' what ' and not the
' that ' of things which we have to consider.
iv] OF THE PREDICABLES 55
The distinctions which we have to consider, therefore, do not afford j
a classification of things, but o£ concepts : and (unlike the cate- I'
Dories) of concepts considered not in themselves but in their relation \
one to another. V
But things are known to us through concepts ; and an enquiry
into the relation of concepts is an enquiry into the nature of things,
as we conceive them to be.
The statement that things are known to us through concepts
needs a little explanation. It has been frequently pointed out that
the English language uses only the one verb, ' know/ to represent
two different acts, which in some languages are distinguished by
different verbs l : 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 connattre and savoir ; German the words kennen and wissen.
Knowledge of acquaintance does not come barely through concepts ;
however much may be told me about Napoleon, and however clear
a conception I may have been enabled to form 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
individual that is to be known. But knowledge about a thing comes
by concepts; and without this there is no acquaintance, though
this by itself does not 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
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
1 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.
56 AN INTRODUCTION TO LOGIC [CHAP.
Smith, he can regulate his business accordingly, without knowing
Smith.
It will now be understood in what sense we know things
o
through concepts : we are not thereby acquainted with them
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 : completely knowable and not parti
ally l. Take, for example, the concept of a timepiece : a timepiece
is a machine in which the movement of wheels is so stimulated and
regulated as to cause a hand or 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 un
changing, while my watch wears out or gets broken ; and it is com
pletely 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
have a satisfactory concept of what a timepiece is for all that.
It may be asked, 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, to which some reference has
already been made in speaking of the opposition between Realism
and Nominalism 3. An elementary treatise must be content to be
brief and dogmatic. Concepts, it must be 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
1 Concepts do not necessarily realize this last requirement ; but whereas
the individual cannot be completely known, a concept might be understood
completely.
* Or does it (as some have held) exist apart at once from particular
things and from our minds ?
s Supra, p. 41.
TV] OF THE PREDICABLES 57
tell the time of day in the manner set forth in the concept 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 thing's is the nature of the things ; nor would it
otherwise be they that my knowledge dealt with. But though
concepts have existence in things, as well as in our minds l, the
manner of their existence in the two cases is different, in an
important respect. In our minds, 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 object. But in
the thing these features are not isolated. The individual object is
at once and together all that can be predicated of it separately and
successively (except as far indeed as predicates are true of it succes
sively). In thinking of my watch, for example, I may think of it
as a timepiece, as an heirloom, as being two inches in diameter, and
so 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 2. The individual object is all that
can be predicated of it (and there is no end to what might be
predicated, if we knew its whole 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
1 This does not of course mean inside our skulls.
2 The word thing here is used first of the individual, the subject of pre
dication, then of the universal, 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.
58 AN INTRODUCTION TO LOGIC [CHAP.
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 13 / where the subject A is
not a proper name, but a general concrete term, or an abstract term.
The predicate H must be either definition, genus, differentia,
property or accident 1 of A : one or other of these relations must
subsist between the two concepts A and J5, in any individual
characterized by them.
The statement just advanced clearly concerns the nature of our
thought about objects 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 dis
covered the relations denoted by them.
If we take any term that is an universal, and not an individual,
and make it the subject of a judgement, 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 predi
cated of everything whereof the other can be predicated 2 ; 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 commensurate
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
1 dog ', and not with the relation of these terms to Tray)— it may
be pointed out that when the subject of a judgement is an indi
vidual, the predicate is hardly ever commensurate 3 : for the predicate
is an universal, predicable of other subjects besides this individual :
mine is predicable, for example, of other subjects than Tray ; whereas
* But cf. p. 62, n. 1, inf. The Porphyrian list of predicates will be con
sidered later.
2 And therefore, of course, neither of anything of which the other cannot
be predicated.
3 Only if it is a predicate which from its nature can belong to no more
than one individual, as e.g. the attributes of God.
iv] OF THE PREDICABLES 59
this individual is predi cable of none of those : nothing else that
I can call mine is Tray. Now where the predicate of a judgement
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, or an Accident.
The definition of anything is the statement of its essence * :
what makes it that, and not something else. In the following judge
ments, the predicate claims to be the definition of the subject : ( An
organism is a material body, of which the parts are reciprocally
ends and means ' ; ( a church is a building erected for the service of
God according to the principles of the Christian religion 3 ; ' mo
mentum 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 distinguished from every
thing 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 exchange, then gold, having
value in exchange, is wealth, and so forth.
The genus is that part of the essence of anything which is pre-
dicable also of other things 2 differing from it in kind 3. 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
(lev yap rov rl fan KOI ovarias, Ar. Anal. Post. 0. iii. 90b 30. We
may ask the question rl eVn ;• — what is it ? — of an attribute (like momen
tum) as well as a substance (like a man or a lobster) ; and the answer will
be a definition. In strictness we can define the owia of an individual, if
at all, only as meaning the kind to which it belongs ; cf. the previous ch.,
pp. 40-44.
2 ' Thing ' here again does not mean a particular thing.
3 revos 6%' fan TO KUTU rrXftdfcoi/ *ai diafpepovTW ra> tldfi f'v TO> rl (an Karrjyo-
povp.(voi>, Ar. Top. a. v. 102* 31. The notion of a kind is here presup
posed. Some discussion of it will be found below, pp. 77-89.
60 AN INTRODUCTION TO LOGIC [CHAP.
you cannot transfer it l ; 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 sub
jects, is clearly not commensurate 2. Genus is sometimes explained
as a larger class including the class defined within it ; figure, for
example, as a class including triangle, square, and many other
subordinate classes besides : building as a class including churches,
stables, barracks, and so forth. This explanation cannot be con
sidered a good one, for reasons to be presently stated ; 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 3) 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 predicated in cases
where no genus except that to which the subject belongs is sus
ceptible 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.
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
\ The honest man, however, commands in many situations a higher
price, and so far some economists would reckon honesty as wealth.
2 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. 69-73, 123.
8 In the plural if the genus has divers determinable points that have to
be specified differently in the different species. Cf. inf., p. 86.
iv] OF THE PREDICABLES 61
pentagons, &c., are all placed in the class of rectilinear figures
because they have that character in common, triangles, on the
other hand, are differentiated from the remaining classes included
within that of 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 ' 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 l
(and therefore obviously commensurate with it), but not part of its
essence, and so not included in the definition of it. 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 is half the
area of the parallelogram on the same base and between the same
parallels ; a line is either straight or crooked (here the alternatives
together are common and peculiar) ; and so forth.
All other attributes of any subject are accidents. An accident
may be 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 2. 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.
1 The subject being, it must be remembered, an ' universal ', not an indi
vidual. 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 the dog
in every instance. Aristotle sometimes spoke of an attribute peculiar to an
individual, and not to a kind or universal, as a property ; and also of attri
butes peculiar to one out of a certain definite number of kinds, and therefore
serving to distinguish it from them (though found perhaps again outside
their number) as relatively properties ; thus it is a property of man re
latively 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. € i.
2 Cf. Ar. Top. a. v. 102" 4-14. Cf. Top. e. i.
62 AN INTRODUCTION TO LOGIC [CHAP.
The doctrine just illustrated presents many points for considera
tion, of which the following- are perhaps the most important : —
1 . how to understand the analysis of a definition into genus and
differentia ;
2. the ground of the distinction between the essence of anything
and its properties ;
3. the antithesis between accident on the one hand and all the
other heads of predicables on the other.
It will be most convenient to consider the third of these points first.
TV hen we classify the members of a genus or class, we sometimes,
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 arrange my books, for example, into historical, philosophical,
philological, scientific, and miscellaneous — 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 l ; but it is not a heading like ' miscellaneous ' ; there is
a very definite and important difference 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,
2vp.[:ifftr)K(>f fie ftrriv 6 prjdfv ptv TOI/TOOI> far!, u.'re opos u/.re tdtov unrf ytvos,
Ar. Top. n. v. 102b 4.
2 Coincident is really a better translation of (rvfjLpfprjn6s than accident.
1\
] OF THE PREDICABLES 63
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
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 nothing1 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 sufficient
knowledge the presence of all its attributes in any individual might
be explained ; but the explanation would be largely historical ; we
should need to know the history of that individual, in order to see
how it was that so many different and apparently unconnected
things all came to be predicable of one and the same subject. On
the other hand, where two predicates are conceptually connected,
there it is not by knowing the history of an individual that we
determine whether, if one is predicable of it, the other will be.
We have here the great difference between science and history :
science consists in tracing the connexion of universals ; history in
tracing their coincidence in individuals. The two no doubt utilize
one another. It is by noticing how attributes are historically found
conjoined or disjoined in divers individuals that we learn which are
really connected together ] ; while again the discovered connexions
of attributes, or the ' laws ' which science establishes, help to explain
the history of individuals. And when the assemblage of historical
events is resolved into instances of the connexion between matters
which, if we understand their nature, we can see to be involved
one in another, history becomes scientific.
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
1 The illustration of this forms a considerable part of what is called
Inductive Logic ; we shall find that many connexions are inductively estab
lished whose necessity remains unconceived.
64 AN INTRODUCTION TO LOGIC [CHAP.
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
a relation between universals : my dog 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 one thing x the cause of another, the real relation
between them 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 7, 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 recipro
cally necessary ; no heat without molecular motion, and no mole
cular 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 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,
1 Thing being here again thing of a kind, or universal, not individual.
l\
] OF THE PREDICABLES 65
then, that we do not always mean the same thing 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 are accidents, whose cause does
not lie in the nature of A as such, 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 causal connexion
between a subject and a predicate is satisfactory is another
question, involved principally in that of the value of his account
of f 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 Revolu
tion (whose cause must be as unique as that event itself is), but of
an event of a kind, such as consumption, or commercial crisis, 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 commercial community, given which there must
and without which there cannot be a commercial crisis ?
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, the ground for whose existence in the
subject does not lie in the nature of that subject as such. 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 plough is predicated as an accident. But a man drives a
plough. That is an accident ; for the subject now is not Hodge,
but man, and it is not in the nature of man as such that the ground
or reason of driving a plough lies ; else should we all be at the plough-
66 AN INTRODUCTION TO LOGIC [CHAP.
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, con
tributes 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 predicate may belong to the subject of which it is predicated
accidentally either
(1) when the ground for its existence does not lie completely in
the nature of that subject as such 2, or
{2) when the ground for its existence does not lie at all in the
nature of that subject as such 2.
The first interpretation would rank as accidents of a subject 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 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 disconnected
the conjunction of circumstances through which it came about,
where the nature of the subject as such2 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
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 acci
dent ; but the second sentence -will stand without qualification.
2 It is necessary to say of the subject as such, in order to keep in view
that it is not the individual, but the subject as something of a kind, about
which we ask whether its nature contains in any degree the ground of the
predicate. To be knocked down by a locomotive may be an accident, as
regards a cow as such, i.e. as cow; but it would be absurd to say that the
particular cow contributed nothing to the accident, since it could not have
been knocked down if it had not been there.
iv] OF THE PREDICABLES 67
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 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.
The antithesis between accident and the other heads of predi-
cables needs perhaps no further illustration. We may return to
the first of the three points enumerated on p. 62, viz. how to under
stand the analysis of a 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, so that we have a determinate concept of
it ; 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 a true notion of him,
and that unessential. Moreover, even if we could, we should still
only have got a notion of what he in fact is, but a second person also
might be ; for every notion is universal. What makes him this indi
vidual and not another we should not have defined, 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 ;
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
F a
68 AN INTRODUCTION TO LOGIC [CHAP.
we have already said that concepts express the nature o£ 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 J : that
they set forth the meaning (or, as it is also phrased, the connotation 2)
of a name, but not the nature of a thing. Yet 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 ; nor by considering a thing as far,
sour, pink, soft and circular, can we construct the concept of one
thing. 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 anything. 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 con
stitute the essence of one thing, or state, or quality, or relation.
And the reason for the parts of a definition being one3 is this:
that they are not attributes independent but coincident, but the
^enus is the general type or plan, the differentia the ' specific '
mode in which that is realized or developed. Let us take again the
1 e. g. Mill, Logic, I. viii. 5.
3 On ' connotation ' cf. infra, c. vi.
3 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.
iv] OF THE PREDICABLES 69
definition of a triangle. It is a rectilinear figure ; but that by
itself is an incomplete notion. There cannot be a rectilinear figure
without a definite number of sides, though any definite number 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
suggests a collection, whereas the genus of anything is not a collec
tion to which it belongs but a scheme which it realizes, or a 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
70 AN INTRODUCTION TO LOGIC [CHAP.
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
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.
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
vequally to the habit of calling the species a class including individuals.
iv] OF THE PREDICABLES 71
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 l, 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 c 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) belonging
to it, only realized in each in a special way. The differentia 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
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. But even a class
at school is not a chance collection, but a collection of bovs supposed to
share the same level of attainments.
72 AN INTRODUCTION TO LOGIC [CHAP.
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 hair 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 l, 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 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 O\\Q fund amentum 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 leading
idea of the thing, and then to render this definite by stating in
what way the leading idea is realized or worked out. And the
differentiae are of the essence of the things, because they belong to
the working out of this leading idea. 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 an organized body,
and classify its various forms in such a manner as to show how this
scheme is 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
1 Cf. infra, c. v. p. 101.
?
iv] OF THE PREDICABLES 73
these according1 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 ' (${5Aa), the platyhelmia or
flat-worms, annelida or worms, arthropoda, mollusca, echinoderma
and chordata; of chordata, according to the form which the nerve-
cord assumes, into hemichorda, urochorda, cephalochorda and verte-
brata; and of vertebrates, according to the different forms which
the general principle of vertebrate 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 organized body, it is
not of course meant that historically, in our experience, that is
what we first become acquainted with. We first become acquainted
with individual plants and animals ; and we are familiar with their
various species — with horses, dogs, and cattle, oak and apple and
elm — long before we have settled with ourselves what is the leading
idea, and how it is developed and worked out in them all, so as to
make them the kinds of things they are. The genus is that with
which, when we have acquired an insight into the nature of these
rious kinds, we then start ; it is first in the order of our thought
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 cfrvo-tL Trporepoy, or Aoyw Trporepov, not fiyJiv
irpoTfpov : first or fundamental in the nature of the thing, and in
the order of our thought, but not what strikes us first. And Aris
totle also expressed its function by saying that the genus is, as it
were, the matter, vXrj, of the species or kind.
In saying that a genus is related to its species as matter to form,
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 compara
tive complexity of metazoa, in coelentera and coelomata ; but it would be
difficult 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 coelomates 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 sub
divisions of the vertebrata this can be done more adequately than for the
subdivisions of the chordata.
74 AN INTRODUCTION TO LOGIC [CHAP.
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 vertebrate, 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
superfluous, if they help to guard against the idea that a genus
is something 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
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 objects, we should first examine what we mean
iv] OF THE PREDICABLES 75
[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 objects, that there
is a plan, purpose, or idea suggested to us in what we call the less
developed, but not adequately exhibited there as we conceive it, and
that this same plan, purpose, or idea is more adequately exhibited
in what we call the more developed object, we have no right to call
them more and less developed at all. The relation therefore is not
between the objects as individual, but between their characters;
we cannot identify with the less developed individual the plan,
purpose, or idea which is less developed in it ; there is the same
plan at different levels of development in each individual ; and the
evolutionary history of individuals must be a manifestation of
a plan or of intelligence in them, unless we are to say that there is
no real development in them, but only change, and that to call this
change development is to read into things a fancy of our own.]
[In the first chapter, the antithesis of form and matter was
employed in explaining how a common character might belong to
divers objects. Two shillings, for example, may be said to be of
the same form, while the matter in them is different : and two
propositions to be of the same form, so far as each asserts a pre
dicate of a subject, while their matter — i. e. the actual subject and
predicate in each — varies. 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 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, this is still
the case. We regard a shilling as an object having a certain form
(that might also be stamped in gold or copper) impressed upon
76 AN INTRODUCTION TO LOGIC [CHAP.
[a certain matter, silver : and say that both are necessary to its
being- a shilling-. Now the matter here is really silver as of no shape.
A disk of silver may be put into the die and stamped : but such
disk is not the mere matter of which a shilling is made ; it is the
matter in a different form : but because the silver may have the
form of a shilling, and may have the form of a plain disk, it is
possible for us to distinguish between the silver, which is present
alike in the disk and in the shilling, and the form which the silver
assumes in the minting. The matter of a shilling is thus not silver
in another shape, but silver without regard to its shape : the metal
as it is present equally in the disk and in the shilling ; now silver
does not actually exist except in a particular shape ; and in think
ing of it in abstraction from its shape, our thought of it is incom
plete. 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
vertebrate ; 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 object.
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 light 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 of the same die) ; and though we say they differ in
matter, we mean that though of the same matter, they are different
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
iv] OF THE PREDICABLES 77
[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 individual objects. Matter is indeed, strictly
speaking, not a particular thing or an aggregate of particular
things, but a generic conception. We recognize various species of
it, which we call elements : the elements are different forms of
matter ; |ind 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 form any conception of the common or
generic character in abstraction trom 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
triangle and being a three-sided rectilinear figure are l ; 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 anything
must belong to it ; for else it would not be that kind of thing, but
something different.
We may now take up the last of the points raised on p. 62 — the
second in the order in which they were there stated : 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 it
is, of course it would be something different, were any element in
its essence wanting ; but what makes it what it is?
1 Aristotle would express this by saying that TO x\&>pbV may be rer paywvov,
but TO x^pn flvm is not TO TiTpaywvw fivai — the green is square, but green
ness is not squareness ; whereas triangularity is three-sided-rectilinear-
tigurehood.
78 AN INTRODUCTION TO LOGIC [CHAP.
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 what it is called ; and that the
world might have been spared much useless controversy, 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 *, the nominal essence. Pushed to its
logical conclusion, such a doctrine makes all the distinctions of pre-
dicables arbitrary ; for if the nature of the thing denoted by a
general name X is not to determine the signification of the name,
we can attach to the name what concept we please, and it will rest
with us whether the concept shall be one with which a given pre
dicate is conceptually connected or not, and therefore whether it
shall be an accident of X, or stand in some other relation to it.
And if we were to regard only the definitions of geometry, it would
appear a gratuitous paradox to maintain, that men determined
arbitrarily what to include in the definition of circle or triangle,
and what to omit. Every one recognizes that you declare better
what a 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 gene
rated by the revolution of a straight line round one of its extremi
ties remaining fixed, than by saying that it is a 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 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 object. The definition of abstract
notions like wealth or crime or liberty has lent some support to the
same view. In these cases, the object 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
1 v. Essay, Bk. III. c. iii. § 15.
iv] OF THE PREDICABLES 79
arguing1 to its nature from our definition, we have rather to deter
mine whether it is to be called a crime, or wealth, or a state of
liberty by considering 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 * 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 t 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 substance
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 an object 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
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 some substance which in any individual object is
what has the 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. 41-44, supra.
80 AN INTRODUCTION TO LOGIC [CHAP.
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 of a kind are the predicates common and peculiar to all
the individuals 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
definition 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 over
looked ; it is, however, vicious in theory ; for it implies that we
already know what gold is, or what makes a particular object
a piece of gold, and can by that knowledge select the objects 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 is to be settled by an examination of the
things that are gold ; what things are of gold is to be settled by
knowing what gold is.
Hence our selection must be arbitrary ; for we have no principle
to make it on. We may take a particular specific gravity, 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
iv] OF THE PREDICABLES 81
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
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 uni
versally connected, because we believe that with fuller knowledge
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 pecu
liarities in a species are inferred to be ' correlated \ because the same
conditions seem to affect them both, 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, in the case
at least of 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 devia
tions from the type, excluded under the title of monstrosities or
sports or unnatural births, were not allowed to disturb the sym
metry 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, as in the case of the
mule, and that when the cross was uniformly infertile, the species
JOSEPH
82 AN INTRODUCTION TO LOGIC [CHAP.
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 the essence of a species
becomes theoretically impossible. It is possible to describe a type ;
but there will be hundreds of characteristics 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, the distinction between essence and property is
similarly infected. But that distinction is obnoxious to another
objection, already noticed on p. 80 : 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 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 sub
ject alone, why is it not regarded as a part of its nature ? if it is
grounded in part in the nature of the subject, in part in the fulfil
ment of 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 a figure includes so much as need be stated in order
1 Cf. supra, p. 66.
iv] OF THE PREDICABLES 83
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 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 line round one 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 angles CAB, EBA -.
equal to the angles DAB, FBA, CD and /A
EF must be parallel, and if not, not ; and ^ /
vice versa : we assume also in one propo- 4-
sition all that we have already proved 7
in others. It is not from the mere contemplation of a figure as
defined, 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 is involved not
solely in the essence of the figure as set out in its definition, but in
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 equal on both sides 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 bring the figure into
being before us. 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
G 2,
84 AN INTRODUCTION TO LOGIC [CHAP.
non-mathematical sciences. And it creates its objects by construct
ing them — i. e. by drawing lines ; and in this possesses a natural
principle upon which to distinguish between property and essence.
For though, in geometry, properties are commensurate with their
subjects, and may be reciprocally demonstrated, yet everything
depends upon the power mentally to see the lines ; 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 application until the figure can be
pictured. Let a circle be a 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 gene
rated by the revolution of a straight line about one of its extremi
ties 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 f 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.
iv] OF THE PREDICABLES 85
Geometry therefore deals with subjects capable of definition : 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 ques
tionable, so far as the properties of a figure do ideally belong to it
always, just as much as the figure always exists ; they are as neces
sary 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 which we must start with, 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 neces
sary in order that we may see before us 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 there
with.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 their
construction in different instances; and they exist under con
ditions which are not constant (like the nature of space) but
infinitely various. Under these circumstances, we cannot expect to
find the determination of the essence of a kind, and the separa
tion 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,
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.
86 AN INTRODUCTION TO LOGIC [CHAP.
our problem deals with the elements. It will be instructive to look
for a moment at the Greek treatment of this question. There
were 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
jilting 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 it in our
definition ; we might define a snake, for example, as a certain kind
of vertebrate; but the notion of a vertebrate involves it; and it is
necessary if the definition is to furnish us with the concept of
a material object 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 unmixed 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, or its specific gravity, 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.'4 It is impossible to
1 Or perhaps, regular solid.
2 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 87
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 attri
butes as appear, in some 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 specific gravity 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 specific gravity, 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 salts : 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 be of
importance in 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 in particular circumstances are not properties
in the full sense. We may indeed regard it as the property of an
element to exhibit a certain reaction in certain circumstances l • but
whereas the ' circumstances J under which geometrical figures exist
and possess their properties are in every case the same (being the
general nature of space), the circumstances relevant to the manifes
tation 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,
1 Cf. Ar. Top. e. i. 128b 16 dnodiSoTai 5e TO ?3toi/ i? /ca#' avro KOI del fj irpbs
erepov KO.\ TTOT«'.
88 AN INTRODUCTION TO LOGIC [CHAP.
since causal connexion is the root-idea of the notion property, we
rightly regard these attributes as properties rather than accidents.
For although the subjection of an element to any particular con
ditions rather than others is strictly speaking accidental, since it
depends upon 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 : but an
accident to lie in the cellars of the Bank of England, for that belongs
not to gold, but only to particular masses of gold, and why those
masses should lie there instead of any others cannot be determined
scientifically, nor by any reasonings applying to gold universally.
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. The very idea
of an element negates the possibility of any difference between
different specimens I ; and 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. 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.
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
1 This may seem inconsistent with the occurrence of the so-called ' allo-
tropic ' forms of elements ; but as a matter of fact, the speculations as to
the arrangement of the atoms in* a molecule, to which the phenomena of
allotropy have given rise, confirm the remark in the text. It is found
necessary to account for the diversity of properties in the allotropic forms
by supposing that atoms indistinguishable in their own nature are capable
of divers combinations ; it is not the elementary substance, but the com
bination of atoms of the elementary substance, to which the properties are
now attributed ; and that combination is not supposed the same in the
allotropic forms, though the elementary substance is.
iv] OF THE PREDICABLES 89
life could go on in the individual at all ; then this nucleus would
form the essence of the kind. But such is not the case. The
conformity of an individual to the type of a particular species
depends on the fulfilment 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 keen
ness 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 defini
tion, such as we have it in geometry, we must substitute classifica
tion ; and for the demonstration of properties, the discovery of laws.
A classification attempts to establish types ; it selects some parti
cular characteristics as determining the type of any species ;
these characteristics must be (a) of the same general kind for each
type, or, as it was expressed on p. 72, 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 must connect themselves 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 sup
position 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
consist in demonstrating its properties. To discover the properties
of kinds belongs to the empirical and not to the scientific stage
of botany or zoology. Science asks rather what it is about 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 laics 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
90 AN INTRODUCTION TO LOGIC [CHAP.
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 ;
and our subject will not be the concrete kind, but a set of con
ditions 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 example,
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 organic
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.
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 ^sp^ey to grow a certain kind of feather,
much used by ladies in their hats ; but only at the pairing season.
4. id quod pertinet omni et soli et semper : in this sense it is
a property of a 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
iv] OF THE PREDICABLES 91
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 objects 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 : of 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, lank. 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 objects because they serve
a certain purpose, or exhibit a certain structure ; and all else in the
nature of the object 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 an object must
possess as gold, or as a crab ; the whole nature of the concrete
object 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
92 AN INTRODUCTION TO LOGIC [CHAP.
they denote is most complex; thus it is easier to define army
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 know
ledge 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 compara
tively little knowledge is needed in order that the definition of
a bridge may be fully understood. It will be readily seen, that
what has been said of the difficulty of determining either
property or essence in regard to natural kinds applies also to such
terms as we are now considering in proportion 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 commensurate 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 connexion (or coincidence)
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
IV] OF THE PREDICABLES 93
implies a change in the point of view. The problem now is not as
to the relation between two universals predicated one of another,
but as to the relation in which the various universals predicated of
an individual stand to their subject : for it is of individuals only
that a species (such as man, or horse, or parrot-tulip) is 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 predicate 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 with the wider
genus of mammal, vertebrate, 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 dis
cussed them so earnestly; nor can any philosophy refuse to face
the controversy between them. But it was a misfortune 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 theory is that while
beginning by distinguishing the relation 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
1 There is a suggestion in Aristotle's Topics of this point of view, for he
allows that ?di»v may mean a peculiarity that distinguishes an individual
from others ; cf. the passage quoted, p. 87, n. 1 supra and e. i. 129a 3-5. But
his doctrine as a whole implies that the subject term is general.
2 In technical language, what is an ivfima species and what a species
subalterna ; it was said that a species subalterna ' praedicatur de differentibus
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 deter
mine 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 same problem restated. Looked at from the other side, the species
subalterna can of course be called the genus subalternum : cf. Crackenthorpe's
Logic, Bk. I. c. iv.
94 AN INTRODUCTION TO LOGIC [CHAP.
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
the individual belonging to the species. But we cannot distinguish
between property and accident, so long as the subject whose
predicates we wish to refer to these heads is an individual.
A property is necessary to its subject, and an accident is not j but
all the attributes which belong to Cetewayo are equally necessary
to him as Cetewayo ; on what ground then are some to be called
properties, and others accidents? An accident is an attribute
which coincides l in an individual with another general character, or
universal ; its accidental relation lies towards that other universal,
and not towards the individual, in which its presence is, historically,
necessary. A property is an attribute found in an individual,
but grounded in certain general characteristics of that individual ;
and it is proper not to the individual as such, but as having those
characteristics, and therefore to everything which has them, or to
that kind of thing universally. It is only therefore in reference
to a kind of thing as subject that we can ask whether a given pre
dicate is to be ranked as accident or property. 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 ? 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.
Thirdly, the Porphyrian doctrine gave rise to a division of acci
dents into separable and inseparable which, if an individual be the sub
ject, is confused, if an universal, self -contradictory.2 An inseparable
1 If sometimes translated what happens (<rvpj3aim) to an individual, yet it
is said to happen, just because it need not belong to him according to the
conception we have so far formed of him ; and it is therefore only coinci
dent in him with the characters included in that conception. Cf. supra,
p. 62, n. 2.
2 'iSi'co? 8e dta<j)(peiv \fyfrai erepov erepov, orav a^wpto-rw (rv^f^KOTi TO erepov
TOV eYepov 8ia(ptpci. a^eopio-roi/ Se (rvfjL&ffirjKbs olov •yAauKdYr;? 77 ypvTrorrjf r) ovXi)
(K rpavpnTos eWKippa>0e«ra, 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 — ical TO. pcv av/i/Se/S^Kora eVi ra>v
iv] OF THE PREDICABLES 95
accident of an individual is an accident of the species 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 as subject, 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 circum
stances 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 an universal, then
TrpnTjyovpevtos {x^iVrarm, ib. c. x ; and also that they are predicated pri
marily of individuals — aXXa TTporjyov /ze vats p.ev TO>V aTo/zooi/ (sc. KaT^yopfirat,
from the context) Kara dtvrfpov de \6yov *ai TCOV Trfpie ^OVTWV ra aro^ua, 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 o-u/z/Se/fy-
KOS 8e eo~Tiv 6 yivtrai Kal anoyiverai \a>pls TTJS TOV inroKfip.evov (pBopas. ftiaipelrai
de els fiuo' ro fj.€v yap aiTov xa>Pl(J"rov e'aTi, ro de a%<0picrTov. TO pev ovv Ka0€v8(iv
(Tv/i^f/3^KOf, TO 8e ne\av tlvat d^copi'ora)? TO> Kopam Kai T&> AttfiWi
C, dvvarat 5e €Tnvor]()r)vai Kal xopat- \CVKOS Kal Ai^i'an^ a7ro3aXa>i> rfjv
(bBopas TOV vTroKd/jifvov. (Accident is what comes and goes with
out the destruction of the subject. It is of two kinds, separable and in
separable. 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 de /ze'Aaz/ TOU re etdovs r&v
KopaKtov Kal TWV Kara [j-epos (sc. KiiTTjyoptiTai), a~vp.^f^r)Kos ov a^d)pio"Toi/, Kal TO
Kivf'io-dm avdpumov rt KOI ITTTTOV, ^copio-Toi/ ov o-u/Lt/3f^^«or. (To be black is pre
dicated both of the species of crows and of crows severally, being an inse
parable accident, and to move of man and horse, being a separable accident.)
96 AN INTRODUCTION TO LOGIC
the expression is a contradiction in terms. It is sometimes 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 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 inseparable accident of a species is really an attribute
which we find to characterize a species so far as our experience
extends, without knowing whether its presence depends on con
ditions necessary to the existence 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.
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 attributes and
individuals 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 individual. We need a terminology in which
to express these differences. We do form complex conceptions of
objects, and of attributes or states, that cannot be analysed into
a mere assemblage of simple qualities, but only per genus et diffe-
rentiam. These are the facts which justify this somewhat difficult
part of logical theory.
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,
about the practical difficulties that lie in the way of adequately
defining many kinds of 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 be commensurate with that which is to be
defined : i. e. be applicable to everything included in the species
defined, and to nothing else.
2. A definition must give the essence of that which is to be defned.
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 triangle : in virtue of being an institution for
the education of the young, that any place 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 be always
such as are the ground of others rather than the consequences.
Thus an animal is better defined by the character of its dentition
98 AN INTRODUCTION TO LOGIC [CHAP.
than of its habitual food ; since the kind of food that it can eat
depends on the formation of its teeth, and not vice versa.
(b) That we must not give only some comparatively isolated attri
butes 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 third rule is :
3. A definition must be per genus et differentiam (sive differentiae).
The better the definition, the more completely will the differentia
be something that can only be conceived as the 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 piece of timber
forming 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 the concept of a lintel, I notice this further as
a characteristic of it ; whereas really, until I have taken this into
account, I have no concept of 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 the whole notion ; we have
in our minds a pretty substantive concept (if the phrase may be
allowed) without the differentia ; and therefore this appears as a
further characteristic, which is really selected because it is diagnostic.
4. 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
what the thing defined is, not what it is not. A scalene 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 a negative definition is in itself inadequate, and it would
in most cases leave us quite uncertain what the subject positively
1 Cf. Ar. Top. £. v. 142b 22-29. But properties, according to Aristotle
(An. Post. /3. x), are defined by specifying the subjects in which they inhere,
and the cause of their inherence in their subjects.
v] RULES OF DEFINITION AND DIVISION 99
is. If real property were defined as property that cannot be trans
ferred from place to place, we should not necessarily realize 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 an imagined hurt ? A definition in
negative terms is, with one exception, always faulty ; its futility
depends on the precision of the positive meaning which the negative
terms may happen to convey.1
The one exception to the faultiness of a definition in negative
terms is furnished by concepts that are themselves privative or
negative. 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.2 But it must not be assumed that because a term is
negative in form it need be negatively defined ; intemperance is the
excessive indulgence in strong drink.
5. A definition must not, directly or indirectly, define the thing by itself.
A thing 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
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 be really defined
1 Cf. the discussion of positive and negative terms, supra, c. ii, pp. 28-33.
2 From Watts's Logic.
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 an animal, male and female ; in property, real and
personal, &c. Contraries and opposites generally may be wrongly used to
define one another in the same way.
100 AN INTRODUCTION TO LOGIC [CHAP.
at all ; if a man does not immediately understand that number is
either odd or even, 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 differ
ence between straight and curved. In such cases, to explain one
counter-alternative by the other, though not definition, is 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 with
out 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.
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
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 a tablet as possible.
1 Top. C. iv. 142* 34. 2 Logic, III. v. § 6.
v] RULES OF DEFINITION AND DIVISION 101
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 laymen, but may express the ideas
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 riot 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 the process of dis
tinguishing or 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
object 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. If we rightly divide
the genus into its species, the species will be parts about which we
shall find that the largest number of general propositions can be made.
Division l is closely allied to Classification ; and both to Defini
tion. The difference between Division and Classification seems to
be principally this : that when we classify, we start with the
particulars of a genus, and throw them into groups, according to
their resemblances and differences ; when we divide, we start with
the genus, and distinguish the species within it by the differentiae
of which the genus is susceptible. In other words, Division moves
downwards from the more general to the more special, Classification
upwards from 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 may move in
both directions at once ; and the process of dividing a genus is at
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, to which the name Division is also applied.
102 AN INTRODUCTION TO LOGIC [CHAP.
the same time one of classifying the thing's 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 inflmae 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
divided are sometimes called its constituent species 2, 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 : —
1 Cf. p. 92, n. 2, supra. According to one doctrine, nature has determined
where division should stop, and infimae species are fixed by nature. Cf.
p. 81, supra.
2 In Latin, membra dividentia, as the species are conceived to share the
genus amongst them.
v] RULES OF DEFINITION AND DIVISION 103
Nebula
Irresolvable Resolvable
(i.e. clusters of stars)
! I
-
ii I I
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 object 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 include 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 we secure this, we do not properly divide ; for the parts
that which one divides must be separate from each other.
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 dis-
104 AN INTRODUCTION TO LOGIC [CHAP.
ting-lushes '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, wfro 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 *, upon one principle, or f undamentum divisionis.
The fundamentum divisionis, the principle or basis of a division,
is that aspect 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. Pro
ceeding upon the first basis, we should divide into artillery, cavalry,
infantry, and engineers; 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, yeomanry and militia, volunteers, and reserve. When
the division is carried further than one stage, the same funda
mentum divisionis should be retained in the later stages which was
used in the first. If the division of soldier into artillery, cavalry,
infantry, and engineers 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, 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.
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 volunteers. It is called
a cross-division, because the grouping required by one basis cuts
across that required by another; in distinguishing privates, for
1 Cf. infra, p. 116. 2 Cf. supra, c. iv. pp. 72, 87.
\] RULES OF DEFINITION AND DIVISION 105
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
introduces confusion.
It is plain that in a cross-division, the constituent species will
not exclude each other. The only possibility of 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 V in
which it exhibits the character B ; hence a and V will not exclude
each other.
There are two apparent exceptions to be considered here: one
to the statement that the employment of two or more funda-
menta dkiswnis at once produces a cross-division, the other to the
statement that the members of a cross-division are not mutually
exclusive.
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, the hot and
moist, the cold and dry, the cold and moist. 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 must
exhibit each character in some mode, and no character in more
1 Cf. supra, c. iv. p. 86.
106 AN INTRODUCTION TO LOGIC [CHAP.
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 four alternatives under the first head, three
under the second, and four under the third, we should obtain a divi
sion into forty-eight members. These would be mutually exclu
sive ; 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.
In our first exception, a cross-division seemed to be employed when
it was not ; in the second 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 with those into which it is divided upon another.
Thus flowering plants may be divided according to their method of
fertilization into exogenous and endogenous ; and according to the
mode of germination in the seed into dicotyledonous and monocoty-
ledonous. It happens that all exogena are dicotyledonous, and all
endogena monocotyledonous ; so that if the genus were divided
into exogena and monocotyledona, 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 constituent 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 con
nexion between these differences in mode of fertilization 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.
There is a form of division called Dichotomy, which is of neces-
v] RULES OF DEFINITION AND DIVISION 107
sity exhaustive, and the species yielded by it of necessity exclude
each other; for it divides the genus at every stage into two mem
bers (as the name implies), which respectively do and do not
possess the same differentia ; everything in the genus must there
fore 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, sub
stance 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 never be used. Its use is in analysing or defining some
one subordinate species. It may, however, sometimes be used to
show that a division which is not dichotomous is necessarily exhaus
tive, and the constituent species exclusive of each other.
The reason why dichotomy is out of place in a classificatory divi
sion 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,
and engineers, was carried further by particularizing the way in
which the artillery may be constituted for different lighting pur
poses, or the cavalry armed, &c. But one side of a dichotomy is
always characterized negatively, by the non-possession of the attri
bute which characterizes the other side ; and there is therefore no
positive notion which we can develop in the subdivision of this
side. 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 far more cumbrous than one
108 AN INTRODUCTION TO LOGIC [CHAP.
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- Pleasure- Waste
| munication ground
Arable Pasture Orchard
I
Of bush-fruit Of tree-fruit Of hops
2. Land
Building-land Land not used for building
1 1
Farm-land Non-farm-land
i 1
1
Arable
Not arable
1
1
Forest
Not forest
j
Pasture Not pasture Means of communication Not means of communication
I L_
f~ ~~l I I
Orchard Not orchard Pleasure-ground Not pleasure-ground
Of bush-fruit Not of bush-fruit Waste Not-waste
Of tree-fruit Not of tree-fruit
j !
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
stocks, 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
v] RULES OF DEFINITION AND DIVISION 109
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.
A negative conception affords no basis for further subdivision, and
a division which attempts to classify by dichotomy is for ever
subdividing negative conceptions.
[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. Such a division does not proceed on a single ftinda-
mentum divisionis. In the proper division of land, the basis taken
was the use to which land is put, and that was retained throughout ;
but in the division by dichotomy, the basis taken was first the use
of land for building, by which it was divided into building-land and
the rest : and the rest was divided on a different basis, viz. the
use of land for farming : and so on. Again, 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 order
in which the subaltern genera are placed (except where a positive
concept is divided) is also quite arbitrary ; building on it might as
reasonably be called a mode in which land is not farmed, as farming
a mode in which it is not built on. Lastly, it is claimed for divi
sion 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
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.
110 AN INTRODUCTION TO LOGIC [CHAP.
[Semitic races are also non-Turanian (so that the constituent species
are not mutually exclusive) ; and that if the last objection is con
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 thai
is none of these ; this last heading1 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 ; 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 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
peculiar nature of number, and not merely the general ( laws of
Of. S. H. Mellone, Introductory Text-book of Logic, c. vi. § 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.
v] RULES OF DEFINITION AND DIVISION 111
thought ' y 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
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 triangle should be divided into three and not two. U nf or-
tunately 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
III i
Essence Not essence Part of essence Not part of essence
(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 combinations
remain, as in the case of the four elements already given.
Element
I
I I
hot cold
I. I I I
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 which we may attempt to construct a definition. We may
take instances of that which is to be defined, and try to detect
112 AN INTRODUCTION TO LOGIC [CHAP.
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 definition rather by working downwards from
:i 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 com
mensurate notion. At every stage of our division, the differentia
taken must if possible be a modification of the differentia next
before it ; it must 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 started1; 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 el?e contained within the genus we
thrust aside together, as what does not exhibit the differentia
characterizing that subject. Had we further to consider and sub
divide it, we could not be satisfied with characterizing it only nega
tively ; 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 abaci* sio 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 tuler ; the genus
to which it is to be referred is stem.
1 Cf. infra, pp. 115-116, 118-120.
v] PJLES OP DEFINITION AND DI 113
Stem
X\
Bssyiag .'.->*. sfsfpBg
/\ ^_
ondergnmnd not ondergnmnd
much thkkened not much thickened
po«e«hi? leaf 4wd« not powearing leaf-bods
in the form of 'ejes* MI the form of 'eye* '
In this dirision, we reach as oar definition of a tuber ' a stem
creeping underground, much thickened, and possessing leaf-bods in
theform of eyes'. At erery stage by an tfAswww M^*ft ? we rejtttfi
from further considera^km a lau^ part of the genus we had so far
reached : first all stems not creeping, then all creeping stems not
Ejpinf; JtOBM Mi ««eh thick
ened,^.; aiidat«fayit^^w»faMiTidedthatpaitof the _
which we had retained by a iliimaiii that specified further the
form to which we had 00 fcr brought it
It might hare hsfpeafJ, fl«» creeping AM had a MM to
denote them, say OM«f^ J ; and thai undergrowid Cttliiaili
had a special name, say Hypvktkamil*; that these when much
thickened had again a different MUM, say PackyimaU; and that
tubers were fmhy *••!• IMJ jinssr ssr ^ VaMmds in the fot» o£ eyes.
fa thk ease, the dmion would be set out in somewhat different
form, as follows —
114 AN INTRODUCTION TO LOGIC [CHAP.
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 creep
ing 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 l 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 a
good classification ; but just as a study of the logical form of classi
fication does not enable us to classify any particular order of pheno
mena, so we are not enabled to define any particular subject, merely
Anal. Post. /3. xiii. 97a 23 sg.
v] RULES OF DEFINITION AND DIVISION 115
by familiarizing ourselves with the scheme of a definition of
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. 113 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, &c.
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 (SicupertKr/) of one genus is constitutive (o-uarariKT/) 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
(imoTTovv and avow) and if the footed are divided into biped and quad
ruped, the latter differentia biped is a differentia of footed, as such;
116 AN INTRODUCTION TO LOGIC [CHAP.
[for to be a biped is a particular way of having- feet. In the species
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 object
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 we are really introducing a new differentia. In such
a case, 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 ax\t\. 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 o-uju/Se/SrjKos and not Kara TO opQov. We may notice too, that
whereas a differentia which is a continuation of that before it is
never applicable 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 mem
bers (e. g. feathered &\A featherless might be applicable to quadruped
no less than to biped). The fullness and complexity of natural
kinds is, however, such that we cannot always avoid the introduction
of fundamentally 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. 118-120.]
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 kind* ;
itself a universal, the specification of it by various differentiae can
only give rise to more determinate universals. The division of it stops
therefore with infimae species, and never proceeds to the enumera
tion of individuals. For if the infima species could be logically
divided into individuals, we must apply some fundamentum dim-
tionit ; and that means, that we should have to distinguish indi-
v] RULES OF DEFINITION AND DIVISION 117
viduals 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 but
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 knife blade and handle.
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 dis
tinction of the parts composing either a determinate individual, or
any individual of a kind : as Great Britain on the one hand can be
divided into England, Scotland, and Wales, a plant on the other
into root, stem, leaf, and flower, or a forest into its component
trees.
In Metaphysical Division, we distinguish in a kind its genus
and differentia, or the various attributes predicable of it, and
included in our notion of it ; thus we may divide man into animality
and rationality, or sugar into the colour, texture, solubility, taste
and so forth that characterize any piece of sugar. This is ob
viously a division that can be carried out in 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
1 Thus in the Arbor Porpliyriana the enumeration of the aro^a Socrates,
Plato, &c., in the infima species man is no part of the logical division. Cf.
Porph. Isag. C. ii aro/za Se Xtyerai TO. roiaura, on «'£ IdioTrjTwv o-vv(OTT]Kfv
lav TO adpoio-p.a OVK ai/ eV «XXov TWOS Trore TO avro yfvoiTo TO>V Kara p.fpos' at yap
2co<fparouy idioTr)T(S OVK av cV aXXou TIVOS TO>J> Kara p.fpos yevoivr av at aurai. (By
individuals are meant such things as are constituted each by peculiarities.
the precise collection of which could never be the same in any second
particular; for the peculiarities of Socrates could never occur identically
in any other particular individual.)
118 AN INTRODUCTION TO LOGIC [CHAP.
exhibited in different cases in a museum. But in Metaphysical
Division, 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 *, 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 part — we cannot either
say that a leaf or stem is a plant, or that a plant is a leaf or stem.
[A few words may be added on the relation of Logical Division,
and its rules, to Classification. Just as the theory of Definition, with
its sharp distinction of essence and property, breaks down amidst
the complexity and variety of concrete things, so it is with the
theory of Division. Ideally when a genus 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, and ellipse ; 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; it would be the skeleton of
a classification, and 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 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 satis-
1 irapavvfjia Se Xeyerai otra cnro TWOS diafpepovTa rrj Trraxm rfjv Kara rovvofia
irpovrjyopiav e^ei, oioi> two r^s •ypa/i/iariKT/s 6 ypanfj.aTiK.bs Kal airb TTJS avdpfias
6 avdptios, Cat. i. la 12. (That is paronymous which receives its designation
from something with a difference in inflexion, as a grammarian from
grammar and a courageous man from courage.) The Latin for Trapww/zoi/ is
denominatum or denominativum, according as the subject or its attribute is
meant.
v] RULES OF DEFINITION AND DIVISION 119
[factorily classifying1 them at all. Classification is, as Jevons called
it1, 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 incompatible 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 of the ( laws of nature '
themselves 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 those objects which belong 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 of the order of phenomena which we are classifying, and
argues that the facts could only be thus on the assumption of
connexions of attributes such as the proposed classes imply ; 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
is exhaustive, and the constituent species which it establishes are
not to overlap ; but a classification may have to acknowledge that
there are individuals which might with equal right be referred to either
of two co-ordinate classes, 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 imagination ; the consideration of a process which, outside
geometry, can scarcely be illustrated by examples except by mutilat
ing facts, is denounced as a barren pastime. And there is justice
in the denunciation, 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 precepts,
'hat is the best classification which conforms to them most closely,
e case of the logician may be compared with the case of the
>meter. The geometer studies such figures as he conceives, and
believes that his conclusions are true of the squares or triangles
lat exist eternally in space, bounded by the distances between
)ints therein ; but he does not imagine they would apply without
[ualification to a square table, or a triangular lawn. The figures
1 Principles of Science, c. xxx. p. 689, 2nd ed.
120 AN INTRODUCTION TO LOGIC
[of these concrete objects 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 concrete 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 classifica
tion : 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 have to deal.]
CHAPTER VI
OF THE INTENSION AND EXTENSION OF TERMS
IT was observed by Aristotle *, that in one sense the genus is in
the species, in another sense the species is in the genus. f 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 verbal is what we intend by it, or
what we mean by it when predicated of any subject 2 : the ex
tension is all that stands subordinated to it as to a genus, the
variety of kinds over which the predication of the term may
extend? If by term we mean the concept, or what is thought of,
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 defining
it, and break up its extension in dividing it.
It is clear that as between two terms subordinated one to the other
in a classification, the higher, or superordinate, must always 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
1 Phys. 8. iii. 210a 17-19. Cf. p. 118, supra.
a 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 propo
sition '. Cf. infra, c. ix.
8 For another use cf.'p. 128 sq., infra.
122 AN INTRODUCTION TO LOGIC [CHAP.
f conic section y to hyperbola and parabola, as well as to ellipse 1.
Many hold also, that the superordinate term, as it is of greater
extension, so is of less intension ; less being meant by calling any
thing an animal than by calling it a man ; or by the term f 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/ 2
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 f Christian '
simply, for we conceive that there may be Christians not Arme
nians, 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 it,
that the doctrine of the inverse relation of intension and extension
applies. It would be ridiculous to compare in this matter such dif
ferent concepts as democracy and steam-engine ; it is even unmeaning
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 com
prised the larger number of subordinate species.
Porph. Isag. c. viii ert TO. p.ev yevrj nXeovafci rrj TU>V VTT' avra clScov Trepioxfj,
ra 06 cidrj rS)v yevvv rrXeovd&i rals oiKfiais 8ia<popals. (Further, genera exceed
species in the compass of the species under them, species genera in the dif
ferentiae belonging to them.)
* Jevons, Principles of Science, 2nd ed., c. ii. p. 26. Cf. Sir W. Hamilton,
Lectures on Logic, viii. 1! xxv ; Thomson, Laws of Thought, § 28 ; Bain,
Logic, Deductive, p. 51 ('the greater the one the less the other').
vi] INTENSION AND EXTENSION OF TERMS 123
Applying only to terms subordinated one to another in a classi
fication, the doctrine is an attempt to explain the nature of classifi
cation, 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 this idea 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 ? do
I form 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 attri
butes 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 : —
Jb
I
ac
ad
1
1
1
1
abe
abf
1
abg
1 1
ach aci
1
adj
1 1
adk a<
But we have seen x 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
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 2.
If we look at terms which are really in a relation of genus and
1 Cf. p. 69, supra.
2 And therefore the introduction of differentiae into a division which are
not differentiae of those before them is not Kara TO op06v, cf. supra, p. 116,
though they may still be such of which only the genus from which we started
is susceptible.
124 AN INTRODUCTION TO LOGIC [CHAP.
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 am at present doubtful how
to choose. But if so, the generic concept would seem to exceed
the specific in intension ; ( animal ' means ' man, or horse, or ox, or
ass, 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 ac
quaintance with the steam-engine in the form of railway locomo
tives. 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 run
ning 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 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 alternative possibilities ; and the experience which leads
him to extend the term to new kinds of objects 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 object ; but in itself it does not come to have less
meaning.
vi] INTENSION AND EXTENSION OF TERMS 123
The doctrine of the inverse relation of extension and intension in
terms seems therefore wrong1; it misrepresents the nature of a
classification. But a doctrine which has been accepted so widely of
Jate *, and seems 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. Hence in the term of wider, as compared with that
of narrower, extension there is often little definite ; and 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 the notion of man or horse rose in one's mind, 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 notion.
2. Our actual classifications, as we have seen, fall short of
perfection 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 constituting a genus, and then distribute into species the objects
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 flowering plants (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
1 There are, however, eminent names on the other side, e.g. Mr. F. H.
Bradley, Prof. Bosanquet, and R. L. Nettleship. Cf. especially section xi of
the 'Lectures on Logic' in The Philosophical Remains of R. L. Nettleship.
126 AN INTRODUCTION TO LOGIC [CHAP.
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
Dicotyledon, 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
adjectival 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 approximate) 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 commensurate with it (and therefore narrows the
extension), and in the second place is not implied in it in any way
as a possible development of it : 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
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.
vi] INTENSION AND EXTENSION OF TERMS 127
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 triangle, with its species equilateral,
isosceles and scalene. Can we not and do we not form a notion of
triangle which includes those points in which equilateral, isosceles,
and scalene agree, but none of 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 l, ' 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 notion, 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 : i. e. that here at any rate the
element of variety was 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
1 Philosophical Remains, i. p. 220. The italics are mine.
2 Plat. Men. 71 D-72D ; Ar. Pol. a. xiii. 1260a 20-28.
128 AN INTRODUCTION TO LOGIC [CHAP.
necessary connexion, it will have the character of the jejune ex
tract 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 in reference to an iwjima species, or a notion
within whose unity we recognize no conceptual variety, intension
and extension are indistinguishable. The equilateral triangle may
differ in the length of its sides ; and we may if we like regard this
difference as constituting a variety in the notion of equilateral
triangle. But if we do not — if we conceive the particular length
of the sides to constitute no difference in the equilateral triangle —
then we recognize no such variety in the unity as makes the
distinction of intension and extension possible. The nature of
equilateral triangle is not shown in species that are distinguished
within that unity, but in that unity itself. The two aspects of the
meaning of the term coincide, or rather, do not fall apart.
But it may be said that even if there are no distinguishable
species of equilateral triangle, there are very many distinguishable
equilateral triangles. Two interlaced equilateral triangles are
a favourite symbol in the decoration of Christian buildings ; and the
number of equilateral triangles delineated on the walls and in the
windows of churches alone must be past counting. Do not all these
and others form the extension of the term, and are not they
distinguishable from its intension ?
We have treated the extension of the term as f the variety of
kinds over which its predication may extend'; the variety which
we conceive within a unity. We have dealt throughout with
a relation of general terms or notions ; the development of variety
within the unity of a conceptual or logical whole has been regarded
as stopping with whatever we take as infimae species. The exten
sion of a term is, however, sometimes understood to be not the various
conceptually distinct forms which are included within the unity
of a single whole (like the various virtues, or species of animal or
plant, or kinds of conic section, or sources of income), but various
individual instances in which a common nature is realized. Accord
ing to this view, the extension of man is not Aryan and Semitic,
Negro and Berber, &c., but Socrates and Plato, Caesar and Pompey,
&c. ; the extension of triangle is not equilateral, isosceles and scalene,
but the triangles on particular church walls and windows or
vi] INTENSION AND EXTENSION OF TERMS 129
elsewhere ; the extension of colour is not red, blue, and green, but
the particular display of colour in every portion of the sky, or blade
of grass, or fragment of an army jacket. And the contrast of
extension and intension is no longer the contrast of variety and
unity in a notion or concept, but that between individuals and the
common character which makes them individuals of a kind.
This view has never prevailed in respect of abstract terms. No
doubt qualities have their instances ; the whiteness of this page and
that of the next are each an instance of whiteness. But it is the
function of abstraction to consider the quality in its identity, and to
ignore the difference between the concrete instances in which it is
manifested ; let the quality differ qualitatively, as the whiteness of
milk does from that of snow, and we may be interested in the
difference ; but if it differs only numerically, as the whiteness in one
patch of snow from the whiteness in the next, we ignore it. We
may be separately interested in the various concrete things which
exhibit the same quality, but the very purpose and nature of the
abstraction which we perform in considering the quality is to treat
it as the same in these instances, and to ignore their difference.
With concrete terms it is otherwise ; an attention to the identity of
man in Socrates and Plato does not exclude our interest in them as
separate individuals ; and it is of concrete terms that individual
instances are sometimes taken to constitute the extension.
Now we need not quarrel with this use of the word ; but it is
important to see that we are introducing a new distinction. The
relation of man to animal, or of negro to man, the relation which we
recognize between species and genus, is not the same as the relation
of Socrates to man or animal, the relation between an individual
and its kind or universal. The inverse relation of extension and
intension of which we have spoken does not hold, except between
notions or universals ; if the extension of a term is the individual
instances, it is meaningless. The individual instances may be more
or fewer, but what is meant by the common term predicated of them
all remains the same. We saw how the intension of the term animal
might from one point of view be said to increase, as a man becomes
acquainted with fresh forms of animal life ; and how from another
point of view, because what at first he 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 whichever
130 AN INTRODUCTION TO LOGIC [CHAP.
way we look at it, it is only acquaintance with fresh forms of
animals that produces this result : a mere increase in the numbers
of one's acquaintance would produce no such effect. The intension
of the term baby does not increase and decrease with the fluctua
tions of the birth-rate 1 ; when guineas were called in, the term did
not alter its intension. Intension has nothing to do with actual
existence. There may never have been a perfectly just man ; and
yet we mean something by perfect justice. The dodo is extinct, but
dodo would not have less intension if the bird were as common as
the sparrow.2 As it is, the chaffinch is commoner than the goldfinch,
but there is not any consequent difference in intension between the
two terms.
We may therefore mean as we please, by the extension of a con
crete term, either the distinguishable species or the individuals
included under it ; but we must not treat the relation of extension
and intension as the same in both cases. It is true that concrete
individuals of one kind are distinguished from one another by their
characters ; and if we attend sufficiently to these distinctions, then
as our acquaintance extends our conception of the variety of which
the kind is susceptible enlarges. Unobservant people may be
familiar all their lives with earwigs, without recognizing the richness
of earwig nature as diversely displayed in divers individuals. The
least observant of us have the richness of human nature forced to
some extent upon our attention. But so far as our growing
experience of life leads us to realize more fully the variety of human
nature, it is not because the men we meet differ numerically, but
because they differ in character from one another. With a kind like
man, where the differences of character between different individuals
are so closely noted, it might seem that as the individuals are con
ceptually distinguished, therefore in passing from man to Socrates
and Plato we are only carrying on the same process of thought
which we had employed in distinguishing within the genus animal
the species of man and horse and ox. That is not so. Man is not
1 Bradley's Logic, p. 158.
2 If intension and extension varied inversely, and by extension were meant
the various individuals, then the intension of dodo should become infinite
when the species became extinct. Perhaps it might be replied that past as
well as present individuals are included in the extension ; but if there never
has been nor can be a body moving freely in space, that term at least
should have an infinite intension.
vi] INTENSION AND EXTENSION OF TERMS 131
less an universal notion because it is more specific than animal; and
if we were merely further specifying our conception of man in the
case of Socrates, Socrates would be an universal notion too. But
Socrates is an individual ; and I cannot arrive at individuality by
any specification of a general notion. Socrates is distinguished
conceptually from Plato ; but that is not the whole of the distinction,
for they exist in the concrete.
In place of the words Extension and Intension, various writers
have used others to mark the same distinction ; and in particular,
since the publication of J. S. MilFs Logic1 , the words Denotation
and Connotation have come into favour for Extension and Inten
sion respectively. Mill claimed for these that they possess an
advantage in the existence of the corresponding verbs, to denote
and to connote, which other expressions do not possess ; we may
speak of a term denoting or connoting this or that, but we should
have to use a periphrasis and say that so and so constituted the
intension, or was included in the extension, of a term. Though
this is a real advantage, yet in other respects the terms which he
selects seem to be ill chosen. Extension suggests, what we want to
convey, the range of species over which the application of a generic
term extends; Denotation does not. Moreover, usage allows us
equally to say that a species or an individual is denoted by a term ;
if either is the more natural expression, it is perhaps the latter ;
and so the very reference to individuals which we wish to avoid is
foisted on us. Again, Intension naturally suggests what we intend
or mean by a term ; Connotation suggests not that, but some sub
sidiary meaning, a meaning additional to some other. It would,
perhaps, be convenient if the term Connotation were dropped, or
restored to its original signification (according to which nomen
connotativum meant an attributive term), and if Denotation were
distinguished from Extension as reference to individuals from refer
ence to subordinate species. We could then say that animal
denoted Socrates and Bucephalus, but that man and horse were part
of its extension.
Such an emancipation from what seems to be an unhappy
phraseology may, however, be too much to hope for. But from
a doctrine which Mill used his phraseology to express it is neces
sary that we should emancipate ourselves. Mill drew a distinction
1 v. I. ii. § 5.
K 2
132 AN INTRODUCTION TO LOGIC [CHAP.
between connotative and non-connotative names, which he described
as being f 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 '. There are, however, no non-connotative
names.
The distinction had better be stated in his own words. f A non-
connotative term is one which signifies a subject only, or an attri
bute 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 *, connotes, the attribute
whiteness. The word white is not predicated 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 connotative. 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 considered as connota
tive ; for attributes themselves may have attributes ascribed to
them ; and a word which denotes attributes may connote an attri
bute of those attributes. Of this description, for example, is such
a word as fault ; equivalent to bad or hurtful quality. This word
is a name common to many attributes, and connotes hurtfulness,
an attribute of those various attributes.2 . . . Proper names are
not connotative: they denote the individuals who are called by
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. 140-142.
a Mill instances ' slowness in a horse ' as an attribute denoted by the word
'fault'. It is clear that if 'fault' is connotative, 'virtue' should not have
been given as an example of a non-connotative name. The italics in this
quotation are his.
vi] INTENSION AND EXTENSION OF TERMS 133
them ; hut they do not indicate or imply any attributes as belong
ing to those individuals/
Thus Mill considers to be connotative —
(a) general concrete terms ;
(#) attributive terms ;
(c) abstract terms, if they are names of a genus of attributes ;
and to be non-connotative —
(a) proper names ;
(b) abstract terms, if they are names of a simple or a logically
undivided l attribute.
Designations, i. e. descriptions of an individual involving con
notative terms, he considers connotative ; abstract terms which are
logically undivided, but not indefinable, like velocity or momentum,
he does not specially discuss ; they ought to be connotative, if (as
he holds) definition unfolds the connotation of a name ; they ought
to be non-connotative, if (as appears to be the case) they ' signify
an attribute only ', and not an attribute ascribed to other attri
butes; but as he has forgotten his view of definition in this
section, we seem justified in following the indications of the con
text and classing them as non-connotative.
We have to consider, therefore, two classes of names which
according to this doctrine have no connotation (or intension) :
proper names, and abstract terms which are not generic, i. e. not
predicated of other abstract terms which would form their exten
sion. We may begin with the latter.
According to Mill, fault is a connotative term, because it
denotes slowness in a horse, and other hurtful attributes, while
connoting their common attribute of hurtfulness. Vice would be
connotative, denoting indolence, intemperance, jealousy, and so
forth, and connoting their common character as vices. (It is to be
observed that all terms are assumed to denote something, and the
question is whether they do or do not connote something as well.)
Slowness, on the other hand, is non-connotative, and so is indolence
or jealousy • for these merely denote each a single attribute.
It would be very strange, however, if this were true. What
I mean by calling Othello's passion a vice forms the connotation
of that term; vice is connotative by what it means in regard
1 i. e. one of which we do not distinguish and name subordinate species.
134 AN INTRODUCTION TO LOGIC [CHAP.
thereto; but when I call his passion jealousy, though that in
cludes calling it a vice (for vice is part of the notion of jealousy),
we are told that the term has no connotation ; ' vice ' is a connota-
tive term ; but ' the vice of readily suspecting the unfaithfulness of
those you love ' is not.
The fact is that Mill starts from the distinction between con
crete individuals, and their common character on the ground of
which they are called by the same name ; and he takes a name
to be connotative, if it has a common meaning distinct from the
individuals of which it is predicated. Thus man is connotative
because its meaning is not identical with John or Peter ; and white
because its meaning is not identical with milk or snow. He then
confusedly supposes indolence and jealousy to be individuals denoted
by the common term vice, slowness and stupidity by the common
term fault ; and since we can distinguish the common meaning of
the terms fault and vice from the particular attributes of which
they are predicable, he treats them as connotative terms; while
indolence aiid jealousy, slowness and stupidity are non-connotative
like John and Peter.
Now we shall see that John and Peter are also connotative
terms ; and therefore that even if indolence and such-like terms
were comparable with them, they would not have been shown
to be devoid of connotation. But they are not comparable. In
dolence and jealousy are not individual attributes ; if we are
to talk of individual attributes, we must mean the indolence
exhibited by a given person at a given time and place : as the
jealousy which fired Othello's heart when he strangled Desde-
mona ; and so far as indolence and jealousy can be predicated of
these and other indolences and jealousies, we can distinguish the
common meaning of the terms from the particular manifestations
of that meaning. They will therefore be as connotative as any
general concrete term. We have seen, however, that in abstraction
we are not considering the particular manifestations of an identical
quality ; we are looking upon indolence as one thing, not different
things every time that it is exhibited. Therefore the distinction
between the concrete individuals and their common character, from
which Mill starts, is altogether out of place, and a view of conno
tation based on that cannot apply to abstract terms. We must
fall back upon the relation of concepts, which was developed at the
vi] INTENSION AND EXTENSION OF TERMS 135
beginning- of this chapter by the help of the words intension and
extension. Let us call these respectively connotation and denota
tion if any one prefers it ; but what we shall have to say about
connotation and denotation in abstract terms is as follows.
An abstract term has a meaning : it means a certain attribute l,
as an unity. This is its connotation. But we may recognize a
diversity within this unity, or forms of this unity conceptually dis
tinct — the kinds, e. g., of vice or virtue. If so, these form its
denotation. The term may be predicated of any part of its denota
tion separately, and so far as we distinguish the divers parts from
the unity of which they are parts (e. g. indolence from vice as such),
it does not denote precisely what it connotes. But when we come
down to attributes within the unity of which we distinguish no
diversity, the distinction between what a term denotes and what it
connotes disappears. Indolence, so far as we recognize no separate
species of indolence, is just one attribute : not one like a concrete
individual, but as an universal. The term connotes that attribute ;
and that is what it denotes or is the name of. It can be predicated,
as a name or word, of the attribute it means. As a thing (i. e. here,
an attribute) it is itself, and not a genus of different things.
Suppose we recognized (as indeed we may) degrees of indolence ;
so far as we thought of them as different when we spoke of
indolence, material for the distinction between what the term
denotes and what it connotes would be furnished afresh. We might
still have no separate names for indolence of divers degrees, but in
spite of this the term would have connotation. Are we to say
that when we cease to think of these degrees of indolence, it has
connotation no longer? What has become of the meaning (for
connotation is meaning) which it had before ? Clearly it must have
meaning. What we have to explain is how it can be predicated of
that which is not precisely what it means. This arises through the
recognition of a conceptual diversity within a conceptual unity.
Where that is not recognized, the problem does not arise ; but the
term still has meaning, or connotation.
The other class of terms which Mill regards as non-connotative
are Proper Names. His view is equally untenable in this case, but
1 I use the word attribute because Mill uses it ; but it includes such
complex 'attributes' as apolitical constitution. And what is said in this
paragraph is true as well of concrete terms so long as they are general.
136 AN INTRODUCTION TO LOGIC [CHAP.
for different reasons ; and there is more plausibility in it. For
there is an important difference in instructiveness between proper
and general concrete names, which ought not to be overlooked,
though it ought not to be stated as lying in the non-connotative
character of the former.
Mill denies that proper names are connotative, because they tell
you nothing about the individual which they denote ; whereas
general names give you information about it. * A proper name/ he
says, * is but an unmeaning mark which we connect in our minds
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 ' ; and he contrasts c connotative ' names as ( not mere marks,
but more, that is to say, significant marks '. A general name is
used of an individual on the ground of some character which the
thing is believed to possess ; and that forms its connotation, which
it possesses independently of its use about this individual : a proper
name is given upon no such ground, but merely in order to
distinguish the individual it is given to from others.
The premisses here are correct, but they do not justify the conclu
sion drawn from them. A proper name need be given on the ground
of no attribute l ; for we may set aside as irrelevant to the real issue
the case which Mill instances of a name like Dartmouth, intended
to imply that the town is at the mouth of the Dart, and compounded
out of elements whereof one is general ; in the case of the river
Dart itself , at any rate, no such significance is to be found in the name.2
On the other hand, general names are used on the ground of some
attribute. I should not call London a port, except to indicate that
ocean-going ships resorted there. Yet it does not follow that
proper names are non-connotative. For the proper name is only
unmeaning before it is given ; by being given, and becoming a
mark, it acquires a meaning. And the general name was equally
unmeaning before it was ever given ; but being general, it can be
given to more things than one, and having acquired a meaning by
1 Except, indeed, that of individuality : to be an individual is an attribute
of the individual denoted, and Mill should have allowed that this was
connoted.
2 Most proper names are selected for a definite reason ; a child christened
Septimus is generally the seventh child ; a mountain may be named after
its discoverer, a college after its founder, or a society after some one of
whom its members wish to be considered the disciples.
vi] INTENSION AND EXTENSION OF TERMS 137
its original imposition, has a meaning1 in advance of its subsequent
use about other individuals ; and that is why it is instructive.
The account which Mill gives of a proper name is substantially
indistinguishable from Hobbes's definition of any name, which Mill
himself had accepted in the first section of the same chapter.
According to 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 '. Being a word taken at pleasure, it can
have had originally no meaning x ; else that meaning would have
restricted our choice. It acquired a meaning when we marked with
it the object which we would have it to signify. And whether we
wish to mark with it an individual object, or a kind of object, makes
so far no difference. All names, whether general or proper, are
as Aristotle called them, c/xoral (rrnj.avri.Kal Kara crvvdriKrjv2, origin
ally, and before they are assigned to an object, they are (fxavai only,
sounds without meaning. In being assigned to an object, or becoming
marks, they eo ipso acquire meaning ; for an unmeaning mark is not
properly a mark at all, though I may of course be ignorant of the
meaning of it. The broad arrow f which is occasionally seen on
gateposts, milestones, &c.} is a mark ; the traveller would know
that it was not a mere flaw in the wood or stone ; he might not
know what it meant ; but he would know 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 consequence 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 ;
1 The case of derivative names is, of course, different.
8 'Articulate sounds having signification by convention.' — de Inteiy. ii.
16* 19.
138 AN INTRODUCTION TO LOGIC [CHAP.
the name would have given her precisely the same information ;
how could the name be unmeaning1? The doctrine that proper
names have no connotation is refuted by every criminal who
assumes an alias.1
Proper names, it was admitted, are not assigned (as general
names are employed) on account of their meaning. They only
acquire their meaning by being assigned to an object. But in
being assigned to an object they must acquire connotation. The
error which it is important to avoid is that a name can denote
without connoting; for that implies that a thing can be, and be
distinguished, without any attributes distinguishing it. I may
frame the sound Glamby : it is doubtless non-connotative ; but
neither does it as yet denote anything. So soon as I give it as
a name to my house or my horse, my dog or my daughter, it will
denote that thing, and also connote it for me ; for here, as in the
case of non-generic abstract terms, we may say that the term
denotes what it connotes. The two kinds of term have important
differences. Proper names are given to individuals ; and what the
individual is we can never know completely. The proper name
therefore cannot be defined; and a great deal of its connotation
may be said to be left as it were in the dark ; the name connotes
an individual characterized by all which distinguishes it from
others; but we do not know all that. Practically we may say
that the connotation is anything which enters into our notion of
the individual, and therefore so far as no two men have the same
knowledge of Glamby, that name will have partially different
connotation for different men. The same remark might be made,
however, in some degree about general names. And if Glamby
were a mark denoting an individual, but connoting nothing, how
should any one whom I told to go to Glamby know whether I sent
him to a person or a place ?
It is hardly necessary to labour the point further. If the
connotation of a name were a fixed and constant meaning, borne by
it in every case of its application, and therefore general, it would
be fairly said that proper names were non-connotative. For they
have no constant meaning, except in reference to the same indivi
dual; and so far as they belong to several individuals, they are
equivocal. But an equivocal term is not a term without meaning ;
1 Cf. Prof. Bosanquet, Essentials of Logic, Lect. v. § 6
vi] INTENSION AND EXTENSION OF TERMS 139
it is a term with more than one meaning. And whatever has
meaning- has connotation. The connotation of a proper name can
only be learnt by knowledge, personal or through report, of the
individual denoted; such report must of course be made by help
of general terms. But the connotation of a general term is in the
last resort learnt through personal acquaintance with or report of
some object of the kind denoted. Only being general it serves
now to convey information about individuals without the need
of personal acquaintance.1
[A little further examination of the passage quoted on p. 132
will show how thoroughly confused Mill's account of the matter is.
A connotative name, he says, is one which denotes a subject and
implies an attribute: a non-connotative name denotes a subject
only or an attribute only. He clearly intends here to distinguish
between subjects and attributes; and by a subject he means an
individual. ' By a subject is here meant anything which possesses
attributes. Thus John, or London, or England are names which
signify a subject only/ But whether such a subject of attributes
is a bare uncharacterized that, and all its predicates are attributes :
or whether it is a subject of a certain kind, of which its further
predicates in other categories are to be called the attributes, Mill
does not say in so many words. The former is, however, implied ;
for the word man connotes all that makes John a man; and the
account of substance in the next chapter bears this out. Yet we
are told that fault is a connotative term because it denotes, e. g.,
slowness in a horse and connotes the hurtfulness of this quality;
the names of attributes f may in some cases be justly considered as
connotative ; for attributes themselves may have attributes ascribed
to them '. According to the definition of a connotative term given
at the outset, slowness ought to be a subject and not an attribute,
if. fault is connotative.
Mill has confused the logical relation of subject and predicate,
which allows you equally to say that slowness is a fault and London
is a city, with the metaphysical relation of substance and attribute,
also sometimes called the relation of subject and attribute ; and he
has not any very coherent view of what he means by a subject as
1 Very often the form even of a proper name gives a clue to the nature or
nationality or sex of the object denoted ; and surnames, so far as they denote
the members of one family, are not altogether equivocal. Every one knows too
how proper names come to acquire a general meaning : Caesar is a familiar
instance ; and we have all heard of a Daniel come to judgement, and that
Capuam Hannibali Cannas fuisse. The reader will easily allow for all such
considerations, none of which support the view impugned in the text ; but
as a proper name may be used without any such acquired signification, the
question has been argued independently of them.
140 AN INTRODUCTION TO LOGIC [CHAP.
[= substance. He has consequently also failed to distinguish the
relation of genus and species from the relation of general to
singular, or universal to individual. Thus terms like white or
virtuous are connotative, because their form implies a subject
(whether a substance or not) distinct from whiteness or virtue, of
which they are to be predicated ; colour is connotative, while
whiteness is not, because that is a genus, and this is an infima
species; city is connotative, while London is not, because city is
general or universal, and London is singular or individual.]
[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 primario et
aliquid secundario/ 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 something which
has the quantity) : and certain other words : v. Prantl, Geschichte
der Logik, 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
fomnis terminus connotans aliud ab eo, pro quo supponit, dicitur
appellativus et appellat illud quod connotat per modum adiacentis
ei, pro quo supponit'.1 Thus meus and turn stand for something
which is mine or yours ; but they connote or signify further and
'appellant me ette tanquam adiacentes' (id. ib. xx. Ill, vol. iv. p. 30).
In the same way elsewhere we are told that * rationale ' ' connotat
formam substantialem hominis ' (xx. 232, vol. iv. p. 63 : cf. Anm.
459, p. 109). Album and agens are given elsewhere 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 with
out 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),
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 (' pro-
_metas secunduin 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 not as
albedo.
vj] INTENSION AND EXTENSION OF TERMS 141
['it " connotes", i.e. "notes along with" the object [or implies],
something considered as inherent therein/ The Archbishop suggests
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 substantives in form, yet
adjectives are the principal class of connotative terms, in the
original sense of that word.
Connotation and denotation were thus originally not opposed to
each other, and the terms were by no means equivalent (as they
have come to be treated as being) to intension ana extension. And
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, therefore, that it notes the
primary, connotes the secondary, signification ' (Analysis of the
Human Mind, vol. i. p. 34). 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) may stand for either an individual or an universal ; for
an individual when I say ' this man ', for an universal or species
when I say that man is mortal. (Occam would have said that in
the latter case it stood for all the individuals.) But even when
I say 'this man', meaning John, the name man does not denote
two things, man and John ; for John is a man ; and if I abstract
from that, John disappears too ; I have no notion of John as some
thing with which I can proceed to combine in thought another
thing, viz. man. 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 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. James Mill, who thought that objects
were 'clusters of ideas', and that we gave names sometimes to
clusters (in which case the names were concrete) and sometimes
to a particular idea out of a cluster (in which case they were abstract),
could also say that white ^ when predicated of this paper, denoted
two things — the whiteness, and the cluster not including whiteness
142 AN INTRODUCTION TO LOGIC
[which I call paper. But John only denotes one thing- — the cluster of
ideas which make John; and man only one thing, the cluster
of ideas common to John and Peter. J. S. Mill, however, distin
guished what is common to John and Peter from John or Peter,
and said not indeed that man denoted two things, but that it
denoted one and connoted the other. But if he had been asked what
John, the subject, was as distinct from man, his attribute, he
would either have had to say that he was not something different
from man, any more than slowness is something different from
a fault, though fault was also held by him to denote one thing- and
to connote another; or that John was just the uncharacterized
substance, in which those attributes inhered, the unknown subject ;
or else that he was what remained of the concrete individual when
his humanity had been left out of his nature. None of these
answers would be very satisfactory. Again, coloured is connotative,
in the original meaning of that word, because it is predicable, say
of a horse, and to be a horse is something else than to be coloured ;
in J. S. Mill's usage, because it is predicable of brown, though to be
brown is to be coloured. Mill treats as two, when he opposes a term's
denotation to its connotation, things like John and man, brown and
colour, whereof the latter is simply the universal realized in the
former, and the former nothing- without the latter : as well as
things like horse and colour, which are conceptually two. Originally,
only a name that was predicated of something thus conceptually
a distinct thing from the attribute implied by predicating it was
called connotative ; and it is only where there are thus conceptually
two things, together indicated by the name, that the word ownotative
has any appropriateness.
(Cf . also on the history of the word Connotative a note in Minto's
Logic, p. 46.)]
CHAPTER VII
OF THE PROPOSITION OR JUDGEMENT
A GENERAL acquaintance with the nature of the judgement or
proposition 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 the modes in which we already think
of things. Now judgement is the form in which our thought of
things is realized, and it is only in judgement that we form concepts.
The varieties of the concept, as they are distinguished in the doctrine
of terms, the different relations of one concept to another which
form the basis of the distinction of predicates, would be unintelligible,
unless it were realized that, in the first instance, concepts come before
us only as elements in a judgement. They live, as it were, in a
medium of continuous judging and thinking ; 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 concrete, 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 it
would be 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 — i.e. varieties
arising in the manner of our judging about any subject, not in the
matter which we judge of.1
A general definition of judgement raises many metaphysical
problems, which cannot be fully discussed in such a work as this.
But a few things may be pointed out about it.
1 This antithesis must not be pressed too far, as was pointed out above,
c. i, pp. 5-7. To regard it as absolute, as if what we judged of made no
difference to the manner of judging, is the error of those who attempt
to treat Logic as a ' purely formal ' science. But I do not think that, with
this caution, the statement in the text need mislead.
144 AN INTRODUCTION TO LOGIC [CHAP.
Every judgement makes an assertion, which must be either true or
false. This capacity of truth or falsehood is the peculiar distinction
of judgement, expressed grammatically by the indicative mood.
Imperatives, optatives, exclamations, and interrogations are not
judgements 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 judgements ; but we cannot ask of the imperative * Come ',
is it false or true 't — it is not a judgement. Again the question ' Art
thou he that troubleth Israel ? ' is not a judgement ; 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 judgement; 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 gesture; and in
such cases, though something doubtless ' passes in the mind ', the
exclamation can hardly be regarded as an attempt at asserting1
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 grammatical 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.
A judgement makes one assertion ; an assertion is one, when there
is one thing said of one thing — £i> /ca0' ero's, i.e. when the subject is
1 The reasoning which would make all exclamations imply a judgement
was extended to actions by Wollaston, when in his Religion of Nature
Delineated he regarded all wrongdoing as a particular mode of telling
a lie.
vn] OF THE PROPOSITION OR JUDGEMENT 145
one, and the predicate one ; though the subject and predicate may
be complex to any degree. Thus it is one judgement that f 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 ; there is one grammatical sentence, but 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 judgement is often said to be composed of three parts,
subject, predicate, and copula ; the copula being the verb substantive,
' is/ €(TT{V, estj ist, sometimes, though mischievously, represented in
Logic books by the mathematical sign of equation, = . 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 judgement.
Common speech does not always employ the copula. Take the
line ( It comes, it comes ; oh, rest is sweet'.1 Here in the judgement
' Rest is sweet ', we have subject (rest), predicate (sweet) and copula
all severally present; whereas in the judgement (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 such a 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 use a periphrasis, and say,
c he is one who plays the violin ', or ' he is a violinist '. But it is
clear that the copula 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 in thought, whether I say Beati immaculati in via or
Beati sunt immaculati in via. The inflexion of the predicate verb, or
the inflexion of the predicate adjective together with the form and
balance of the sentence, replaces or renders superfluous the more
precise exhibition of the copula ; it 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 express it. We
symbolize the judgement generally by the form ' A is B ' ; we may
1 C. S. Calverley, Lines on the St. John's Wood Omnibus.
JOSEPH L
146 AN INTRODUCTION TO LOGIC [CHAP.
write it ' A B\ but that is an abbreviation; to write it 'A = B* is1
an error.
If the copula is thus present, openly or surreptitiously, in every
judgement, what is its function, and can it be regarded as one of
three parts composing a judgement ? 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 property
and I may think of robbery, but they may remain apart in my
thought — subjects successively contemplated, like breakfast and a
morning's work ; if I say that ' property is robbery', I show that
they are not unconnected concepts, 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
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, the copula
may fairly be called a third and distinct member; but the whole
proposition ' A is £ ' 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. In our
thought, the copula is the synthesis (or linking) of judgement : it is
the form of the act, as distinguished from subject and predicate,
which are the matter. In our language, 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 judgement is analysable into subject and predicate ;
though in the act of judgement we recognize their unity, yet they
are also 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 f 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
vn] OF THE PROPOSITION OR JUDGEMENT 147
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 judge
ment 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 : Cogifo, ergo sum, I think, therefore I am.1 The use of the
verb of existence as copula suggests that every judgement predicate*
existence, that if I say that ' 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 idea; if I
say that ' a griffin is a fabulous monster ', or that ' 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 some
times to signify predication : with no more identity of meaning in
these two uses, than there is between est = 'is' and est = f eats'.2
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, affirm themselves as true. But a judgement which
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.
2 Cf. J. S. Mill, Logic, I. iv. i.
148 AN INTRODUCTION TO LOGIC [CHAP.
affirms itself as true claims to express, so far as it goes, the nature
of things, the facts, or the reality of the universe. In doing this it
may be 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 affirm her existence in the past ; and the
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 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 the
triangle ; though these different things play different parts in the
whole.1
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
1 Some writers have used the notion of a ' universe of discourse ' 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 conception which would be
false about savages themselves. It is said that these are different 'universes'
of discourse; 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. 32, n. 1, supra.
vn] OF THE PROPOSITION OR JUDGEMENT 149
accident that the verb of existence is employed to express the
act of judgement. I may entertain a concept, say that of Public
Schools ; I may think of them as tending to stifle originality in
boys, but without deciding in my mind whether they do so or not ;
so far, the complex concept of public schools as tending to stifle
originality in boys floats as it were before my mind, but it is not
declared to express the facts ; if I judge, one way or the other, that
public schools do or do not tend to stifle originality in boys, then
I believe that my notion of them expresses them as they are — that
it is no mere notion of mine, but the character of the real school-
world ; and to express that a combination of which I think is real
and true, I use the verb to be. Public schools are liable (or not
liable) to stifle originality in boys, because the liability (or non
liability) of public schools to do so is, or exists.
§[t will be observed that in the last paragraph the copula was
to imply, not to predicate, existence. For existence by itself is
not a significant predicate, as we have already seen, 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 subject of every judgement. A judgement as a whole
always has a content — the concept of the subject as qualified by the
predicate : and this content is believed not to be a mere idea
entertained by the person judging, but to be true, i. e. to be the
nature of the real ; and all true judgements are true together, because
reality is manifold, and each judgement seizes some portion of its
nature. To ask, Can I make such and such a judgement ? is to
ask whether reality is correctly apprehended (in part) in the concept
of such a subject so qualified. To make the judgement is to
apprehend reality in that way, to affirm of it the content of the
judgement ; and it is because of this reference to reality involved in
every judgement, that we use in expressing a judgement the verb
to be.
This view that reality is the ultimate subject of every judge-
150 AN INTRODUCTION TO LOGIC [CHAP.
[ment must not, however, 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 ' Belladonna dilates the pupil J may be an answer either
to the question ( What dilates the pupil ? ' or • What do you know
of belladonna ? ' In either case the grammatical subject is bella
donna ; bufc 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 judge
ment 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, tor it can in
turn be predicated of something else. Some have thought (and
this seems to have been Aristotle's opinion) that there was no single
metaphysical subject, but as many as there are concrete individuals.
And in the Categories l he defines the concrete individual as that
which can neither be predicated of nor inhere in anything further.*
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
culled the existential judgement — the judgement whose predicate
1 ii. 1* 3-9, v. 2a 11-14.
* 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 /card avp&eftriKos (cf. Met. A. viij : 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, when we enunciate such judgements
as these, we cannot help at the same time thinking of the predicate as
qualified by what figures as subject.
vn] OF THE PROPOSITION OR JUDGEMENT 151
[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 one system of reality. The content
of an existential judgement cannot indeed be predicated 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 men ; when
I say ' Est qui non curat habere } ' , 1 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 what is predicated of the concrete
individual is not true of him in complete isolation from all else, and
therefore that 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 judge
ments. We cannot maintain the view that the metaphysical subject
of every judgement is always in the last resort a particular individual.
' Civilization is progressive/ Doubtless civilization is only seen m
the lives of men ; but it is seen in the lives not of this and that
man singly but of the community 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. 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
152 AN INTRODUCTION TO LOGIC [CHAP.
[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 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
how we think; 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 subject2 with which we start is
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 A synthesis, and the affirmation of the result for real,
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 synthesis,
and the affirmation of the result for real, must be meant. The verb
to be naturally lends itself to this meaning. The mathematical
symbol of equality has a different meaning ; it is not a sign of pre
dication, but an incomplete predicate; it implies, of one thing,
quantitative identity with some other. If I say A — B, the predicate
is not B but ' equal to B3 : 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
1 The view that Reality is the ultimate metaphysical subject of judgement
is of course familiar to all readers of Mr. F. H. Bradley's or Professor
Bosanquet's logical work.
2 i.e. the logical subject.
3 Sigwart has pointed out that the movement of thought in a judgement
is different for a speaker communicating information and for 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 sup
plementation : to him the predicate comes as new information, which he
has now to combine with the concept of the subject hitherto formed by him.
The judgement is for him an act of synthesis first, and in retrospect, when
he has completed it, of analysis ; to the speaker it is an act of analysis first,
and in retrospect, when he has completed it, a synthesis by which he
recovers the whole fact from which he started, v. Logic, § 5. 1.
vn] OF THE PROPOSITION OR JUDGEMENT 153
and predicate in their combination are declared true of the real. To
the words which signify the subject and the predicate separately is
added a word which signifies that they are combined as subject and
predicate one of the other in a judgement. 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 are the matter
judged. Hence it is, at least generically, the same, while subject
and predicate change ; and for this reason the scheme of a judge
ment ' A is J3 ' represents subject and predicate by symbols, but
retains the ' copula ' itself. We write A and B for subject and
predicate l, 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.
The act of judgement is, however, only generically the same in
every judgement ; it is the same in so far as it involves a synthesis
of subject and predicate, and affirms the result of that synthesis for
real. It may differ in the nature of the synthesis of subject and
predicate. If therefore we speak of judgement as a common form
realized, for every difference in the subject and predicate, in different
matter, we must admit that there are also differences in the common
form. This was pointed out in the first chapter, as precluding what
is called a purely formal treatment of Logic. We cannot study the
form of thought with no reference to its content, because on the
nature of the content depends in part the form. Having got some
notion of the form of judgement, so far as it is always one and the
same, we must now proceed to consider some of the variations of
which it is susceptible, so far as these belong to its form, and not
merely to the content. Differences that belong merely to the
content (as between the judgements 'men are animals' and 'roses
are plants ') we can of course ignore.
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 have for long been commonly distinguished accord
ing to Quantity, Quality, Relation, and Modality.
In respect of quantity, 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 judgement 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 judgement
is also called singular. In the latter, the judgement may affirm
or deny the predicate of the subject either universally, i.e. in every
case, e.g. ' All equilateral triangles are equiangular', 'Nemo omni
bus horis sapit ' : in which case it is called universal ; or partially,
i.e. in particular cases, 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.
By a part of the subject is meant here a logical part, i.e. some
instances or species included in the extension of the subject J, some
part of all that it denotes ; thus when I say that some larkspurs
are perennial, I mean some species of that genus : when I say that
some animals cannot swim, I mean some species of animal, or some
individuals of some species. Now the singular, particular, and
universal judgements may be represented as referring respectively
to an individual, to a part of a class, and to the whole of a class, i.e.
to one, some and all of a certain number. Or since an individual
is incapable of logical division, and a singular term, as denoting
one individual, cannot refer to less than all that it denotes, singular
judgements may be ranked with universal judgements, and con
trasted with particular : both the former referring to the whole of
1 Cf. infra, p. 159, n. 1.
VARIOUS FORMS OF THE JUDGEMENT 155
what their subjects denote, while the latter refers to a part only.
We shall see later, in dealing with syllogism, that singular judge
ments may for certain purposes be treated as if they were universal,
because they equally render possible certain inferences. But at
present it is important rather to realize that such attempts to treat
the differences between singular particular and universal, or
singular + universal and particular, as merely quantitative do
not do justice to the differences in the thought contained in
them.
A logical whole or class (if we are to give it that name) is — as
we have already seen — ill conceived as a collection of individuals.
It is rather an unity, or identity running through things which are
different. It may form the subject of our thought and of our
judgement ; but it differs from an individual not as all from one of
a collection, which would be a quantitative difference, but rather
notionally, as what is universal from what is individual. The
difference between singular and universal judgements is therefore
not essentially quantitative. Again, the individuals contained
within a class are not, as individuals, an unity but a collection ;
between some and all of this collection the difference is quantitative ;
but that is not the proper difference between a particular and
an universal judgement, for the universal judgement regards
primarily the class as kind, and not as a totality of individuals.
The difference therefore between particular and universal judgements
is not essentially quantitative. On the other hand, the difference
between individual and particular judgements is often quantitative.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
1 The Aristotelian division (or rather Platonic — for it occurs in Plato's
Joliticus) of political constitutions is another example in which differences
>t really quantitative have been presented under a quantitative form,
monarchy, an aristocracy, and a democracy, though said to differ accord
ing 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 kmd. It must be added
that Aristotle does not put forward any purely quantitative division of
judgements (cf. de Interpr. vii. 17a SSeVei ci' cari TO. pev KudoAou rav Trpay/xurcof
rd Oe nad' tiuurrov— since of things some are universal and some severalj,
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.
156 AN INTRODUCTION TO LOGIC [CHAP.
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
universal 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 judgement
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
judgement 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 1, the words all, none, some
are appropriated to that service. A judgement without any mark
of quantity is technically known as an indefinite judgement; because
it is not clear whether the whole, or only a part, of the extension
of the subject is referred to, and so the scope of the judgement is
undetermined; the examples just given, Women are jealous, A flower
is a beautiful object, are therefore indefinite judgements.
At the same time, the words all and none, as signs of the
universality of a judgement, have disadvantages of their own.
For a judgement is really universal, when the subject is universal
or general, and the predicate attaches to the subject (or is excluded
from it) necessarily ; 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 judgement. Each is a judge
ment made about a number of individuals : it states an historical
fact, and not a scientific truth. It would be convenient to call such
judgements collective2 or enumerative judgements ; for they really
collect in one the statements which may be made about every
1 A form like ' Man is mortal ' is clearly universal ; but represented in
symbols it will not unambiguously show its universality.
2 Cf. Bradley's Logic, Bk. I. c. ii. §§ 6 and 45. In the Table of Contents
he speaks of ' collective ' judgements in this sense.
vni] VARIOUS FORMS OF THE JUDGEMENT 157
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 judgement
is meant as universal, 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
judgement no longer referred 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. If we contrast
such judgements as All my bones are out of joint and All triangles in
a semicircle are right-angled^ the difference is very plain.
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 a general or abstract
term, a concept or kind of thing. The enumerative judgement
(and this is true in some degree of the particular judgement also)
approximates to the type of the singular rather than of the uni
versal.1 For though the subject be a general term, and I predicate
about all the members included under that term, yet I do so
because I have examined them as individuals, and found the predi
cate in them all, not because of any necessary connexion between
the predicate, and the common character of these individuals which
the general term signifies. French ministry is a general term ; bat
(for all that I see) it is not because being a French ministry
involves being short-lived, that I assert all the French ministries
to be short-lived; it is 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 collective 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
1 Cf. Bradley 's Logic, Bk. I. c. ii. § 45.
158 AN INTRODUCTION TO LOGIC [CHAP.
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 holds of any and every instance, alike past present and
future, examined or unexamined. An enumerative judgement
holds only of those instances which we have examined, and summed
up in the subject. All reformers are hated : if that is merely
enumerative, it affords me no ground to anticipate hatred if I
undertake reform ; it affords me no explanation of the hatred with
which reformers have been met. But if it is a true universal, it
explains the past, and predicts the future. Nevertheless an uni
versal judgement has nothing, as such, to do with numbers of
instances ; if the connexion affirmed in it be necessary, the judge
ment 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 ^s are B ' expresses it adequately.
The particular judgement may be interpreted as referring either to
individuals not enumerated or to an universal not fully determined ;
and it will approximate more to the enumerative, or more to the
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, Logic, Bk. I. c. ii. §§ 43-6; Bosanquet, Logic,
vol. i. pp. 278-292; v. also Bradley, Appearance and Reality, p. 361.
vm] VARIOUS FORMS OF THE JUDGEMENT 159
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 pigments 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 outward form of a particular judge
ment to show whether the speaker is thinking rather of indivi
duals whom he does not name, or of conditions which he does
not specify; though the content and context of the judgement will
often guide us on this point.
It will be readily seen that there is the same sort of difference
between the particular judgement interpreted of individuals not
enumerated, and the particular judgement interpreted of conditions
not fully specified, as exists between the enumerative and the true uni
versal judgement. If the women vaguely referred to as some were
enumerated, I could say All the women on my list have ruled king
doms ; 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 judgement, or between the
enumerative and the universal, may be expressed by saying that in
the one case the judgement is interpreted in extension, in the other
case in intension. A judgement is interpreted in extension, when
we are thinking primarily of the various instances (individual or
specific *) included in the subject to which the predicate refers ; it
1 It will be remembered that in discussing the extension and intension of
terms, it was pointed out how the extension of a term meant, properly,
subordinate terms conceptually distinguished, and not merely the instances
of a kind regarded as only numerically distinct. Thus in the extension of
the term shilling would be included shillings of different die or standard
fineness ; but the extension of the Queen Victoria Jubilee shilling would not
be subdivided. At the same time it was recognized that we may fix our
attention either on the common character which all shillings of that issue
have, or on the multitude of different shillings having that character : for
things of a kind are a one in many, or a many in one— one form in many
instances, many individuals in one type. When we think of the many more
than of the one, we may be said to consider the term in its extension ; when
of the one more than of the many, in its intension. And indeed individuals
of a kind, in order to be distinguished at all in thought, must be con
ceptually distinguished : whether only by number (as we might think of the
first, second, third, &c. shilling struck from the die) or by place (as we
160 AN INTRODUCTION TO LOGIC [CHAP.
is interpreted in intension, when we are thinking primarily of the
subject as concept, of the character implied in the subject term,
with which the predicate is connected. f Some A is J3 ' is inter
preted in extension, if I think of this that and the other A : in
intension, if I think of A's of a certain character. ' All A is B Ms
interpreted in extension, if I think of every one of the A's : in
intension, if I think of the character of A as such.
What has been said on the quantity of judgements may be
summed up as follows. Judgement predicates either of individuals
or universals. In the former case, when it predicates of one indivi
dual, the judgement is called singular : when of every one of a collec
tion or enumeration, it may be called collective or enumerative. In
the latter case, when the predicate is affirmed (or denied) of the
subject without respect of instances, and therefore in any and every
instance, the judgement is called universal ; when otherwise, it is
called particular. But an universal judgement is 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 imperfectly
denote, or the conditions we imperfectly specify, in the subject.
A judgement may be viewed primarily in intension, as asserting
a connexion of content, or in extension, as asserting a certain
character in individuals. The former aspect predominates in the
universal, the latter in the enumerative, and even more in the sin
gular judgement : 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. Some
of 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 judgements simply as either
universal or particular : universal, when the whole of a kind *, or
might think of the shilling in nay pocket, in yours, &c.) ; though when the
grounds of distinction are no longer proper to the kind (as distinctions of
first and second, here and there do not belong to shillings qua shillings),
they are ignored in classification.
1 i.e. a kind or any 'universal'; but I have avoided the word 'universal'
here, and preferred kind (though otherwise a less apposite term) in order
to avoid confusion between the universal concept referred to in the
judgement, and the universal judgement referring to the whole of this
universal.
vm] VARIOUS FORMS OF THE JUDGEMENT 161
when an individual is referred to (for in both cases the subject is
completely indicated), particular when a kind is referred to only
in part (and the subject therefore incompletely indicated).
In respect of quality, judgements are distinguished as affirmative
or negative. An affirmative judgement assigns a predicate to
a subject; a negative judgement puts it from it. But the
distinction between affirming and denying is too familiar to need
and too simple to admit of expressing 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 ; the content of our
thought is declared to express the character of the real, its 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.1 But the judgement is
not about my idea; I may reflect on that, and say that the
idea I had formed of a dead-nettle was a wrong one ; at present
I am judging about the dead-nettle, not about any past idea of it.
And when I say that it does not sting, what am I saying about it ?
in it, what is this property of not stinging ? surely, it may be urged,
just nothing : so that the negative judgement expresses 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 limitation 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. There is always a positive character
as the ground of a negation. Snow is not hot, because it is cold ;
1 Moreover this would really mean that I now judged a previous judgement
to be false : about which the original question would at once arise.
162 AN INTRODUCTION TO LOGIC [CHAP.
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.
To say that negative judgements presuppose affirmative does
not 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 proposition.
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 that,
everything would be everything else ; that is as positive, as these
several modes of being themselves.
Negation, as Plato saw lf is as necessary as affirmation, if there are
to be any differences or discriminations within reality ; that A is not 7?
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
Determmafio est negatio. Whether this is a tenable conception 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 con
tended 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.]
It has sometimes been proposed to treat the negative judgement,
1 Soph. 256 E TTfpi €KO.O~TOV apa rS>v fldcov JTO\V pev fan TO ov, arrfipov de ir\r)6si
TO fjirj ov. 257 B OTTOTCIV TO p.^ ov Ae-yto/je j>, o>? eoiKfv, OVK firnvTiov TI \€yofj,fv TOV
oi/rof, aXX' eTfpov novov. (' 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.')
vm] VARIOUS FORMS OF THE JUDGEMENT 163
A is not B, as an affirmative judgement, A is not-B1, 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-7^
is a positive concept ; and if not-7? is a positive concept (say C),
it is only because B and C are reciprocally exclusive attributes ; but
if they are reciprocally exclusive attributes, then C is not B and B
is not C -, nor can these negative judgements be done away by
repeating the same manipulation, and writing C is not-7?, B is not-C.
For if C means the very same as not-i?, then not-C means the
very same as not-not-^, and the proposition B is not-C means no
more than B is not-not-7?. That, however, is absurd; for C is
a positive concept, and the consciousness of the distinction between
it and B and of their reciprocal exclusiveness cannot be reduced to.
a consciousness that B cannot be denied to be itself. The argument
thus expressed symbolically can be easily applied to a concrete
case by any one who chooses to substitute for B and C odd and even
or dog and horse ; though there is less temptation to think not-a-dog
a positive concept, than not-odd, as it leaves us to select in the dark
among a large number of still remaining alternatives.
Judgements are distinguished according to relation into categori
cal, hypothetical, and disjunctive. We have been considering hitherto
categorical judgements. A categorical judgement merely affirms
or denies a predicate of a subject : dogs lark, dead wen tell no tales.
An hypothetical judgement connects a consequent with a condition
which it does not, however, imply to be necessarily 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 : rocks are either igneous, aqueous,
or metamorphic.2 The hypothetical judgement is sometimes called
conjunctive, as conjoining the truth of the consequent with that of the
antecedent: while the disjunctive disjoins the truth of one alternative
1 Such judgements, with an infinite term (cf. p. 30, supra] for predicate,
have been called infinite judgements.
2 For any given rock, these are alternatives : for rocks collectively, they
are three forms which are all realized : cf. p. 168.
164 AN INTRODUCTION TO LOGIC [CHAP.
from that of the others. Both are sometimes called complex judge
ments, in contrast with the categorical, which is called simple.
In an hypothetical judgement, the antecedent and consequent
may have the same, or different, subjects : the scheme of the
judgement may be either ' If A is B, it is C 3 (If corn is scarce,
it is dear), or { If A is B, C is D ' (If money is scarce, the rate
of discount rises). Again, either antecedent or consequent may
be either negative 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 distinction of affirmative and negative, though applying
to the antecedent and consequent severally, does not apply to the
hypothetical judgement as a whole.
Where the subject of the antecedent and the consequent is the
same, the hypothetical judgement may commonly be reduced to
categorical form : ' If A is B, it is C' may be written ( A that is B
is C' ; If corn is scarce, it is dear, becomes Scarce corn is dear. Even
when antecedent and consequent have different subjects, a little
manipulation will sometimes produce an equivalent judgement
categorical in form : If wishes were horses, beggars would ride might
be written Beggars whose wishes were horses would ride. For the
hypothetical judgement asserts a predicate of the subject of the con
sequent, under a condition expressed in the antecedent ; and if that
condition can be expressed as an adjective of the subject of the
consequent, then of that subject, so qualified, we may assert the
predicate in the consequent categorically. But we do not thus
reduce hypothetical to categorical judgements : the hypothetical
meaning remains under the categorical dress. Scarce corn is dear is
not really a judgement about scarce corn, but about corn : we
realize that corn is something which may be scarce, and is dear
when scarce; and so the dependence in corn of a consequent on
a condition is the burden of our judgement about it.
The difference between the categorical and the hypothetical
judgements — between affirming or denying a predicate of a subject,
and asserting the dependence of a consequent on a condition —
becomes clear in the case of unfulfilled conditions, in past or future
time. If I had served my God as I have served my king, He would not
hare given me over in my grey hairs : no doubt this implies the
categorical judgement God does not forsake those who serve Him
vm] VARIOUS FORMS OF THE JUDGEMENT 165
faitlifidly \ but it cannot be reduced to this, for it implies also
Therefore He would not have forsaken me, if 1 had served Htm
faithfully ; and we cannot eliminate the hypothetical judgement.
Kpoloros "A\vv 6"ia/3as ptyaXyv apyj]v KaraXvo-tL 1) If Croesus crosses the
Halys, he will ruin a great power ; here it is not stated whether
Croesus will cross the river or not ; so that as the fulfilment of the
condition upon which the assertion in the consequent depends is left
in doubt, there is nothing but the dependence categorically asserted.
It may be urged that at least the dependence is categorically
asserted ; and therefore the hypothetical judgement is categorical
after all. This is a very good answer to any one who attempts to
abolish the distinction between the two judgements by declaring
that all judgements are in reality hypothetical ; for it shows that the
hypothetical does presume the categorical. But it does not invalidate
the distinction of the hypothetical from the categorical ; for that
distinction rests upon the difference between asserting a dependence of
consequent upon condition, and asserting an attribute of a subject ;
if it is granted that the hypothetical asserts the former, though it
do so categorically, yet it differs from the categorical judgement.
It has been said 2 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 ofLydia, 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 distinction between
categorical and hypothetical assertion is formal in the sense that it
meets us, whatever be the subject we may think about ; and to exclude
it from Logic on the ground that, as compared 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 science, and cannot be tolerated in Logic.
1 This oracle shows that the outward or grammatical form of a judgement
is no sure guide to the meaning ; for it may be translated ' Croesus will
cross the Halys and ruin a great power ', in which case it becomes
categorical: the two translations are clearly different, though the same
Greek line covers both senses.
2 Cf. Mansel, Prolegomena Logica, pp. 232, 251.
166 AN INTRODUCTION TO LOGIC [CHAP.
There is a metaphysical problem suggested by the hypothetical
judgement, which must be briefly noticed. If Hannibal had marched
on Rome after Cannae } he would have taken it. This judgement
makes an assertion ; in doing so it declares something to hold good
of the real, for it declares its own content to be true. But what
does it declare true of the real, and what historical fact (as we may
put it in such a case) 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 that the one event was due to the other, for
neither happened. If he had marched on Rome then, he would have
taken it ; but that is not a fact in his history, or in the history of
Rome ; it is an unfulfilled contingency ; and how can that be real ?
Every hypothetical judgement presents this problem ; for it asserts
that under certain conditions something would exist or have
existed, but not that the conditions are realized, nor therefore
that it does or will exist or has existed. Nor does its truth
require this; in order that an hypothetical judgement should
be true, neither condition nor consequent need be realized ;
and yet if an hypothetical judgement is true, it is true of
reality, and reality, we may urge, is actual ; what then does the
hypothetical judgement affirm to be actual in the real ? A character,
says Mr. F. H. Bradley *, which is the ground of the connexion
hypothetically asserted in the 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 ? We speak freely of unrealized possibilities, as if they
existed as well as realized actualities. We are not always conscious of
the metaphysical difficulties involved : how are we to think of what
we so freely speak of ? When we reflect, in Logic, upon the hypo
thetical form of judgement, we become conscious of the problem.2
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
* Logic, Bk. I. c. ii. § 50 : cf. § 52.
2 The reader must not suppose that these paragraphs deal at all com
pletely with the problems raised by the hypothetical form of judgement.
Nothing, for example, has been said about the quantity of hypothetical judge
ments. It has been urged by some that they are all universal ; and doubt
less they imply an universal connexion somewhere* Yet they can clearly
be made about individuals.
vin] VARIOUS FORMS OF THE JUDGEMENT 167
a physician), ' Either A is B or C is D ' (lie either fears his fate too
much, Or his desert is small1. 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 an hypothesis, so this 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 C \ and ' A is either not B or
not C ' : 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 C', and ' Either A or
B is not C'. But it should be noted that ' Neither ... nor ' is no
disjunction at all, but a conjunction of negations. On St. PauPs
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 judgement whether the
alternatives offered are meant to be mutually exclusive. If A is
either B or Ct 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.
It has been suggested that the disjunctive judgement is in reality
a combination of hypothetical; that ' A is either B or C' means
1 If A is not B, it is C ; if A is not C, it is B ; if A is B, it is not C;
if A is Cy it is not B\ Doubtless these four propositions are
involved (supposing B and C to exclude each other) ; but we do
not therefore get rid of the peculiar nature of the disjunctive
1 This might be equally expressed 'He either fears his fate too much,
or deserves little ' : indeed in sense the alternative predicates are predi
cated of the same subject, not (as in the proposition Either Tacitus ivas
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.
168 AN INTRODUCTION TO LOGIC [CHAP.
judgement. 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 alternative hypotheses. 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 judgement makes an assertion, like a categorical ; but
what it asserts is a relation of a consequent to a condition. A dis
junctive judgement involves hypothetical, but it presents them as
alternatives and asserts the truth of one or other of them.
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.C/ 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 judgement 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 1 ; 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 consider
ing negative judgements, that a thing is definitely this or that by
not being something 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 judge
ment. In respect of modality, judgements are distinguished as
assertoric, problematic, and apodeictic ; the first is sometimes op
posed 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
1 Of course there is a disjunction in the facts, in the former case as well,
so far as that a year must be either the 429th or the 427th or some other
number, from any point of time whence we choose to begin our reckoning.
For the fuller treatment of this form of judgement also the reader is
referred to more advanced works.
vm] VARIOUS FORMS OF THE JUDGEMENT 169
conveniently retained as a form of modal judgement. Judgements \
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', apo-
deictic — ' the train must be late ', ' the sun cannot be late '. The
distinctions 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
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
It is clear that the modality of the judgement whose subject
and predicate are X and Y does not in any way affect or modify
the predicate Y. When I say that the train is actually, or possibly,
or necessarily late, it is not the predicate late which is actual, pos
sible, or necessary, — but the train being late ; for there are not those
three kinds of lateness. ' The blossoms of that chrysanthemum are
possibly white ' : 'the blossoms of that chrysanthemum are actually
white ' ; it is clear that ( actually ' and { possibly ' do not qualify the
predicate white, as the adverbs 'purely ' orf brilliantly' might do;
there is no such colour as possible white, as there is a brilliant
white or a pure white. ' Water runs down hill ' : * water must
run down hill ' ; these are not different ways of running, like run
ning fast and running slowly. Grammarians tell us that adverbs
qualify verbs and adjectives ; but these adverbs, actually, possibly,
and necessarily, seem to form an exception to the rule. They
qualify neither a verb nor an adjective, though these be predicates
of the judgement, but the judgement itself.
For the real meaning of these expressions — ' X is actually Y',
( X is possibly, or may be 7', ' X is necessarily, or must be Y' —
1 Except so far as in some subjects, like arithmetic, a judgement is nearly
always made with consciousness of its necessity : cf. infra, p. 175. 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 F' is not contradicted by the problematic negative
4 J£may not be Y\ but by the apodeictic 'X cannot be F': and similarly
the problematic negative by the apodeictic affirmative.
170 AN INTRODUCTION TO LOGIC [CHAP.
is rather this : 4 that X is Y is actual ', ' that X is Y is possible ',
' that X is T is necessary '. They involve reflection upon the judge
ment that X is T, and express differences not in the nature of X or
of the predicate belonging to it, but in the nature of our grounds
for affirming X to be Y. ^ We may speak of differences of modality
in judgements, if we like, as differences in the mode in which, for
us, the judgement is grounded. Yet such an expression is open to
misinterpretation. For when I say that X may be Y, I do not
judge at all that X is Y, but that there are insufficient grounds for
so judging. We must, however, scrutinize these forms of expres
sion more closely ; for the illustrations so far chosen do not bring
out their different meanings, having been chosen merely with the
purpose of showing that modality qualifies neither the subject
nor predicate of what appears to be the judgement in which it
occurs.
Nothing is more fundamental in our thought than the constant
search for necessity in our assertions : the desire to see that the
matter of fact asserted could not be otherwise than we assert.
In this search we are not content with what is commonly called
experience. I may find in my experience that a man whom I had
trusted does me a wrong, but I want to know further why he did
it. So it is with any other event of which I have no explanation.
My explanation in such a case would lie in connecting the event
with another ; we are perpetually tracing connexions between one
fact and another, and cannot conceive anything to be completely
isolated from everything else. ' Nothing in this world is single ;
All things by a law divine In one another's being mingle ' ; this is
the faith that underlies all effort after knowledge. All judgement
expresses the connexion of things, or of one attribute with another
in things ; about a thing isolated altogether from everything else,
united with no other by any common characteristic, judgement
would be impossible.1 But we realize only gradually the intercon
nexions of fact. In many judgements intended by us to express
the facts as we apprehend them, we find upon reflection that the
connexion of the subject and the predicate is not intelligible to us ;
we then seek some ground for the fact asserted ; and if we cannot
avrtov \6ywv earlv d(f>dvi(ris TO 8ia\veiv eKacrrov dno TravToav '. Plato,
Soph. 259 E. ('All speech vanishes altogether if each thing be severed from
everything else.')
vm] VARIOUS FORMS OF THE JUDGEMENT 171
find it by seeing more clearly into the fact, we look for it in
another, i. e. in a wider system to which the first belongs. Often,
however, when we make a judgement we do so without full reflec
tion upon what is asserted and upon the grounds for it ; and such
judgements, barely asserted, are called assertoric; and the expres
sion of them, ' X is F' (' crows are black', fthe train is not
arrived'), is bare of any words that indicate reflection on the
grounds for our assertion. It is true that such judgements, report
ing what we perceive, are not made arbitrarily ; but the appeal to
perception does not satisfy us ; for though we may be unable to
doubt that a rose is red when we see it, and seeing it justifies our
assertion, yet it does not show why the rose is red, and the fact
remains one for which we see no ground.
But the assertoric form of judgement, X is Yt may express two
different mental attitudes. We may affirm or deny unhesitat
ingly, but without any thought in our minds of possible grounds
for what is asserted. We may repeat our affirmation or denial
as unhesitatingly as before, when the question whether there are
sufficient grounds has occurred to us, even though we have not
found any to satisfy us. Some men detect water with the divining-
rod. That is very extraordinary • how do you account for it ? I cant,
but they detect it. Here the assertoric judgement is challenged,
and repeated ; in the interval, we have reflected on the grounds for
our judgement, and found none : none, that is, that make the fact
asserted intelligible, though we may still think we have grounds for
making the assertion in our experience of events that we cannot
account for except by connecting the detection of water with the
use of the divining-rod. We therefore still use the assertoric
form ; yet the force of it is not quite the same, though the words
in which we express ourselves are; and we must be careful to
notice the difference, since in Logic it is not the form of words that
matters, but the form of thought.
The difference lies in the absence or presence of the thought of
the grounds of our judgement. If there is no thought of them,
we make the judgement without looking beyond it; if there is
thought of them, we look beyond the judgement in making it,
even when we look in vain. It might perhaps be best to call
^judgement pure, rather than modal, when it is made without any
thought of its grounds ; and to call it assertoric, and so assign to it
172 AN INTRODUCTION TO LOGIC [CHAP.
a species of modality, only when it is asserted with the thought of
grounds that are not forthcoming. In this case, the introduction
of the word actually would mark a judgement as assertoric ; but the
ordinary categorical form, X is (or is not) 7, might represent
either a pure or an assertoric judgement. Very often the emphasis
of the voice, or the use of italics, serves to distinguish the pure from
the assertoric sense of such a form of judgement. If I say c The
stimulation of the retina by waves of ether is correlated with
sensations of colour ', I may barely intend to state a fact, without
thought of looking beyond it for grounds ; but if I emphasize the
' is ' or write it in italics, I should be understood to affirm it as an
actual fact in spite of my inability to give grounds for it; the
general thought of grounds accompanies the judgement, but in
a different form from what occurs in the problematic or apodeictic
judgement.
By the expression ( grounds for our judgement ' in the last
paragraph has been meant grounds for the matter of fact judged ;
and at the risk of repetition, it may be well again to distinguish
between this, and grounds for judging. For the difficulties in the
subject of modality centre in this distinction, and if our discussion
cannot hope to solve the difficulties, it may at least be well to
indicate where they lie. Even if I do not see how a man is made
aware of the presence of water by the divining-rod, I may have
reason for judging that he is, if I have known water found by men
who had no other means of detecting it. In scholastic phrase,
I have here a ratio cognoscendi, but not a ratio essendi : a reason for
acknowledging the fact, but not a reason for the being of the
fact.1 Of course the ratio essendi is the best of all rationes cogno
scendi ; of course also my ratio cognoscendi may turn out inadequate
on closer scrutiny. And if a judgement made without any thought
of its grounds — what we have now called a pure and not a modal
judgement — be reasserted in assertoric form, it is seldom that it is
purely assertoric. Either we find our reasons for asserting it
insufficient, and it has acquired the character of a problematic
judgement; or we have begun to explain the fact, and then the
judgement is on its way to become apodeictic. f There were species
I have translated cognoscendi by 'acknowledging', because in the full
sense of knowledge I do not know a fact which I do not see in its own
nature to be necessary.
vm] VARIOUS FORMS OF THE JUDGEMENT 173
once intermediate between the ape and man. How do you know v
that, since no specimen has been found ? Much may have existed,
of which no trace has survived/ This reply gives a tinge of the
problematic to the original judgement. Suppose a different reply :
' The structure of man bears the same relation to that of the ape as
prevails between species in other cases where specimens of inter
mediate forms, now extinct, have been preserved/ This is
something of a ground in the nature of the facts for accepting the
original judgement; there must therefore, we might say, have once
been forms intermediate between man and ape. Our 'must' in
such a case expresses a different kind of necessity from what it
expresses in a really apodeictic judgement; but still, it does
express a kind of necessity. It is rare that a judgement is re
affirmed after challenge with unshaken confidence, and yet with no
thought of any ratio essendi. fl feel ill' is such a judgement.
If a man challenges my assertion, I cannot justify it, but only
reaffirm it. But the barely assertoric attitude, when once the
mind has been awakened to the thought of the grounds of its
judgement, is rare. Our pure judgements, when we have got so
far as to ask their grounds, generally present themselves as either
problematic or apodeictic. This might be considered to justify us
in calling a pure judgement, i. e. one made without reference to its
grounds in our thought, assertoric : instead of reserving that name
for the case in which a judgement is made in the consciousness
that judgements need grounds, and yet is neither problematic nor
apodeictic. Nevertheless the distinction between the two cases
ought to be observed ; and is in fact expressed by the addition to the
pure judgement ' X is Y' of the adverb that marks the assertoric
form of modality, in the expression ' X actually is Y3.
If we turn to the apodeictic and problematic judgements, the char
acter of the assertoric will become clearer by the contrast. The apo
deictic may be considered first. When we say f X must, or cannot, be
Y1 (' X necessarily is, or is not, Y'), we imply that there are grounds
known to us for X being, or not being, Y. As a rule, these
grounds are conceived to lie outside the content of the judgement
XY1 : i. e. we do not upon reflection see immediately that X must or
1 We may symbolize thus the judgements whose subject and predicate are
.Yand F, and which are thus 'materially' the same, but whose 'formal'
character— modality, quality, quantity— may differ.
174 AN INTRODUCTION TO LOGIC [CHAP.
cannot be 7, upon a mere consideration of the nature of X as such ;
we see it to be a consequence of other truths, which in their turn
may be asserted either apodeictically or assertorically. The water
must rise in the common pump, when the piston is raised : why
must ? because of the pressure of the atmosphere. It is the con
sciousness of that ground for its rising which leads us to affirm the
water's rising apodeictically, whereas the mere observation of fact
would only lead us to affirm it assertorically. But are we sure, it may
be asked, that the atmosphere must have weight ? for if not, we
can only say that the water must rise j^and when the atmosphere
has weight. We cannot here discuss the sufficiency of the grounds
on which we regard the general propositions of science as demon
strated ; but it is clear that if the grounds of an apodeictic judge
ment are themselves affirmed only assertorically, there is a doubt
thrown on the apodeictic judgement. It is necessary, if the judge
ments on which it is grounded are necessary.1 ' Animals must
sleep, because they cannot be continuously active.' But how do we
know that they cannot be continuously active ? And suppos
ing a reason were given, we might ask how it is known to be
necessarily true, and so ad infinitum. An apodeictic judgement
would thus be merely a judgement made with reference to grounds
from which it followed, and which we accepted as true ; but since
these grounds might not be true, there would be no judgement
absolutely necessary, because none safely grounded.
The remedy for this state of affairs would lie in the existence of
judgements which we saw to be necessary (i. e. saw must be true)
without going beyond them : the ground for the judgement ' X
must be Y* lying in the content of that judgement.2 We have
1 We may call the necessity of a judgement, which we see to follow from
certain grounds, but whose grounds we cannot affirm necessarily, an hypo
thetical necessity. The consequent of every hypothetical judgement is
asserted- as hypothetically necessary— ' if A is B, -X"is T' might be written
'if A is B, X must be Y\ When the grounds can be affirmed necessarily,
then the judgement referred to them maybe called apodeictically necessary.
It should, however, be noted that in the hypothetical judgement 'if A is J?,
X is Y\ we may or may not see that the consequent is involved in the
condition ; the connexion may be a bare fact for us, or one that we see to
be necessary: and necessary, either immediately, or on further and assign
able grounds.
2 No truth is isolated; and there is none (not even such a truth as
2x2 = 4) which would still be equally true if all other things per impossibile
were different (e.g. if 2 + 2 = 5 and 2x3 = 7). So far, no judgement is
unmediated, or immediately necessary. But there are judgements whose
vm] VARIOUS FORMS OF THE JUDGEMENT 175
already been made familiar, in discussing- the heads of predicates,
with the notion of judgements in which the subject and predicate
are conceptually connected : some such judgements are imme
diately necessary. That a line must be either straight or curved
is a judgement of this kind. A man may assert as fact that
lines are either straight or curved, being led to that assertion by
the memory of past experience : but if he pause to reflect on the
ground for the assertion, he may realize that not only have the
lines he has seen or imagined been all of them either straight or
curved, but they must be so.
An apodeictic judgement then is one whose truth is not merely
affirmed (for every judgement affirms its own truth) but seen to be
grounded, either in itself, or in other judgements accepted as true.
It is to be noted that many judgements which are really or in
thought apodeictic are commonly expressed in assertoric form. In
mathematics, for example, every step is by the mathematician seen
to be necessary; almost all mathematical judgements are apodeic
tic 1 ; insomuch that it is often summarily said that mathematics
deal with f 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 ' 2 x 2 is 4 ',
not ' 2 x 2 must be 4 ' : ( the interior angles of a triangle are '-
not c must be ' — ( equal to two right angles '. On the other hand,
many judgements expressed in apodeictic form are differently
thought. Not only does the form l X must be Y' leave it uncer
tain whether the judgement is asserted as immediately necessary,
or as grounded in knowledge outside itself — a matter of which we
cannot be unaware in our thought when we judge ; but also the
outside grounds of the judgement may be grounds that merely
require the fact asserted or explain it : may be raliones cognoscendi or
rationes essendi. At times we even use the apodeictic form of propo-
necessity is seen in a particular case, as we see that 2x2 must be 4 in
a particular counting, though it is not seen to be unconnected with all other
judgements, but rather to be bound up with others. And the matter of fact
in which we find necessity might be something much more complex — a far
bigger system— than the numerical relations of 2 x 2.
1 Almost all; for a few judgements, such as formulae for the finding
of prime numbers, have been believed to be universal, and turned out to
break down for certain values. These were not apodeictic. If it had been
seen that the formula must yield a prime for any value, it could not have
broken down.
176 AN INTRODUCTION TO LOGIC [CHAP.
sition to hide our doubts : we are conscious of grounds for a judge
ment, and grounds against it, and 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
1 It is so '. All these diversities of thought lie concealed under the
apodeictic formula, Xmust be Y ; but it is always implied by that
formula that our attention is directed to the grounds for the asser
tion XY.
The problematic judgement, on the other hand, implies that the
truth oi the judgement depends on grounds whose existence cannot
be asserted. (X may be 7' means that we have not sufficient
grounds for asserting positively that X Y is true. Thus it involves
the same attitude of reflection as the apodeictic judgement, or as
the assertoric (if we distinguish the assertoric from the pure) ; but
as a result of reflection, the relation of the content of our judgement
to what we know is seen to be different, and precarious.
In order to understand the meaning of the problematic judge
ment, we must distinguish between those which are general (i. e.
which have a general term for subject) and those which are sin
gular. For where the subject is a general term, the problematic
form may or may not express a judgement that is problematic in its
logical character. A problematic judgement, as is obvious, expresses
uncertainty ; but uncertainty has been regarded as a state either of
facts, or of our mind in regard to facts. As a state of our mind,
uncertainty arises through ignorance; and it is this uncertainty
which renders a judgement problematic, in the logical sense in
which that is one of the modalities of judgement. As a state of
facts uncertainty might mean either of two things ; but only one
of these can be meant when the judgement is singular; and the
judgement is not in both cases logically problematic. Yet the
formula ( X may be Y9 is used in all these cases.
The judgement ( Rain may fall to-niorrow ' is a singular judge
ment : being concerned not with a particular thing or person, but
still with a particular day. This judgement is problematic in the
logical sense ; for it does not imply that the fact, whether rain is
to fall to-morrow or not, is uncertain, but only that we are ignorant
of the present condition of some at least of those factors (wind
and clouds, heat and moisture, lie of land, and currents of air) on
viu] VARIOUS FORMS OF THE JUDGEMENT 177
which to-morrow's event depends. The fact is really certain, but
we are uncertain ; the rain falling or not falling to-morrow is now
necessary, but to us problematic. With sufficient knowledge we
could say ' Rain must (or cannot) fall to-morrow '. But sufficient
knowledge is beyond our reach. .
Again, ( The Sultan may behead his vizier to-morrow/ This is
still problematic, for it implies that we have not sufficient grounds
either for affirming or for denying that he will do so. But in
the opinion of many, there is here a further uncertainty in the
fact itself. For the issue depends in part upon the Sultan's will ;
and many hold that the future actions of the human will do not
lie contained as it were necessarily in the present ; and therefore
that no amount of knowledge would enable us to calculate and
predict with certainty the acts of men, or events depending in part
upon the acts of men, as it would enable us to calculate and predict
events dependent purely upon physical causes. According to this
view there is a ' real contingency ' in human action.1 Such real
contingency would of course carry with it, that our judgements
about future contingents must be problematic in the logical sense ;
we cannot know for certain what in itself is undetermined. But
the problematic nature of our judgement in such a case does not
spring from our ignorance, since no increase of knowledge could
remove it ; it springs from the nature of the facts ; and the differ
ence in the nature of the facts between their real contingency in
the one case, and their necessary interconnexion in the other, is not
a difference of logical modality. Indeed, if we regard the human
will as a principle of new beginnings, or source of events whose deter
mining conditions cannot be found in events preceding them, we
might even say that a particular future human action is necessarily
contingent. It is to be observed, however, that this uncertainty in
the event itself can only belong, if at all, to future events. 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 judgement ( The Sultan may
now be beheading his vizier ', just as much as of f Rain may now
be falling '. All these alike are problematic only in virtue of my
1 There are other views of human freedom which make the future acts of
men as certain in themselves as any other.
178 AN INTRODUCTION TO LOGIC [CHAP.
uncertainty about the facts, and not of any uncertainty in the facts
themselves.
The upshot of this is, that in singular judgements the
problematic form 'X may be 7' expresses always our want of
grounds for making an assertion, but not necessarily any want
of certainty in the facts themselves. All events — the acts of man1
alone perhaps excepted — happen necessarily when they happen,
the conditions on which they depend being what they are; but
these conditions being largely unknown to us, we have not sufficient
ground for asserting the events ; hence our assertions assume a
problematic form, fX may be Y'l meaning, that while we know
nothing inconsistent with the assertion that X is J", we do not
know enough to justify us in saying that it must be so ; though if
it is so, it is so necessarily. Only in human action and what
depends on human action some would admit a real contingency ;
and would understand the formula ' X may be Y* to include in
such case an assertion of uncertainty in the events themselves.
Let us now take a problematic judgement which is not singular.
'Cancer may be incurable/ Here we mean that though cancer
either is incurable or not, we have not sufficient grounds for a
decision. The judgement is based on ignorance, and is logically
problematic. But the same formula sometimes has a somewhat
different meaning. ( Currants may be either black, white, or red ' : c a
man may die of joy'. We do not mean here that we are uncertain
whether currants are black, white, or red, though knowing they must
be one or other ; for on the contrary we know that they are all three,
in different cases. Nor do we mean that we are uncertain whether
or not joy can kill a man, but that sometimes it does so. If you
tell me that you have a currant bush in your garden, I can say it
may be black, white, or red ; as to that particular bush I am un
certain. But I make this disjunctive judgement about it because
of my knowledge that there are those three colours in currants.
Such a judgement therefore is not problematic in the logical
sense ; for as referred to the species, or general term, which is the
subject of it, it implies not my uncertainty, but my knowledge of
the alternatives. Here the facts may be called uncertain, in the
sense of being multiform or variable, but not in the sense (in
which a particular fact, if really contingent, is uncertain) of not
1 Or of any other being that has freedom in the same sense.
vm] VARIOUS FORMS OF THE JUDGEMENT 179
being the necessary outcome of pre-existent conditions. This
variability arises either through the diversity of species necessarily
included in a genus (as when we say that a conic section may be
either an ellipse, a parabola, or an hyperbola) or through the
multitude and complexity of the elements in the world that go
in constantly shifting combinations to the production of what we
regard as single things or events. Any two elements (the word
here must not be confined "to its technical chemical sense), taken
arbitrarily in isolation from everything else, would as we believe
interact with each other always in the same way. Science
endeavours to determine the interactions that would occur between
such isolated or ( abstract' elements, and so to enunciate its pro
positions universally. But in fact we cannot readily secure such
isolation. History, or the course of events, depends on all sorts
of elements as it were jostling in concrete, and so presents per
petually varying combinations or conjunctures. This gives rise,
as we previously saw, to the accidental or { coincidental ' : which is
also sometimes called the contingent l ; and in the sense that the
same conditions, in the kaleidoscopic movement of events, are
combined now with these and now with those others, there is
uncertainty in facts. We might know enough to say what precise
conjunction of physiological and other factors is necessary in order
that a man should die of joy; but the occurrence of this con
junction depends on historical conditions that are sometimes ful
filled and sometimes not. Hence we make a judgement which is
problematic in form, ' a man may die of joy ' : meaning that if
certain factors combine with his joy, a man will die. We have no
right to connect a predicate Y universally with a given subject X,
if its presence in X depends on the coincidence of other factors ;
and so long as in our judgement we do not specify all the con
ditions necessary in order that X should exhibit the predicate Y,
our judgement will assume the form ' X may be Y '. These con
ditions may or may not be known to us. ' Water may boil below
212° Fahrenheit': this depends on its being sufficiently heated,
and at an atmospheric pressure sufficiently low : both of them con
ditions not necessarily connected with the occurrence of water below
1 In this sense, the region of concrete facts, where such ever-shifting
combinations are found, is sometimes called ' contingent' matter, as opposed
to the 'necessary matter' e.g. of mathematics : cf. p. 175, supra,
N 2
180 AN INTRODUCTION TO LOGIC [CHAP.
212° Fahr. But the conditions here are known ; and we give our
judgement the problematic form, not on account of our uncertainty
of the grounds on which the content of the assertion depends for
its truth, but because we know that those grounds are not always
present. Here then the problematic form is due to an omission
of the conditioning details. The particular judgement is sometimes
particular for the same reason, because we omit some of the con
ditions, given which the predicate might be affirmed of the subject
universally. In other cases of course the particular judgement is
all we are able to enunciate, and we do not know under what con
ditions the predicate could be affirmed universally of the subject.
' Some triangles have the square on one side equal to the squares
on the other two ' — viz. when that side subtends a right angle ;
( some children are taller than either parent ', but here we cannot
give the condition on which it depends. The same difference is
observable in the case of these quasi-problematic judgements ; as
may be seen if the foregoing particulars be put into the form
CX may be Y*. 'A man may smile and smile and be a villain'
means much the same as if it were said that some men smile and
smile, and yet are villains ; but we do not know more than the fact
which shows this conjunction to be possible; we cannot state the
condition on which the conjunction of a smile with villainy depends.
In dealing with the quantity of judgements we saw that in the par
ticular judgement 'Some X is Y3 we may either be thinking of indi
viduals of the kind X, not separately enumerated, or of some general
determination of the kind X, not specified, which would involve its
being Y\ that in the former case, it is rather of the nature of the
singular judgement : in the latter, it is on its way to become
universal. Particular judgements of the latter kind have been
called ( modal particulars \ because of their close similarity to the
quasi-problematic judgements which we are now considering.
They can indeed be expressed in the form f X may be Y' as easily
as in the form ' Some X is Y'. There is only this difference
between the two expressions ; each implies that under certain con
ditions, not specified, though possibly known, X would be Y\ but
the latter implies that these conditions are sometimes actually
fulfilled, the former does not necessarily do so1.
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 181
Where a judgement problematic in form states the alternatives
within a genus, as if I say that a line may be straight or curved,
the architecture of a church classical or Norman or Gothic, it
is really, as referred to the genus, a necessary judgement if we see
that the alternatives are necessary, but assertoric if we merely accept
them as actual. As referred to any particular subject, like the
boundary between the United States and Canada, or the parish
church of Clayfield Porcorum, it is problematic ; because it implies
that I have grounds for offering these alternatives, but not for
going further and deciding as between them. Where, though the
judgement is not disjunctive, yet X is general, and the unspecified
conditions under which X is Y are known, the meaning of the form
'Xmay be Y' has really nothing problematic about it — i.e. it corre
sponds to no uncertainty in our thought with regard to the content
of the judgement. Where the conditions are unknown as well as
unspecified, it has the logical character of the problematic judgement
so far as it implies that we are uncertain under what conditions
X is Y, but is assertoric so far as it implies that we know that there
are such conditions, because X is sometimes Y. The singular judge
ment ' This X may be Y' ('This water may be unwholesome') is
problematic in the logical sense, because it means that we are
uncertain whether the conditions under which X is 7 are fulfilled
in the case before us.
A problematic judgement therefore does not imply by its form
that any particular event is in itself uncertain l ; though some hold
that there is a real uncertainty about events involving human will.
The matter of fact asserted in a problematic judgement whose
subject is a general term may be uncertain, in the sense that the
given subject does not carry with it the predicate, but will only
exhibit it under conditions that are not constantly and necessarily
combined with it. But a judgement is not logically problematic
unless it expresses our uncertainty with regard to the connexion of
a predicate with a given subject. All singular judgements of the
form ' X may be Y' are therefore logically problematic ; but
general judgements of that form are not really problematic, when
the form only serves to cover the omission of the known conditions
1 To say that an event is uncertain of course often means only that we
uncertain about it.
182 AN INTRODUCTION TO LOGIC [CHAP.
under which X is T universally, or to specify one of the alternative
forms under which X is known to occur.
[The distinction between singular and general problematic judge
ments finds a parallel also in the case of apodeictic judge
ments ; but as confusion is not so likely to arise there from want
of noting it, the discussion of apodeictic judgement was not
burdened by it. Any one remembering what was said in c. iv
on the difference between conceptual and historical necessity will
see that a singular apodeictic judgement is one in which an
historical event is recognized to be necessary on the ground of
previous historical events accepted as actual; these last may in
turn be shown to have been necessary, on the ground of other
events before them : but such a process of demonstration recedes
into the past ad infinitum, and so we never get more than hypo
thetical necessity. A general apodeictic judgement, on the other
hand, is a really universal judgement — a judgement asserting
a connexion of content or of universals, irrespective of occasion
or time.]
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 that my judge
ment refers to; the truth I assert may be that I am unable to
discover the truth about this reality. I may judge without looking
for the grounds of 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
reference to the grounds for what is asserted. On the other hand,
I may reflect on the relation which the content of a suggested
judgement bears to what I already know, or take, to be true;
and if I find it involved in such truths, my judgement is called
apodeictic, and expressed in the form'JTmust (or cannot) be Y'.
Judgements whose truth is seen to be grounded in the nature of
their own content are also affirmed apodeictically. Those apodeictic
judgements which are grounded in facts not forming part of what
they affirm themselves 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 the content of a suggested judgement involved in condi
tions about which I am ignorant or uncertain, I assert it to be
possible; such a judgement is called problematic, and expressed
vm] VARIOUS FORMS OF THE JUDGEMENT 183
in the form ' X may (or may not) be Y '. The problematic judge
ment does not imply that particular events are unnecessary in their
happening, though, when general, it does imply that an event of
a certain kind depends on a conjuncture, or contingency, which is
not universally necessary. It is possible that when reflecting on
the grounds for what we assert, we cannot find any except that we
perceive or remember it, 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 '.
This assertoric judgement, being not a bare unreflective assertion,
but expressing besides our mental attitude towards the content of
a judgement, is different from the assertoric judgement, above
called also pure, that contains no reflection upon the grounds for
what is asserted or for its assertion; 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
nected1; 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 form
the content of our really apodeictic judgements; and if their belief
could pass into clear vision, judgements at present problematic or
assertoric would be replaced by apodeictic.
[There are a few other adverbs (besides possibly, actually, and
necessarily) which may be introduced into a judgement in order to
express reference to the grounds for asserting it and an estimate
of the truth of its contents : e. g. probably, truly, falsely, really :
although all 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,
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.' Artie Logicae Rudimenta, c. ii. § 2. 1 (Hansel's
4th ed., p. 47).
184 AN INTRODUCTION TO LOGIC [CHAP.
[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 content of
the judgement in which they occur) 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 l ; they 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 judge
ments of any modality. No doubt differences of tense are a some
what 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
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 and Anal. Pri. a. ii. 1, but the word rponos
(= modus) is said to occur first in the Commentary of Ammonius ; v.
Ammonius in Ar. de Interp. 172r, (quoted in part Prantl, vol. i. p. 654) = Berlin
ed. p. 214 Tponos p.ev ovv (<TTI (pwvr) o-tjfMaivova-a arras virdpftfi TO KarrjyopoviJLevov
ro> vTroKei/ieVo), olov TO Taxecos, OTOV Aeyotyiev " f) (reXrjvr) ra^ecoy aTroKa&'oraTai ", 17
TO KaAoos ev TO) " SaJK/jan;? K.a\u>s SiaXeyeTai ", fj TO Trdvv ev TO) " Il\dTQ>v At'copa Trdvv
<piAei", T) TO del ev TOO "6 fjXios del Kii/firai". dpidp.bs 8e avT&v (pixrfi pev ov<
fo-Tiv aTreipoy, ov JJL^V 8e neptXijTrTos ye r)fJ.lv, &(nrep 6 TO>V K.a06\ov vTTOKeifjievav y
KaTifyopou/nez/coy, dvapiOp,rjTO)V de avrav OVTW. TfTTapas de /JLOVOVS 6 'ApicrTOTe\r)S
7rapa\afjL^dvei TTpbs Trjv 6ea>piav TO>V peTo. TpoiroiV TrpoTao'ecav, TOP avayKalov TOV
dvvaTov TOV ev8e^op.evov Kal errl TOVTOLS TOV ddvvciTov . . . : ' Mode is a word signify
ing 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 impossible. . . .' This state
ment 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 TpoTroy 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 milst attach to the 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 propositionis ;
and it is obviously wrong to suppose that any adverb will make the pro
position in which it occurs modal ; nor can differences of tense do so,
though they express a modification of the predicate.
vni] VARIOUS FORMS OF THE JUDGEMENT 185
[amounts to saying that 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, to which the
existence of a predicate is susceptible in a subject. 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.
t In all judgements/ says Kant 1, f 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
j5 belongs to the subject A, as somewhat which is contained
(though covertly) in the conception A\ or the predicate £ 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 (affirmative) are
therefore those in which the connexion of the predicate with the
subject is cogitated through identity 2 ; those in which this con
nexion is cogitated without identity, are called synthetical judge
ments. The former may be called explicative 3, the latter augmenta
tive 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,
1 Kritik of Pure Reason, E.T. (Meiklejohn), p. 7.
2 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.
3 Or ampliative.
186 AN INTRODUCTION TO LOGIC [CHAP.
although in a confused manner ; the latter add to our conception
of the subject a predicate which was riot 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.
1 All bodies are heavy ', on the other hand, is a synthetic judge
ment; 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. In
particular, it has been pointed out, and it is important to recog
nize, that no judgement is purely analytic; every judgement is
a synthesis of distinguishable elements. Let the predicate B of
an analytic judgement be contained in the conception of the
subject^ — extended for example in the conception of body. Suppose
the constituent elements of the conception A to be BCD, as those
of body are substance and extension. Yet the judgement ' A is B '
(all bodies are extended) is not equivalent to the judgement 'BCD
is B ' (all extended substances are extended). The latter does merely
repeat in the predicate what is contained in the subject-conception ;
and inasmuch as the subject-conception has already been exhibited
as a synthesis of elements, among which the predicate is one, the
judgement only goes over old ground. But the former judgement
performs a process of analysis, and does not pick out one element
from an analysis already made. Now this difference is important ;
because in performing an analysis of the subject-conception, we
realize at the same time that the predicate must be conjoined
with the other constituent elements in the subject, in order to
make the subject-conception. ' A is B ' means f to the constitution
of Aj B must go with CD ' : all bodies are extended means ' to the
constitution of body, extension must go with substantiality '. Kant
indeed tells us that until the analytic judgement is made, the
predicate B is only covertly contained in the conception A : so
that it is really the work of the judgement to recognize B (as an
element along with other elements) in the conception A. On the
other hand, the synthetic judgement is from one point of view
analytic. c Cats purr ' ; it is true that I learn this only by experi
ence, and that purring is not otherwise necessary to constitute the
vm] VARIOUS FORMS OF THE JUDGEMENT 187
conception of a cat: but to me, who have learnt long ago that
cats do purr, purring has become part of my conception of a cat,
and when I make this judgement, I am picking out one element
in my conception, in order to assert its connexion with the others.
Except therefore to some one who knows what cats are, but not
what noise they make, and knows what purring is extraneously,
the judgement that cats purr is not purely synthetic. And even
to him, in the act of making it, it becomes also analytic ; for no
sooner has he united the predicate ' purr ' with his conception of
a cat, than it becomes an element selected from among the other
elements of his more enlarged conception.
Every judgement then is at once analytic and synthetic; for
the act of judgement at once holds different elements apart and
recognizes them as elements in a single whole. As held apart,
it requires an act of synthesis to see that they make one whole :
as recognized to make one whole, it requires an act of analysis
to find and hold them apart.
In distinguishing analytic and synthetic judgements, then, Kant
has not distinguished judgements in which there is only an act of
analysis from those in which there is only an act of synthesis.
What he has really done is to distinguish those in which the pre
dicate is part of_the definition of the subject from those in which
it is not. For he really had in his mind only judgements whose
subject is general, or at any rate if his distinction can be applied to
singular judgements, it is only so far as a particular thing is
designated in the subject by a general term, or concept under
which it is brought. ' This body is extended ' would be analytic,
and ' This body is heavy ' synthetic, because the predicates are
respectively explicative and augmentative of the concept body.
Yet if we look to the particular experience which is the ground
of the judgement ' This body is heavy ', we shall have to acknow
ledge that it analyses what is given as a concrete whole ; so that
although the judgement is synthetic so far as concerns the relation
of the predicate to the subject-concept, it is analytic as concerns its
relation to the object of perception, the body in question. Such
judgements have in fact been called in consequence ' analytic judge
ments of sense ', though they are emphatically synthetic in the
Kantian sense, as being grounded on the conjunction of manifold
elements empirically in an object, and not on a relation between
188 AN INTRODUCTION TO LOGIC [CHAP.
subject and predicate which is necessary for thought, because
( cogitated through identity ' and so incapable of being denied
without self-contradiction.
Now Kant, in drawing the distinction, was interested precisely
in the question of the necessity belonging to certain judgements, in
virtue of which our thought recognizes them as true without appeal
to confirmation from repeated experience. His ' analytic ' judge
ments have this necessity because they are analytic ; the problem,
he says, is to see how any ' synthetic ' judgements can have it.
So far as these merely state the conjunction in things of attributes
which are distinguished and found together in them, they lack the
character of necessity, whether we call them synthetic or analytic l ;
but he held, and rightly, that there are some judgements in which
we do apprehend the necessity of the predication, without the
connexion being ' cogitated through identity '. Such are the
judgements ' 5 + 7 — 12 ', or ' Two straight lines cannot enclose
a space '.
A question next arises regarding those judgements in which the
predicate is already covertly contained in the subject-concept, and
which are therefore incapable of being denied without contradiction,
and so conceptually necessary; has this come to pass merely by
the fact that we have chosen to include certain elements in the
subject-concept, which we thereupon cannot consistently deny of
it ? We saw, in discussing Definition, that we have sometimes
to determine arbitrarily what elements are to be included in
our definition of a concept ; and if this were always the case with
definitions, it would appear that Kant's analytic judgements are
necessarily true merely because of the meaning which we have
given to the subject of them. On the other hand, if the elements
in the definition are not arbitrarily selected, but are seen to hang
together necessarily in the constitution of the thing defined, then
the analytic judgement which predicates of a concept a part of its
definition is justified by the same insight into the necessary con
nexion of distinguishable characters as justifies a synthetic judge
ment which is not empirical. Let us take an example of a subject
in whose definition the elements are arbitrarily 2 put together. In
1 Synthetic of elements, or analytic of a whole.
2 Arbitrarily, not because there is no motive, but because there is no
necessity.
vm] VARIOUS FORMS OP THE JUDGEMENT 189
the Elementary Education Act of 1870, § 3, an elementary school
is by definition ' a school, or department of a school, at which
elementary 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 10cL 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 lOd. or over should rank as an
elementary school, and not because we have such a knowledge of
what an elementary school must be as to see that it could not be
elementary, and charge a fee so high. Whereas if I say that
a figure has sides, that is true not because it is agreed to call
nothing a figure which has not, but because I see that lines can be
put together into the unity of, and are required in, a figure.
It follows that some judgements ranked by Kant as analytic
may involve just the same insight into the necessary connexion
of elements in an unity as is found in the class of synthetic judge
ments which most interested him — viz. those that are grounded not
upon repeated experience but upon the apprehension of necessity ;
while others are true only in virtue of the meaning we have chosen
to give to words; neitEer Is any judgement purely analytic or
purely^synthetic. His distinction therefore is not well expressed
by these terms. If, however, we take the terms explicative and
augmentative (or ampliative), we may say that all his ( analytic '
judgements are explicative of what is already involved in thinking
the subject, but we may question whether all his ' synthetic *
judgements are ampliative, unless singular judgements, which
analyse a present experience, are excluded ; nor does the term
' explicative ' apply any otherwise to those judgements where the
elements in the subject are arbitrarily put together than to those
where they constitute a real unity for our thought. Now the
former are, as we have seen, true by convention as to the meaning
of words, and so they may be called verbal ; and to verbal judge
ments we may oppose as real all whose truth does not rest upon
the meaning given to words, but which state something about the
nature of things : whether what they state is seen to be necessary
— in which case they may be either analytic or synthetic in the
190 AN INTRODUCTION TO LOGIC [CHAP.
Kantian sense — or rests upon mere experience of fact — in which
case Kant would call them synthetic. This does not commit us
to the view that all definition is verbal, but only that if a so-called
definition does no more than arbitrarily to include certain elements
in a concept, like the definition of 'elementary school ' quoted
above, then it is verbal. On the other hand, if we wish to mark
the distinction between judgements in which the predicate is part
of the definition of the subject, and those in which it is not, we
may call the former essential and the latter accidental. The
term ' essential ' may be extended to cover those cases where the
definition is arbitrary *, and some essential judgements will then
rest merely on the law that forbids self-contradiction ; while others
will involve the same apprehension of the necessary connexion of
elements in an unity as Kant's necessary ( synthetic ' judgements ;
some, that is, will be verbal and others real. The term ' accidental ',
if ' accident' be taken, as by Aristotle in the phrase KaO* avrb
(rvfj,p€(3r]K6$j to include what is demonstrable of a kind, will cover
all Kant's ' synthetic ' judgements, whether they are grounded on
an experience which, so far as we can see, might have been other
wise, or on insight into a necessary relation of concepts 2. It will
be seen that the three antitheses, of analytic and synthetic, essen
tial and accidental, verbal and real, cannot really be regarded as
equivalent ; for neither are they made on the same fundamentum
divisionisj nor do they respectively bring together and keep apart
the same individual judgements.
Two comparatively unimportant classes of judgements may be
mentioned before closing this chapter — exceptive and exclusive
judgements. An exceptive judgement is one which excepts from
its application a certain part of the extension of the subject 3 : as in
dough's satirical version of the second commandment — 'No graven
images may be Worshipped, except the currency/ An exclusive
1 Arbitrary because -what we are defining is something of our own institu
tion, or because our so-called definition is a compromise of the nature
explained pp. 85-88, supra. In the strict sense of definition, none is arbitrary :
things are what they are.
2 i. e. in Kantian language, whether they are synthetic a posteriori or
a priori.
3 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.
vm] VARIOUS FORMS OF THE JUDGEMENT 191
judgement 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/ It is clear that within a given whole, it
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 judgement under the head of Exponibilia, i. e. pro
positions whose full meaning could only be expounded in more
judgements than one. Thus 'None but the brave deserve the
fair * implies two statements, that the brave deserve the fair, and
that those who are not brave do not. The infinite judgement 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.
CHAPTER IX
OF THE DISTRIBUTION OF TERMS
IN THE JUDGEMENT: AND OF THE OPPOSITION
OF JUDGEMENTS
WE saw in the last chapter that all judgements, in respect oi
their quality, were either affirmative or negative ; and in respect oi
quantity, might be treated as either universal or particular. The
latter division indeed strictly applies to those judgements only whos(|
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. The purposes in question
are the determining the distribution of terms, together with whai
depends on that. A term is said to be distributed, when it is usecj
in reference to its whole extension, or to all that it can denote.
Now the subject of a singular judgement denotes one individual
only, and the judgement refers to that ; the subject of an universa
judgement is general, and may denote any number of individuals
but since the judgement is universal, it applies to them all|
Therefore in both singular and universal judgements, all that th«
subject can denote is referred to, or, in other words, the subject i,|
distributed ; and, in considering the distribution of terms in a judge]
ment, we may accordingly rank the singular with the universal.
As every judgement must have both quantity and quality, an<|
in each respect there are two alternatives open, there are fou
varieties of judgement in respect of these two characters combined
An affirmative judgement may be universal or particular : a negativ
judgement may be universal or particular. It is customary ill
1 We have already seen, in discussing the extension, or denotation, ol
terms, that confusion may arise between the relation of a generic concept tf
the more specific concepts included under it and the relation of the universal
to the individual. But in considering the distribution of terms, it is nol
always necessary to bear in mind this distinction. I may therefore sal
indifferently that a term is i.sed with reference to its whole extension, or
all that it can denote, even if we reserve the latter expression (denote
tion) to signify the individuals of which a term can be predicated.
DISTRIBUTION OF TERMS, ETC. 193
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 „ „ „ „ „ „ /;
a particular negative „ „ „ „ „ „ 0.
Thus the affirmative judgements are A (universal) and / (particular) :
the negative judgements are E (universal) and 0 (particular) ; and
his may be remembered by noting that A and /, which indicate
;he universal and particular affirmative judgements, are the first
wo vowels in the verb f #ff/rmo ' : E and 0, which indicate the
miversal and particular negatiye judgements, the vowels in the
'erb ' nego '.
All universal judgements (A and E) distribute their subject: all
negative judgements (E and 0) distribute their predicate. No
>articular judgements (/ and 0) distribute their subject: no
ffirmative judgements (A and /) distribute their predicate. Thus : —
in Ay the subject is distributed, the predicate undistributed ;
in E, „ „ „ distributed, „ „ distributed ;
in /, „ „ „ undistributed, „ „ undistributed;
in 0, „ „ „ undistributed, „ „ distributed.
t is important to understand and become familiar with these
baracteristics of a judgement.
A term, as was explained just now, is said to be distributed wlien
t is used with reference to all that it can denote l. The term ' book '
s distributed, when used in a proposition that refers to all books :
ndistributed, when used in a proposition that does not refer to all
ooks. It is obvious that an universal proposition about books
whether affirmative or negative) refers to all ; and that a particular
roposition does not: all books are written lef ore being printed : no
was printed before 14502: some books are published unsewn:
me books are never published. That the subject of universal pro-
ositions is distributed, and of particular propositions undistributed,
i.e. denote univocally : an equivocal term is to be regarded as a different
rm in each sense.
* The proposition must be taken to refer to European books and movable
pe : the first dated examples being of 1454.
194 AN INTRODUCTION TO LOGIC [CHAP.
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 booh; 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 Ley den),
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 c these books ') a collection of singulars ;
and the proposition should rank with universals. But 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 l 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 objects,
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 particular
thought of individuals. In saying that a triangle has its angles
equal to two right angles, I am not referring to all the particular
triangles that have ever existed or may exist ; I am thinking of their
common character as triangles, which being one and the same in
them all may be spoken of in the singular number.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 to the individuals which the term triangle
1 I do not deny that a particular 'representative' triangle innst be
conceived in making the judgement.
ix] DISTRIBUTION OF TERMS, ETC. 195
can denote I am not referring. 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 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 not distributed or undistributed because it
refers to all or only some preachers ; for a term is only 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 predicated. Now the extension of the terms ' praiser
of virtue* and l practise r of virtue3 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 are therefore included
in the extension of the predicate ; but what is thus included is not
predicated of preachers. In the judgement X is 7, I predicate Jot*
X, but I might predicate it also of Z\ X and ^are both included
in the extension of Y, or in what J~can denote ; but when I affirm
Yj I do not affirm it in its whole extension; for then in saying
( X is ¥ ', I should mean that it is X and Z, and in saying ' Z is J'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
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
reference to a part only of its extension, and when it is used
o 2
196 AN INTRODUCTION TO LOGIC [CHAP.
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 statement 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 it is manifested.
It is impossible to predicate 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, and ellipse ; 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 only 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 forms 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.
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.
ix] DISTRIBUTION OF TERMS, ETC. 197
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 judge
ments 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 I can affirm, 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, and ellipse, I can say that a cycloid is
neither an hyperbola nor a parabola nor an ellipse.
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 judgement 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 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 vertebrates
are not mammals, some part of the vertebrate-
area will lie outside the whole mammal-area ;
whereas if some vertebrates are mammals, some
part of the vertebrate-area will coincide either with the whole
or with a part only of the mammal-area; and if all mammals are
vertebrates, the mammal-area will fall completely within the
vertebrate-area. But all the objections which lie against repre
senting 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
198 AN INTRODUCTION TO LOGIC [CHAP.
[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.]
[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} /, 0, we get eight, as
follows : —
V. All X is all 7. All organisms are all mortals.
A. All X is some 7. All men are some mortals.
Y. Some Xis 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.
77. No X is some Y. No men are some mammals [ e.g. not
monkeys].
0. Some X is no 7. Some vertebrates are not any mammals.
(i). Some A^ is not some 7. Some mammals are not some verte
brates [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 mean
the same thing, anjd 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 none of these eight forms of proposition expresses anything
that we ever really mean when we make a judgement (though
some 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 7' ;
ix] DISTRIBUTION OF TERMS, ETC. 199
[we are told to state it 'All X is some Y'. All men are gome
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 objects (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 any other kind dies ; and though we may be aware
of it when we say that men die, it is no part of the judgement
men die. There is much that we are aware of when we judge that
men die, besides the content of that judgement — that the sun is
shining, for example, or our feet aching; yet nobody would sup
pose this to be included in that judgement, merely because we are
aware of it in making the judgement. There is no more reason
to suppose the fact that other creatures besides men die to be
included in the judgement all men are mortal, because we are aware
of it in making the judgement. All men are some mortals is not
one judgement, 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 f 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 commensurate,
but which are not definitions, such as all equilateral triangles are
equiangular. These also we are told to represent in the form ' 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
200 AN INTRODUCTION TO LOGIC [CHAP.
[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 the 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 indivi
duals are different, or tautologous, if they are the same.
e All 3 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 c All living things reproduce their kind ' is true, then it is true
of any living thing and therefore of peas. I may introduce 'per
fectly ' into the predicate, and then it will be true that peas reproduce
their kind perfectly. But I cannot introduce f all' into the predicate.
For then, since all living things are all things that reproduce
their kind, peas would 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 collec
tively. 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. Uni
versal judgements whose terms are commensurate do differ from those
whose terms are not, and do form a very important class of judge
ments ; and there is no special recognition of them in the ordinary
fourfold classification of judgements (A, E, 7, 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 the
De Interp. vil. 17" 12 eV! fie rov KaT^yopov/jLevov Ka66\ov KUTyyopei
KaOo\ov OVK fcrrtv aXydes' ov8ep.ia yap Kardf^ao'is d\rj6rjs ecrrm, fv ij TOV Kar
povptvov KaddXov TO KadoXov KdTrjyopfiTai, olov eort nas avOpviros Ttav (q>ov.
(a^pwros-, 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
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
ix] DISTRIBUTION OF TERMS, ETC. 201
[intention of terms. Professing to complete what is defective in the
current recognition of different kinds of proposition, it leaves
important differences itself unrecognized. We have seen that a
proposition of the form ' All X is Y' represents two kinds of judge
ment essentially different in thought, according as it is really
universal, meaning * X as such is Y', or only enumerative, meaning
1 All the X's are Y'. Of this difference, whether in universal
judgements whose terms are commensurate (U) or not (A), this
doctrine takes no note ; but sets up instead two kinds which misrepre
sent 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 Y3 or f 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 A' that are Y are the Y that are X. Some sower*
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, then as before we have
two judgements packed into one sentence. What is one judgement,
and what is the character of a judgement, are questions to be deter
mined 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.
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'(rj). The
former may stand ; for as we have seen, if X is not J, it is not any
affirmation is true when universality [in extension] is assigned to the
predicated universal, e.g. All men are all animals.' Of. Ammonius in loc.
f. 82, who points out that then each man would be all animals.) Anal. Pri.
a. Xxvii. 43b 17 avrb fie TO enop-evov ou X^TTTCOV oAoy fn€(rdat) Xtyco 6' olov di>$pa)7ra>
Traf £a>oi/ fy fj.ov(TiKri Ttdcrav eVwr^i^f, dXXa fjiovov OTrXa)? aKO\ou8flv, Kaddrrep /cat
TTpOTfLvd/jLcda' KOL yap (ixprjVTOv Odrepov KCU ddvvarov, olov ndvra iivtiptoirnv emu
irav t«oi/, r) dinaioa-vvrjv array 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.1)
202 AN INTRODUCTION TO LOGIC [CHAP.
[case or kind of Y. The latter may well puzzle us. It denies of X
some part of the extension of 7; 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 Fare 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 Y'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 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 ' Some X is all 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 0 ; and these are so inter
preted as to lay undue stress on the aspect of extension in the predi
cate. The truth is that if we prefix to the predicate of a proposition
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 really do. We cannot predicate of
the extension of one term the extension of another. If a set of
individuals, or of species, forms the subject of a judgement, another
set cannot form the predicate. ' All X is some Y' is meaningless.
' Some 7,' we are told, means f 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 Xis the former part ; it is false to say that it is the
latter.
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 £» 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 Xis all F'— meaning that no Xis 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 Xare all F'
and 'Some X are all F'. But they have the advantage over those of
being true. Cf. p. 204, n. 1.
ix] DISTRIBUTION OF TERMS, ETC. 203
[Still, it is urged, the judgement compares the extension of two
classes. ' All X is all 7' means that the class X and the class 7 are
co-extensive ; ' All X is some Y' means that the class X is included
in the class Y, 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 no
comparison between two 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 7's were collected in one place,
all X's would be found in the crowd ; then, when we said that all X
is some 7, we should mean that all X were included in the crowd of
Y's. But now our predicate is no longer 7, and has become ' included
in the crowd of 7'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 7's be meant. Clearly part ; so that our judgement
will run ' All X are some things included in the class 7 (or crowd of
7'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
ftome 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
Y'. 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 Y'. So the
process goes on ad infuitum. You cannot predicate of one class the
whole or part of another. You may compare the extension 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
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 judgement
compares the extension of two terms, or includes a subject in or ex
cludes 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 relation of
terms in a judgement by the relative position of circles on paper,
204 AN INTRODUCTION TO LOGIC [CHAP.
[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 extension,
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.1]
1 Archbishop Thomson (Laws of Thought, pp. 187-189), though not contest
ing the doctrine of the quantification of the predicate, excludes the forms
of proposition rj and o> (' No X is some Y,' * Some X is not some Y') on the
ground that though conceivable they are not actual cases of negative
predication. ' It is not inconceivable that a man should say " No birds are
some animals" (the 77 of the Table), and yet such a judgement is never
actually made, because it has the semblance only, and not the power,
of a denial. True though it is, it does not prevent our making another
judgement of the affirmative kind, from the same terms ; and "All birds are
animals " is also true. Though such a negative judgement is conceivable,
it is useless ; and feeling this, men in their daily conversation, as well as
logicians in their treatises, have proscribed it. — But the fruitlessness of
a negative judgement where both terms are particular is even more manifest;
for " Some X is not some Y" is true, whatever terms X and Y stand for, and
therefore the judgement, as presupposed in every case, is not worth the
trouble of forming in any particular one. Thus if I define the composition
of common salt by saying " Common salt is chloride of sodium ", I cannot
prevent another saying that "Some common salt is not some chloride of
sodium ", because he may mean that the common salt in this salt-cellar
is not the chloride of sodium in that. A judgement of this sort is spurious
upon two grounds ; it denies nothing, because it does not prevent any of the
modes of affirmation ; it decides nothing, inasmuch as its truth is presup
posed with reference to any pair of conceptions whatever. In a list of
conceivable modes of predication, these two are entitled to a place.' In this
passage, the ridiculous nature of r; and <•> is excellently shown ; and the
observation that they have the semblance only and not the power of
a denial is very just. But how then can they be negative judgements?
A negative judgement is an act of thought that denies, not a sentence that
looks negative on paper. It may be noticed that not only can we say ' Some
salt is not some chloride of sodium ', but with equal truth ' Some salt is not
some salt '. Now that means ' One piece of salt is not another ' : a perfectly
' conceivable mode of predication ' — only, there is no quantification of the
predicate in it. It is true that there is a difference for thought between
distinguishing individuals from one another, and denying an attribute of a
subject : a difference which escapes in the common symbolic form ' X is not
Y\ The difference arises through the content; for we cannot think and
judge about the relations between individuals as we think and judge
about the relations between universals, or of attributes to a subject. Hence
it is by something of a fiction that we include all possible judgements
under four forms A, E, I, and O: the fiction being that singulars may
be treated as universal. It is well to bear in mind that the form of judge
ment is really different (although the difference comes through the matter,
as was just now stated ; for form and matter, we may repeat, are not rigidly
ix] DISTRIBUTION OF TERMS, ETC. 205
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
another. The four forms of proposition A, E, I, 0 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 pro
positions.1
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—0, 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 — 7, 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
Mussulmans do not fear death.
Contrary and contradictory are terms in common use, though
sometimes treated as equivalent ; the origin of the terms subaltern
separated, like a mould and the jelly in it, so as that the form is the same
whether the terms are singular or universal) ; yet for certain purposes in the
theory of syllogism we need not attend to the difference. But the real variety
in the form of our judgements is not recognized by quantifying the predicate :
a process which, instead of bringing out the true features of thought, dis
torts and falsifies even the commonest judgements.
1 Contraries are what stand furthest apart upon a scale of some kind— TO
[j.aXio'Ta. ftif&mKOTn fv TO) aurw ytvd '. 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
noi-A (blue and not-blue, &c.) being called contradictory terms. But we
have seen that mere not- A is no term at all : there must be some positive
content. (See however Bradley, 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.')
206 AN INTRODUCTION TO LOGIC [CHAP.
and sub-contrary may be seen in the above-given, and ancient, ' dia
gram of opposition', /is placed under A, and 0 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 7,
E and 0 are called subaltern, because in each pair one is subordi
nated to the other : 7 and 0 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
proposition, affirmative or negative, it is only necessary to establish
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
contrary 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 0 and 7 respectively; and Logic confines the title of contra
dictory opposition 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
given as 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, 7, or 0 is given as true, 0, I, 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
ix] DISTRIBUTION OF TERMS, ETC. 207
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 0 is true, and given the falsity of / or 0,
A or E is false ; but given the falsity of A or E, I or 0 remains
doubtful, and given the truth of /or 0, A or 7? 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 /, 0 is true, and
vice versa; but given the truth of 7, 0 remains doubtful, and
vice versa.
Of two contrary or of two contradictory propositions one may
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. l 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, f 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
proposition ' 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 *, 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
1 Aristotle notices this in Anal. Pri. £. xv. 63b 27 TO -yap nv\ TO> ou nvl
KOTO rrjv Xe'£tj/ mriKeirai povov (' For some are is only verbally opposed to some
are not ').
208 AN INTRODUCTION TO LOGIC
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 remain
ing- three, the process of inference (if inference it is to be called)
is immediate.
CHAPTER X
OF IMMEDIATE INFERENCES
INFERENCE is a process of thought which, starting with one or
more judgements l, ends in another judgement made necessary by
the former. The latter, 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 judgements, 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, etymo-
logically 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 con
clusion.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
of immediate inference, of which the principal are Conversion,
Permutation (or Obversion) and Contraposition.
1 Or, more generally, elements, if we allow (with Bradley, Logic, pp. 370-
373) that, e.g., 2 + 2 = 4 is inference. But the above is not intended as a
final definition of inference.
2 For the function of the middle term in syllogism, cf. infra, c. xi.
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 propo
sition. It is doubtful, however, whether, so far as there is any inference in
it at all, it is really always immediate, either in this or in the etymological
sense. Cf. the discussion pp. 217 sq.
210 AN INTRODUCTION TO LOGIC [CHAP.
A proposition is converted, when its subject is made the
predicate, and vice versa, its quality (affirmative or negative) re
maining unchanged : as, for example, when from ' No true Mussul
man eats pork' we pass to 'No one who eats pork is a true
Mussulman'. The original proposition is called the convertend,
and the new proposition its converse.
Whether, and in what way, a proposition can be converted,
depends on its form, A, E, /, or 0 l : because the process of conversion
is invalid, unless it conforms to the following rule, that no term
may lie distributed in the converse, which was not distributed in the
convertend? An A proposition is converted ~by limitation : an E or
an / proposition simply : and an 0 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 Y, becomes J2, no T 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 Y is X, becomes J, some X is Y : e. g. ' some dia
monds are black ' — { some black stones are diamonds ' ; ( some ever-
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.' Of. pp. 213, 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 substan
tival 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 sub
stantival 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 L
x] OF IMMEDIATE INFERENCES 211
green shrubs flower brilliantly' — 'some brilliant flowering shrubs
are evergreen'; '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 E ; 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 distri
buted, 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 'conversion by limitation'. So A, all X is Y, becomes 7,
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 '.*
In the last example, any one who knows geometry will be
tempted to convert simpliciterj 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 Ay Ej I, or 0 ; in this respect ' all isosceles triangles have
equal angles at the base' is indistinguishable from 'all isosceles
triangles haye 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 there
fore does it follow logically from the former, that all triangles having
equal angles at the base are isosceles. The form of proposition
1 all X is 7 ' 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 pre-
dicable of the other, because the relation of a predicate to its subject
1 With this paragraph, cf. supra, pp. 199, 200.
P 2
212 AN INTRODUCTION TO LOGIC [CHAP.
may be either accidental or essential. It must at the least be acci
dental, and therefore from its bare form, we are entitled to convert
an A proposition as if T were an accident of X; but we are not
entitled to do more. For this reason, conversion by limitation is
called conversion per accidens (fcara a-u/z/Se/fy/cos) ; if Y is an acci
dent of X, i. e. coincides 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 X1
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 0 pro
position is not convertible, except by negation : a process which will
be explained later (p. 215). This is not always realized, when we use
symbols, and forbid the passage from ' some X is not Y ' to f some Y
is not X3 ; 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 f 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 3 and f some men are not monks }) are
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. 'jail 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 this sense, that the conditions necessary to the genera
tion of an animal must coincide with the special conditions necessary for
the generation of a man, if the animal is to be a man. The expression
coincide is not strictly suitable (nor therefore can the relation of man to
animal be strictly called accidental), because it is only in thought that the
conditions necessary to the generation of an animal can be separated from
the special conditions necessary to the generation of some particular
species : 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.
2 Though certain persons on the Continent seem to believe otherwise.
x] OF IMMEDIATE INFERENCES 213
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
sideration of the distribution of the terms in the convertend, with
out considering1 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 judge
ment 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 whose terms are singular is called an A
proposition, but it cannot be converted per accident : f 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 vwithout meaning ; ' Chatham was eloquent ' becomes ' an elo
quent 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.
Again, ' Demosthenes and Cicero were the greatest orators of anti
quity ' 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, f some Christians are men ' an improper
214 AN INTRODUCTION TO LOGIC [CHAP.
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
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 3 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 exten
sion, 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 7. 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 textbook 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-
sion1, there is no transposition of terms, but the quality of the pro-
\ Jeyons, 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 '.
x] OF IMMEDIATE INFERENCES 215
position is changed, and the predicate at the same time replaced by
its contradictory. It consists in fact of substituting for an affirma
tive or negative proposition an equivalent negative or affirmative of
opposite quality, by means of negating the predicate.
Thus—
A, All X is 7, becomes E, No X is not- T : All right angles are
equal, No right angles are unequal; Barkis is willing
Barkis is not unwillin'.
E, No Xis 7, becomes Ay All X is not- 7: No dogs allowed, All
dogs forbidden ; Lear is not mad, Lear is not-mad.
/, Some X is 7, becomes 0, Some X is not not-7: Some stretches
of the road are level, Some stretches of the road have no
gradient.
0, Some X is not 7, becomes /, Some X is not-7: Some learned
theories are not sense, Some learned theories are nonsense ;
Some swans are not white, Some swans are not 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 converted again, and this
process of permuting, converting, and permuting is called Contra
position.
All forms of proposition except / can be converted by negation ;
the process is inapplicable to 7, because it becomes 0 by permu
tation, and a particular negative, as we have seen, cannot be
converted. For the same reason / cannot be contraposed.
In conversion by negation —
A becomes E: MIX is 7 /. No X is not- 7 .-. No not- 7 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 7 .-. All X is not- 7 .-. Some not-7 is X.
No stimulant nourishes .*. All stimulants are innutritious.
/. Some things innutritious are stimulants.
0 becomes 1 : Some X is not 7 .*. Some X is not-7 .•. Some
not-7 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-
216 AN INTRODUCTION TO LOGIC [CHAP.
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.
In contraposition l —
A becomes A : All X is 7 .-. No not- Y is X .-. All not- Y is
not- JT. All Arabs are hospitable .*. All who are not-hos
pitable are not- Arabs.
E becomes 0 : No X is Y .*. Some not- 7 is X /. Some not- 7 is
not not-.!7. No unfriendly man is happy .*. Some who are
not happy are not friendly.
0 becomes 0 : 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 0 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-Z; 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
1 Contraposition has not always been distinguished from conversion by
negation : e. g. Wallis, II. 7.
x] OF IMMEDIATE INFERENCES 217
the process of thought involved in contraposition is a common one,
(although the mode of expression may be awkward) if we look at
it from the point of view of hypothetical judgement. Given that
all lovers are jealous, it is possible to infer that all the not- 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-Z is not-X/ We
may interpret in a corresponding way the contraposition 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 Y3 it may
or may not be X' : and that is the force of ' Some not- 7 is not-X',
regarded as a modal particular. Similarly with 0 ; ' 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. Mill1 is
not alone in so regarding them all. In his view we have been
dealing merely with equivalent prepositional 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
We must at the outset bear two things in mind : firstly, that
in all inference there must be some movement of thought ; we must
conclude with something not quite the same as what we started
with; though the obviousness of the inference is no ground for
1 Logic, II. i. 2. 2 Cf. Bradley's Logic, Bk. III. Ft. I. c. ii. §§ 30-37.
218 AN INTRODUCTION TO LOGIC [CHAP.
[denying- that it is inference. Secondly, that the same form of
proposition, A, E, I, or 0, may be diversely intended, and express
different judgements, as we have already seen. /, for example,
the particular affirmative, may be intended to assert the compati
bility of attributes, or to make a statement about unnamed indi
viduals. If I say that some cities are episcopal sees, I may either
have in mind particular cities not named, say Durham, Winchester,
and York, and make my assertion about them ; or I may wish to
affirm generally that the status of a city and an episcopal see are
compatible. In the former case, Durham, Winchester, and York
are thought of for their own sake; in the latter, as instances
establishing the judgement. We may say that a proposition,
taken as making an assertion about individuals, whether these
are specified by name, or indicated as some or all of a specified
kind, is intended historically; when it is taken as asserting a
relation, whether of compatibility or of necessary connexion (or
separability or necessary disconnexion) between universals, that it is
intended scientifically. We shall find that the presence of inference,
in some of the processes which we have to examine, depends on
there being a transition from one to the other of these modes of
understanding the proposition.
In the conversion of A to /, if convertend and converse are both
understood historically, or both scientifically, there is no inference.
All ruminants part the hoof .'. some animals that part the hoof
ruminate. If by the former statement I mean that various species,
which I could enumerate if I had leisure, but prefer to designate as
all ruminants (i. e. all the ruminants), part the hoof, then I must
know in making it that those cloven-footed species ruminate.
The subjects of my thought are cows, stags, and camels, and so
forth ; 1 affirm that they part the hoof ; but I have recognized
that they are all the ruminants, and can be so designated. In
the converse, I am still thinking of the same animals ; I designate
them as cloven -footed, which I previously affirmed them to be;
and I affirm that they ruminate, which I had previously recognized.
It is true that my former proposition spoke of ' all ', and the latter
of ( some ' • and it might be urged that there is inference in
seeing that I am not entitled to say that all cloven-footed animals
ruminate. But surely I recognize this from the outset; when
I say that all ruminants part the hoof, I know that is not equiva
lent to saying that all cloven-footed animals ruminate ; it can
hardly be called inference to refrain from asserting what I know
I have no right to assert * ; and it is to be observed that when
I assert that some cloven-footed animals ruminate, I do not
positively assert that some do not ; I merely restrict myself within
the limits of what I have a right to assert.
1 Cf. Bradley, loc. cit.
x] OF IMMEDIATE INFERENCES 219
[Again, scientifically, the convertend asserts that whatever rumi
nates parts the hoof ; and the converse, that what parts the hoof
may ruminate. And I cannot know one property to be necessarily
connected with another, without knowing them to be compatible,
or capable of coexisting in the same individual. There is therefore
no movement of thought, no transition to anything new, in passing
from the former proposition to the latter. If, again, the inference
be said to lie in the limitation, in seeing that the right to infer
a cloven foot from rumination does not involve the right to infer
rumination from a cloven foot, the answer is as before ; this should
be known from the outset, and there is no inference in not inferring
what you have no right to infer.
But now, suppose the proposition ' All Xis Y9 to be understood
historically, and the converse ( Some Y is X' scientifically; then
there is inference. If in fact all the ruminants do part the hoof,
then generally rumination is compatible with a cloven foot. Set
out in full, the argument would be that cows, and stags, and
camels, and so forth, which ruminate, part the hoof, and therefore
an animal that parts the hoof may ruminate. But the inference
is no longer immediate. It is really in the third figure of syl
logism.1
Similarly if the convertend is understood scientifically and the
converse historically : because whatever ruminates parts the hoof,
therefore any given animals which ruminate will do so, and they
will be animals which exhibit both characters, so that some cloven-
footed animals ruminate. This also is inference, but not imme
diate ; for we are applying a general principle to particulars which
fall under it, as in the first figure of syllogism.
The simple conversion of / is to be similarly regarded. If ' Some
X is Y 3 be intended historically to assert that some things, which
are X, are 7, then it means also that some things, which are J, are
X: to realize one statement is to realize both, and there is no
inference in passing from one to the other. If it be intended
scientifically, to mean that Yis compatible with X, then it already
means also that X is compatible with Y. But if it be intended
historically, to mean that some things, which could be named, and
are X, are also Y, and the converse be intended scientifically, to
assert in general that X is compatible with Y, then there is infer
ence, but it is not immediate. We infer generally that Y may be
X, because certain individuals are in fact both X and Y • it is not
from one relation between X and Y that we infer another, but
from the relation of both as predicates to the same third term
(those individuals) as subjects, we infer the compatibility between
X and Y themselves. If, however, the convertend be intended
scientifically, to assert the compatibility of Y with X, then the
1 Cf. infra, pp. 234, 257.
220 AN INTRODUCTION TO LOGIC [CHAP.
[converse as an historical statement does not follow. There is
nothing to prevent the Secretary of State for War being President
of the Board of Trade; the latter office is compatible with the
former; but it cannot be inferred that some Presidents of the
Board of Trade have been Secretaries for War.
With the simple conversion of Et the case seems to be different.
Here, if both convertend and converse be taken scientifically, there
seems to be inference. 'No X is T .'. No Y is X', understood
scientifically, means, 'If anything is X, it is not Y .'. If anything
is Yj it is not X' This inference is of the same kind as what we
found in the contraposition of A, and shall meet with again in
hypothetical reasoning. Again, if both be taken historically, there
seems to be the same form of inference. ( No mountain in England
is 5,000' high /. No mountain 5,000' high is in England ' ; I am
not here, as in the conversion of A, considering the same individuals
as my subject (though starting from a different character in them)
in convertend and converse. I realize that if a given mountain
5,000' high (say the Rigi, whose height I might know but not
its situation) were in England, that would contradict the proposi
tion that no mountain in England is 5,000' high ; therefore the
Rigi cannot be in England ; and this seems to involve hypothetical
reasoning. But if the convertend be intended historically, we
cannot infer the converse in its scientific intention. Because as
a matter of fact ' No X is Y', it does not follow, so far as we can
see, that what is Y is necessarily not X. If no Sikh smokes, but
this is a mere fact about every Sikh, it does not follow that no
smoker could ever be a Sikh. On the other hand, let the con
vertend be understood scientifically, and the converse historically,
and there will be inference, for the converse in its historical
intention is only reached by first inferring the converse in its
scientific intention, and applying the universal principle so obtained
to all the actual cases of Y; again, however, the convertend, as
understood scientifically, fails to assert the existence of any actual
cases.
The process of Permutation involves the use of the infinite or
negative term not- Y in the predicate in lieu of Y. 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 disjunctive judgement ' A is either B or
C ' does not always imply than it cannot be both. But Permuta
tion rests upon disjunction ; Y and not-Y are alternatives, and
it is assumed that if Y is affirmed or denied of any subject, not- 7
can be denied or affirmed accordingly. Bearing in mind these
l Otherwise, the term is F, and the form not- Y only shows that Fis being
denied of something in a judgement.
x] OF IMMEDIATE INFERENCES 221
[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
propositions. If we are told that X is not Y, and Y and not- Tare
alternatives, one of which must attach to it, then since it does not
exhibit 7, it must exhibit the other, not- 7. 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 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 C, but Y and not- 7. Is there any inference in saying that
because X is not 7, it is not- 7 ?
It will be allowed that the conclusion would not hold unless X
were either 7 or not- 7. But it may be said that this, the f principle
of Excluded Middle', though true, is not a premiss of inference.
No one knows what he means in saying that X is not Y3 unless he
sees that in that case it is not- 7: any more than he can know
what he means in saying that X is 7, unless he sees that in that
case it is not not- 7. 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- 7 were purely negative, this view of the
matter would demand assent. • But 7 and not- 7 are in practice
always alternatives within some definite limits. 7 may be blue, and
then not- 7 will be of some colour not bhie : or 7 may be English-
speaking, and not- 7 speaking some language not English. And in
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- 7, then indeed there is no inference, but only equipollency.
' Steam is not visible .*. it is invisible ' seems a mere substitution 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
222 AN INTRODUCTION TO LOGIC [CHAP.
Sbhe content l ; and if it contains real inference, the inference is
isjunctive.
The permutation of an affirmative proposition may, like this last,
be no real process of inference. We pass here from ' X is Y '
to f X is not not- 17'. 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 7, it
will display one of the others ; but if it does display 7, 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- 7 is quite unlimited in range, and includes everything whatever
except 7, it will not follow that because JTis 7, it is not also not- 7;
because we can predicate of a goose that it hisses, we are not
precluded from applying any predicate but hissing. The only
sense, therefore, in which it is true to say that X is not not- 7, is
one in which we deny no alternative, but only deny the denial of
7; and that is just equivalent to the affirmation of 7, 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 7 is one, then permutation takes us from the affirmation
of 7 to the denial of the rest ; and this is again disjunctive
reasoning, wherein the conclusion will be more or less definite
according to the definitiveness of our knowledge of the alterna
tives to 7. But so far as there is inference here, there is no use
of an infinite term; where not- 7 is really infinite or unlimited,
the only sense in which the permutation of an affirmative proposi
tion is logically justifiable is one in which it involves no step of
inference.2
We have already dealt with Contraposition so far as it can
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 the 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.
2 This is no doubt why Wallis (cf. p. 216, n. 1, supra) did not distinguish
contraposition from conversion by negation. ' Hanc forrnulam locum habere
decent in Particular! 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.1 loc. cit.
x] OF IMMEDIATE INFERENCES 223
She treated as a mode of inference from hypothetical propositions,
t is hardly necessary to deal at length with conversion by
negation. The conversion of 0 by negation is permutation, and then
the simple conversion of J. The general result of our investigation
is, that from the symbolic form of these processes it cannot be
determined whether they contain any real inference or no; that
where there is real inference, it is either, as in the conversion of E
and the contraposition of A, of the kind that we shall study
in dealing with hypothetical arguments : or, as in the permuta
tion of E and 0, of the kind that we shall study in dealing with
disjunctive arguments : or, as in the conversion of A and /, and
that of 0 by negation, it involves suppressed syllogism. Imme
diate inferences, therefore, so far as they are inferences, are not
a distinct kind of inference ; so far as they seem distinct, and
specially unquestionable, it is because they merely bring out another
aspect of what we have already intended in a proposition, without
any fresh step in thought. This result may throw some doubt upon
the appropriateness of the name by which they have become
known.]
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 inferences,
which have been called immediate, that cannot be exhibited by
symbols at all, but only in concreto. One of these is known as
Immediate Inference ly Added Determinants : in which we add the
same qualification to both subject and predicate in a judgement,
and hold the result of our operation to be true, on the strength of
the truth of the original judgement; e.g. ' A negro is a fellow
creature .-. a negro in suffering is a fellow creature in suffering \l
Another is called Immediate Inference by Complex Conception : in
which the subject and predicate of a given judgement 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 judgement,
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 : —
1 Thomson, Laws of Thought, § 55.
224 AN INTRODUCTION TO LOGIC
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 Sopkistici 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 arguments
are not all built on the principle of American watches, with inter
changeable parts *, 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 applicable to 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 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
his followers .claimed) the first to reason syllogistically, defines
a syllogism as follows : Ao'yoy ti> w TtQivrav TLVUV erepoV rt T&V
K€ifj.€v<t)v e£ avayKr]s (rvju/3au>ei rw raOra slvai 1 : that is to say,
'discourse in which certain things being posited, something else
than what is posited necessarily follows on their being true '.
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
mlject 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 C : or a bullet, a horse, and a man ; but
the relations between the terms are in the one case relations of
1 AnaLPri. a. i. 24* 18: cf. Top. a. i. 100> 25, where the same definition
recurs, with the substitution of fitu T&V nei^vw for TO> Tavra ««u.
'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£ dvavKTis.
3 Bradley's Logic, Bk. II. Pt. I. c. iv. § 10, et alili.
JOSEPH
226 AN INTRODUCTION TO LOGIC [CHAP.
quantity, in the other of velocity. A and B are not related as 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
quantity, the latter of velocity ; and from the given relations of
A and C 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 Zof Z ; then JTmust 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 1 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, Zmay
be a predicate affirmed or denied both of JTand 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,
xi] OF SYLLOGISM IN GENERAL 227
and is an animal that lives exclusively upon a vegetable diet ; therefore
an animal that lives exclusively upon a vegetable diet may be strong.
Here we have two terms, strong (X) and being 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, ispredicable
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 andpredicate
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 * ; 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 Philistines ; 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 a predicate
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.
1 i. e. in a wider sense than it is used in when the attributes of anything
are distinguished from its substance or kind.
228 AN INTRODUCTION TO LOGIC [CHAP.
Understanding- the word in this comprehensive sense, we may say
that the theory of syllogism is the theory of inference in the domain l
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 canual relations of one thing to another ; but in its
present use, it includes every predicate. The advantage of using it
is this, that it explains what we mean by predicate. Things may be
related in space, time, quantity, degree, consanguinity, or as cause
and effect : all this conveys a pretty definite meaning to us. They
may be related in the way of subject and predicate ; but what, we
may ask, is the relation of a predicate to its subject ? it is that of an
attribute — a character attributed or belonging to it. In explaining
predicate as attribute we substitute, we may say, a word expressing
a real, for a word expressing a logical relation. Blue is an attribute
of the gentian really and always : a predicate, only when one judge*
that the 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
1 By a domain here is meant a certain order or system of relations, of 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 little system of
relations embracing group after group of terms, but not necessarily con
necting any of the terms of separate groups ; whereas time and space,
which connect group after group of events or objects, 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 Aristo
telian sense of a kind of predicate as determined 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.
xi] OF SYLLOGISM IN GENERAL 229
reasoning, except the inferences called immediate.1 No one has
done more to dispel this illusion than Mr. Bradley, in his Logic ;
though perhaps the zeal of an iconoclast has prevented him from
dwelling enough on the fact that the syllogism formulates reason
ing 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 made logicians dwell on it with something of an
artist's concentration ; and the truth of science has sometimes been
sacrificed to the 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 rela
tions in that way to the same third term. But the judgement which
relates two terms as subject and predicate may be universal or par
ticular, affirmative or negative. 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 a very general problem presents itself to us,
which may be stated thus — writing & for any subject, P for the pre
dicate which is to be brought into relation to it, and 3/for the third
or middle term whose relations with S and P are to bring them into
relation with each other. What must be the quantity and quality
of the propositions (or premisses) connecting S and P respectively
with Mt and how must M be related (i. e. as subject or as predi
cate) to S and P in these premisses, in order to establish in the con
clusion a proposition whose terms are S and P, of the several forms
Ay E, /, and 0 ? In other words, what forms of premisses will
prove that all S 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, wkat relations in the way
of subject and predicate between two terms S and P respectively and
a common third term M will establish wkat relations in the way of
«7 J
subject and predicate bet^veen 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 e. g. Hobbes, Art of Rhetoric, Bk. I. c. i, ' all inferences being syllogisms ' :
v. Molesworth's ed., English Works, vi. 423.
CHAPTER XII
OF THE MOODS AND FIGURES OF SYLLOGISM
A. Nomenclature. 1. In any syllogism, there are two propo
sitions taken as true, and another inferred or following from them.
The latter is called the conclusion (Lat. quaestio or conclusio,
Gk. 7jy>o'/3A.7j/xa or oujutTrepacrjaa) : the former the premisses (Lat.
praemitsa, Gk. Trporao-et?).
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 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
1 Not necessarily, because, as we shall see, from two false premisses may
follow a true conclusion. But a conclusion correctly drawn from false
premisses implies ignorance in the reasoner, though not ignorance of
reasoning.
MOODS AND FIGURES OF SYLLOGISM 231
a Logic of Truth, and offered it to the world under the name of
Induction.1 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 2, i. e. we do not trouble ourselves to
ask what in particular the terms are at all ; and hence we cannot
be asking whether the judgement which connects them is true.
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 ' pre
misses 'j 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.
It makes of course no difference to the form of premisses which
1 Cf. Mill's Logic, III. iii. 9.
2 As J. S. Mill does in expounding his Inductive Methods : but his symbols
are very inadequate.
232 AN INTRODUCTION TO LOGIC [CHAP.
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 s 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 Trpofihrwa and Tr/oorao-eis. For "him, the conclusion
was generally regarded as something to be proved1: the premisses,
as something proffered in proof of it; and so he asked rather,
' 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 ( TJiese 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. 235 seq., where this is explained at
length.
xn] MOODS AND FIGURES OF SYLLOGISM 233
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 mqn 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 term 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
determining the major premiss is to look for the premiss which
contains the predicate of the conclusion.
3. Syllogisms are said to differ in figure (a-xTJjua) according to
the position of the middle term in the premisses.2 (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 S. S ( = 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
.-. S P
1 Cf. Locke, Essay, IV. xvii. 8 (fourth or later edition).
2 Cf. c. xi, supra, pp. 226-227.
234 AN INTRODUCTION TO LOGIC [CHAP.
If we wished to indicate in our symbols the character of the
propositions 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 S is M
.-. All S is P
the latter of the type
No M is P
All S is M
.-. No S is P.
(ii) The middle term may be predicate in both premisses, the
figure of the syllogism being indicated as follows : —
P M
S 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 x 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. 29a 19-27 (cf. p. 258, n. 3, infra).
xn] MOODS AND FIGURES OF SYLLOGISM 235
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
H 8
.-. S P
The theory of syllogism has been much darkened by this addition.2
For in erecting these arguments into a separate figure it is implied
that the distinction between major and minor term is arbitrary,
one of place and not of function. The meaning of that distinction
must be considered 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 f predicate of the conclusion ' ? Are
ic names chosen arbitrary ? And would it have been equally appro
bate 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
line position in both premisses, either premiss may be regarded as major,
ithout affecting the situation of the middle term : and hence there is no
sibility of erecting a separate figure bearing the same relation to them
the fourth does to the first.
236 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 predicated
of scholar, or vice versa ; and there is no more reason for making
one term subject than the other. ' Some poulterers are not fish
mongers ' 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 f 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, and not the species of
the genus : it is not the genus colour, but colour in some particular
case, not the genus stone, but some particular mineral that is blue
or that is diamond. Commonly, except where they are merely
coincident attributes 2, the predicate is a wider term, or more generic,
1 Unless a definite particular colour is meant.
2 Terms, though they be general concrete terms, like statesman or fish
monger, may yet express only a special or ' abstract ' aspect of the nature
xn] MOODS AND FIGURES OF SYLLOGISM 237
than the subject in judgement; it is something1 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. And by the name major he wished to indicate
not (as is sometimes said) that the predicate denoted the larger
class ; for he did not think of a predicate as a collection of things,
including a smaller collection (denoted by the subject-term) within
it ; he meant, that it was the more comprehensive notion : em
bracing as it were all the subjects of which it could be predicated,
but as a character in them and not a class in which they were.1
of the thing- they denote, if they are not in the category of substance :
cf. supra, p. 25, n. 1.
1 In adopting these expressions, however, Aristotle had not in mind what
in the Posterior Analytics he rightly recognizes as characteristic of science,
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, like any other predicate, 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 base of the
triangle 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 concrete nature of the subject, and
Becomes a necessary part of the subject-concept. While a demonstration is
till wanted by us, to show us that the angle in a semicircle is a right angle,
re have no ground for supposing that that is not a property of angles in
ome other segments as well: so soon as we realize that it can be the
M'operty of none other, we have incorporated the demonstration with the
ibject-concept (of the angle in a semicircle) and major, minor, and middle
238 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 an
intermediate concept. 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, a 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 wish to prove ; and the nomencla
ture that is fixed by the first figure is extended to them all.
We can now see that Galen was wrong in adding a fourth
figure to the syllogism. Where the same term M is predicated of
one term Z and is the subject of which another, X, is predicated l,
there X is the more comprehensive term, and Z the less compre
hensive : X is really and in our thought the major, and Z the
minor. We do not change this fact, by framing a forced and
artificial judgement, in which the naturally minor term is predicated
of the naturally major. Let us take an example.
All organisms are mortal
Man is an organism
.*. Man is mortal
is a syllogism in the first figure. But the premisses allow us to
conclude that some mortals are men. None the less, man is not
really a predicate of mortal ; this conclusion affirms of the subject
mortal a predicate man, that is naturally related to it as its subject
or as minor term to major. Nor is it otherwise, even where the
premisses allow no conclusion to be drawn in which the naturally
major term is predicate. Take one of the examples given on p. 235 ;
from the premisses
All persons who have the franchise are eligible to Parliament
No woman has the franchise
terms have for us lost their isolation. Demonstration, when complete and
while completely realized by the mind, maybe said to collapse into a judge
ment whose terms are interfused. But the major term, while waiting to toe
demonstrated, is still the more comprehensive notion, even in regard to
a subject with which it is to be proved commensurate ; while if it is not
commensurate, it remains the more comprehensive. Cf. p. 307, infra.
1 I use the symbols Z and X for S and P here, in order not to seem, by
taking letters which suggest ' subject ' and ' predicate ', to prejudge the
question, which term should be made the subject.
xn] MOODS AND FIGURES OF SYLLOGISM 239
we can draw no conclusion as to whether women are eligible to
Parliament; but we can conclude that some persons eligible to
Parliament are not women. Yet what an unnatural judgement
is this. To be a woman is not conceivable as an attribute of
eligibility to Parliament; but eligibility to Parliament is con
ceivable as an attribute of women ; hence we might properly say
that some women are not eligible to Parliament ; but it is forced and
artificial to say that some eligibles to Parliament are not women.1
Though we say it, we feel that we are making that a predicate
which should be subject, and that a subject which should be
predicate. It is true that this conclusion is got, and is all that
can be got, out of the premisses : but it is of no scientific value.
Either the fact is that no one eligible to Parliament is a woman —
and that ought to be expressed conversely, that no woman is
eligible to Parliament ; or else if some persons eligible to Parlia
ment are women and some are not, we want to know what women
and what men are eligible ; but no one who had any knowledge of
what qualifies and disqualifies for election to Parliament would
express any part of that knowledge in such a proposition as that
' some eligibles to Parliament are not women '.
The introduction of the fourth figure then rests on the erroneous
idea that a term is made a major or minor term by being thrust into
the position of predicate or subject in a proposition ; whereas in fact
a term is made predicate rather than subject when it is in its own
nature, by comparison with the subject, a ' major * term : i. e. a term
more universal, abstract, generic, or comprehensive, than the other.
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.
5. The last paragraph spoke of moods and figures of the syllogism.
The difference of figures has already been explained to depend on
1 According to Aristotle, we can only speak so nara n-u^e^Kos. The
proper subject of which to predicate attributes was in his view substance,
and of which to predicate any genus, its species or the several examples of
these. Where this order was inverted, the judgement did not state what
its subject was in its own nature, but to what it was incident. Doubtless
this is often what we want to state, as in such a judgement as 'The composer
was Handel' ; but in syllogism a term predicated of that to which another
is subject is not naturally made the subject whereof to affirm or deny
this last.
240 AN INTRODUCTION TO LOGIC [CHAP.
the position of the middle term in the premisses. The difference of
mood depends on the quantity and quality of the propositions com
posing 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 that we shall employ in solving
the problem. We must next consider the solution.
B. The only method of originally determining what combinations
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 com
mitted 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
xii.] MOODS AND FIGURES OF SYLLOGISM 241
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 mathematically
possible to combine two premisses, when each of them may have
either of four forms, we can ascertain which in each figure are
conformable 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.
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 H is P
Man is an organism All S is M
.'. Man is mortal 1 .*. All S is P
b. 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 l
1 With actual terms, an universal proposition is often more naturally
'xpressed 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
IOSEPH K
242 AN INTRODUCTION TO LOGIC [CHAP.
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 S is P
ii. the minor negative ; no conclusion follows :
Lutherans are Protestants All M is P
Calvinists are not Lutherans No S 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. loth affirmative :
i. major universal, minor particular ; the mood is valid
and the conclusion /:
What raises prices injures the consumer All M is P
Some import-duties raise prices Some 8 is M
.-. Some import-duties injure the consumer .*. Some S 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 S is M
.-. Excise-duties (or Legacy-duties) are levied at death /.
6. loth 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 * 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
S is M, 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.
xn] MOODS AND FIGURES OF SYLLOGISM 243
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 penta- No S is M
gon) is not a quadrilateral
/. The triangle in a semicircle (or The penta
gon) 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 Mis P
Some compounds are not living Some S 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 0 :
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
iii. major affirmative and particular, minor negative and
universal-, no conclusion follows :
Some traders are freeholders (or are members
of Parliament) S ome M is P
No parson trades No S 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
244 AN INTRODUCTION TO LOGIC [CHAP.
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 S 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 S 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 S 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
rnoods, 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. Anna. 52). They passed into general currency through the Summulae
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
xn] MOODS AND FIGURES OF SYLLOGISM 245
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
Some traders are {freeholders
I 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 in the
latter capacity, while a rector or vicar is legally a freeholder. But
it is possible again to infer that
o ( freeholders )
Somex > 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 (101 8-? 1079), 2vi>o\//>iy els rr)V 'ApioroTf'Aoiiy XoyiKnv fTTKTTrjfjLrjv (accord
ing 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 Summulae Logicales des Petrus
Hispanus und ihr VerMltniss zu Michael Psellus, published in the Festschrift
zum elfhundertjahrigen Jubilaum des deutschen Campo Santo in Rom, Frei
burg im Breisgau, 1897, pp. 130 sq. ; cf. also hie Papst Johannes XXI. pp.
16-19, Miinster i. W., 1898), reason is shown for thinking that the ascrip
tion of the Synopsis to Michael Psellus is erroneous, and that it is really
a translation of the Summulae : the Augsburg MS. 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. ascribes the work to Psellus ; all the rest
Srofess to be translations from the Latin ; seven give the name of Petrus
ispanus as author, and four that of Georgius Scholarius (Geunadius) as
translator. Cf. also Sir William Hamilton's Discussions, 2nd ed., pp. 128,
671 sq. : who, however, wrote before Prantl's work appeared.
246 AN INTRODUCTION TO LOGIC [CHAP.
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 indirect moods, i. e. moods in which
the minor term is concluded of the major instead of the major of
the minor, viz.
AEO All
IEO
No 8 is M
.-. Some P is not 8
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 ac
knowledges 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 l :
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 experimenting 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. note, pp. 257-262, infra.
xn] MOODS AND FIGURES OF SYLLOGISM 247
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 predicate) 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 con
clusion were not related to the same third term, there would be no
relation established between themselves, and so again, no syllogism.
For example, we can draw no conclusion barely from the premisses
Reptiles are vertebrate and The crocodile is a lizard. Any one who
knew that lizards are reptiles might infer that the crocodile is
vertebrate : but the inference requires the premiss Lizards are
reptiles 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) Reptiles are vertebrate
Lizards are reptiles
.-. Lizards are vertebrate
(ii) Lizards are vertebrate
The crocodile is a lizard
.*. The crocodile is vertebrate
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 lettuce is not a vegetable.1
A breach of this first rule is technically known as the fallacy of
Qvaternio 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 with
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. Saurians
are vertebrate, and the crocodile is a lizard .'. The crocodile is vertebrate.
248 AN INTRODUCTION TO LOGIC [CHAP.
reference to its whole extension ; and undistributed, when used with
reference to a part of its extension only. Thus in the proposition All
jealous men are suspicious, the term jealous man is distributed (for I
expressly refer to all that falls 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 distributed.
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 eagles, 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, with the middle term undistri
buted, in the third figure. Granted that some cripples are Tories,
1 This is sometimes expressed as follows : though the expression is apt to
be misleading (cf. pp. 249, 250). 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,
'tametsi enim nemini dubium esse possit quin, quae in medio termino
conveniunt, ea et inter se conveniant,' &c.
xn] MOODS AND FIGURES OF SYLLOGISM 249
and some cripples are tailors : I cannot hence determine whether or
not some tailors are Tories : for the cripples that are tailors may not
be the same cripples as are Tories, and if not, the inference would
be false. But if in either premiss the middle term were distributed :
if cripples were referred to in the whole extension of the term, and
all cripples were spoken of : then a conclusion would follow. For
whether all cripples 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 a particular judgement — one of the other.
A breach of this rule is technically known as the fallacy of
undistributed 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 vertebrates
fly, and some are rodents : but they are not the same vertebrates ;
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 i-ts distribution. This has
already been noticed in discussing the ' quantification of the predi
cate '.l 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 :
FlG.l.
1 Cf. c. ix. pp. 198 6-<z., supra.
250 AN INTRODUCTION TO LOGIC [CHAP.
[The inclusion of one area, wholly or partially, within another
symbolizes an affirmative judgement, universal or particular : it is
plain that the area S may fall wholly within M, and M partially
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 into 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 reasoning
proceeds in some way by help of an identity. It is not true that
the point of identity need consist in the same objects 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
it is on this, no doubt, that the inference hinges ; 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. Prom 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
rodenty or vice versa : neither carnivorous of ruminant, or vice versa :
we cannot infer anything as to the relation of carnivorous and
rodent.
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.
xn] MOODS AND FIGURES OF SYLLOGISM 251
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
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 used with reference to part of its extension
only ; 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
extension of the term as if it were information about the whole.
If alibis P, and some S is M, we can only infer that some S, 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) not being thought
in extension, there is some danger here again lest we should misunder
stand a reference to its distribution. 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.
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
S 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.
252 AN INTRODUCTION TO LOGIC [CHAP.
[My premisses do not primarily give me information about
gambling1 • nevertheless, if there were no gambling except a corner in
wheat, the minor term would be commensurate with the middle,
and what 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
extension than the middle ; for there are many other modes of
gambling besides making a corner in wheat. It is used therefore with
reference 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. Prom two particular premisses nothing can be inferred,
and
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, of course, not the case. 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.
xu] MOODS AND FIGURES OF SYLLOGISM 253
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,
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 (/ and /), or both negative (0 and 0), or one affirmative and the
other negative (/and 0). But in a particular affirmative propo
sition neither subject nor predicate is distributed ; so that the
combination of premisses // contains no distributed terms, 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 / 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 similar line of reasoning will establish rule 8; no combina
tion of premisses, whereof one is particular, contains enough
distributed terms to allow of an universal conclusion. For again,
either both are affirmative (A and /), or both negative (E and 0), or
one affirmative and the other negative (A and 0 : E and /). The
two negative premisses may be struck out as before. The combina
tion of A with / contains only one distributed term, the subject of
the universal affirmative (A) ; 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
254 AN INTRODUCTION TO LOGIC [CHAP.
conclusion must be particular. The combinations A and 0, E and 1
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
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
xn] MOODS AND FIGURES OF SYLLOGISM 255
conclusion — i. e. whether universal or particular 1 — the others yield
in it.
Now as there are four kinds of proposition, so far as quantity
and quality are concerned — A, E, I, and 0 — and our premisses must
be two in number, there are sixteen combinations of premisses
mathematically possible. It is not, however, necessary to try the
validity of all sixteen combinations in each figure in turn; for
eight can be shown to yield no conclusion on grounds which are
applicable to all four figures alike, and without reference to the
position of the middle term.
The sixteen combinations of premisses mathematically possible are
as follows : they are 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 El II 01
AO EO 20 00
Of these, the combinations EE, EO, OE, 00 may be struck out,
because both premisses of a syllogism cannot be negative ; II, 10,
01 (and 00 again) because both cannot be affirmative ; while IE
(if we do not consider indirect conclusions) would involve an illicit
process of the major term : for the conclusion being negative would
distribute the major term, while the major premiss is a particular
affirmative proposition, and therefore, whether it stood as subject or
predicate, the major term would not be distributed in it.2
There remain eight combinations of premisses, on whose validity
we cannot pronounce without reference to the figure and the
position of the middle term, viz.
AA AE AI AO EA El I A 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.
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.
2 It is hardly necessary to give instances to show that these combinations
of premisses are impossible : but a beginner should invent instances for
himself, in order to become familiar with the meaning of the symbols.
256 AN INTRODUCTION TO LOGIC [CHAP.
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
bute the major term P ; the major term must therefore be distributed
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.
In this figure, therefore, the premisses AE, AO are invalid, by
rule 1: I A, OA by rule 21; AA, EA, AT, AO are valid. The
conclusions which they yield will be respectively A (universal
affirmative), E (universal negative), 7 (particular affirmative), and
0 (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, ATI, AOO. 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, All, AEO,
IEO, whose names are Baralipton, Celantes, Dabitis, Fapesmo,
Frisesomorum.
In the second figure the middle term is predicate in P M
both premisses : hence in it 8 M
1. One premiss must be negative, for otherwise the middle 8 P
term would be distributed.
2. The major premiss must be universal: for since one premiss is
negative, the conclusion will be negative, and so distribute the major
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, AU Gothic arches are pointed, it cannot be inferred that All Gothic
arches are (or are not) four-centred (I A, OA).
xir] MOODS AND FIGURES OF SYLLOGISM 257
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, AT, I A are invalid, by rule 1: the
premisses OA (and I A again) by rule 2 1 ; EA, AE, El, 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 S P
as in Fig. 1 (the major term, in both figures, being similarly placed
in its premiss).
This rule excludes the premisses AE, AO2: the remaining com
binations, AA, AT, EA, El, IA, 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 AA2, I AT, All, EAO, OAOt MO:
their mood-names are Darapti, Disamis, Datisi, Felapton, Bocardo,
Ferison.
[It is impossible at this point to pass over the fourth figure, in
which the middle term is predicate of the major premiss, and
subject of the minor, thus (1) P M
MS
.-. S P
It is clear, however, that if the premisses of a syllogism in the
first figure be transposed and the conclusion converted, we get just
the same arrangement of terms, (2) S M
M P
.-. P S
1 e.g. from Some (or All] daisies have a great number of flowers within
a single calyx, All (or Some) composita have a great number of flowers within
a single calyx it cannot be inferred that Some, or All, composita are daisies
(AA, AI, IA} : nor from Some annuals are not (or are) hardy, All poppies are
hardy, that Some poppies are not (or are] annuals (OA, I A).
* 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
hare wings or that Some creatures that can fly have no wings (AE, AO}.
JOSEPH
258 AN INTRODUCTION TO LOGIC [CHAP.
[the only difference being that P is now the symbol for the subject,
and S for the predicate of the conclusion, instead of vice versa.
Now the order in which the premisses are written down makes no
difference to the real relation of the terms in them to one another.
In (2) P is still functionally the major term ; and the premisses are
KT P
really premisses in the first figure, „ ,-> from which a conclusion is
drawn wherein the minor term becomes predicate to the major.
Thus any mood in the fourth figure can be looked at as a mood
in the first figure, predicating the minor term in the conclusion
of the major : in other words, as an indirect mood of the first
figure.
It was stated at the beginning of the chapter that, according to
the authority of Averroes, the first person to regard such moods as
belonging to a distinct figure was Galen.1 Averroes himself
disagreed with that view of them, and in this he was followed by
Zabarella 2, one of the greatest of the scholastic commentators upon
Aristotle, whose De Quarto, Figura Syllogismi Liber is still worth
reading on the subject; though in the reasons 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. 274).
Aristotle, as already remarked, recognized the possibility of
concluding indirectly in the first figure, though only by the way.
He remarks in one place 3 : ' It is clear that in all the figures, when
there is no proper syllogism, if both premisses are affirmative or
both negative nothing at all necessarily follows, but if one is affirma
tive 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 £ is A, and no C is S ; for, converting the premisses, it is
necessary that some A should not be 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. With
regard to Figs. 2 and 3 it is plain from Aristotle's language that
though the major premiss cannot be distinguished by the position
1 Prantl, i. 570-574.
2 And by others, e. g. Lambert of Auxerre, thirteenth century med., quoted
Prantl, iii. 30, Abschn. xvii. Anm. 121.
3 Anal. Pri. a. vii. 29a19 AqXov de KOI on ei> aTracri TOIJ cr^/iao-ii/, orav pr] •yi'j/Jjrai
(ruXXo-yicr/Lidy, KaTr)yopiK£>v /xcV r) o~T€pr)TiKoi>v dfjL(f)OTfp<t)V OVTU>V rSav opa>v ov8ev oXtoy
•yu/erai dvayKalov, KarrjyopiKov Se /cat o~T€pr)TiKov} <a66\ov \T)<p8evTos TOV o~T(pr)TiKov
aei yiVerai avXXoyicr/zos' TOV eXdrrovos aKpov Trpbs TO ncl£ov, oilov ci TO fj.ev A navTi
Tto B 77 Tivi, TO Se B fj.r)d€vl rep I" avrt<rrpf(^>o^t,eVa)i/ yap ra>v Trporacrecoi/ dvdyKrj TO F
Tivl TCO A fjif} vTrdpxflv' Ofjioicos 8e KOTTI ra>f crepcoi/ <r^r//xurco^' del yap yivfTai dia
Trjs dvTio-Tpocprjs cruXXo-ytcr/xoy. It is plain that OTav M^ yivrjTat o-vXXoyf<r/uor
means * when there is no natural, direct, or proper syllogism or conclusion '.
xn] MOODS AND FIGURES OF SYLLOGISM 259
[in it of the middle term, since this occupies the same position in
both premisses, whether as predicate or as subject of major and of
minor terms, yet in his view it was not arbitrary which term is
regarded as the major; it would be the term which, as compared
with the minor, is of wider extension, or as Zabarella says, higher
in predicamental order. Thus if I say that
Some roses are fragrant
and The Baroness Rothschild is not fragrant
I can conclude that some roses are not Baroness Rothschilds. Now
naturally, rose is a predicate belonging to the particular variety
Baroness Rothschild, and not Baroness Rothschild a predicate to
be affirmed or denied of rose. We may be said, therefore, to be
concluding the minor of the major. But in many and probably in
most cases of syllogism in these figures it would be difficult to say
which of the two terms was naturally major and which naturally
minor, for they are not generally terms belonging to one series in a
classification. Hence we can transpose the premisses ; and in any
case this produces no appearance of a new figure, as transposing the
premisses in Fig. 1 does, because the middle term still retains the
same relation to what is now treated as major term which it held
towards what was before so treated. We now have
The Baroness Rothschild is not fragrant
Some roses are fragrant
/. Some roses are not Baroness Rothschilds
which is in the recognized mood Festino of the second figure.
Similarly AEO would be regarded as Cesare, by transposition of the
premisses; and in Fig. 3 AEO as Felapton, and IEO as Ferison.
But in Fig. 1, if we transpose the premisses in the moods AEO and
IEO, we no longer have the right position of the middle term.
They must therefore be regarded either as moods of the first figure
concluding indirectly, E being the minor premiss : or if E be con
sidered major premiss (as containing the term which is predicate in
the conclusion) they must be referred to a fourth figure in which
the major term is subject of the major premiss and the minor term
predicate of the minor premiss.
Elsewhere 1 Aristotle points out that ' whereas some syllogisms
are universal [in their conclusion] and some particular, those which
Anal. Pri. /3. i. 53a 3 eVfi ft ol p,tv Ka66\ov rwv o-iAXoy/o-/uo>t> elalv oi Se KOTO.
H*pos, oi p-cv Ka06\ov TrdvTes del TrXfi'o) av\\oyi£ovTaL, T&V 8' cv pepei ol pfv KOTT)-
yoptKol rrXeuo, of 5' dnfXpaTiKol TO crvfnrfpaap.a p.6vov. ai fiev yap aXXtu Trporcivfis
avTt(rrp€(pov(nv, f) fie OTfprjriKrj OVK avriarp^fi. What Aristotle says here
would cover the Subaltern Moods (cf. p. 262, 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.
S 2
260 AN INTRODUCTION TO LOGIC [CHAP.
[are universal always have more conclusions than one, and so do
those which are affirmative among the particular, but those which are
negative among them have only the [direct] conclusion. For the
other propositions convert, but the [particular] negative does not '.
He means that any syllogism concluding to Ey No 8 is P, im
plicitly gives also the conclusion No P is 8, and any concluding to
A or /, All S is P or Some 8 is P, implicitly gives also the conclu
sion Some P is 8. We have therefore here a recognition of the
possibility of the first three indirect moods of Fig. 1, Baralipton,
Celantes, and Dabitis : whose conclusions are merely the converse
of those which follow directly in Barbara, Celarent, and Darii.
But in Fig. 2 the converse of Cesare is given in Camestres, and
vice versa, and according to the conclusion drawn, you would be
said to be arguing in one mood or the other. There is no affirma
tive conclusion in Fig. 2 and no universal conclusion in Fig. 3 ; but
the converse of the conclusion /in the latter figure can be got, if both
premisses are universal, by merely transposing the premisses in the
recognized mood Darapti ; while if one is particular, the converse of
Disamis is given in Datisi, and vice versa. This transposition of
premisses enables us to refer all these conclusions to recognized
moods, while we can still say both that the premiss containing the
predicate of the conclusion is the major, and that the middle term
occupies its regular position in the premisses. But with these three
indirect moods in Fig. 1 (as with the other two) we must either give
up the rubric, that the premiss containing the predicate of the
conclusion is the major premiss, or else allow that we have a new
arrangement of terms, in which the middle is predicate in the
major premiss and subject in the minor.
It was very early seen that what Aristotle in these passages
notices generally about the three figures works out rather differ
ently in the first figure and in the other two ; and an explicit
recognition of the five indirect moods as supplementary moods of
Fig. 1 is attributed to his nephew and successor in the Lyceum
Theophrastus.1 If the fourth figure is really the erection of
Galen, logicians for some five centuries enjoyed immunity from
the burden of it. For it can hardly be doubted that Galen's
implies a defective insight into the character of the thought which
these forms express, and treats the syllogism more as a matter of
verbal manipulation. In the fourteenth chapter an endeavour
is made to explain the grounds on which this verdict rests. It
is hardly more than the logical issue of the external and me
chanical way of regarding syllogism, which underlies the reference
of these moods to a fourth and separate figure, when we find some
of the later scholastic writers erecting separate moods on no better
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.
xn] MOODS AND FIGURES OF SYLLOGISM 261
[ground than the order in which the premisses are enunciated, with
out there being- any actual difference in the premisses or conclusion.1
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. If either premiss is negative, Ike major must lie 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 le 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 lie par
ticular : for the minor term, as predicate of an affirmative proposi
tion, will not be distributed in the premiss, and must not be
distributed in the conclusion, which will therefore be particular.2
Hence the premisses OA are invalid by the first rule : AI and AO
by the second2; AA, AE, EA, E1,IA are valid; but AA will afford
only a particular, instead of an universal, conclusion. The moods
are thus AAI, AEE, I AT, EAO, EIO ; and their mood-names, as
moods of the fourth figure, are Bramantip, Camenes, Dimaris,
Fesapo, Fresison.
The complete memorla technica, with the fourth figure replacing
the indirect moods of the first, is commonly given in English text
books nowadays as follows 3 : —
1 e. g. Petrus Mantuanus, quoted Prantl, iv. 178. Petrus, in the edition
of 1492, gives as an example of a syllogism in Cesare, ' Nullus homo est
lapis, omne marmor est lapis, igitur nullum rnarmor est homo.' If the con
clusion drawn is ' Nullus homo est marmor ', he calls the mood Cesares ;
but he comes later to Camestres, as a different mood. 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 Cracken-
thorpe, p. 197 (ed. 1670), who appears to treat the moods of Fig. 4 and the
indirect moods of Fig. 1 as two different things.
2 e. g. from the premisses Some change is not motion, All motion is change,
it cannot be inferred that Some change 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 part)/ in poicer are not in the Cabinet, that Some of
the Cabinet are not members of the Government.
3 I have not been able to trace this form of the mnemonic verses any
further back than to Aldrich's Artis Logicae Rudimenta. 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
262 AN INTRODUCTION TO LOGIC [CHAP.
[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,
Nomen habent nullum, nee, si bene colligis, usum.
The meaning1 of the last two lines is explained in the next
paragraph.]
1 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
a particular conclusion in any of these cases ; and the syllogism is
then said to have a weakened conclusion, or to be in a subaltern mood
(because it concludes to the subaltern of the universal proposition
that might be inferred from it). 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 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 pre
misses 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 Jigures. It might merely have been pointed
out, e. g., that in the first figure A A would yield an A conclusion,
AE involve an illicit process of the major term, AT yield an /
conclusion, AO again involve an illicit process of the major, EA
moods of Fig. 1 appearing neither in that capacity nor as moods of Fig. 4.
Sir William Hamilton (Discussions, p. 666) also otters ' 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.
xn] MOODS AND FIGURES OF SYLLOGISM 263
[yield an E, and El an 0 conclusion, IA 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 made necessary
to avoid 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. A science should
recognize principles; and 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 (bvvarot) and syllogisms which were perfect (re'Aeiot). 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 may 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, though sanctified by
the tradition of many centuries, is really necessary, in order to
validate the imperfect figures.
Directions for Reduction are concealed in the mood-names of
' 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 r^ll method of establishing the validity of a syllogism per impossiUle is
applicable to all the imperfect moods ; but the direct method is preferred
where it is available.
REDUCTION OF THE IMPERFECT FIGURES 265
Reduction, as already stated, is either direct or indirect. Direct
Reduction of an imperfect mood to the first figure consists in
showing, from premisses that are either the same as in the original
syllogism, or inferred immediately by conversion from these, that
the original conclusion, or one from which it can be immediately
inferred, follows in a syllogism of 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 occu
pies 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
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 Disarms (Fig. 3), by converting the minor premiss A, we
should get the combination //, 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 trans
posed 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
.-.Notfis?
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 :
266 AN INTRODUCTION TO LOGIC [CHAP.
Insects have six legs
The spider has not six leg's
.-. The spider is not an insect
Now if we want to get the same conclusion in the first figure, we
cannot convert the major premiss ; for that would give vis 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 quality : 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 8 is M
.-. The spider is not an insect .-. No S is P
Here the major premiss can be converted simply, being E: and
transposition is not required. The premisses
No animal with eight legs is an insect
The spider has eight legs
are of the form of Celarent, and yield at once the original con
clusion.
If we consider the indirect moods of the first figure (the moods,
as others regard them, of the fourth figure) in order 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), we shall see that
they fall into two groups. Three, Baralipton, Celantes, and
1 Though it would follow by an ' indirect conclusion ' in Frisesomorum
that some insects are not spiders.
xm] REDUCTION OF THE IMPERFECT FIGURES 267
Dabitis, simply draw the converse of the conclusion which the
same premisses yield directly; all we have to do therefore is to
draw the direct conclusion and convert it. But Fapesmo and
Frisesomorum yield no direct conclusion. If every copy of the
Times contains an advertisement of the Encyclopaedia Britannica,
and the newspaper I buy is not the Times, I cannot infer that it
contains no advertisement of the Encyclopaedia Britannica. The
only conclusion is that some papers containing an advertisement
of the Encyclopaedia Britannica are not the newspapers I buy.
Now to get this conclusion directly in the first figure I must
transpose the premisses, so that ' newspaper I buy ' may be in the
major premiss, and 'copy of the Times' in the minor. But this
will bring the middle term into the wrong position, unless at the
same time I convert both premisses; then indeed I shall get the
syllogism
No copies of the Times are the newspapers I buy
Some papers containing an advertisement of the Encyclopaedia
Britannica are copies of the Times
.'. Some papers containing an advertisement of the Encyclopaedia
Britannica are not the newspapers I buy
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 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 J 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 exchange position.
TO eXfvOepov, TO §' fXcvdepov TO fityv^oi/ KpivavTf s, Thuc. ii. 43.
268 AN INTRODUCTION TO LOGIC [CHAP.
[On the other hand,, in the last two moods transposition will now
be unnecessary ; for the fourth figure already regards the universal
negative premiss in Fesapo and Fresison (= Fapesmo and Friseso-
morum) 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 required of the major term
in its premiss by 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 converted;
whether we have to convert the conclusion obtained in the first
figure by 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 l
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
clusion2, signified by the preceding vowel must be converted
simply.
4. p ( = per accident)) which indicates that the same must be
converted by limitation.
5. c ( = per contradictioneni) , 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 7, is a particular affirmative, and the minor,
being indicated by A, an universal affirmative ; the conclusion
1 Except the initials, these are explained in the old lines —
Simpliciter verti vult S, 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 got to be
obtained as it is), but the conclusion of the validating syllogism.
xm] REDUCTION OF THE IMPERFECT FIGURES 269
similarly a particular affirmative. Our syllogism is therefore to be
of the type : —
Some M is P /
AllMisS A
.-.Some Sis P I
In reducing1 it, the m of the mood-name indicates that we must
transpose the premisses, and the «? that we must convert simply the
premiss indicated by the vowel after which it stands ; the I) that
we shall so obtain a syllogism in Darii, thus : —
All M is S
Some P is M
.-. Some P is S
The simple conversion of this conclusion, enjoined by the s after
the third vowel in Disarms, gives us
Some S 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 premisses,
as the first figure requires, one of the premisses in the second and
third figures must be converted. In these moods, the premisses are
respectively an universal affirmative and a particular negative pro
position. The latter, 0, cannot be converted either 'simply or per
accidens] the converse of A is /; and so by converting that we
should obtain two particular premisses. These syllogisms can, how
ever, be validated by the process of Indirect Reduction.
Indirect Reduction, or Reduction per impossibile, 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 is
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
270 AN INTRODUCTION TO LOGIC [CHAP.
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
therefore 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
it with the major, we, deduced a conclusion contradictory of the
minor. The letter c in the mood-name means that the mood is to
be reduced indirectly by substituting for the premiss indicated by
the vowel after which the c is placed the contradictory of the con
clusion.1
[All the imperfect moods could be validated in this indirect
manner,2 : take, e. g., Darapti — All M is P, All Mis 8 .'. Some S is P ;
if this is false, then No S 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 combine the
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 S is not M .'. Some S is not P: Ferio, No not-M is P. Some S
is not-M .'. Some S is not P; from Bocardo we obtain a syllogism in Darii :
Bocardo, Some M is not P, All M is S .'. 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 burden
ing 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 con
tradicting the converse of one of the original premisses.
xm] REDUCTION OF THE IMPERFECT FIGURES 271
[contradictory thereof with one of the premisses, it is only by a
syllogism in the second or third figure that we can deduce a con
clusion inconsistent with the other premiss ; e.g. in Barbara (All
M is P, All S is M .-. All S is P) ; if the conclusion is false, then
Some S is not P ; and All M is P ; /. Some S is not M — which
contradicts the original minor ; and again, Some S 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.]
CHAPTER XIY
ON THE PRINCIPLES OF SYLLOGISTIC
INFERENCE
WHEN I argue that because A=£ and H=C, therefore A = Ct
my reasoning proceeds upon the same principle as when I argue
that because X— Y and T=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, U = C .'. 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 l
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 0 although the quantities are
none of them equal. If A is greater than B, and £ is greater than
Cy 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 C 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.
\et where, as in this case, it requires some violence and ingenuity
1 Todhunter's Euclid, for example, is written under the impression that
this is the right way of stating such an argument.
PRINCIPLES OF SYLLOGISTIC INFERENCE 273
to bring- a quantitative inference into the form of a syllogism, it is
not habitually done ; and since men have been content not to force
into the form of syllogism the inference ' A > B3 B > C .*. A>C3,
it may be surmised that they would not have so dealt with the
inference ' A = B, B = C .-. A = C\ if it had not been for the
apparent ease of the transformation. But appearances may be
deceptive ; it must therefore be noticed secondly, that in the syllo
gism 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 C 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 C are both equal to £, and therefore the
major required is < Things equal to £ are equal to one another \
And the minor term ' A and C ' is not really a subject of which we
demonstrate an attribute ; it is two subjects, which are shown to
stand in a certain reJation 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, 7, and Z, I should not be able to re
cognize 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 C' a true minor term. In the argument that
1 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 = C*,
than are contained in the premisses ' A = B and JB=C}.
274 AN INTRODUCTION TO LOGIC [CHAP.
We may therefore dismiss the attempt to reduce this argument
to syllogistic form, and recognize in the axiom not a premiss but
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 attribute,
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 enumerate 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. negator] 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
affirmatur (s. negatur) universaliter de aliquo, idem affirmatur (s. negatur)
etiam de omni de quo illud praedicatur1. This form seems (as Manscl
xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 275
If we take syllogisms in the first figure — and it is enough to
consider Barbara and Celarent — the meaning of the principle will
remarks of Aldrich's) to be more nearly a translation of the passage in
Aristotle's Categories than of that in his 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
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. 24b 26-30 TO 5e eV oAo> dvai erepov (Ttpto Knl TO Kara
TravTOS KaTTjyopfIo~dni 6(iT(pov 6a.Tfpov ravrov fo~Ttv. \fyo/j.fv de TO Kara irai>Tos
KciTr)yope'io~6ni, orav p.rjo'ev y \aftflv T&V TOV VTTOKfiueVou Ka$' ou Bnrepov ov
\f\6Tja-fTm' KOI TO Kara pndfp&c tao-avrws ('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 Trai/roy,
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. The fact that
he uses the formula TO \ieaav to-T\v ev 6Ao> ro> TT/JOOTW as well as TO np&Tov
KnTrjyopfLTai Kara nai'Tos TOV fj.€(Tov 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) shows that he looked upon the universal as a whole or unity, and
not a mere collection. Again he says of that figure, el yap TO A Kara navTos
TOV B KOI ro B Kara navTos TOV F, avdyKT) TO A Kara TravTos TOV F KUTijyope'io-Oni'
TrpoTfpoj/ yup eipr/rai VMS TO Kara travros Keyopnt ('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. 25b 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 every C must be A ; but the
universal proposition need still not be viewed as a statement about
particulars. 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 enumerative judgement about known particulars ; 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 content within the object,
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 ever}T particular falling under it.
There is another passage in Aristotle sometimes quoted as the source of
the Dictum, viz. Cat. iii. 1D 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 : OTOV erepov KuB CTepov Kar^yopffTai IDS Ka6' vnoKftp.fi'ov,
oaa Kara rov Karqyopov/ueVou Xeyerat -navra Kat Kara TOV v7roKfip.(vov prjOrjcrfTdi, oluv
276 AN INTRODUCTION TO LOGIC [CHAP.
be plain. All (or No) B is A, All C is B .'. All (or No) C is A. Here
it matters not for what real terms A} B, and C stand, any more than
KOTO TOV Tivof dvdpMTTOV KaTrjynpe'iTaL, TO de £o>oi> Kara TOV dvdpwnov'
ra TOV TWOS dvOwrrov KaT^yo^B^r^Tai TO (aov' o yap TLS ('ivdpanros
OUKOIV Km Kara TOV TWOS dvOpwrrov KaT^yo^B^r^Tai TO (aov' o yap
Km ai'0pa>7roy fVn Km (aov ('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 ; 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 '). Taken apart from its context, this sentence might seem
to be an enunciation of the Dictum. But its context dispels this presumption.
There is nothing about syllogism in the Categories at all. Aristotle has
been distinguishing in the previous chapter between different kinds of being
(o<>Ta). What he says involves the distinctions — to put it into other
language — between the individual and the universal, the concrete and the
abstract. In his own language some things Ka6' vnoKetpevov Xeyf™'> «"
vnoKetp-evto de ovdfvi forty : others fv v7roKei/ie'j>a> p.ev eVrt, K.a6* VTroKciptvov &e
ovdevns \eycTat: others KaF v7TOK(ip.evov re XeyfTcti gat ev vnoKei^fvo) ftrriv :
Others ovr1 eV vTTOKfi^eVw eoriV, ovre Knff virnKfiptvov \eyeTai (i.e. some things
are predicated of a subject— it is their subject de quo — but dp not inhere in
any subject; others inhere in a subject, but are not predicated of any;
others are both predicated of a subject and inhere in a subject ; others
neither inhere in a subject, nor are predicated of any). Here it is obvious
that the leading distinction- is between TO *a0' vrroKei^vov Xeytadat and TO ev
vTTOKfiueVw tivat : between being predicated of a subject, and inhering in it.
The distinction is akin to that between essential and accidental predication.
Man is predicated of a particular man, and animal of man o>? KG& vni>K€iiJ.evov,
as the subject de quo, because man is what he is, and animal what man is ;
remove the predicate, and the subject would not be left ; the predicate as
it were overspreads the whole subject. In the same way grammar is
predicated of Priscian's distinguishing science, and science of grammar a>?
Kad' vnoKd^evov, because grammar is what his science was, and science is
what grammar is. Here man is a concrete and grammar an abstract term ;
but either is predicated <»$• «n0' vnoKet^vov of its own particulars— they are
the subject de quo ; and predicates which are of their essence, or tell us
what they in themselves are, are predicated o>f Ka6' inrnKfi^vov of them.
On the other hand, grammar is found in the soul, and colour in a body, as
inhering, OK «v vnoKti^vv ', and if they are predicated of these ^subjects, we
are not saying what the soul is, or what a body is, essentially ; _ these
attributes indeed can only exist in a subject (and therefore Aristotle
explains TO eV vTroKei^fvco or the inherent as 6 ev TIVI ^ o>? p.fpos vTnipxov
dftvvcirov x&>pi? ttvni TOV cv o> fariv — 'what being in a particular not as a part
of it cannot exist separate' from that in which it is '), but their removal does
not involve the disappearance of the subject of which they are predicated.
The grammatical science of Priscian therefore, though there is no subject
of which it is predicable as de quo, <os *nff vTroKetpfvov (for^it is a particular
instance of that attribute, or universal), yet exists eV V7ro/<ei^e'i/a>, as an
attribute in his ' soul ' ; but Priscian himself is neither predicable of any
subject wy Ka#* vTTOKeipevov (being a concrete individual), nor (for the same
reason) does he inhere or exist in anything further.
Having said this, Aristotle proceeds to add the sentence quoted at the
head of the last paragraph ; which must clearly be interpreted with reference
to the distinctions which he had in his mind at the time ; and the point
seems to be this. There are things which we might hesitate about placing
in either of the four classes which Aristotle has discriminated. They are
what we should call generic concrete terms, like animal. These are
xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 277
in the axiom it mattered what real quantities were intended. What
ever they are, suppose that A can be affirmed or denied of all B, 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
primarily predicated not of the individual— e. g. the individual man
Socrates — but of the species man ; we say that a man is an animal, not that
Socrates is an animal. Now man is not the v-rroKfiufvov, but Xfytrat K<I&
vTroKfipevov ; and therefore it cannot be primarily said of animal that it KU^'
vrroK€ip.ei/ov Xeyerai. Yet we cannot treat it like a generic abstract term
such as science, and say that it attaches to man o>? Katf vnoKci^fvov and to
Socrates u>s fv vnoKfmfVM. Still less can we treat it like the concrete
individual, and say that it neither ev v7roKfip.ei>(t> f'ori nor *a$' inroKeip.fi>ov
Xe'yfrat. But we need not erect a new class of things which Kara Karriynpov^vov
At'yerru ; for in cases like this, where that of which anything is predicated is
in turn predicated of something else us KdO" vnoKfip.ivnv, that thing is itself
predicated u>s Ka6J vnoKfinevov of the same subject. Animal therefore, no less
than man, Katf vnoKfip-evov Xeycrui, though predicated usually of man or
horse, and not of Socrates or Bucephalus. The case would be different, if
that of which anything were predicated inhered in something else cb? 4v
vnoKfifjifVti): we could not then predicate it of the subject, as we predicate
it of what inheres in the subject. Science may be predicated of grammar,
and grammar was something inherent in the soul of Priscian ; but we cannot
say that the soul of Priscian was a science, like the grammar in it. Science,
however, is provided for already in Aristotle's list, as something which Knff
v7roKfip.evov re Ae'yerai Km ev v7roK(ip.(V(f t'ori'v : and animal and its congeners
are no less provided for, if we realize that, though predicated primarily of
predicates, they are ultimately and really predicated of the subjects of these.
The section is therefore far from enunciating the Dictum de omni et mdlo.
The vnoKfiufvov is the concrete individual, and not a minor term (though it
is true that it might be also a particular instance of an attribute). The
transference of a predicate A from B to C is considered only in the case
where A is predicated of B, and B of C, o>? Kaff vTro/m/Wi/ou : but the Dictum
is innocent of any such restriction. If Priscian was a grammarian, and a
grammarian is scientific, Priscian was scientific ; but here in the minor
premiss it is not true that crepov K<id' erepov KnrrjyopfiTm cos Ka6' v7TOK€Lfji€vov.
If Priscian was a man, and All men are jealous, Priscian was jealous ; but
here jealous, in relation to man, is not one of those things oo-a Kara rov
Ka.TTjyopovp.evov Xeyerru ; man is that, fv o» e'anV. Now the Dictum covers
these syllogisms no less than the syllogism ' All men are animals, Socrates
is a man .-. Socrates is an animal ' — if indeed Aristotle would have called
any of them syllogisms (cf. infra, p. 296). But the remark which we are
considering cannot cover the first two, nor could Aristotle have thought of
it for a moment as covering them ; the difference between accidental and
essential predication was much too prominent in his mind. There is there
fore no ground for saying that this passage enunciates the Dictum ; whether
he 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.
278 AN INTRODUCTION TO LOGIC [CHAP.
C ; the business of reduction is to bring1 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
admitting of the application 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 oi.
all, or no, Z?, and B is said of C. Clearly it is because we believe
that B is A} and C is B — not because B is called A, and C is called
B — that we assert the conclusion. However, this nominalist inter
pretation of the Dictum is not necessary ; it is not as thus interpreted
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
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 petit io principn.
By petttio 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
xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 279
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 syllogism 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 rumi
nants 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 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 l ;
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, I mean not that B as such is A, but that
all the B's are A, I must certainly have examined the case of C (if
that is one of them) before making the assertion; and therefore
the major premiss, All B is A, rests (inter alia) on the present
conclusion, C 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
1 Cf., e. g., Mill's 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
280 AN INTRODUCTION TO LOGIC [CHAP.
whole of a number of particulars ; it is really an enumerative, and
not a true universal, judgement.1 We make it, not because of any
insight that we have into the nature of the predicates 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
understood, and one in which it no longer makes an assertion about
the whole 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 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 are implied to belong to any subject, when
we call it by some general name. 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 con
nexion between the other attributes for which a parcel of matter is
judged to be gold, and this of yellowness. Given such and such
attributes, we call it gold ; and therefore gold has all these. Let
any one of them be wanting, and we should not call it gold ; there
fore 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.2
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 unexceptionable syllogisms. All other general propositions have,
by the extremer critics, been interpreted in the way mentioned in the text.
1 For this distinction, cf. supra, p. 158.
2 Cf. Locke's Essay, III. vi. §§ 6, 19, and also pp. 78 sq., supra, oil Definition.
xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 281
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 he thought that the ordinary
man would find it hard to say what precisely he did mean ; and
anyhow, that this was all that the evidence, and the means of
knowledge open to us, justified him in meaning. It is not our
present business to discuss this ; we have not to ask how many of
the general propositions enunciated in the sciences have any right
to be regarded as really universal propositions, nor what means there
are (if any) of proving universal propositions about such matters of
fact. We are concerned 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 cle omni et nullo at least
lends colour to such an interpretation. We have now seen that
there is another interpretation, according to which the major
premiss becomes a verbal proposition. On this view, its general
truth does not depend on an examination of all the instances
included under the subject of it, and may therefore be known
antecedently to such an examination. It depends, however, on an
arbitrary convention about the meaning of names ; the syllogism too
will still be a petitio prmcipii, 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 the substance, in which I have found the other qualities
which the name implies, is gold, 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 as 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
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
282 AN INTRODUCTION TO LOGIC [CHAP.
We need not dwell longer on the view that a general proposition
asserts 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 counte
nance it.
We saw that the crucial question here concerned the nature of
the major premiss ; is it universal, or merely enumerative ? is it
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 tt
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
demonstration, could not possibly have understood the major premiss
in this way.1 He thought that, although we might know as a fact
that B 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 JB. B is a middle term,
because it really mediates between C and A ; it performs for C the
office of making it A, and is the reason why C is A, not merely the
reason wliy ire know C 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 esxendi
and the ratio cognoscendi. When I say that wheat is nourishing,
because it contains nitrogen and carbon in certain proportions, I give
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).
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.
xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 283
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 saying- it is 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 ratione* easendi, so far as possible ; though it may be noted that in
what is, in many ways, the most perfect of the sciences, viz. Mathe
matics, we reason very largely from rationes cognoscendi. If A = B,
and B=C, then A — C-, but it is not because A and C are both
equal to .Z?, 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.1
It is not all syllogisms, in which the middle term gives the
reason why the major belongs to the minor. It does so only in
the first figure, and not always there. Because a syllogism falls
into the first figure, whenever the middle term really is a ratio
essendi, Aristotle called it the scientific figure, <rxwa brurnMiovuffaf
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 is scientific, because a syllogism which makes
you know why C 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)
1 But we cannot
2 Anal. Post
it true.
nnot give this reason for the equality of the units.
. a. xiv. 79a 17. The rest of the chapter is by no means all of
284 AN INTRODUCTION TO LOGIC [CHAP.
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 the whole class. 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 the central idea of syllogism is that it works through concepts,
or universals. The major premiss asserts, not the presence of A in
every B (and therefore in C, among them), but the connexion of A
as such with B as such J : hence wherever we find B} we must find
A ; if we know, or can show, that C is B, then eo ipso it is A.
B is one thing, present in many ; an attribute that is the same in
the various subjects in which it occurs, and therefore involves
in every case what it involves in any. How we are to discover
what B involves is a problem of Induction, in the modern sense
of that term. But if we know it, and if we know or discover in
a subject C that the condition B is present, we know and conclude
that C is A. Where B is only something from which we can infer
A, as we infer the distance of the sun from its rays being parallel,
B is still an universal, tv curt TroAAow : an attribute which for one
reason or another we take as a sure indication of another attribute,
and which we look on as the same in the various instances of its
existence. There could be no syllogism if the major premiss really
made an enumerative statement about a number of particulars ; the
most that we could say of the major premiss then would be what
Mill says of it, that it is a note or memorandum to which we
subsequently refer in order to refresh our memory and save the
trouble of repeating our observations : as if a man intending to
dispose of part of his library were to put the volumes, which he did
Or the exclusion of A as such from B as such, if the syllogism is
negative.
xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 285
not consider worth keeping-, all in one bookcase ; he might then
infer that any particular volume in that bookcase was not worth
keeping-, merely because he had made a mental note to that effect
about them all, and without looking at the volume again.
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 et 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
ipriu* (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 concrete, and that the syllogism
refers to a concrete subject (res ipsa) what in the major premiss is
stated to characterize its predicates. It speaks also as if one attri
bute were conceived to qualify another in the same way as an
attribute qualifies a concrete subject. And the conception of a mark
or nofa 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 object is present, but themselves contribute to make
it the object 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
1 Cf. Hegel's Logic, § 165, E. T., p. 296 : ' There is no more striking mark of
the formalism and decay of Logic than the favourite category of the "mark".'
2 J. S. Mill (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
286 AN INTRODUCTION TO LOGIC [CHAP.
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.1 The rule is given
in the major premiss, which connects a predicate (the major) with
a condition (the middle term) : the minor premiss asserts the fulfil
ment 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 the whole of a class. It also applies equally
where the middle term is, and where it is not, the ratio cssendi
of the major. And it is free from the objections just urged
against Nota twtae.2 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. If B is the condition of the rule of being A, whatever
is B — for example, C — will fall under the rule of being 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 millo, if rightly interpreted, is free
from the offences charged against it. If the omne be understood
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 bottle of Liebig's Extract is a mark
of the presence of a certain familiar 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 Icing 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 ip*a never meant the major term, the most general or abstract term
in the syllogism ; and the whole interpretation, which necessitates a measure
so violent, is impossible. The formula is really an abridged equivalent of
the passage in Ar. Cat. lb 10-12, quoted p. 275, n. 1, supra.
1 Krit.d. r. Vern., Transcendental Dialect, Introd. II. B. (p. 215,Meiklejohn's
Translation).
Kant himself applied this analysis to hypothetical and disjunctive
arguments 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.
xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 287
as an unity present in many instances — a whole of intension, not
a whole of extension — 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 success
ful 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 condition with which the predicate (or its absence) is universally
connected.
That this, like the axiom of equals, is a principle and not
a premiss of reasoning, is easy to see. Any one denying it would
as readily deny the validity of any particular syllogistic argument ;
but a man may admit the validity of the inference, in a particular
case, without needing to consider this general principle. And, as
no one could see that Two tilings equal to the same 1hiny 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 tie 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
consistency he might decline. A man who denies the validity of
a given syllogism in Barbara may with equal reason deny the argu
ment which attempts to prove its validity. For that argument will
itself take the form of another syllogism in Barbara :
288 AN INTRODUCTION TO LOGIC [CHAP.
All inferences upon this principle (that what satisfies the con
dition 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 type, and show 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
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 le a syllogism 2 :
and therefore valid.
And there have been writers 3 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
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. 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.
2 Cf. Ar. Post. An. 0. vi. 92a 11-16.
3 e. g. Locke, Essay, IV. xvii. 4.
xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 289
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
•AH 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 par
ticular syllogisms, from which that account is of course derived.
Therefore, though it be said that a syllogism is an argument
which applies to any member of a class what is true of them all,
yet even this analysis of it, however faulty, will serve to ' stop
wrangling ' among persons who accept it. For let a particular argu
ment be exhibited as doing this, and it will be accepted as valid.
But the theoretical objections to this analysis of syllogistic infer
ence 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 1 ; 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.
1 Cf. supra, p. 278.
290 AN INTRODUCTION TO LOGIC [CHAP.
It may make things clearer, if the view to be taken in the
following- pages is given summarily at the outset. There are diffi
culties 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 move
ment of a man's thought, though he expresses himself, e. g., in the
second figure, would be more adequately exhibited in the first.1
In such a case direct reduction may be defensible, though still un
necessary; and yet it may be true that, speaking generally, the
direct reduction of the imperfect figures distorts them, and pur
chases 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 reason
ing of the first ; they are independent types. Their validity is con
firmed, in the second figure, by the reductio ad absurdum 2, and in the
third, by the method which Aristotle called eK0eo-is, or exposition.
The fourth figure (or indirect conclusion in the first) is not an inde
pendent 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.
Let us begin with the second figure. Take the syllogism : All
true roses bloom in summer : The 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 re
assure himself, not by transposing the premisses, and converting the
present minor into the statement that No rose which blooms m
summer is a Christmas rose : but by considering, that the 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
1 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 scariet
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.
a Called by Aristotle dnayvyr) ds TO ddwarov.
xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 291
fish has lungs, and Whales (or Some aquatic animals) have lung*, then
Whales (or Some aquatic animals) are not fish. A man sees at once
that if they were, they would 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 c Because they have lungs ' ; and that this implies a syllo
gism in Barbara, with the major premiss WJiat has lungs is not
a fish. Whether this gives the reason why a whale is not a fish
(in which case Barbara 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 fifth
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 Barbara 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 absence thereof, would extricate from the major
premiss of the latter syllogism the major of the former, and
think in Barbara. 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
harmonious, 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
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.
U 2,
292 AN INTRODUCTION TO LOGIC [CHAP.
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 produce
heats 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, &c., 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.1 Moreover, if I were to recur to
the first figure in order to establish this inference, it would naturally
be by con trapesing the major premiss
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 wKales are really the
1 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.1
xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 293
subject of my thought. The same line of reflection may be applied
to the argument, Matter containing active bacilli putrefies : Froze//
meat docs 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 essentially 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 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, that would follow on denying the conclusion, is
developed. There is therefore a movement of thought in the second
figure which is' absent from the first. This is what prevents our
reducing it to the first, and makes a new type of it ; and this is why
its direct reduction, representing second-figure 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 C is
not A, without the necessity of pointing out that C would not other
wise, as it is, be B ? 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
294 AN INTRODUCTION TO LOGIC [CHAP.
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 the perception, in
the second figure, of the contradiction that would ensue if we denied
the conclusion, is not the reason for admitting the conclusion, but
only involved in realizing its validity. An analogy may help us.
A If a straight line, falling on two other
Q/ 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 consideration, 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 towards one another ; and the perception of
this is really part of seeing the necessity of the original pro
position. 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 con
firmation, such as it is, is obtained by looking at the same 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 development of the con
tradiction 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 some
thing involved in the full appreciation of the argument. It follows,
if the second figure is not a mere variation of the first, 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
xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 295
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
premisses, and the conclusion always particular. For this reason it
has been well called the inductive figure; for induction (whatever
else besides their citation may be involved in it) is the attempt to
establish a conclusion by citation of instances. The terms of the
conclusion are always general; they are what we have called
universals. The conclusion declares two general characters to be
connected, or (if negative) that one excludes the other : Sailors are
handy, The larger carnivora do not breed in captivity. In the premisses
we bring 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 justified, 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 C is A ; in traditional phraseology, C 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 overthrow one. The instances of Queen
Elizabeth or Queen Victoria, of Catherine of Russia or Christina of
Sweden, will disprove the proposition that No woman can be a
statesman ; and truth is often advanced by establishing the contra
dictory 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
296 AN INTRODUCTION TO LOGIC [CHAP.
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 statesman, we
can appeal to the four queens mentioned above ; these were states
men, 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 C 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
e*0€cri9, or Exposition. He conceived that the proper mode of
validating a syllogism in the third figure was by direct reduction1,
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 N ', this will be both P and R, so that there will
be some R which is P 2 ' ; 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
1 Except, of course, where the major premiss is a particular negative and
the minor a universal affirmative proposition (Bocardo), in which case we
can only proceed per impossibile or by exposition. Anal. Pri. a. vi. 28b 15-21
2 Anal PH. o. vi. 28* 24-26.
xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 297
reduction often conceals, rather tban expresses, our thought. No
ostrich can jlyy 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 can
equally be the subject of the other. But the character of the
argument 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 therefore superfluous and misleading: the true con
firmation of the validity of the syllogism lying in the perception
that there actually are instances of its truth.
One objection to this view of the third figure needs consideration.
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 appealed
to the case of 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
1 Cf. supra, pp. 158-160, 179.
298 AN INTRODUCTION TO LOGIC [CHAP.
compatibility o£ the two characters, C and A, in one subject. In
the latter case, I can also express my meaning- by the problematic
judgement CmayleA-, which contains no doubt the thought of
unknown conditions under which it will be so. Now suppos
ing 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 1 ; neither is it a syllogism (though it is inference)
to argue, from the 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 B 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 E and A (or not A)} then we have
not got a proper syllogism. Still our conclusion rests entirely
on the production 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 :
1 Cf. Bain's Logic, Deduction, p. 159 (ed. 1870).
xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 299
as a problematic judgement, a statement of the compatibility of
two attributes, or the possibility that one may exist without the
other. 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
malobservation. The instance need not indeed be an individual ;
it may be 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 the species, and not any particular specimen ] .
But very often, and mostly where one premiss is particular 2, and
of course always where the premisses are singular, it is on an
individual instance that we rely ; and one instance, whether indi
vidual or species, is enough. Therefore it is by exposition — by a
production, not of course in bodily form, but in thought, of one
instance — 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,
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 suppose 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
1 It may be objected that it is only in some particular specimen that the
coincidence of these two characters is ever actually realized, and that there
fore it is to a specimen that we must at bottom be referring. This raises
a question that is not peculiar to the third figure. If I argue that the
rhododendron is popular because it flowers brilliantly, it may be said that
this truth is only realized in particular shrubs. The relation of the universal
truth to particular existence, here raised, is important; but it need not
complicate the present issue.
" 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 (Disarms). Here I am speaking, and thinking,
throughout not of individual animals but of their kinds.
300 AN INTRODUCTION TO LOGIC [CHAP.
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
establishing 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 con
siderations besides the instances themselves. 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 peculiarities constant throughout one
species, and failing when we go beyond it ; so that the accumula
tion 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 Guardsman. The readiness with
which we infer connexion is controlled by our general knowledge of
the kind of attributes that are connected ; 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 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 the possibility that one may
appear without the other) 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
xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 301
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 ( = BaraKpton,
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
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
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.
302 AN INTRODUCTION TO LOGIC [CHAP.
[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 vertebrate
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 * by converting both premisses (i. e. by direct reduc
tion) : 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 sub
stitute a less natural mode of expression in the premisses ; e. g.
from the premisses 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 conclu
sion, 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
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 ; and
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
alcoholic ; it is clearly more natural to say that No alcohol is taxed,
1 i.e. of Fapesmo and also Fresison = Frisesomoru m : v. Anal. Pri. a. vii.
29a 21-27.
2 It would complicate the illustration too much to make the exception
required by methylated spirits.
xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 303
[and that exhibits better the contradiction with our premiss. If we
employ the method of tK0e<ris 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, and they
bring it under one of the other figures. Perhaps the first of these
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,
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 our conclusion. It is the meaning or
content of the terms themselves which determines which ovght 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 transposition of the premisses produce one in Dimaris ; e. g.
304 AN INTRODUCTION TO LOGIC [CHAP.
[the premisses 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
propositions 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 essen
tially 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
considerations 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.
It' 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 be the case with Fesapo ; for bad logic, as well as verbal
contortion, is required in order to express a particular affirmative by
an universal converse; and therefore the minor premiss A cannot be
an inverted way of stating 7: the original of Fesapo cannot be
xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 305
[Ferio. With Fresison it is more possible; that is to say, a
syllogism in Fresison may be reached by converting1 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. Cold does not tarnish, Some ancient ornaments are of gold :
we may, however, say, it' we like, that What tarnwhes is not gold,
and Some thing* 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 unnatural form, and would be restored to
natural form by conversion. They are those in which the position
of the middle term, as the predicate 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 essentially the major term — that is, the most general
and comprehensive — does stand as predicate in its premiss, and
what is essentially 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, 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 notion 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
iirst figure, we must no less recognize that they need validating;
and the most natural way of realizing their validity is by the
JOSEPH X
£06 AN INTRODUCTION TO LOGIC [CHAP.
[process of exposition which we found to be the characteristic
method for the third. 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 ad iwpossibile 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 unchal
lenged. 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 without 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 ad
mitting it. The third figure appeals not to relations of concepts, but
to experience of the conjunction of attributes (or their disjunction) 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 conclusions ; 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 con
clusion is only particular, and realized by the help of exposition
or of conversion or reduction ad impossible. It must always be
remembered that the character of an argument is determined 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 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 conversion by which the
xiv] PRINCIPLES OF SYLLOGISTIC INFERENCE 307
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 more remark may be made about the first figure. We
have seen that the charge otpetitio fails, unless the major premiss
be enumerative ; but suppose that it states a connexion seen to be
necessary between A and B as such ; may it not be urged that in
this case no one can judge that C is B without eo ipso recognizing
it to be A as well ? and that if so, there will be no such act of
' subsumption ', bringing C under the condition of a rule, as we
found the first figure to involve ? To this we must answer yes ;
with complete insight we should go straight from B to A in the
subject C, and the major premiss as an independent rule would not
be wanted, and would be represented only by the recognition that
a connexion of A with B, which we see to be necessary, is therefore
universal. Thus it will be found that in geometry we never syllo
gize except when we rely on 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 the hypotenuse equal to the squares
on the other two sides, because it is right-angled ; but if we realized
at once the constructions of Euclid i. 47 and 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 semi
circle, than as a rule applied to that case. The subsumption in
syllogism belongs therefore to thinking which has not complete
insight into the grounds of all its premisses at once.
X 2
CHAPTER XV
OF HYPOTHETICAL AND DISJUNCTIVE REASONING
THE form of argument which we have been examining1 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 the case. In what have been called
Hypothetical and Disjunctive Syllogisms, hypothetical and dis
junctive propositions figure in the premisses. For reasons to be
considered later, it appears, however, 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
proposition, connecting a consequent with a condition or antecedent :
the other is a categorical proposition *, 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, an 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 A is B, C is D
A\sB A is B
.'. AisC .'. CisD
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, iii. p. 310.
HYPOTHETICAL REASONING, ETC. 309
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 changed at full moon, it
does not follow that the change will last V 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.
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
1 This is the denial of a hypothetical judgement, but not itself hypothetical :
being equivalent to saying ' It is not true that if, &c.
310 AN INTRODUCTION TO LOGIC [CHAP.
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 A is C, it is D or If C is D, E is F
If A is B, it is C If A is B, C is D
.-. If A is B, it is D .'. If AisB,EisF
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
consequent, 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 C or If A is B, C is D
A is not C C is not D
.*. It is not B .*. A is not B
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.
It is plain that the observations made above with regard to the
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
xv] HYPOTHETICAL REASONING, ETC. 311
If A is B, it is C
AisC
.'. Itisj5
or A is not B
.'. It is not C
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 having1 occurred is no proof that it occurred in
consequence of this particular condition ; 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 among1 the commonest 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 hypothesis. 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 difference of
religion ; yet if there are other ways of explaining it, what 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
312 AN INTRODUCTION TO LOGIC [CHAP.
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
A is C
may be exhibited in the form
A Bis C
AisC
.'. AisAB
and the argument
If A is B, it is C
A is not £
.•. A is not C
may be exhibited in the form
ABisC
A is not A B
.'. A is not C
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 modu*
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
established 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 logical dependence; and there is not necessarily any
middle term. Where antecedent and consequent, in the hypothetical
premiss, have the same subject — where that proposition is of the
form ' If A is B, it is C3 — a middle term may at times be found,
and the reduction effected ; but where that is not so — where it is of
1 A number of modern textbooks teach this doctrine. For an older
authority ci'.Zah&rella, In Lib. Prior. Anal. Tabulae, p. 158, ' syllogismus hypo-
theticus an valeat necne cognoscitur per eius reductionem ad eategoricum.'
— Opera Logica, Coloniae, 1597.
xv] HYPOTHETICAL REASONING, ETC. 313
the form ' If A is By C is D ' — there a middle term is wanting and
the violent nature of this process of reduction becomes manifest.
f 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 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/ 1 But such linguistic tours deforce 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
supersede, that we assent to it at all; the l reduction' is purely
verbal; our meaning remains unchanged, and cannot be put into
i
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.
314 AN INTRODUCTION TO LOGIC [CHAP.
the categorical form. Nor does the minor premiss stand criticism
any better. What case is cthe 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 l : 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 proposition 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 C is a condition fulfilled in A. flf 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 as it revolves in round
another body presents always the same face to the other
The moon rotates in the same period as it revolves in 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
xv-] HYPOTHETICAL REASONING, ETC. 315
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 hypothetical1; 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 tollens — 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 concerned
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
the earth is also 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 as it revolves
in round another body'; in the minor premiss, X=4body rotating in the
same period as it revolves in 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 case of the moon in its relation to the earth under the
condition of a rule. Aristotle recognizes this: cf. Post. An. 8. xi. 94*
36-b?.
1 Cf. p. 166, n. 1, supra.
316 AN INTRODUCTION TO LOGIC [CHAP.
proposition, that if the moon rotates in the same period as it
revolves in, 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 in question are the moon and the earth, but holds equally
for any two bodies ; so that the more general form of the universal
categorical 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 f Nations who 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 C ', some general principle involved :
we may express this as ' a ft is y '. But if A is some determinate
individual, or case of a particular kind, and if the condition £ is
similarly determinate, we may know that if A is B, it is (7, 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.
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 C is D is not a condition asserted to be realized in the nature
of C itself ; in other words, there is no middle term *. No
1 The inference in a hypothetical argument might hence be called
immediate ; but such an expression would readily give rise to misunderstand
ing. ^ 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 dis
tinguished from syllogism : viz. that in them we passed from a single
proposition to another inferred therefrom, without anything further being
xv] HYPOTHETICAL REASONING, ETC. 317
doubt 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
conclusion a categorical proposition, denying or affirming the other
alternative. In the former case, the argument is said to be in the
required as a means of reaching the conclusion. Hypothetical arguments
are not immediate in this sense. Given that 'If A is B, ifc 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. 0. iv. Ill1' 17-23 et al.) ; but he does not speak of
hypothetical syllogisms. The term rruXXo-yioyios- «£ vrroOiaftos has a different
meaning— viz. a syllogism proving the antecedent of a hypothetical pro
position, and therefore, Try virtue of the acceptance of that hypothesis, proving
the conclusion. Let it be granted that if A is jB, C is D : then any syllogism
which proves that A is B will by virtue of this agreement establish also
that C is D : but without such agreement, it would not have been shown at
all that C is D : that is therefore said to be proved only ex hypothesi. In
a recent 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'£ V7ro&'(r*co?, the College showed by the same arguments
that it was entitled to erect the bridge without acknowledgement.
318 AN INTRODUCTION TO LOGIC [CHAP.
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 C or Either A is £ or C is D
A is B A is B
.*. It is not C .'. C is not D
or Either A or B is C
Ais C
.-. B is not C
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 C Either A is B or C is D Either A or B is C
A is not B or A is not B or A is not C
:. It is C .-. C is D .-. B is C
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
Nicomachean Ethics
Eudemus did not write them
.*. Aristotle did write them.
xv] HYPOTHETICAL REASONING, ETC. 319
The following points should be noted : —
i. It is sometimes contended that the modus ponendo tollens is
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 is
now believed to have been the case. 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 hypotheticals are implied in its disjunctive premiss ; for
we have seen (p. 167, supra) that the disjunctive judgement 'A is
either B or C> may imply, though it is not reducible to, the
hypothetical judgements 'If A is B, it is not £', ' If A is C, it is
not J5/ ' If A is not 3, it is C/ and ' If A is not C, it is B \ If
the alternatives are mutually exclusive, all four will be implied, and
the modus ponendo tollens will be valid. If not, we cannot get, out
of the proposition c A is either B or C y , the propositions ' If A is
B, it is not C3— ' If A is <?, 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
1 The argument may be valid even though the conclusion be false :
the truth of the conclusion further presupposes that of the minor
premiss.
320 AN INTRODUCTION TO LOGIC [CHAP.
must be so actuated j 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.
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 1 ; 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 while noticing that quite inde
pendently of this doubt about the validity of the modus povendo
fallens in any given case, the modus tollendo ponens is of more
importance 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 satisfied except by discovering the murderer. And so it is
with disjunctive 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
1 It might be said that we could give an unambiguous fbrm 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
neems 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.'
2 The subsumption involved may be expressed if we like in a separate
xv] HYPOTHETICAL REASONING, ETC. 321
iii. The mood of a disjunctive argument is not affected, any more
than the mood of a hypothetical argument, by the quality —
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
Ais £
.'. 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 be a failure
Bismarck was not a failure
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 hypothetical ; 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 argu
ment ; 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 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.
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 Boethius) sensu latiore,
to cover both what have in this chapter been called hypothetical and what
JOSEPH y
322 AN INTRODUCTION TO LOGIC
have been called disjunctive arguments; and for hypothetical, in the
narrower 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
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 C or Z>. 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: 6' 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
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 fvOv^iia is used in quite a different sense : he
defines it as a-v\\oyio-p.of e£ CIKOTCOV % (rr)fj.ei(t)v, Anal. Pri. /3. xxvii. 70a 10. Its
nature is discussed in that chapter and in various passages of the Rhetoric.
Roughly speaking, etVo's- is a general proposition true only for the most part,
such as that Raw foods are unwholesome ; in applying this to prove the
unwholesomeness of some particular article of diet, we are open to the
objection that the article in question forms an exception to the rule ; but
in practice we are often compelled to argue from such probable premisses.
A o-jj/Ltetoi/ 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^'iov (Rhet. a. i.
1357b 11); or it is a particular fact appealed to as evidence of another
particular fact, because the existence of one such fact implies the pre
vious 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 o-^etoj/ of his liberality (Anal. Pri. /3. xxvii.
70a 26). In this case, the appeal to a a-rjpflov implies a general principle
which, if it is irrefragable, gives to the a^^elov the nature of an evidence,
or T€Kfj.r)piov (Rhet. a. ii. 1357b 3) ; to argue from a reK^piov is not, however,
to argue from the true cause of the effect ; for this would be scientific
syllogism, and not cvdvMpa. 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 o~u\\oyiafibs e< o-^/ieiou from a o-v\\oyi<rpbs e£
tiKoros. It should be noted that Aristotle includes under cn/pcio? 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 TCKMPIOV; and of this character are what doctors call the
symptoms of a disease (and such reasoning from effect to cause is not
Y 2,
324 AN INTRODUCTION TO LOGIC [CHAP.
as enthym ernes, 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
that when formally expressed it contains, we are arguing syllo-
gistically, 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 name, asks Jason — Servare potui, perdere an possim
roc/as : here the major premiss, Qui servare, perdere possunt, is
understood : Medea supplies only the minor, and — in the form of
a rhetorical question — the conclusion.1 If I argue that f those
cultivate the land best who have a personal interest in its improve
ment, and therefore peasant proprietors are the best cultivators ',
I omit — yet I clearly use, for to deny it would destroy the argu
ment — the minor premiss, that * peasant proprietors have a personal
interest in the improvement of the land '.2 The conclusion may be
'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. 1357b
19) ; there are, of course, symptoms of disease that are of doubtful interpreta
tion. The €v6i>ij.r)n.a is said to be a rhetorical demonstration, or rhetorical
syllogism (Rhet. a. i. 1355a 6, ii. 1356b 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. We might say
the same of the enthymeme in the later sense of the term, in so far as it is
not held necessary, except in the most formal statement of an argument,
always to enunciate both premisses and the conclusion. It is possible that
the later sense arose through misinterpretation of the passage in Anal. Pri.
j3. XXvii. 70a 24-28 — fav nev ovv f) pia XfX^f} ^poraa-is, (TT)p.eiov yivfrai /j.6vov, eai>
8e K.a.1 fj frepa Trpo<r\rj<p6f), (ruXXoyKT/uos', olov OTI HITTO.KOS eXevdepios' ol yap
0iXori)uoi fXfvdfptoi, UirraKos S<f (piXorifios. This, however, seems merely to
mean, that if I say ' Pittacus is generous, because he is ambitious ', I only
state the sign : if I add that the ambitious are generous, I make a
syllogism ; but this syllogism was implied all along, and is an tvGvprifui
because of the character of the premisses, whether it be stated explicitly
or only implied.
1 This example is used in the Port Royal Logic, Pt. III. c. xiv.
2 I am inclined to think it would be found that the major premiss is more
xvi] ENTHYMEME, SORITES, AND DILEMMA 325
omitted from motives of delicacy, or sometimes for purposes of
effect, as in the Greek couplet
Kat rode 4>a>KU/U'8oir Aepiot KCCKOI, oi>x o fj.€v oy 5' ov,
Travres, TrArjy IIpo/cAeoCs* Kal ITpo/cAeTj? Ae/otos.1
It is, of course, possible that an enthymeme may be contained in
what grammatically is only a single sentence ; as in GoneriFs
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.2
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 re
lation to that, a prosyllogism : and a syllogism using as a premiss
the conclusion of another is called, in relation to it, an episyllo-
gism ; where the prosyllogism is expressed in the form of an enthy
meme, the whole argument is sometimes called an epicheirema.3
The following argument contains both a prosyllogism and an
episyllogism, 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
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.
1 'And this of Phocylides : The Lerians are bad men, not this one only
and not that, but all of them except Proclees ; and he is a Lerian.'
2 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, pp. 153-158) traces the antiquity of the non-Aristote
lian use of the term. It goes back to the oldest of the commentators.
3 v. Hansel's Aldrich, p. 97, note t : and Trendelenburg's Elementa Logices
Aristotelicae, note to § 33, cited by Mansel. The term tinx^PW* was differently
defined by Aristotle, who called it o-uXXoyio-pos diaXfKTinos, Top. 6. xi.
162a 16 : it was an assault upon a position maintained in disputation
by the respondent.
326 AN INTRODUCTION TO LOGIC [CHAP.
advance the objects in which we are interested ; and so wealth is
no guarantee of happiness.' 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 prosy llogism 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.
A Sorites 2 may perhaps be defined as a syllogism in the first figure
with many middle terms ; or if it be thought that nothing should be
failed a syllogism that contains more than one act of inference, as
1 The schoolmen gave the name of syllogismus aypticus 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 '.
2 The name is derived from <ra>pdr=heap.
xvi] ENTHYMEME, SORITES, AND DILEMMA 327
a poly syllogism 1 in the first figure with the intermediate conclusions
suppressed. Schematically, it is of the form
Jis5
Sis C
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.2
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.3 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 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
1 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.
2 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 Goclenian Sorites,
after Rodolphus Goclenius, Professor at Marburg at the end of the sixteenth
century, who first called attention to this form of 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. 79a 20, 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.
5 ' Sorites est syllogismus multiplex . . . Est enim sorites prpgressio enthy-
mematica, syllogismos continens propositionibus [=praemissis] uno tantum
pauciores.' Downam's Commentarii in Petri Eami Dialecticam, 1510, p. 653.
328
AN INTRODUCTION TO LOGIC
[CHAP.
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
contain parts is one whose acti
vity is not motion :
A thing whose activity is not
motion is not a body :
What is not a body is not in space :
What is not in space is insusceptible
of motion.
What is insusceptible of motion
is indissoluble :
What is indissoluble is incorrup
tible :
What is incorruptible is immortal.
. The human soul is immortal.
for all motion is divisible
into parts.
for the activity of a body is
always a motion,
for the definition of body is
to be extended.
for dissolution is a movement
of parts,
for corruption is dissolution
of the inmost parts.
1 v. Erdmann's ed., p. 47.
xvi] ENTHYMEME, SORITES, AND DILEMMA 329
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 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 major, in relation to one preceding
it, and therefore must be universal. This will be easily seen if we
resolve the sorites into its constituent syllogisms :
1. beginning from the minor
A is B A is # (i)
BisC £isC(u)
CisD /. A is C
D is E CisD (iii)
E is F .: AisD
.-. A is F D\$E (iv)
.-. A is E
E is F (v)
.-. A is F
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 could
therefore again be particular, and so would ultimately be the
conclusion of the whole sorites; but if any other premiss were
particular, there would be an undistributed middle in the syllogism
into which it entered.
2. beginning from the major
JSiaF (v)
Disfi (iv)
.-. D is F
330 AN INTRODUCTION TO LOGIC [CHAP.
C is D (i\i)
.-. CisF
3isC (ii)
.-. B is F
Aisfi (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 reasoning by the
fact that not only is one of the premisses suppressed, at every step
of the argument except one, but the intermediate conclusions, by
which the final conclusion is reached, are all suppressed ; for the con
clusion of one argument is the suppressed premiss of the next. This
is, perhaps, what has led logicians to give special attention to it.
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 dis
junction an unpalatable conclusion. In one case, however — that of
a simple destructive dilemma2 — the disjunction may be in the con
sequent of the hypothetical premiss, and the other be a categorical
premiss denying both alternatives in the disjunction.3 We may
1 Either an E or an / proposition may be converted simply. With an
I 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
throughout ; hence as soon as we come to combine the conclusion of two
premisses with the next premiss, we should be involved in quaternio
tenninorum. The sorites is therefore essentially confined to the first figure,
though its resolution may involve the second or third.
2 See below, pp. 332-334.
3 The hypothetical premiss is sometimes called the major, in accordance
xvi] ENTHYMEME, SORITES, AND DILEMMA 331
therefore define a dilemma, to cover this case, as a hypothetical
argument offering alternatives and proving something against an oppo
nent in either case. The conclusion may be either the same, which
ever 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
.-.EisF1
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.
If A is E, E is F-, and if C is I), G is H
But either A is B or C is I)
.-. Either E is F or G is //
Thus we might argue — and this too is unfortunately a dilemma
from which it is not easy to see an escape :
If 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
.*. Either abuses which should be exposed must be hushed up,
or truth be sacrificed to sensation.
3. Simple Destructive.
If A is B, either C is D or E is F
But neither is C I), nor is E F
.-. A is not B
with the nomenclature used also of hypothetical reasoning : and the other
premiss the minor.
1 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.
332 AN INTRODUCTION TO LOGIC [CHAP.
O£ 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.
Again, If A is B, C is J) and E is F
But either C is not D or E is not F
.-. A is not B
A Liberal, convinced in 1885 that Gladstone's Home Rule Bill
was dangerous to the best interests of the country, and too much
devoted to his leader to enter into opposition to him, might well
have argued :
If I am to continue in politics, I must feel able to support
both my convictions and my party
But now I must either act against my convictions, or oppose
my party
.-. I cannot continue in politics.
4. Complex Destructive.
If AisB,E is F; and if C is D, G is H
But either E is not F, or G is not H
.-. Either A is not B} or C 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
.-. 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. MansePs definition (which follows
Whately, and has been adopted by others since) definitely excludes
xvi] ENTHYMEME, SORITES, AND DILEMMA 333
[the simple destructive ; according to him (v. his Aldnch, p. 108,
n. i) a dilemma is fa 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 second form above given, at any rate.
The simple constructive (If A is B, E is F; and if C 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 1)
:. EisF
The simple destructive runs
If A is B, C is D and E is F
But either C 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 Jit ex duabus propositionibus pluribusve, ex quibus quidquicl electum
fuitt 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 the dis
junctive, and drives a man into a corner by way of alternatives
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
] So Minto takes it, Logic, Inductive and Deductive, p. 224.
334 AN INTRODUCTION TO LOGIC [CHAP.
[antecedent and a simple consequent, and therefore the other premiss
must be disjunctive and the conclusion simple. The simple destruc
tive dilemma of the form given first above is a hypothetical
argument in the modus fattens ; 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 conclusion
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
seems 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 IB 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 property 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 premisses for it. Now
it is generally difficult, except where one alternative 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
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
xvi] ENTHYMEME, SORITES, AND DILEMMA 335
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
paradox; 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 judgement
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 transposing and negating the consequents in the major
premiss. With a destructive dilemma the parallel procedure would
be to negate the antecedents. But this is not the only way of
rebutting ; you rebut whenever you produce a dilemma with
contradictory conclusion, and you may do that with quite different
336 AN INTRODUCTION TO LOGIC [CHAP.
premisses. Nor can every dilemma be rebutted in this way or in
any other way : not in this, for the alternative conditions are not
always such with which you can connect the contradictory of each
other's consequents. And if a dilemma can be rebutted, one of two
things must follow. Either there must (as in the last example) be
some element of contradiction involved in the 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 ; 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 ? l — 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 ; 2 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 ? Or if there is no such element of contradiction involved in the
situation, then a dilemma can only be rebutted because its premisses
are unsound, and premisses equally or more plausible can be found
for another dilemma proving a contradictory conclusion. 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 '.
To take a dilemma ~by the horns (or by one of them) is to accept
the alternative offered you, but to deny that the consequence, which
the opponent attaches to its acceptance, follows. Perhaps the fol
lowing will serve for an example. It is held by many naturalists,
that species are modified in the course of descent only by the
accumulation of many slight variations, and not per saltum : varia
tions 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
1 The solution is easy unless we suppose that no Cretan ever spoke the
truth ; in which case the situation imagined contradicts the assumption
which it makes.
2 Cf. Lucian, Vit. Auct. § 22 (cited Hansel's Aldrich, p. 151).
xvi] ENTHYMEME, SORITES, AND DILEMMA 337
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 varia
tion 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.1 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
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.
1 See an article on The Age of the Inhabited Earth, by Sir Edward Fry, in
the Monthly Revieiv for January, 1903.
CHAPTER XVII
THE FORM AND MATTER OF INFERENCE
So far we have considered and examined some of the commonest
types 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
latter can be reduced to syllogism, or that syllogism, even if the term
be extended to include them, is the type to which all valid inference
must conform ; though we have maintained, and it will appear more
fully in the sequel, that they are forms of great frequency and im
portance 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
form 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 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 syllogism
in the first figure, and in the highest form which it can assume in
that figure, rests upon a perception of the necessary relation between
certain notions, or universals ; while in the third figure such a per
ception of necessary relation neither need be given in the premisses,
nor can be reached in the conclusion. We saw too how hypothetical
reasoning, where it differs most from syllogistic, differs because it
establishes a connexion between subject and predicate in the con
clusion by means of a condition which is apparently extraneous to
the nature of the subject; and yet how our thought recognized 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.
THE FORM AND MATTER OF INFERENCE 339
None of these things could be explained or understood merely
through symbols : examples were needed not only to show that the
arguments 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 are the
same, but do not symbolize the same thing, when some terms iu our
syllogism are particular concrete objects, whose attributes are set
down as we find them, and when they are all 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, an understanding of the form must wait upon a know- j
ledge of the matter, and the task of Logic will not be complete j.
until we have finished the investigation of what is to be known. »j
In a sense this is true. It may be illustrated by the case of mathe
matics ; no one can understand the conditions on which the cogency
of mathematical reasoning depends except in the process of thinking
about number or space or quantity ; they cannot be seen in applica
tion to heterogeneous subjects. 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 performs when we are thinking about other things
than Logic. Nevertheless 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 com
pletion 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 matter ; 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 multiplicity of
facts to unity of principles. Thus our apprehension of the forms
Z 2,
340 AN INTRODUCTION TO LOGIC [CHAP.
of thought has not to wait upon the completion of our knowledge
so far as that completion means only its extension to fresh matter 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 numerical 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 subject-matter 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 transforma
tion. 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. 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 uncer
tainty will vanish. We may know all this, and know that we have
xvn] THE FORM AND MATTER OF INFERENCE 341
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 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 matter 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
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 they occur commonly in application to
matters 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 feel 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. 1 do not wish to subscribe to this view ; but even its upholders
would admit that such differences may be negligible.
342 AN INTRODUCTION TO LOGIC [CHAP.
been examined. For example, there is the a fortiori argument. ' If
a man love not his brother whom he hath seen/ asks St. John,
( how shall 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
O
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 reasoning, and not the conditions of truth. To reason consis
tently 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 some
times 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 an earlier
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 defines Logic as
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
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. Logic, VI. i. and Autobiography, p. 226.
xvn] THE FORM AND MATTER OF INFERENCE 343
other branches of knowledge. But this we may say, that men who
know the difference between consistency and demonstration, who
know what is required before it can be said that they have know
ledge about thing-s, 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 knowledge. By a study of the conditions
of demonstration we may be led to see how far from being demon
strated 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 1J is neither
a small thing, nor an easy ; and until we have some idea of 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 demonstration : not because such an expo
sition of the form of knowledge is itself an instrument for bringing
our thoughts upon any matter into that form, but because it stimu
lates us to use such instruments 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 material truth of the pre
misses; 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 principles 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
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
inference 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.
344 AN INTRODUCTION TO LOGIC [CHAP.
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 matter. It is,
however, probable that 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 cor
rective, 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}- Such a mode of putting things may suggest
some false ideas. It is impossible to bring one's beliefs into harmony
with facts, except so far as the facts are known to us, and therefore
by the way of bringing them into harmony with one another ; and
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
1 Minto, Logic. Inductive and Deductive, p. 243.
xvn] THE FORM AND MATTER OF INFERENCE 345
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 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. Facts can only be expressed
in judgements which are matter for belief; and such judgements need
not cease to express facts because they are presented as dogmas. But
it is true, as Minto wishes to bring out in the chapter 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 ideas
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
critics, that the study of the syllogism was not all-sufficing : that
no syllogism could guarantee the truth of its premisses ; and that
for a knowledge of the most general principles to which deductive
reasoning appeals we must rely on something else than deductive
reasoning itself. Bacon refers to the 'notorious answer' which
was given to those who questioned the accepted principles of any
science — Cuiqiie in sua arte credendum.1 And there are seasons in
the process of learning when that is a very proper answer ; men
must be content at many times and in many matters to accept
the expert opinion of their day. But this is only tolerable if in
every science there are experts who are for ever questioning and
testing. When tradition stereotypes doctrine, it is as bad for
knowledge as close guilds and monopolies are bad for the industrial
arts ; they shut the door upon improvement. Authority plays, and
must play, a great part in life — not only in practice, but also in
things of the intellect. But the free spirit is as necessary, which
insists on satisfying itself that what is offered upon authority has
claims on its own account upon our acceptance.
1 Nov. Org. I. 82.
346 AN INTRODUCTION TO LOGIC [CHAP.
Why was it that for so many centuries so much was accepted
upon authority which afterwards fell to pieces in the light of inde
pendent enquiry ? Much knowledge of the human mind, historical
and philosophical, would be needed in order to answer this question
adequately. If a few observations may be made upon it here, it
is with a full consciousness of the inadequate equipment of know
ledge upon which they rest. And it may be doubted whether we
can hope fully to explain why some periods and places are richer
than others in men of fruitful and original thought ; at most we
can hope to show what conditions are favourable to such men's
work when they arise. Now to us, looking backward across the
Middle Ages to the more brilliant days of Athens and of Rome,
and looking also at the great increase of knowledge which the last
three centuries have brought, the stagnation of the sciences in the
period intervening is apt to seem a thing surprising. But how
long was it before ancient science began to appear and to advance ?
The power of tradition and authority over the human mind is the
rule rather than the exception.1 And in the break-up of ancient
civilization there perished not only much knowledge, but much
material wealth ; men were of necessity for long absorbed in the
task of restoring this and restoring order ; and it is not wonderful
that they had little time to spend in questioning such scientific
principles as had survived. Moreover, during the darkest times,
the most powerful and the most beneficent institution that stood
erect was the Church ; the most comprehensive and well-reasoned
theory of the world was that which the Church taught; the
strongest minds, almost the only minds that thought at all, were
enlisted in the ranks of the clergy (which was why independent
thought took so largely the form of heresy), and the interest of
men was directed rather to what concerned the soul than to nature
around them. To this it must be added, that through a series of
historical accidents, a great part of the literature of Graeco-Roman
civilization had perished ; but that of the works of Aristotle some
few were known continuously, and the rest recovered, at least in
translations, by the end of the first quarter of the thirteenth
century.2 The works of Aristotle, by their encyclopaedic range,
by the effort after systematization displayed in them, and by their
1 Cf. Bagehot, Physics and Politics.
2 v. Prantl, Geschichte der Logik, III. p. 3.
XVH] THE FORM AND MATTER OF INFERENCE 347
extraordinary intellectual power, were peculiarly suited to rivet
themselves upon the mind at a time when ability was not wanting,
but when detailed knowledge was slight, and there was little else
to serve for an educational discipline. It is not surprising, if
Aristotle and the Church (especially when the Church pressed
Aristotle's philosophy into its service) acquired a preponderant
influence over men's minds. Indeed, it is hard for us to imagine
what self-confidence and courage were necessary, in order to question
any part of that closely concatenated fabric of belief, upon appearing
to accept which depended a man's comfort in society and perhaps
his life in this world, and upon really accepting it — unless he could
find for himself something better — his confidence with regard to
the next. It is no small testimony to the inexpugnable power of
reason, that this system broke down. And it began to break
down largely through the recovery of other monuments of ancient
thought and learning besides the works of Aristotle. This doubt
less stimulated, though it could not produce, the powers of those
men by whom the foundations of modern science were laid — men
like Copernicus, Galileo, Harvey, Gassendi, Descartes. It was not
the reform of Logic which liberated the mind, any more than it
was Logic which had bound it.
It is, then, rather to the habit of believing on authority, the
strength of which it has been attempted in some degree to account
for, than to the prevalence of an erroneous Logic (whose errors
were not really what the ' inductive ' logicians supposed), that the
stagnation of science for so many generations must be attributed.
Given that habit, it was natural that men should spend time and
thought upon a barren elaboration of the more technical parts of
Logic, and leave the traditional assumptions both of it and of
the natural sciences unexamined. When the overmastering influence
of authority began to decay, the science of Logic shared with other
sciences in the revivification that comes from thinking out a subject
freshly and independently.
But, as was said above, the particular matter which first attracted
the attention of the reforming logician was the barrenness of an
exclusive attention to the forms of valid inference ; and the parti
cular improvement proposed was the establishment of a Logic that
should do for the discovery and proof of scientific principles what
had already in part been done for the drawing of conclusions from
348 AN INTRODUCTION TO LOGIC [CHAP.
them. This at least is how Bacon looked at the matter; and others
have so looked at it after him, in this country more especially.
Now it is a very interesting question, how sciences get their prin
ciples, and when they may be considered proved ; but it is not quite
the same as the question, what kind of principles knowledge
requires.
The works of Aristotle dealing with inference are three — the
Prior Analytics^ the Posterior Analytics, and the Topics. Speaking
generally, the first of these deals with syllogism from a formal
point of view — it pays no attention to the nature of the premisses,
but only to the validity of inference ; the second deals with know
ledge, or demonstration : it asks not when a man is bound by the
acceptance of certain forms of premiss to admit a certain form of
conclusion, but when he can be said really to know a thing
absolutely, and not merely on the assumption that certain premisses
are true ; the third asks how positions can be established or over
thrown, what sort of considerations are useful in weighing their
claims to acceptance, and on what sort of grounds men may be
content to accept their principles in matters where certainty is not
attainable. In the first and in the third of these treatises, Aristotle
was analysing and formulating the actual procedure of his con
temporaries ; he did not, upon the whole, go ahead of the science,
the disputation, the rhetoric and the pleadings of his day. In the
second, he was doubtless guided also by a consideration of the
highest types of scientific knowledge then existing; but he was
guided also by an ideal; he was trying to express what knowledge
ought to be, not merely what the form of men's reasonings was.
It may be said that in scholastic Logic, the problems of the
Prior Analytics bulked too large ; that those who revolted against
this raised, without realizing it, problems of the same kind as
Aristotle had already discussed in the Topics ; but that for a long
time the questions of the Posterior Analytics received insufficient
attention. It is these last which are the highest, and go deepest
into the philosophy of the subject. The physical sciences employ
many principles of great generality which they try to prove ; but
there are some assumptions about the nature of the world, which
they accept without asking why they accept them. As instances
of these may be mentioned what is called the Law of the Uni
formity of Nature — the principle that every change has a cause
xvn] THE FORM AND MATTER OF INFERENCE 349
upon which it follows in accordance with a rule, so that it could
not recur in the same form unless the same cause were present, nor
fail to recur when precisely the same cause recurred : or again, the
principle that matter is indestructible : or that the laws of number
and space hold good for everything numerable or extended. There
are other principles less general than these, such for example as the
Law of Gravitation, of which, as aforesaid, science offers proof;
but whether the proof of these amounts to complete demonstration,
and whether the assumption of the truth of those is justified —
these are problems with which the special sciences trouble them
selves little, and which will not be answered merely by analysing
the nature of the inferential processes that do as a matter of fact
lead scientific men to accept the general propositions which they
conceive themselves to have proved.
This is only an elementary book, and makes no pretence to give
a complete answer to that most difficult of logical questions, What is
knowledge ', in its perfect form ? But from what has been said in the
present chapter, it follows that there are two problems to which
some attention ought to be given. One is the question how, as
a matter of fact, we do get our premisses : the other, what are the
requisites of demonstration.1 The first of these may be called the
problem of Induction.
1 v. p. 487.
CHAPTER XVIII
OF INDUCTION
THE history of the word Induction remains to be written ; but it
is certain that it has shifted its meaning in the course of time, and
that much misunderstanding has arisen thereby. The Aristotelian
term eTraywyri, of which it is the translation, signified generally the
process of establishing a general proposition not by deduction l from
a, wider principle, but by appeal to the particular instances in which
its truth is shown. From what sense of the verb €7rdyeiz> this use
of the word sprang is not clear; there are two passages2, where
the verb, in a logical context which makes it clear that the pro
cess of eTraycay?} is referred to, takes a personal subject ; as if it
were meant that in the process a man is brought face to face with
the particulars, or perhaps brought, and as we could say induced,
to admit the general proposition by their help. In another place 3,
it is the universal proposition which is said to be { induced' or
brought forward or brought up (whatever the best translation
may be) ; and perhaps the not infrequent antithesis of e-Traywy?} and
<n>AAoyi<r^os might suggest that the usual object of the verb is the
inductively obtained conclusion ; the conclusion is certainly what
is ' syllogized ', so that the conclusion may also be what is ' in
duced '. It has, however, also been thought that the process
of bringing up or citing the instances, by means of which the con
clusion is to be established, is what the word was primarily in
tended to signify 4 ; and anyhow the process described is one in
which a general conclusion is established in that way, by citing the
instances of its truth.
1 The history of the term Deduction also remains to be written. aTrayvytj
in Aristotle meant something very different (v. Anal. Pri. /3. xxv : there is also
the use cited p. 290, n. 2, supra], and the nearest Aristotelian equivalent to
Deduction is o-uXXoyioyzos1.
2 An. Post. a. i. 71* 21, 24 : a. xviii. 81b 5.
3 Top. a. xviii. 108b 11 : cf. Soph. EL xv. 174a 34.
4 So apparently Bonitz : v. Index AristoteL, a. v.
OF INDUCTION 351
Induction then meant primarily to Aristotle, proving- a pro
position to be true universally, by showing empirically that it was
true in each particular case : or, proving something about a logical
whole, by appeal to the experience of its presence in every part of
that whole ; as you might show that all horned animals ruminate,
or that whenever the tail of a fish is unsymmetrical (or heterocercal)
it is vertebrated, by a dissection of the intestines of every kind of
horned beast, or of the tail of every kind of heterocercal fish. In
such a proof, it would be assumed that the nature of each specie*
of fish or beast might be judged from the single specimen dis
sected; and it is to be noted that Aristotle thought that the
process of induction began with the infima species ; the species in
his view (as we saw in discussing the Predicables) being essentially
the same in every one of its particulars.1 This form of argument
he described in his own technical language as proving the major
term of the middle by means of the minor ; and he showed how it
could be expressed as a syllogism. From the premisses
The cow, the sheep, the deer, fyc., ruminate
The cow, the sheep, the deer, fyc., are horned
I cannot, as they stand, infer that all horned animals ruminate,
because there may be other horned animals besides all that I have
1 Induction certainly starts in one sense, according to Aristotle, with
individuals ; for it starts with what we can perceive with the senses, and
only the individual can be perceived : cf. e.g. An. Post. a. xviii. 81 b 5-9. But
it may be said that what we apprehend in the individual is its character or
type, and that it is to the individual as such and such an individual that we
appeal : cf. An. Post. a. xxxi. 87b 29. In An. Post. 0. xiii. 97 h 7 seq., however,
Aristotle describes a method of searching for definitions— the example which
he uses is ^yaXo^v^i'a (magnanimity) — in which the instances cited in support
of the definition of /xeyaXo^u^ia are not cited as types at all. This has come
traditionally to be called the method of obtaining definitions by induction ;
and the description of it seems based on those discourses of Socrates to
which Aristotle refers as e-rrnKTiKol \6yoi ; but the term (nayayr) does not
occur in the passage. Still in the argument from Example, or irapddeiyfjLa, the
instance appealed to is not cited as the specimen of a kind ; and he calls
this the rhetorical form of Induction. Hence, though the statement in the
text is true, so far as concerns the proof by induction of the properties of
natural kinds (for in regard to that, Aristotle's particulars are infimae
species), it is difficult to maintain that he never regards induction as
starting with individuals as such. How you are to tell what properties
in a specimen are properties of the species is a question which is discussed
in the Topics] and certainly he would not have thought of proposing to
prove that by a complete enumeration. The species of a genus are limited
in number, and can all be cited ; but not so the individual members of
a species. Cf. infra, pp. 356-357.
352 AN INTRODUCTION TO LOGIC [CHAP.
enumerated ; but if I know that this is not the case : if the
members in my enumeration taken together are commensurate
or equate with the term ' horned animals', then the possibility
which forbids the general conclusion is excluded, and I may infer
that all horned animals ruminate : as is shown by the fact that the
minor premiss may be converted simply ; I may say that all the
horned animals are the cow and sheep and deer, fyc. ; and my syllo
gism becomes formally correct. In such a syllogism we are said
to prove the major of the middle by means of the minor, because
(as we saw) the minor means to Aristotle not primarily the subject
of the conclusion, but the term of least generality and nearest to
the individual ; it is by the particular instances that the predicate
ruminant is proved of the subject horned animal. And if we might
regard the possession of horns as the cause of ruminating, then it
would be the proper middle term by which to demonstrate ruminant
of cow or sheep or deer; in Aristotle's own example, where
longevity is proved of gall-less animals by means of man, horse,
mule (and any other particulars that ought to be mentioned
—though for brevity they are not enumerated), it is supposed that
the absence of gall is the cause of longevity.
In symbolic form then we may express Aristotle's Induction
thus : —
ABCD, &c. are P
AB C D} &c. are all the M
.'. All M are P
This, which he calls 6 ef €iray(oyrjs o-i>\Aoyto-/xoj, is commonly
called now the Inductive Syllogism. If it is to be valid, our
minor term must, as Aristotle says, comprise all the particulars ;
r] yap eTraycoyr) bia TrdvT&v*
We have now seen what Induction, as a formal process, meant
in the mouth of the first author who used the term ; and when
Aristotle insisted that it must proceed through all the particulars,
or (as it was afterwards put) ty complete enumeration— the require
ment which, to Bacon and the 'inductive logicians' of modern
times, has given so much offence— he was quite right ; for if you
are going to establish a general proposition that way, you will
clearly not be justified in making it general unless you have made
1 For induction proceeds through all ' : Anal. Pri. /3. xxiv. 68^ 15-29.
xvm] OF INDUCTION 353
sure that your enumeration of the particulars is complete ; though,
as has been said, it is not really an universal proposition then, but
only < enumerative ' : a thing which Aristotle fails to point out.
The burden of the charge against Aristotle is, however, not that
he held that, if a general proposition is to be established by
enumeration of particulars, the enumeration must be complete :
but that he recognized no other mode of establishing general pro
positions. And if this be so, then his Logic falls to pieces. For
syllogism needs a general proposition for its major premiss; and
as Aristotle himself insists, we cannot be said to know the truth of
the conclusion, unless we know first the truth of the premiss l •
doubt of that will involve doubt of what is stated in the con
clusion, so far as this is arrived at by inference, and not by direct
experience independently of the inference. Now how can this
condition be fulfilled, if our knowledge of any general principle
rests on nothing better than an enumerative assurance that it
holds good in every particular case ? Let us take the principle
that all matter gravitates, and symbolize it in the form 'All
M is 6" '. If it is possible to know this without experience of its
truth in every parcel of matter, we may use it in order to
prove that this book must gravitate; and therefore may refrairji
from adding the book to one's kit in going up a mountain, or laying
it upon a flower that is for show, or on the other hand may use
the book to keep one's papers steady in a wind or as a missile
against a neighbour. But if the principle can really only rest upon
a complete enumeration, we must experiment with this book, before
we can assert it ; and then we shall know that this book gravitates
by direct experiment, and our deduction thereof from the general
principle will be superfluous, even if the enumeration be complete —
as it would only be, if this book were the last parcel of matter
to be experimented with ; but even so, the deduction would be
but a hollow show, and begging of the question. For let us
symbolize any particular parcel of matter by \i. We propose to
prove that /u, is G, because all M is G, and fj. is M ; how do we
know that all M is G ? Only because pv /u2, &c. up to //„ are G, and
Hv P2 ... pn are all the J/, and therefore all M is G. Hence we
use the fact that p is G to prove the principle by which we prove
that /LI is G. And the upshot of this is that we can never prove
1 An. Post. a. ii. 72a 25-H.
354 AN INTRODUCTION TO LOGIC [CHAP.
anything by reasoning, until we already know it by direct experi
ence ; so that the use of reasoning, in order to infer that which we
have not learnt by direct experience, must disappear. If we still
try, by appeal to any general principle, to prove anything which
we do not already know, we shall be appealing to a general prin
ciple which we do not know to be true, in order to prove a particular
conclusion which we do not know to be true ; for ex hypothe&i our
knowledge of the truth of the general principle depends upon the
knowledge of what occurs in the particular case in question among
others. Such a procedure hardly commends itself to a sane man.
And if again it were said, that however little we may be logically
justified, in advance of experience, in drawing inferences about
some particular from a general principle, yet our experience when it
comes is constantly confirming the inferences we thus draw, this,
far from being a solution of the logical difficulty in which we have
found ourselves, ought only to be matter of perpetual astonishment,
to a creature that reflects at all about his experience.
Such is the difficulty that arises, if there is no other means of
proving a general proposition than by enumeration of all the parti
culars to which it refers 1 ; and to this criticism Aristotle is obnoxious,
if he recognized no other means. But did he recognize no other ?
Now Aristotle undoubtedly says that we arrive at our first prin
ciples by a process of Induction 2. He draws a famous distinction
between the logical order and the order of experience 3 ; in the
logical order, the general principle is prior to the sensible fact ; in
the order of experience, it is the reverse. To us, the particulars
of sense are known first : the intelligible principles by which these
are explained are known afterwards ; but Nature may be conceived
as starting with principles or laws, and with these in her mind
proceeding to the production of particular objects or events. In
duction proceeds from what is first in the order of experience to what
is first in logical order : from the apprehension of the sensible facts
to the apprehension of the general principles, out of which we sub
sequently construct the sciences. Without sense-experience, there
is no knowledge of intelligible principles ; and the process of obtain
ing that knowledge out of sense-experience is Induction.
1 Cf. what was said above, in discussing the Dictum de omni et nullo.
2 See e.g. An. Post. p. xix. 100b 4.
8 Xdyo) or (pv&e i irportpov and rjiiiv irportpov : cf. p. 73, supra.
xvm] OF INDUCTION 355
And this, taken together with his analysis of the Inductive
Syllogism, might seem to settle the question ; if only we could
suppose Aristotle capable of overlooking the difficulty in which his
whole system would thereby have been involved. But so far from
overlooking, he shows in one passage that he had considered it, and
uses his distinction between what is logically prior, and prior in the
order of our experience, in meeting it1. His view seems to have
been this.
The business of any science is to demonstrate the properties of
a kind — such kinds, for example, as geometrical figures, species of
animals or plants, or the heavenly bodies. As we saw in the
chapter on the Predicables, he was influenced much by the fact that
geometry and biology were the two most progressive sciences of his
day. Science is concerned with kinds, as what are identical in their
many members, and eternal. In demonstrating their properties, it
starts from a knowledge of their definitions ; such definitions cannot
themselves be demonstrated ; and for them we are dependent on
experience, which familiarizes us with the nature of any kind, or of
its properties, by means of particular cases. But though experience
may thus acquaint us with the definition of anything, yet the essential
nature of a thing (which is what a definition gives) cannot possibly
be an empirical fact. It may be an empirical fact that all sailors
are superstitious ; but how can it be an empirical fact that a triangle
is a three-sided rectilinear figure ? For to say that anything is an
empirical fact implies that it might (so far as we can see) have
been otherwise ; and certainly we can conceive that a sailor may be
either superstitious or not superstitious ; but we cannot conceive
that a triangle should not be a three-sided rectilinear figure, since
if that — which is its essence — were removed, there would be no
triangle left to be anything else. It will be asked, how do you
know what constitutes the essence of anything ? The answer is,
that the intellect sees it : sees it, as we might say, intuitively, as
something necessarily true ; and this is the source of our assurance,
in virtue of which we know the principles from which our demon
stration proceeds more securely even than the conclusions we draw
from them. But the intellect does not perceive it at once ; experience
of things of the kind is necessary before we can define the kind.
1 An. Post. a. iii.
A a 2
356 AN INTRODUCTION TO LOGIC [CHAP.
The use of these particulars is, not to serve as the proof of a principle,
but to reveal it : as the counters, for example, which a child uses
in learning the multiplication table, though one among innumerable
instances of the fact that three times three is nine, are to be
appealed to not because the general proposition could not be asserted
unless it were tried and found true in the case of these counters as
well as of all other countable things : for had the child learned with
nuts, it would have been quite unnecessary to confirm the generaliza
tion by an examination of the counters ; but because they serve as
a material in which the child can be brought to realize the truth of
a numerical relation, which it apprehends forthwith with a generality
that goes far beyond these particular counters. They are a means
used because some countable material is necessary in order to realize
the general truth; but the general truth is not accepted simply
because it is confirmed empirically by every instance.
Now we need not ask at the moment whether the sort of
intellectual insight with which we do apprehend the necessity of
numerical or spatial relations * can really serve us in determining
the essence of gold or of an elephant or a tortoise; our present
purpose is only with the nature of Induction, and the different
senses in which the term has been used. And the purpose of the
preceding paragraph is to show that in spite of the analysis which
Aristotle gave of Induction as a logical process, yet when he said
that we get our first principles by induction, he had something else
in his mind. Where your units are species, and you want to prove
something about the genus to which they belong, there you may
proceed by appealing to the fact, that it is found true of every
species in the genus ; there your reasoning may be thrown into
the form of the ' inductive syllogism ', — which is inconclusive unless
every species is included in the premisses. But even there, from
the fact that he regarded the conclusion as an universal and not
merely an enumerative proposition, we must suppose Aristotle to have
1 There are philosophers who would not agree with what has been said of
the nature and grounds of our assurance of the truth of mathematical
principles. Some hold that they are only generalizations from experience,
deriving their high degree of certitude from the great number and variety
of the instances in which they have been found to be true. This doctrine
is maintained in a well-known passage of Mill's Logic, Bk. II. cc. v-vii, to
which he refers in his Autobiography as a crucial test of his general
philosophical position. For a partial examination of the passage, crushing
so far as it goes, see Jevons's Pure Logic and other Minor Works, pp. 204-221.
xvm] OF INDUCTION 357
thought that the mind grasped a necessity in that relation between
the terms of the conclusion, at which it arrived by a process of
enumeration ; directly or indirectly, the connexion of longevity
with gall-lessness was to be seen to be necessary, and freed from
the appeal to man or horse. And where your units are individuals,
and you want to discover the essential nature of the species to
which they belong, there you do not work by an inductive syllogism
that summons all the instances to bear witness to the truth of your
definition ; for how could you summon the numberless members of
a species ? There is still a use for experience ; we may still say
that we know these things by induction ; but the induction now is
a psychological rather than a logical process ; we know that our
conclusion is true, not in virtue of the validity of any inductive
syllogism, drawing an universal conclusion in the third figure because
the subject of the conclusion is coextensive with the particulars,
taken collectively, by means of which we prove it : but in virtue of
that apprehension of the necessary relation between the two terms,
which our familiarity with particulars makes possible, but which is
the work of intellect or vovs.
Such seems to have been Aristotle's doctrine : and thus he
avoided the bankruptcy that would have ensued, had he taught
that all syllogism rested on universal propositions, and that universal
propositions rested on nothing but showing by enumeration that
they held true in every particular instance that could be brought
under them. But it may be said that thus he only avoids the
Chary bdis of moving in a logical circle to be snatched up by the
Scylla of an arbitrary assumption. We are to accept the general
propositions upon which every subsequent step of our inference rests,
because our intellect assures us of their truth. This may satisfy
the man whose intellect gives him the assurance ; but how is he to
communicate that assurance to others ? If a principle is not
arrived at from premisses which another admits, and between which
and it he sees a valid process of inference to lie, why should he
accept that principle? No evidence is offered, whose sufficiency
can be tested. The iptse dixit of an incommunicable intuition
takes the place of any process of reasoning, as the means whereby
we are to establish the most important of all judgements — the
general propositions on which the sciences rest.
Of this charge Aristotle cannot altogether be acquitted ; yet we
358 AN INTRODUCTION TO LOGIC [CHAP.
may say this much in his favour. Such an intellectual apprehension
of the necessary truth of the principles from which demonstration
is to start forms part of our ideal of knowledge 1 ; doubtless it seldom
enough forms part of the actuality. But Aristotle idealized; he
spoke of what, as he conceived, science in the fullest sense of the
term involved, and forgot to state, or failed to see that the sciences
did not realize it. And the prominence which he gave to the
question ( What sort of premisses does knowledge require ? ' led
him to relegate to an inferior position the question ' How can the
sciences as they are validate their premisses ? '
He did not overlook this last question altogether; indeed he
devotes to it a considerable portion of the longest of his logical
treatises, the Topics ; for when he asks by what sort of considera
tions you can prove or disprove that a proposition gives in its
predicate the definition, or a property, of its subject, he is asking
how you can prove scientific first principles. And he knew this ;
and among the uses of Dialectic, or of the disputation whose methods
he elaborates in the Topics^ he places as its most peculiar use the
examination of the truth of scientific principles.2 But he ought to
have seen that, outside mathematics, we seldom have any other means
of establishing general propositions upon the evidence of particular
facts than those of the kind which he discusses in the Topics. For
the rest, his account of the logic of the reasoning by which the
sciences do as a matter of fact support the general principles which
they accept contains hints which are in advance of much modern
' inductive logic ' ; though there is much in his conception of the
character of the general principles which science seeks to establish,
that is now antiquated. Science seeks to-day to establish for the
most part what are called ( laws of nature ' ; and these are generally
answers rather to the question ( Under what conditions does such
1 With this proviso, that for perfect knowledge all the parts of truth
ought to seem mutually to involve each other. In mathematics, where alone
we seem to achieve this insight into the necessity of the relations between
the parts of a systematic body of truth, we find our theorems reciprocally
demonstrable ; and if twice two could be three, the whole system of
numerical relations would be revolutionized. Yet we do not need to wait
till we discover how all other numerical relations are bound up with the
truth that twice two is four, before we are as fully convinced of this truth
as we are capable of becoming. Whether in every science we should desire
that each principle should thus be apprehended as necessarily true, even
when cut off from its implications, may be doubted.
» Cf. Top. a. ii. 101* 84-»4.
xvm] OF INDUCTION 359
and such a change take place ? ' than to the question ' What is the
definition of such and such a subject ? ' or ' What are its essential
attributes ? ' l It is more in respect of the problems to be answered,
than of the logical character of the reasoning by which we must
prove our answers to them, that Aristotle's views (as represented in
the Topics) are antiquated.
We may briefly indicate the nature of c dialectical ' reasoning, as
Aristotle conceived it, and of the ' topics ' which it employed.
Dialectic is contrasted with science. Every science has its own
peculiar subject-matter : geometry investigates the nature and
properties of space, geology the conditions which determine the
character and distribution of the materials which form the crust
of the earth, physiology the functions of the organs and tissues of
living bodies, &c. Each science, in explaining the facts of its
own department, appeals to special principles, or tdtat ap\ai ; to the
specific nature of its own, and not another, subject-matter — to laws
in accordance with which that particular class of facts is determined,
and not another class. The geometrician makes use of the axiom of
parallels, of the notion of a straight line, of the definition of a cone
or circle ; but the nature of chalk or granite is indifferent to him.
The geologist will use such principles as that stratified rocks are sedi
mentary, or that mountains are reduced by denudation ; but he
draws no conclusions from the definition of a cone. The physiologist
in turn has his own probkms to explain, and his own principles to
explain them ; that every tissue is composed of cells which multiply
by division is a physiological principle of which we hear nothing in
geology, while the laws of denudation contribute nothing towards
the explanation of the growth of living bodies.2 Dialectic, on the
1 I think this contrast is substantially true ; though it is possible to bring
many scientific investigations to-day under one or other of the types of
question which Aristotle says we enquire into, yet looking to his examples,
one must confess that (as is natural) he put the problems of science to
himself in a very different manner from that in which scientific men put
them now. Cf; An. Post. /3. i. 89b 23 TO. frrovfjitva tamv icm TOV apiOpov oo-arrfp
fTTKTTdfjLeda. ff/Tov/iev de Ttrrnpa, TO on, TO diori, ft tort, ri (<rnv.
2 One science does often to some extent use the results of another. In
particular, of course, all the other sciences resolve all they can into terms
of chemistry and physics. Yet looking (say) to Physics, Chemistry, Physio
logy, and Political Economy, no one will deny that they must continue
to rest each in part on different principles, even if the later mentioned may
have to take note of some facts whose explanation involves the principles of
the earlier mentioned. Aristotle noted such partial use by one science of
the results of another ; though the state of the sciences in his day prevented
360 AN INTRODUCTION TO LOGIC [CHAP.
contrary, has no peculiar subject-matter ; all the sciences submit
their principles to its investigation; the dialectician may ask
whether a geometer would be right in saying that it is a property
of a triangle to have its exterior angles equal to four right angles :
whether the geologist has rightly affirmed all stratified rocks to be
sedimentary : whether the physiologist would do well to accept
Spencer's definition of life, as ' the continuous adjustment of inner
to outer relations '. And in debating such questions, the dialecti
cian will invoke not special, but common principles, K.OLVOL ap^ai 1-^-
i. e. not principles whose application is confined to the science he
happens to be investigating, but principles of universal appli
cation : as, for example, that what is common to the genus is
not a property of the species — whence it follows, that since all
rectilinear figures have their exterior angles equal to four right
angles, this is not a property of a triangle, or in other words, that it
is because a figure is rectilinear, and not because it is three-sided, that
this can be predicated of it ; it is for the geometer to show that all
rectilinear figures have their exterior angles equal to four right
angles ; the dialectician's business is to show that it cannot therefore
be called a property of a triangle, as such. Or again, the dialectician
may ask, with regard to Spencer's definition of life, whether the
distinction between ' inner ' and ' outer ', on which it rests, is clear ;
for he knows that the terms of a definition should be clear, though
he does not necessarily know physiology ; and if Spencer, or his
him from illustrating it as it would be illustrated now, and his remarks on
the subject are open to a good deal of criticism. Cf. An. Post. a. xiii. 78b
32-79a 16.
1 Cf. Anal. Post. a. x. 76b 11-22, xi. 77a 26-34, xxxii. 88a 31-3b, b9-29.
In the second of these passages, Aristotle gives as examples of * common
principles ' the Law of Contradiction, that the same proposition cannot be
at once true and false, and the mathematical axiom that the differences
between equals are equal. The latter is not really 'common ', but special
to the sciences of quantity ; and if he wished to be consistent with what he
says in /3. xvii. 99a 6-16, Aristotle should have allowed that it means some
thing a little different in geometry and in arithmetic. By no means all of
the communes loci in the treatise called the Topics are ' common principles '
— e. g. the topics given in y, rrepl TOV atpereorepou, which are principles to be
appeale'd to in determining which of two goods is to be preferred : as, that
the more lasting good is preferable, or the more secure, or the greater, or
the nearer. Most of them however are such, though it must be admitted
that Aristotle does not describe his topics as common principles, or kotval
ap^ai : and I think that the distinction which he intends to convey in the
Posterior Analytics by the antithesis of tStai and Koivai dpxai is really what
has been stated in the text.
xvm] OF INDUCTION 361
disciples, could not show precisely what it means, he would say the
definition must be faulty ; and if they replied that ' inner ' meant
within the organism, and ' outer ' outside it, he would ask whether
all material systems which changed inwardly in response to changes
outside them are living bodies ; for he knows that a definition
should not apply to anything except the species defined, and if this
expression does, it cannot be a definition ; or he might ask whether
many of the peculiar processes of living bodies are not apparently
initiated from within the body ; and if the answer was affirmative,
he would again object to the definition ; for though it is not his
business to know whether any of the peculiar processes of living-
bodies are initiated from within or not (and therefore he has to ask the
physiologist how that matter stands) it is his business to know that
a definition must include everything essential to the thing defined ;
so that if there are such processes, a definition of life which excludes
them must be a wrong one. Or, lastly, the dialectician might ask
the geologist if there are not some igneous rocks that are stratified :
not knowing, as a dialectician, the answer to that question, but know
ing that, since igneous rocks are not sedimentary, the existence of
igneous rocks that are stratified would upset the geologist's proposi
tion; while if the geologist were able to answer the question in
the negative, he would so far have come out victorious under
examination.
All these general principles, to which the dialectician appeals,
are called topics l : it is a topic, that what belongs to the genus is
not a property of the species; or that what in some particular
instance is absent from a species is not a property of it ; or that
the terms of a definition must be precise, or that it must be com
mensurate with what is defined. All these principles hold good in
any science ; it matters nothing what the species may be, or what
the property, or what the definition. A man therefore whose mind
is stocked with principles of this kind has points of vantage, as it
were, from which he may proceed to attack or defend any definition,
any predication of a property ; they are topics in common, ' common
places/ points of view whence you may approach to the consideration
of the statements of any science. Just as a man who knows nothing
of the truth of its premisses may be able to detect a flaw in a syllo
gism, so the dialectician, without a scientific knowledge of a subject,
1 TOTTOJ, Zoct, communes loci.
362 AN INTRODUCTION TO LOGIC [CHAP.
may know what sort of questions to ask, if he wishes to test a
scientific man's right to affirm the principles he enunciates.
Aristotle's Topics is written with reference to his doctrine of
Predicables. He regards every proposition as asserting (or denying)
some accident, property, differentia, genus or definition, of its subject ;
and he asks, to what considerations are you to look, if you would
know whether such and such a predicate does stand to such and
such a subject in any one or other of these relations ? Each of these
considerations is a topic. He details an astonishing number of
them. They are of very different degrees of importance and value.
Some are drawn from language. Look, he says, for example, to
conjugate terms ; if noble is a property of just, then justly is
nobly ; perhaps a man who affirmed generally that justice is noble
might admit that it is possible in some cases to act justly and not
nobly.1 Others are based on the principle that contrary things
have contrary properties ; so that you cannot say that the just is
the equal, unless you can say that the unjust is the unequal. Some
aim only at enabling you to determine whether an expression is
elegant, according to accepted rules. But others are principles of
great importance. For instance, there is what we might call the
topic of Concomitant Variation 2 ; that is not a property of a subject
which does not increase or decrease with an increase or decrease in
the subject, and conversely, if you find two things increasing and
decreasing together you may assert such connexion between them.3
Considerations of this kind enable you to judge how different
concepts are related to one another ; and relations between concepts
furnish the principles with which the special sciences work.
It may be admitted that this treatise contains much that is
trivial; that it throws together considerations, or principles, of
great and of little cogency ; that the problems of science assume
other forms than determining the definition of a subject, its
properties, or its accidents (although these problems occur too, and
many problems which we should not express in those forms can be
translated into terms of them). It may also be admitted that
Aristotle had his mind fixed too exclusively upon debate. The
answers to the questions asked were to come from the respondent —
the other disputant ; but in building up the sciences, they must
1 Cf. Top. (. vii. 136b 15. 3 ronos eVc TOV /uaXXov Kal
3 e.g. Top. t. viii.
xvin] OF INDUCTION 363
come from the field and from the laboratory. Aristotle would have
a man test any scientific doctrine that is put forward by interro
gating its maintainer ; the man of science must test those which he
himself or a fellow worker puts forward by interrogating- nature.
It would be easy to do Aristotle an injustice on this head. It may
be assumed after all that the respondent testifies to what he has
seen ; and Aristotle was alive to the importance of collecting and
recording facts.1 But the Topics is a treatise on the art of disputa
tion; disputation aims after all more at silencing an opponent
than at establishing truth ; and though we are told that Dialectic
has its use as much in the examination of the principles of the
sciences as in the conduct of a disputation, it is in the latter spirit
that it is expounded. Nevertheless, in the distinction drawn
between scientific and dialectical reasoning, as illustrated above,
and in its account of the general nature of the considerations to
which one must appeal in any defence of the principles of a science,
the Topics is a work of great logical value.
What, then, has Aristotle to say about Induction ?
1. He gives the name to a formal process of inference, by which
we conclude a proposition to hold universally of some class, or
logical whole, because an enumeration shows it to hold of every
part of that whole. This is what has been since called Induction by
Complete Enumeration, or Perfect Induction ; and he shows how it
might be thrown into the form of an Inductive Syllogism.
2. He points out that our knowledge of scientific principles
springs historically out of our experience of particular facts ; though
its certainty rests ultimately upon an act of intellectual insight.
And he gives the name of Induction to the process in which the
particulars of our experience suggest to us the principles which they
exemplify. But this is not a formal logical process from premisses
to conclusion ; and it is not the induction (in this sense) which leads
us at the end to accept such principles, but our intellect, or vovs.
3. He shows where (presumably in default of the necessary
insight and assurance from our intellect) we may look for reasons
for accepting or rejecting any principles which a science puts forward.
He does not give to this procedure, which is of a formal logical
kind, the name of Induction, but calls it Dialectic; nevertheless
what he says on this head is of much the most importance from the
1 Anal. PH. a. xxx.
364 AN INTRODUCTION TO LOGIC [CHAP.
point of view of scientific method, and comes much closer to what
modern writers understand by Induction.
Thus he admitted that our knowledge of general principles comes
from our experience of particular facts, and said that we arrive at
them by Induction ; but the only formal logical process which he
described under the name of Induction was that ' Perfect Induction '
which clearly neither is nor can be the process by which the sciences
establish general propositions ; while the kinds of process which
they really do employ, so far as they appeal merely to the evidence
of our experience, he described under a different name. It is not
surprising that some confusion has resulted.
The critics of whom Bacon is the coryphaeus, recognizing with
Aristotle that we discover universal truths by induction, attacked
him for saying that we only discover them by complete enumeration,
which he had not said; and finding the name of Induction given
to no other formally valid process than this1, supposed he had
nothing else to say of the processes by which such truths are reached.
Bacon himself attempted to systematize the process of discovering
and proving them in a way which undoubtedly possesses value, and
no less undoubtedly owes much to Aristotle ; but as the Aristotelian
ideas on which it is based do not occur in the Organon in connexion
with tiraytoyriy he hardly realized how much he was borrowing.
His analysis is offered in connexion with an unworkable theory of
the nature of the problems which science should set itself to solve.
To put it summarily, he thought that a list of the several sensible
properties of bodies should be drawn up, and that men should then
try to discover on what particular principle of corpuscular structure
in the bodies that exhibited it each property depended. There was
nothing in the conception of any particular principle of structure,
which would lead you to anticipate that its presence would involve
any one sensible property more than another ; you could not tell,
apart from experience, that a particular motion of the component
particles of a body would exhibit itself to the senses as heat, or that
a particular disposition of its surface particles would show as white,
and another disposition as black. Suppose we were to symbolize
the sensible properties of bodies by Roman letters, and the principles
1 It was also given to Induction by simple enumeration — i.e. to any attempt
to prove a general proposition by merely citing a number of instances of its
truth ; but this is not a formally valid process.
xvm] OF INDUCTION 365
of .corpuscular structure in them on which these depend by Greek
letters : how are you to prove whether a property a is connected
with a or b or z ? Bacon's answer is as follows. He called the
principles of corpuscular structure Forms : whatever be the Form
of a given property a, it must be so related to a as to be present
in every body in which a is present, to be absent from every body
whence a is absent, and to increase or decrease in any body as a
increases or decreases. Our problem then is, as he says, ut inve-
niatur natura alia (the Form) quae cum natura data (the sensible
property) perpetuo adsit, ab&it, crescat atque decrescat.1 How are we
to solve it? No mere enumeration of instances in which a sensible
property a and a Form a are present together will prove that they
are thus related, and that a is the Form of a ; for your enumeration
must be finite, but your conclusion is to be universal. You may
find a hundred bodies exhibiting both a and a : yet the presence of
one may be quite unconnected with the presence of the other, and
you may find a body to-morrow exhibiting one without the other.
We must proceed then by exclusions. Where a hundred instances
will not prove an universal connexion, one will disprove it. This
is the corner-stone of his method : maior est vis instantiae uegativae?
If we had drawn up an exhaustive list of the different principles of
corpuscular structure present in bodies in different combinations, all
we: should have to do would be to find instances in which any of
these was present in a body that did not exhibit the property a,
or absent in one that did exhibit it, or in which it increased or
decreased without a corresponding variation in the degree of the
property, or vice versa. We could then confidently reject that Form ;
and when we had thus rejected every other Form, then we could con
fidently affirm that principle of corpuscular structure which alone had
not been rejected to be the Form (or cause of the presence) of a given
sensible property a. Our assurance would rest not on the positive
testimony of its presence along with a in a number of instances,
but upon the fact that we had disproved all possible rival theories.
It will be seen that this procedure presupposes that we know all
the possible Forms, among which that of any particular sensible
property is to be sought ; and Bacon, though he promised to do so,
1 tfpv. Org. II. 4.
2 Ib. I. 46. Cf. Aristotle, Anal. Pri. a. xxvi. 43a 14 a/*a St 8i)Xov on KOI TO
v eori roO KaTao-Kfviifaiv paov I and more fully, Top. TJ. v.
366 AN INTRODUCTION TO LOGIC [CHAP.
never showed, and could not have showed, how we were to discover
that. The procedure is formulated too under the idea, that the
immediate task of science is to draw up a complete list of all the
distinct sensible properties found in nature, and then look for what
we should perhaps now call their physical basis. This idea was
mistaken. But the fundamental principle of the method by which
Bacon proposed to ' interpret nature ', the principle on account of
which he gave it the name by which he called it, Exclusiva, is
correct ; it is that where you cannot (as in Mathematics) see that
a proposition must universally be true, but have to rely for the proof
of it on the facts of your experience, there there is no other way of
establishing it than by showing that facts disprove its rivals.1
Bacon called this method inductive ; it may be as well to point
out at once that formally the reasoning involved is just that of
a disjunctive argument. The alternative hypotheses (with Bacon, the
alternative hypotheses as to the Form or physical basis of a particular
sensible property) are so and so : such and such of them are false ;
therefore the one remaining is true. How we are to discover what
the alternative hypotheses are, he does not explain to us ; we are to
prove that the rest are false by appeal to the facts of our experience ;
these facts he would have men methodically collect and tabulate, and
in making use of them he relies upon the general principle that
nothing can be the Form sought for which is ever present in the
absence of the property whose Form it is alleged to be, or absent in
its presence, or variable when it is constant, or constant when it
varies ; when he has got his premisses, his conclusion follows accord
ing to the ordinary principles of disjunctive reasoning.
Bacon wrote in the dawn of modern science, and proclaimed with
splendid confidence its future triumphs. His predictions have been
fulfilled, perhaps to the extent, though not on the lines, that he
anticipated. Spes eat una, he wrote, in inductione vera 2 ; and as men
watched the continuous progress of the inductive sciences, they
came to think that induction was really some new form of reasoning,
ignorantly or perversely rejected by our forefathers in favour of
1 There are many very valuable remarks in Bacon's account of his ' Exclusiva'
about the kind of instances which are of most evidential value (and he
therefore calls them Prerogative Instances) ; but a discussion of them would
hardly be relevant to the present argument.
* Nov. Org. I. 14.
xvm] OF INDUCTION 367
the deductive reasoning, which they associated with the name of
Aristotle, and now held to be in comparison an idle thing. To
praise induction became a sign of enlightenment ; but the praise of it
ran ahead of the understanding.
Those who did the most to advance the sciences had not the need
or inclination to pause and analyse the arguments which they were
so successfully building up ; nor would it imply any disrespect to
add, that many of them probably had not the power of doing so.
It is no more necessary that a great scientific genius should be able
to give a correct account of the methods he uses than that a great
artist should be able to expound the philosophy of art ; those can
often do things best who are quite unable to explain how they do
them. The chief scientific name in the history of speculation upon
the logic of the inductive sciences in this country is that of
Sir John Herschell ; four writers in all, if we exclude those
still living, have made the principal contributions to the subject.
David Hume, in a brief section of his Treatise concerning Human
Nature (Of the Understanding, Part III, Sect, xv), gives c Rules
whereby to judge of causes and effects ' which contain the pith of
much subsequent writing ; but the work, as he said himself, ' fell
stillborn from the press ' ; this section was not incorporated in the
later and more popular ' Enquiry ' ; and it had no influence on
the exposition of Induction. Sir John HerschelFs Discourse
concerning the Study of Natural Philosophy and the various works
of Dr. Whewell did, on the other hand, much to stimulate interest
in the subject; especially since Whewell propounded an explicit
theory of it. The help which he had derived from both is acknow
ledged by J. S. Mill, whose System of Logic for many years held
the field as an exposition of inductive reasoning. To that more than
to any other work is to be traced the prevalence of the opinion, that
inductive reasoning, or Inductive Logic as the theory of it, is
a discovery of the moderns — an opinion which certainly contains
less truth than falsehood. The name induction may be said with
him to have stood for more than a particular form of inference ; it
was the battle-cry of a philosophical school, the school, as it is called,
of experience. But as a result of this, and of its previous history, it
has become one of the most confusing terms in Logic. It stands
firstly for that induction by complete enumeration which Mill
denies to be properly induction at all, but from which his influence
368 AN INTRODUCTION TO LOGIC [CHAP.
was unable to withdraw the name after the prescription of so many
centuries. It stands secondly for the logical processes employed
in the inductive sciences, so far as these infer from particular facts
the principles that explain them ; as to what the nature of these
logical processes is, Mill had a theory different from WhewelFs,
and others have since had theories different from Mill's. Thirdly,
Mill, who admits that there are certain general principles assumed
as true in the reasonings of the inductive sciences, gives the name
to what he conceives to be the logical process by which these
principles themselves are reached : a process that starts, in his view,
barely from a great number of particular facts, and without the
help of any general principles at all bases upon these facts the
general principles whereon all other inductive inference rests.
Many of Mill's critics have thought, and have thought rightly —
for it is better to state one's position explicitly at the outset — that
if the process by which these principles are reached were as he
describes it, it could only be called an illogical process.1
It would have been possible to omit the foregoing historical
sketch, and to offer a purely dogmatic account of what Induction is,
and what it is not. But against such a course there were two
reasons. In the first place, a new writer has no right to do such
a thing. It is indeed necessary for him to put forward that account
of the nature of the reasoning of the inductive sciences, which he
believes to be true ; but not as if he was only delivering an accepted
tradition. And in the second place, unless the reader knows some
thing of the history, he can hardly fail to be confused by the
diversity of senses in which he finds the word Induction used.
Men have rightly felt that an antithesis could be drawn between
the inductive and the deductive sciences ; though they can be
classed only according to their predominant character, since no
sciences, except the mathematical, are exclusively the one or the
other. On the strength of this they have most unfortunately
erected an antithesis between Inductive and Deductive Logic :
1 The second part of Jevons's Principles of Science ought perhaps to have
been included along with the four works mentioned above (cf. also Lotze's
Logic, Bk. II. c. 7). Among contributions on the part of living writers to
the criticism of Mill's doctrines (for the great acceptance which his views
obtained has made criticism of him a prominent feature of much subsequent
writing on Induction) may be mentioned Bradley's Logic, Bk. II. Part ii.
cc. 2 and 3, and an excellent discussion in Professor Welton's Manual of
Logic, vol. ii. § 155.
xviii] OF INDUCTION 369
unfortunately, partly because Logic is one; the science which
studies the nature of our thought embraces equally the processes
of thought that enter into the construction of the deductive sciences
arid of the inductive ; but unfortunately also, because it has led to
much misunderstanding of the nature of inductive reasoning itself.
Inductive Logic has not really laid bare any new forms of reasoning ;
we have already seen that Bacon's Induction is a disjunctive
argument. The true antithesis is, as Aristotle saw, the antithesis
between Dialectic and Demonstration ; or in more modern phrase,
between Induction and Explanation.1 Or if any one likes to keep the
antithesis between Induction and Deduction, and to call inference
deductive when it proceeds from conditions to their consequences,
and inductive when it proceeds from facts to the conditions that
account for them 2, he will find
a. that the two processes cannot be kept rigidly apart. Whoever
infers from the facts of experience the conditions which account
for them must at the same time in thought deduce those facts
from those conditions.
b. that what has been called Deductive Logic, what Inductive
Logic has been contrasted with, analyses forms of inference
which, if the antithesis between Induction and Deduction be
thus understood, must be called inductive. This will appear
more fully by and by ; it will be admitted now that, if it is
true, though we allow a difference between inductive and
deductive reasoning, we had better give up opposing Inductive
and Deductive Logic.
1 The two antitheses are not quite identical, because some dialectical
arguments are not inductive, and explanation is not demonstrative unless
the premisses from which it proceeds are known to be true. The reasoning
from those premisses is however the same, whether the premisses are known
or only believed to be true (cf. c. xxiii, infra}.
2 Induction is often regarded as proceeding from particular facts to the
establishment of general principles, under which those facts are then
brought by sulsumption, and so accounted for. And though we may also
inductively establish from one particular fact the existence of another
conditioning it, yet such a conclusion does imply a general principle of
connexion. But it must be remembered that this reasoning starts from the
assumption that there are universal connexions (cf. next ch., and p. 502,
infra}. Moreover to have written general principles for conditions in the
text would have narrowed unduly the scope of Deduction, which frequently,
as in Mathematics, proceeds from one fact to another without any applica
tion of a general principle to a particular case subsumed under it. Cf.
infra, pp. 401 n. 1, 487 n. 2, 505 n. 2.
CHAPTER XIX
OF THE PRESUPPOSITIONS OF INDUCTIVE
REASONING: THE LAW OF CAUSATION
'WHY is a single instance, in some cases, sufficient for a com
plete induction, while in others myriads of concurring instances,
without a single exception known or presumed, go such a very little
way towards establishing an universal proposition? Whoever can
answer this question knows more of the philosophy of logic
than the wisest of the ancients, and has solved the problem of
Induction/1 However we may think of the knowledge possessed
by the wisest of the ancients, the question which Mill asks is no
doubt an important one. By what right do we ever generalize
from our experience ? and how can we tell when we have a right
to do so? To these questions we must now attempt an answer.
Afterwards we may note what other processes of thought besides
generalization enter into the sciences ; and then we shall be able
to realize better the true nature of that antithesis between induc
tion and deduction which was spoken of at the end of the last
chapter.
The present chapter will address itself to the question, by what
right do we ever generalize from experience. This is the primary
question. Syllogism never generalizes. Unless it is provided
with universal propositions for premisses, it cannot arrive at them
in its conclusions, and even so, its conclusion is never more general
than its premisses.2 It is just this fact which raised the difficulty,
1 Mill's Logic, III. iii. 3, concluding paragraph. Strictly speaking,
a single instance never is sufficient— if we had really to rely on it alone
without help from conclusions already drawn from other parts of our
experience. Cf. Jevone, Pure Logic and other Minor Works, pp. 295-299 ; and
also Lotze, Logic, §§ 252, 253.
2 The third figure, when both premisses are singular propositions, may
seem to furnish an exception to this statement, and it would hardly be
a sufficient answer to recall the fact that this is the inductive figure ; for
PRESUPPOSITIONS OF INDUCTION 371
how to get the universal propositions which syllogism needs to
start with. If experience gives us only particular facts, how are
we to get universal conclusions out of them ? A mere enumeration
of particulars will justify a conclusion about no more than the
particulars which have been enumerated, whereas we claim in any
generalization to go beyond the observed facts on which the general
ization is based, and to draw a conclusion true in any possible
instance whatsoever. By what right do we do this ?
The answer is that all induction assumes the existence of uni
versal connexions in nature, and that its only object is to determine
between what elements these connexions hold. The events of our
experience are no doubt particular, but we believe the principles
which -they exemplify to be universal; our difficulty lies in dis
covering what principles they exemplify ; in that, a close study of
particular facts will help us ; but were we to be in doubt whether
there are any such principles or not, no amount of study of par
ticular facts could resolve our doubt.
There are many ways in which this assumption may be ex
pressed. It will be well to consider some of these, and to ask
what precisely it is that we assume. We may then show that (as
has just been said) it is hopeless to attempt to prove the assump
tion by any appeal to experience ; and ask ourselves what justifi
cation we have for making it.
The commonest expression for it is the Law of Universal Causation,
or (more briefly) the Law of Causation-, again, we say that we
believe in the Uniformity of Nature ; but the same idea is implied
in the distinction between essential and accidental circumstances, or
in asking what circumstances are relevant to the occurrence of an
event, or what are the material circumstances in the case. For only
those circumstances can be called material, or relevant, or essen
tial, without which the event would not have occurred, or whose
non-occurrence would have made some difference to it; and the
occurrence or non-occurrence of any particular circumstances can
make no difference to an event, unless there is some connexion
the question is whether a syllogism can generalize, and it is hardly con
sistent with saying no, to add that it can only do so when its character is
inductive. But the statement may stand, because all conclusions in this
figure are particular or contingent. We may aim at generalizing— at finding
a judgement which is true universally; but we have failed, with such
premisses, to do it.
B b 2
372 AN INTRODUCTION TO LOGIC [CHAP.
between them and it. Were everything in nature loose and un
connected, it would be impossible to say that an event occurred
because of any one thing rather than another. All these phrases
therefore imply Causation, and imply Uniformity.
Both the Law of Causation and the Uniformity of Nature are
phrases open to misunderstanding. There is a sense in which it is
the business of induction to discover laws of causation ; in the
plural, the term refers to the various particular principles of con
nexion exemplified (whether we detect them or not) in the course of
nature; it is equivalent to Laws of Nature, or Natural Laws, such
laws, for example, as that matter gravitates, or that organisms
reproduce themselves after their kind. Used absolutely and in the
singular, however, it means the principle that there are such par
ticular principles, and hence we speak of the Law of Universal
Causation, intending to assert that everything has a cause, and that
no change occurs except under conditions with which its occurrence
is connected universally. And it is because we believe its occurrence
to be connected universally with such conditions, whatever they
are, that we speak of the uniformity of nature. We do not mean
to deny variety, but only to assert the unbroken reign of law.
That which collectively we call nature is a vast assemblage of sub
stances of divers kinds diversely intermingled : interacting with
one another in ways that depend upon their abiding character and
their shifting situation ; what we call single things are highly
complex, and their properties and behaviour depend upon their
composition, and upon the circumstances in which they are placed ;
we may believe that whenever a thing of precisely the same kind
is placed in precisely the same circumstances as another, it will
behave in precisely the same way; nor is more required by the
principle of the Uniformity of Nature ; and yet we may doubt
whether such precise repetition ever occurs. Watch the move
ments of a waterfall, how it breaks into a thousand parts which
seem to shift and hang, and pause and hurry, first one, and then
another, so that the whole never presents quite the same face twice ;
yet there is not a particle of water whose path is not absolutely
determined by the forces acting on it in accordance with quite
simple mechanical laws. No one would suppose that because these
mechanical laws are unchanging, the waterfall must wear a mono
tonous and unchanging face ; and so it is, on a larger scale, with the
xix] PRESUPPOSITIONS OF INDUCTION 373
course of nature. Nature is uniform in the sense that under like
conditions like events occur ; and in fragments, as it were, she is
ever presenting us with the repetition of conditions that have been
fulfilled before; so that in fragments there is recurrence of like
events enough. But sooner or later, because the surrounding cir
cumstances are not quite the same as before, the course of like events
is broken in upon ; from the beginning the likeness was probably
not complete. Were it indeed possible for the procession of events
to bring back precisely the state of things which had existed at some
moment in the past, then it must follow, from the principle of the
Uniformity of Nature, that the same procession would recur, and
terminate again by reinstating the phase in which it had begun ;
so that the history of the world as a whole would really repeat
itself indefinitely, like a recurring decimal, and to a spectator who
could watch it long enough, might seem as monotonous as the
music of a musical box which, as it played, somehow wound itself
up, to pass always from the conclusion to the recommencement of
its stock of tunes. But nothing of this kind occurs ; and the unifor
mity of nature is consistent, as Mill said, with her infinite variety.
But it may be said, the Law of Causation is one thing, and the
Uniformity of Nature is another ; every event may have a cause ;
but the same cause need not always produce the same effect, nor the
cause of the same effect be always the same. The human will, for
example, is a cause ; but it does not always act in the same way
under the same circumstances ; to-day in a given situation I may
act meanly ; yet it is possible that in a situation of the same kind
I may act better to-morrow.
The freedom of the human will is a peculiarly difficult problem,
not to be argued here ; doubtless there are some who so understand it
(if understanding is then the proper word) as to make it an exception
to the Uniformity of Nature. Some would say that, in this sense,
it is not to be called a cause at all ; that to assert it in this sense is
to assert mere chance, the happening of events for no reason, the
very negation of cause ; for they hold that there is no causation
which does not act uniformly. Others would make an exception to
that principle in this one case ; but even if we were to allow it, we
should still have to say that, except so far as a cause is of the nature
of the human will, there is no meaning in a cause which does not
act uniformly.
374 AN INTRODUCTION TO LOGIC [CHAP.
Let us ask what is involved in the conception of a cause not
acting uniformly : we shall see that it is the same as if we denied
the existence of causal connexions altogether. For suppose that
every event had a cause, but that there was no reason why the
same event should have the same cause or produce the same effect
on different occasions. There need therefore be no appearance of
order in nature at all, but things might happen just as if all
changes were fortuitous. As it is, we believe that plants produce
seed after their kind ; we do not expect to gather grapes of
thorns, or figs of thistles ; where we see garden fruit upon a wild
stock, we look for a graft, convinced that the same stock will
only bear different fruit in virtue of some material difference in the
conditions. If any plant might produce any seed, or any seed any
plant, and it was impossible to discover, in such circumstances as
graft or soil — because no reason of the kind existed — why the same
plant produced now one seed and now another, or the same seed
now one and now another plant, the.n we should just deny that
there was any cause for the things that happened. We should not
say that there was always a cause, though the cause need not act
uniformly. If two plants, whose nature is really the same, can
determine the growth of totally different seeds, how can we call
either the seed 0/'that plant at all? Grant that a seed may some
times be produced by a plant of its own kind, and sometimes by
a plant of another kind, without any difference of circumstances,
and merely because causes do not act uniformly, and you have
really granted that anything may produce anything ; flint and steel
may produce seed instead of a spark, and oil raise the waves or
quench a conflagration. But to say that anything may produce
anything is to empty the verb ' produce ' of all its meaning. For
the causal relation is a necessary relation, such that if you have one
thing you must have another. To add that it does not matter what
the other is, destroys the force of the must. The distinction
between essential and accidental, material and immaterial, relevant
and irrelevant, will vanish. So long as causal connexions are uni
versal, there is a meaning in it. That is essential to health, with
out which health is impossible, and that is accidental to it which
(though doubtless it has its effects) has no effect upon health. But
if exercise, which is essential to my health to-day, should suddenly
and without any change in my condition give me epilepsy to-
xix] PRESUPPOSITIONS OF INDUCTION 375
morrow, while the loss of a letter in the post somewhere in the anti
podes should on the following day cure my epilepsy, then it would
be impossible to say that anything was accidental, or anything
essential, to the same result for two minutes together. And the
discovery of the causal connexions that determine the succession of
events now would certainly be of no use in enabling any one to fore
cast the future ; because the connexions themselves might have
altered in the meantime. It is difficult to see how all this differs
from denying that there are any connexions.
Causal connexions then are necessary and universal ; to assert
causation is to assert uniformity of connexion. Were it otherwise,
to discover them would mean only to discover the connexion subsist
ing at a particular moment ; and we could not tell that such con
nexion would subsist the next moment. For this reason, we could
not generalize, even though we believed in the Law of Causation ;
nor indeed could we so much as discover what connexions did
subsist at any moment. For since anything might produce any
thing, there would be nothing to make us connect a change with
one rather than another o£ the events that were observed to occur
immediately before it. No light would be thrown upon the
problem by comparison with other instances, since, ex hypothesi,
the cause might be different there. As it is, if the sun comes out
when I hear the clock strike, I do not suppose that the striking of
the clock causes the sun to shine, because it so often strikes with
out relieving the gloom, and is so often silent when the sun
comes out. But when I reason thus, I assume that if one event
were really the cause of the other now, it would be so always. If
it can be the cause now, and not another time, how am I even to
tell whether it is the cause now or not ? We spoke of the human
will as an alleged exception to the rule that the same cause must
always produce the same effect. We may notice here that just in
so far as it is allowed to be an exception, human actions are
allowed to be incalculable. And if everything were endowed with
a will like man's, and all these wills were free in the sense in which
some suppose that man's will is, then we should have no logical justi
fication for any generalization whatsoever. But those who claim
this freedom for the human will would attach no value to it unless
the act to which a man was determined by his free choice produced
effects that were necessary in accordance with universal laws.
376 AN INTRODUCTION TO LOGIC [CHAP.
There is no need then to distinguish the Law of Causation from
the Uniformity of Nature; for — bating the possible exception of
the causality of the human will — a cause which does not act uni
formly is no cause at all ; and if we are looking for the presupposi
tions of inductive inference, it is plain that the only connexions
whose existence would justify such inference are uniform con
nexions. But two cautions must be given here. First, it must
not be imagined that uniformity is the fundamental element in the
conception of causal connexion, but necessity or law. Secondly, we
must be careful not to confuse a conditional with an unconditional
necessity.
j)avid Hume, whose enquiry into the meaning and origin of our
idea of Causation was epoch-making in the history of modern
philosophy1, could find no other meaning for the statement that one
event is the cause of another than that in our experience the one is
always immediately followed by the other ; and according to him,
the thought and expectation of this uniformity of sequence is all that
is present to our minds when we assert causation. In agreement
with this view, J. S. Mill (who differed from Hume on this matter
chiefly in not drawing the logical consequences from the same
premisses) defined a cause as the invariable and unconditional ante
cedent of an event. The word unconditional in this definition may
seem to betray ideas inconsistent with the resolution of the causal
relation into one of time ; but Mill explains an unconditional
sequence to be one that is subject only to negative conditions 2, and
the negative conditions of any phenomenon ' may be all summed up
under one head, namely, the absence of preventing or counteracting
causes ' 3 ; so that those circumstances are the cause of an event,
upon which it follows whatever other circumstances may be present
as well 4 ; and the relation remains one of invariable sequence after
all. Now it is not denied that if any set of conditions a is the
cause of an event x, x will be produced as often as the conditions a
are fulfilled ; and in this sense the sequence will be invariable ; but
we cannot intend to assert primarily that, when we say that a is
1 Treatise, Of the Understanding, Part III; and Enquiry concerning Human
Understanding, §§ iv-viii.
' Logic, III. v. 6. 3 Ib. III. v. 3.
* More precisely, when there is nothing preventing it ; and by the notion
of preventing Mill presupposes the relation he is trying to explain ; but if
we are to avoid this petitio, we must interpret his statements as above.
xix] PRESUPPOSITIONS OF INDUCTION 377
the cause of x. For if a is the cause of #, the relation subsists
between them in every case of their occurrence ; it subsists between
this a and this x ; and it is clear that the relation between this
a and this x cannot be the uniform sequence of all instances of x
upon instances of a. The action of light of certain wave-lengths,
&c., upon a chemical surface prepared in a particular way may be
the cause of the production of a photographic negative of a particular
peak in the Himalayan mountains. I cannot mean by that that the
production of all such negatives has been preceded by a similar as
semblage of conditions on each occasion, since mine may be the only
photograph ever taken of the peak in question. No event could
have a cause until it had beenjgpeated at least once, if the essence
of the causal relation lay in uniformity of sequence ; nor could thajb
relation ever be one subsisting between a and a? in a determinate
instance ; and it is difficult to see how a causal relation which sub
sists between no determinate instances of a and x could subsist at alj.
So far then from the causal character of a sequence being derived >
from its uniformity, its uniformity is derived from its causal j
character. We avail ourselves of __ the uniformity which must char
acterize causal sequences so far as they are repeated, tp_deterniine
which of the sequences that we observe are causal ; and that is why
the repetition of an event under diversity of conditions is of such
assistance to us in determining what conditions are essential, or
material, to its occurrence. But an event that was absolutely
unique must just as surely have its J^ause, though we may be unable
to discover what it is. For the causal relation has nothing to do "7
with number of instances, so far as its existence — though not so far j
as its detection — is concerned; it is bound up altogether with the
nature or character of things, and the nature of anything is not
a question of the number of such things that may be or have been
Tcashioned. We have seen indeed that a cause which does not act
uniformly is no cause at all; but we may now see that were it
otherwise, a thing would have no determinate nature. If a thing
a under conditions c produce^ a change a? in a subject s — if, for
gxample, light of certain wave-lengths, passing through the lens of
a camera, produces a certain chemical change (which we call the
taking of a photograph of Mount Everest) upon a photographic film
— thejvay in which it acts must be regarded as a partial expression
of what it is. It could only act differently, if it were different.
378 AN INTRODUCTION TO LOGIC [CHAP.
As Jong therefore as it is a, and stands related under conditions c to
a subject that is s, no other effect than # can be produced ; and to
r that the same thingaitingonthe same tiling under the same
conditions may yet proarul;eadfiff^ say that a thing
need not be what it is. But this is in flat conflict with the Law of
Identity. A thing, to be at al!A mustTe something, and can only be
• /T^7***^^M •• ^••"••"•••^^•""^•••^'^•^"'•"^••^•^•••••"•^•••••••••••••^••••••••Mft^
what it is. To assert a causal connexion between a and x implies
that a actsasjt does because it is whatjtjs ; because, in fact, it is a.
Solong therefore as it is a, it must act thus ; and to assert that it may
jict otherwise on a subsequent occasion is to assert that it is some-
jthing else_than the a which it is declared to be. It may be replied
that no two things ever arethe_same; and — what that reply must
commit you to — that no one thing ever is the same for two succes
sive moments. The fact ofchange is not disputed, nor the diffi
culty of finding two things that are qualitatively the same. But
'if the ffffect of the second is^different, that must be because of its
qualitative difference from the first, and not merely because it is
a secon^l ; and so far as t_it ^qualitatively the same, the effect must
J3e the^ same alsp : it being understood of course that to sameness of
effect qualitative sameness is equally necessary in all the material
conditions. To. deny this is to deny^ the possibility of reasoning
altogeth ernfrlf we cannot truly make the same assertion about ~~^
a number of things, then, as Aristotla observes^ there will be__np <
universal, and so no middle term, and no demonstration.1 For s
tin universal judgement connectsa certain attribute with a certain
subject in virtue of their content and without regard to the fre
quency of their existence. If we can do this, we can_jmake_the
same assertion about_alMjiings of such and such a kind ; if we
cannot do it, we are left with nothing but particular things whose
attributes must be ascertained from inspection or experience of
themselves ; and not by transference of what we have once found
true of such a kind of thing to others of the kind. What holds
for the relation of subject and attribute holds in this respect
eo ipso for that of cause and effect. To suppose that the same
cause — other things being equal — can have different effects on two
occasions is as much as to suppose that two things can be the
same, and yet so far their attributes different. To reply that two
things cannot be the same, and that the same cause cannot be
1 Anal. Post. a. xi. 77a 5-9.
xix] PRESUPPOSITIONS OP INDUCTION 379
repeated, is either to miss the point, or to abandon reasoning-. If it
is meant that two complex things cannot be qualitatively the same,
nor can conditions precisely the same in kind ever recur, such an
objection misses the point. One need not maintain that such iden
tity, or such recurrence, in fact occurs, though it is not perhaps incon
ceivable that it should ; all that is maintained is, that so far as
things are qualitatively the same they have the same attributes, and
so far as conditions precisely the same in kind recur, they must, if
there is such a relation as cause and effect at all, have the same effect.
If, on the other hand, it is meant that there is no qualitative same
ness in what is numerically different, we can only say that if so,
there is no reasoning. But this denial of identity between different
things is what is really at the bottom of the attempt to resolve the
causal rej at i o n .into. u iiifp nil i t y_o f sequence. For the causal relation
which connects a with xt connects a cause of the nature a with an
ejfect of the nature x. The connexion is between a and x as^uch,
and therefore must hold between &ny )g and £ny\#. if^ they really
are a and x respectively ; in other words, it must be uniform. The
denial of this is just the denial of universals ; while if there are
universals — the same content in numerically divers things — th e
relations between them must be universal, If, on the other hand,
we1 are to substitute for a relation one and the same in all its
instances a mere similarity between the relations that connect the
respective terms of many different instances — if for the relation
BeiEween a and x as such we are to substitute the uniformity
between the relation of this a to this x, and of that a to that #, and
of the other a to the other x, then we are substituting for the common ~^ ./,
content of many things a bundle of things united by nothing1 in ^ 7^
common. How then can we speak oi_lhem^s things of a kind, or
uniform except in the fact that they are
sequences ? l Thp causp of a,n event might then indeed be any
thing to whic^ ft stood in a relation_of sequence at all, and need no
more be the same on different occasions than its antecedent need be;
since we should have agreed that it was impossible that the sequence
of the same thing as upon the same thing a should ever be repeated.
We may pass now from this to the second of the two points
mentioned on p. 376. If it is thus necessary that causal relations
1 Strictly speaking, even sequence could not be a feature common to two
successions.
380 AN INTRODUCTION TO LOGIC [CHAP.
should be uniform, it is all the more important that in speaking of
the Uniformity of Nature we should not confuse conditional with
unconditional necessity.
We saw above that the Uniformity of Nature was consistent
with any degree of variety in the coarse of events ; but that
it implied that the principles in accordance with which these events
occur, or what we often call the Laws of Nature, are unchanging'.
In other words, the uniformity which a particular law requires in
events can admit of no exception ; for an exception would mean,
that events did not necessarily happen in accordance with the law ;
and a law that changes is no statement of the way in which events
must happen. Nevertheless, we often use the term Law of principles
which we should not be prepared to declare unchanging1 ; which, as
we might say, do not hold good always. In the strictest sense of
the word, no doubt, a law must hold good always and uncondi
tionally x ; but we use it in a looser sense as well. It is important
to realize this distinction, and also to consider how far, when we
speak of the Uniformity of Nature, we mean to assert that what
are commonly called ' natural laws ' are unconditional.
The first law of motion is an example of a natural law which
would perhaps be regarded as unconditionally true — that every body
persists in its state of rest, or uniform rectilinear motion, until it is
interfered with by some other body. The same might be said of
the law of universal gravitation, that all bodies attract one another
with a force that varies directly as the mass, and inversely as the
square of the distance. Compare with these the principle that-
acquired characters in a plant or animal are not inherited. Supposing
this to be true (for it is still sub indice), yet it is not true uncondi
tionally. We are not in a position to say that living things could
not be so organized, in respect of their reproductive system, as to
make acquired characters heritable, but only that, with the organi
zation which we find, they are not heritable. That organization
therefore conditions the truth of our principle. Just as the prevailing
necessity for sexual union in the reproduction of all multicellular
organisms does not exclude arrangements in some species which
make them parthenogenetic, so there might possibly be conditions
1 Cf. J. S. Mill's definition of Laws of Nature in the strict sense as ' the
fewest and simplest assumptions, which being granted, the whole existing
order of nature would result ' (Logic, III. iv. l).
xix] PRESUPPOSITIONS OF INDUCTION 381
under which the non-heritability of acquired characters held good
no longer. And as conditions may change, those realized at one
time not being realized at another, so the conditional principles
which prevail may change with them. It appears to be the case
that living matter can only be produced from other living matter ;
there is no spontaneous generation of it from the inorganic ; omne
rivum ex vivo. But many scientific men have supposed that though
this is true and necessary now, yet in an earlier period of the earth's
history, under very different conditions of temperature and so forth,
it was not so.
Conditional principles are necessarily derivative : i. e. their trutlv,
so jar as they are true, follows from some unconditional laws, which
nnder^ given conditions involve them as their consequence. They
therefore admit, theoretically if not as yet actually, of explanation.
But derivative principles, or principles admitting of explanation,
are not necessarily conditional. For when we call a principle
conditional, we mean that the truth of our principle depends upon;
conditions which are not stated in it. If jwejbring the conditions
into the_statement, then, though it remains derivative, it is conditional
no longer. Supposing that we knew precisely those conditions of
organization in animals and plants which made acquired characters
non-heritable ; then the statement that in animals or plants of that
organization acquired characters were not inherited would be uncon
ditionally true, although no doubt it would admit of explanation.
It would probably not be called a law of nature, because it would be
derivative ; but it would have all the necessity of a law of nature.1
The Uniformity of Nature then involves the truth, without
exception or qualification, of all unconditional laws ; but conditional
principles admit of apparent exceptions, without derogation to its
truth ; and if we are ignorant of the conditions within which these
conditional principles hold good, we cannot tell when the exceptions
may not occur. To return to our previous illustration : if we do
not know under what conditions of organization acquired characters
are and are not heritable, we must be prepared to admit evidence
that in some cases they have been inherited. Where, however,
exceptions occur to some conditional principle, they constitute no
exception to the truth of the Uniformity of Nature ; but only imply
1 Cf. c. xxii, infra ; the non-reciprocating causal relations there discussed
are all conditional.
382 AN INTRODUCTION TO LOGIC [CHAP.
that the conditions, under which that principle held good, are not
fulfilled in the exceptional case. And the exception leads us, not to
deny that ' Nature is uniform ', but to revise or to determine more^
precisely the particular principle which we have found invalid. It
is "only unconditional laws that can have no exception.
It becomes therefore important to determine, if possible, when
we have discovered an unconditional law. We may disregard here
those derivative laws, which we may be capable of explaining from
others more general than themselves; for the question whether
they are unconditional is the same as the question whether the
more general laws from which they are derived are so. Now, if we
have no better reason for accepting a law as unconditional, than
that by assuming it to be true we can account for the facts of our
experience, then, though we might provisionally accept it, we can
hardly be content with our warranty ; for perhaps some other law
might also account for the facts. But if (and this, as we shall see
hereafter, is a distinction of the first importance in inductive theory)
— if, without assuming it to be true, it is impossible to account for the
facts of our experience, we should have to suppose it unconditional;
though such impossibility may be hard to establish. Still, we
should not be fully satisfied ; for had the facts been otherwise, we
need not have admitted the law ; and we do not see, except on the
hypothesis that the law is true, why the facts might not have been
otherwise. Complete satisfaction would only come, if the law
which the facts had forced us to recognize should, when considered,
appear self-evident.
Are there any unconditional laws known to us? There is no
doubt that the fundamental principles of physical science are often
so considered. It is held that we have discovered certain physical
laws prevailing throughout the material universe, in accordance
with which every event in the material order takes place ; that these
laws are mechanical ; and that nature is, in truth, and in the last
resort, a purely mechanical system. And this view is supposed to
be confirmed by the character of the principles with which physical
science works. A great deal is purely mathematical; and about
mathematical principles at any rate we can say that they are
unconditional because self-evident; no apparent exception would
make us doubt them or revise them ; we should only doubt the fact
which was supposed to constitute the exception. And some of the
xix] PRESUPPOSITIONS OF INDUCTION 383
most general physical laws ha/ye often been held to possess the same
self-evidence ; the first law of motion, and the laws of the con
servation of energy and the conservation of mass, are instances.
That anything should occur in the material system unconformably
with these principles would then present the same kind of contradic
tion as that two and two should make five. The explanations of
physical science, at least so far as they rested onjaws of this kind,
On the other hand, there are very serious difficulties in the way
of admitting the finality of the explanations which physical science
offers of events in the material system. These difficulties arise
from the relation of some of these events to human, and also to
infra-human, consciousness. Experience reveals to us a corre
spondence between certain changes of a material kind in the nervous
system, and changes in our consciousness. No satisfactory theory of
this correspondence has yet been found; it cannot be said that
what is involved in treating as unconditionally true the principles
of physical science is satisfactory in theory. For if all physical
changes are to be explained as determined altogether according to
physical laws, then they are purely mechanical ; the existence of
consciousness has made no difference to anything which has occurred
on the surface of the globe; we are, in Huxley's language, what
Descartes thought the lower animals to be, conscious automata ;
and the laws of matter and motion would of themselves have
sufficed (if we may borrow an illustration from Professor James l)
to produce the manuscript of Shakespeare's works — and indeed
every edition of them — though Shakespeare had been no more than
a lump of matter as devoid of thought and feeling as the pen he
wrote with, or the automaton of Vaucanson.
Such a conclusion is undoubtedly paradoxical, but paradox does
not by itself constitute a refutation. It is, however, impossible to
account on physical principles for the facts of consciousness. They
cannot be 'physical processes ; and a mechanical theory demands not
only that a physical event should depend only on physical conditions,
but that physical conditions should determine only a physical result.
Mass and energy are to remain constant in amount, but to undergo
redistribution in accordance with certain laws, which can be expressed
1 Principles of Psychology, i. 132.
384 AN INTRODUCTION TO LOGIC [CHAP.
in a mathematical formula enabling us to calculate the precise
degree of change in one direction that will be involved in a given
degree of change in another direction.1 In these redistributions there
is no room for knowledge or feeling among the ' forms of energy ' ;
for mechanical conditions are to have their complete mechanical
equivalent, in terms of matter and of motion, potential or actual.
Thus to a physical theory of the world consciousness remains un
accountable ; such a theory therefore cannot be complete or final.
Now philosophy suggests that in the last resort, instead of
explaining consciousness in terms of physical law, we shall have to_
see in physical law a manifestation of intelligence. The whole
material order is an object of apprehension ; therein, however,
it stands related to minds that apprehend it ; it and they together
form the complete reality, or res completa; and they cannot be
understood except together. There is, however, another paradox
here ; for what understands is mind, and so one term in this
relation has to understand both itself and the other term.
It is not our business to discuss here this central metaphysical
problem. But we are concerned with the conception of an uncon
ditional law; and a self-evident principle must be unconditional.
With- regard to the claims of physical science to have discovered
principles really unconditional we must therefore either say that
they are not self-evident, or admit that they are unconditional.
If we adopt the latter alternative, then we shall hold that whatever
transformation our view of the material order may undergo, yet the
interconnexions of events within it, the connexions of cause and
effect there traced, will as it were be taken over en bloc, unbroken
and undistorted, by any interpretation of the universe which takes
knowledge as well as its objects, mind as well as matter, into
account. A moving body may be something else than a moving
body ; but its motion will for ever appear determined in accordance
with physical laws. If, however, we adopt the former alternative,
the principles of physical science may not be unconditional.
Now we are perhaps sometimes too hasty in supposing that we
see the necessary truth of physical principles. The speculations of
men of science themselves have lately called in question the doctrines
1 Hence M. Poincare has recently said that a physical law is a differential
equation. Address on the Principles of Mathematical Physics, St. Louis, U.S.A.,
Sept., 1904: v. the Monist, Jan. 1905, p. 3.
xixj PRESUPPOSITIONS OF INDUCTION 385
of the conservation of energy and of mass ; l though doubtless
without questioning the possibility of getting some physical formula
that will be unconditionally true. It might be said that in the
first law of motion it is self-evident indeed that a body will persist
in its state of rest or uniform rectilinear motion until something
interferes with it, but not that interference can only come from
another body ; that the mathematical reasoning in physical science
is necessary, but not the physical principles which supply the data
to which mathematical reasoning is applied ; and that the doctrine
that a body can only be interfered with by another body is one
of these. If these physical principles are only conditionally true,
the same will hold of their results ; and changes may occur in the
material order not accountable in terms of physical conditions, and
not conformable to physical ' laws '. Nevertheless, because these
physical ' laws ' are not unconditional, there is nothing even so
that conflicts with the Uniformity of Nature.
We need not here determine which of these alternative positions
to take. But it must be pointed out with regard to the latter,
that if physical laws are conditional in the way suggested, there is
an important difference between them, and the conditional principles
with which we are already acquainted. For in the case of a con
ditional principle like the non-heritability of acquired characters, we
conceive that the laws on which it depends might be found, and
would be in eodem genere with the principle itself ; i. e. the principle
stated with the conditions to its truth (and stated then in a form
unconditionally true) would be derivative in an intelligible way
from principles more general, but from principles that hold like
itself of what is material. On the other hand, if the fundamental
physical laws are only conditionally true, yet it is impossible to
derive them from physical principles more general than themselves ;
and so the kind of explanation which is possible of other conditional
principles (when their conditions are taken into account) from
principles of the same sort with themselves, whereof they are really
but examples, is here precluded. Supposing that there are, if we
may so put it, spiritual conditions upon which the movements of
bodies in the last resort depend, and under some of these the first
law of motion holds good, and not under others, then physical
science at any rate cannot deal with those conditions.
1 Cf. Poincare, op. cit.
JOSEPH C C
AN INTRODUCTION TO LOGIC [CHAP.
For this reason, physical science will ignore this alternative. If
the non-mechanical conditions upon which physical changes depend
(supposing that such there are) cannot be ascertained and formulated
in a way which enables physical science to take account of them, it
will treat them as non-existent. It is of no use to regard a factor,
whose mode of action is unascertainable. It must remain for science
what the will is upon one theory of human freedom — a source of
purely incalculable and to it irrational interference. But irrational
interference is just what cannot be supposed to occur. No doubt
an interference which admits of explanation according to law is not
irrational ; but if the law is unascertainable, it is as good as irra
tional. And this attitude of physical science has the practical
justification, that if events are once admitted to occur in the material
order whose conditions are unascertainable within that order, there
is no point at which we can draw the line. Only by assuming that
it can explain everything is it possible to find out how much it can
explain in physical terms.
What has been maintained then is this : — It is part of the
conception of Cause to act jmiformly^ : and so far, the Universality
oiTCaiisation and the Uniformity of Nature are the same^thing,
But it consists with the Uniformity of Nature that many principles
which we use to explain events should be only conditionally true ;
these admit of exception ; but no unconditional principle admits of
exception. If a principle is self -evident^jt must be unconditional ;
and the fundarnenFal principles of physical science are commonly
treated as unconditional. On the other hand, there is much in the
world not explicable from principles of physical science. But it*
any of them are self-evident, what follows from them must be
retained, and not contradicted, in any complete explanation which
takes into account what physical science leaves on one side. And if
the principles of physical science are only conditionjJl^Jj:ue^yel_s.o
far as the conditions under which they do and do not hold good are
unascertainable, physical science may fairly treat these conditions
as non-existent.
After these explanations and qualifications we may say indif
ferently that the inductive sciences presuppos^ ^p Law ^ il*v"mrsal
Causation orJhe_JJjiifor^ But as it has been
held T)y~some to be the task of induction to prove this principle J,
1 Cf., e. g., Mill, Logic, III. xxi.
xix] PRESUPPOSITIONS OF INDUCTION 387
it may be worth while to show that that is^ impossible. It is
alleged upon the view now to be considered that our experience .of
the great extent to which like antecedents have like consequents is
the ground upon which we believe that this is universally the case.
Against this we may point out in the first place, that such an infer
ence assumes the course of events in one time and place to be
a glide to their course in other times and places T which is really
the very principlejthat is to be_proved As Lotze has urged, if
a reason can be given for the inference, it rests on some previous
assumption ; and if no reason can be given for it, what is its force ? 1
Next, it is to be noted that two very different kinds of argument
are confused. It is supposed that to infer the uniformity of nature
from the observed succession of like consequents upon like antece,-
dents is an argument of the same kind as to infer an universal con
nexion between two events a and x from the frequency with which
one has been succeeded by the other. This, however, is not the case.
"We infer under such circumstances an universal connexion between
a and x, because upon the assumption that there is some set of con
ditions upon which every change follows uniformly, it seems the
only^thing consistent with the facts of our experience in the case of
x to suppose the conditions to be a. Upon the assumption that
there is some set of conditions upon which every change follows
uniformly, the uniformity in general has not got to be inferred ;
while, if that assumption is to be made in neither case, an universal
connexion between a and x could not have been inferred. There is
therefore no parity between the two arguments. That may indeed
be seen if we attempt to put them into symbolic form. In the one }
case we reason that because a has in many instances been followed >
by x. therefore the connexion a-x js^mwftrgT In the other we"^
reason that because a has in many instances been followed by x. "
and I by y, and so forth, therefore jjiere is something by which <
every other event, such as p, q, or r, will be uniformly followed. ^
Again, the uniformities which are said to be the empirical basis of
our generalization are not really matter of direct experience. We
have said above, that the particular connexions which we believe to
prevail jn^ nature havejbeenjnf erred with the help of the assump
tion that all changes occur in accordance with laws. But if any one
likes to question this, he must at any rate agree that most of the
1 Metaphysic, Introd. § v.
C C 2
388 AN INTRODUCTION TO LOGIC [CHAP.
uniformities in which we believe have been inferred somehow : very
little has come directly under our observation. We believe that
winds are caused by differences of atmospheric pressure : these differ
ences of atmospheric pressure are themselves inferred rather than ob
served ; but waiving that, for what proportion of winds have they
been noted ? We believe the sound of the notes of a piano to be
caused by the striking of strings : for what proportion of the notes
which we have heard have we first seen the strings struck by
the hammer ? It is needless to multiply such examples : but when
it is alleged that we are justified in inferring the uniformity of
nature to hold good universally because we have direct experience
of it over vastly the larger portion of the field, it is important to
point out that our direct experience of it is singularly small, and
that the vastly greater proportion of what we believe ourselves to
have ascertained is matter not of experience but of inference.
Now we may offer the empiricist his choice. If this inference is
made bv the help of the assumption of thejuriformity of nature.
its results cannot bemused to prove that assumption. If it is maole
without that help, by his own admission it falls to the ground, for_
the inference of any particular uniformity is supposed to need that
assumption ; and so he is not left with experience sufficient to justify
his generalization. We may present the argument against his posi
tion in yet one more light. The essence of his contention is, that
we must come to the facts of experience without any preconceptions ;
we must have no antecedent view of what is conceivable or possible.
For all that we can tell to the contrary until experience has
instructed us, anything whatever is possible; and if it occurred with
sufficient frequency, anything would be conceivable. Now, it will
be admitted that if there are a number of independent alternatives
a]]j^L^fcj20^si^ w^k onty OPe °^
them leaves us quite unable to decade between the rest. But if, as
the empiricist insists, all things are antecedently- equally possible^
tl^n._allj2rpportipns of regularity to irregularity in the world are_
equally possible antecedently. All events may occur in accordance
with uniform principles : or there may be no event which ever has
the same_consequent twice ; and between these two extremes an
infinity of alternatives may be conceived, among which we cannot
select except upon the evidence of experience. The extent to which
regularity, or uniformity, prevails may therefore be limited in any
xix] PRESUPPOSITIONS OF INDUCTION 389
conceivable way, whether as regards place, or time, or subject.
There is no reason why the succession of like consequents upon like
antecedents, while exemplifiedjitother times and places, should not
fail inthe hitherto unexplored parts of Central Asja, or on all
Fridays subsequent to the Friday in next week. Nothing less,
than this is involved in the refusal tp_£rejudgej}xperience. But if
that is so, experience itself can never enable us to prejudge. For
why should any degree of uniformity observed till now in the suc
cession of events induce us to expect such uniformity to continue ?
It was antecedently as possible that such uniformity should con
tinue till to-day, and then terminate, as that it should continue till
to-day and still continue. The fact that it has continued till to-day
has disproved what until to-day was a possible hypothesjs,jyiz. that
it might terminate sooner ; but between its terminating to-day, and
still continuing — two independent and antecedently equally probable
alternatives with which that fact is equally consistent — it does not in_
the least enable us to decide, This argument will hold good, at
whatever point in the series of time to-day may fall ; so that we
never get any nearer being able to infer a degree of uniformity
which goes beyond what has been actually observed. It seems
conclusive therefore against the view that the Uniformity of
Mature can be an jnduction from experience, if by the term induc-
tion any legitimate process of inference is understood.1
1 The last argument may be put in a way that will perhaps to some seeiu
clearer as follows :
1. An event which is equally consistent with two hypotheses affords no
ground for deciding between them.
e. g. if A and B keep a common stock of boots, and each uses every
pair indifferently, footprints that fit one of these pairs afford no ground
for deciding whether A or B has passed that way.
2. It is admitted by those who regard unifonnili/ in nature as empirical,
that antecedently to experience all issues, so far as regularity and irregu
larity in the succession prevents are concerned, are equally probable.
BjTan issit-eia meant a certain course of events, however long.
3. These alternative issues must be regarded as perfectly detached altej-
nativesj i. e., antecedently to experience, the rejection of one issue would
not give any ground for or against the rejection of any other. To assume
that it would is to assume, antecedently to experience, the existence of such
degree of uniformity as enables you to say that if one specific issue happens,
another must or cannot.
4. That events should occur with any specified degree of regularity down
to the end of the year 2000 A.D., and with less or no regularity, or in
apparent conformity to different rules, thenceforward, is one such issue ;
390 AN INTRODUCTION TO LOGIC [CHAP.
With what right then do we assume it ? The answer to this
lias been given in discussing what we mean by it. To deny it is
to resolve the universe into items that have no intelligible connexion.
If the universe and the events in it form a systematic whole, then
any change must be determined by something in the nature of that
whole; and for the same change to occur on different occasions
except under the same conditions is not consistent with its having
a determinate nature. It is not, of course, denied that changes
partially the same may occur under conditions partially different ;
and the task of disentangling the identities in what is partially
different is one of the tasks of the inductive sciences ; but ceteris
paribus — a proviso about which it is very difficult for us to know
in individual cases how far it is fulfilled — the same conditions must
produce the same effect, and the same effect must have been due to
the same conditions. The universe is otherwise unintelligible or
irrational. If any one likes to accept that alternative, it may be
impossible to reason him out of it ; for he has disallowed at the
outset the appeal to reason. At least let him not maintain that,
while the alternative is conceivable, experience proves that it is
not the case.1
that they should occur with the same specified degree of regularity down to
the end of the year 2001 A.D., and thence with less or none or other, is
another such issue. And these issues are perfectly detached alternatives
a priori. Let them be called X and Y.
5. The empirical observation of that specified degree of regularity down
to the end of 2000 A.D. is equally consistent with the hypothesis that X, or
that F, expresses the truth. Therefore it affords no ground for deciding
between them.
6. It would therefore be equally likely at the end of 2000 A.D. that the
events should thenceforward exhibit none or less of the regularity that they
had hitherto exhibited, or conform to quite different rules, as that they
should continue to exhibit the same regularity even for a year longer.
7. The dividing date might be taken anywhere ; and one might take
equally a dividing place, or department of fact.
8. Hence the actual issue never affords any ground for preferring the
hypothesis of a^ continuance of the observed regularities to any hypothesis
of their discontinuance, complete or partial, with or without the substitution
of other regularities, in any period, region, or department of fact, in which
they have not been empirically verified.
1 In speaking of causality in the present chapter, prominence has through
out been given to the conditions which determine successive events. But so
far as scientific explanation appeals to principles of interaction]'^ regards
a thing as determined by what is contemporaneous with it and not by what
is antecedent. Moreover, if the whole series of events in time can be
xrx] PRESUPPOSITIONS OP INDUCTION 391
regarded as an expression of tbe activity of that which is in some way
exempt from subjection to succession, then what appears in time as future
may have to be taken into account in giving a reason for the present and the
past, though of course the future cannot determine the present in the same
way as what precedes it does. The present chapter is perhaps already more
than sufficiently metaphysical. But it is Important to realize that the
ground of our belief in the Law of Causation has nothing to do with
succession. It rests rather on the perception that a thing must be itsefl'.
If it is the nature of one thin*? to produce a change in another, it will
always produce that change in that other thing ; just as. if it is the nature
'ot a triangle to be half the area of the rectangle on the same base and
Petween the same parallels, it will alwaya be half that area. And modern
science largely eliminates the relation of succession from 'its statement of
scientific laws.
CHAPTER XX
OF THE KULES BY WHICH TO JUDGE OF
CAUSES AND EFFECTS
WE saw in the last chapter that all inference from experience
rpsf,ftf| on our belief in universal connexions in native. If there are
no circumstances material to the occurrence of a landslip, it would
be foolish to expect that any examination of the circumstances
under which landslips have been found to occur would enable us
to determine under what circumstances they will occur in the
future. But if such universal connexions do exist, the examination
may help us to detect them ; and if we can detect them, we ipso
facto generalize.
Our problem then is how to detect them; and indeed the dis
covery of causes is the popular conception of the task of an induc
tive science. But cause is a relation x ; and how are we to determine
what stands to what in that relation ? The relation itself cannot
be perceived. Events as they occur by no means display to obser
vation the lines of causation that connect them. What we call
the puerile fancies of the savage mind, which thinks that the incan
tations of a medicine man will produce rain, or the glance of
a witch wither the crops — or at a later stage of civilization, that
walking under a ladder, or overturning the salt, will bring disaster —
these would never have arisen, if you could observe with what effect
such incidents are connected, as you can observe that the medicine
man is gesticulating, or the salt lying on the table. We may
observe the events, but never their connexions ; these can be only
indirectly ascertained by considering whether the events occur as
they should if they were connected.
It is here comes in the working importance of the uniformity
which is involved in the conception of a causal relation. All
manner of events are occurring simultaneously at every moment ;
i. e. one thing is called a cause on the ground of its relation to another.
RULES OF CAUSE AND EFFECT 393
and the events of one moment, taken in the lump, must be the
causes of those at the next.1 But which is the cause of which, the
single experience of their succession will not determine. A man may
run for an hour round his garden on a frosty night, and when he
wakes up ,next morning may notice that his legs are stiff, and the
dahlias in his garden blackened. If he had really no other expe
rience of such events than in this succession, he might equally well
conclude that the frost had made him stiff and his running black
ened the dahlias, as vice versa. But it is involved in the causal
relation that if two things are really cause and effect, the one never
occurs without the other ; and hence by comparison of that expe
rience with others, he might conclude that running round the
garden did not blacken dahlias, because at another time they
had not gone black after he had been running round it ; and that
frosty nights did not make his legs stiff in the morning, because he
had waked up after another frosty night without any stiffness in
them. So far he would only have disproved the connexions to
which his mind at first had jumped. To prove that frost does
blacken dahlias, and that it was the running that made his legs
stiff, is a more difficult matter; for the mere fact that one has
been followed by the other many times constitutes no proof. Yet
the repetition of the same event under different circumstances is
constantly narrowing the field of possibilities ; for no two events
can be precisely cause and effect, of which one in any case occurs
without the other; so that if we can show that out of all the
circumstances under which the blackening of dahlias has been
observed to occur, a frost is the only one that has not also on
another occasion either occurred without such an effect befalling
the dahlias, or failed to occur when it has befallen them, we may
conclude that there is nothing except the frost to which their
blackening can be attributed.
1 It may be said that an event of to-day may be due partly to some event
that occurred a long time ago : for example, a man may inherit a fortune on
his twenty-first birthday in virtue of a will made before he was born. We
shall see later that it is by no means always practically convenient to call
the immediately preceding conditions the cause : and the remoter cause may
without offence usurp the name. But the legatee becomes possessed of his
fortune because he has just attained the age of twenty-one to-day ; and the
will may be regarded as having initiated a persistent legal position as
regards the money ; so that the statement in the text may be deemed
sufficiently accurate in the context which it is intended to elucidate.
394 AN INTRODUCTION TO LOGIC [CHAP.
In this example we find the simple principle upon which the
reasoning1 of induction rests : though the successful prosecution of
inductive science requires very much besides such reasoning. The
cause of any phenomenon 1 — in the strictest sense of that relation^-
is so related to it, as to occur whenever the phenomenon occurs,
and never when it does not ; and to vary or be constant as the
phenomenon varies or is constant, when susceptible of variations
in quantity or degree. From this it does not follow that because
in a limited number of instances some two particular phenomena a
and x have been' observed to be present and absent, to vary and
be constant together, they are related as cause and effect; since
there may be another phenomenon^ which also satisfies the con
ditions, and it is impossible so far to tell whether a or_^or the
combination of them is the cause of x. But it does follow that
nothing is the cause of x which fails to satisfy the conditions;
and it is upon that consideration that all discovery of causes from
experience rests. In saying this we do indeed but repeat what
was said in reference to the ' New Induction ' of Bacon.
Thus inductive reasoning rests upon the definition of Cause 2 ;
for unless we know what causal relation is, we cannot know that
certain phenomena do not stand to each other in that relation. And
from the definition of Cause proceed what may be called Topics of
Cause, or rules whereby to judge whether two phenomena are thus
related to each other or not : just as from the definition of Property
proceeded what Aristotle called Topics of Property, or rules whereby
to judge whether a given predicate was or was not a proprium of
a given subject. But you can only prove that they are not-related
as cause and effect by proving that there is nothing else with which
either of them can be causally connected.
J. S. Mill formulated four ' Methods of Experimental Enquiry ',
1 1 use the word phenomenon on account of its generality : an event, like
the fall of a thunderbolt, may be called a (natural) phenomenon : or
a thing, like the thunderbolt itself: or an attribute, like the velocity of its
fall : or even a law, like gravitation. The word certainly does not mean in
its current usage, as is nevertheless sometimes stated, anything that can be
perceived by the senses ; it seems to be used to cover any particular thing,
property, principle, or event which can be made matter of scientific investiga
tion or used in explaining what is investigated. It is convenient to have a
comprehensive term of this kind, and the context will frequently indicate,
where necessary, whether thing or property, eve^t nr principle, is meant.
2 Cf. Poste, Sophistici Elenchi, Appendix D,"p7221.
xx] RULES OF CAUSE AND EFFECT 395
or as he also called them, 'Inductive (or ' Experimental') Methods/
to which he attached considerable importance in his System of
Logic.1 He called them the Method of Agreement, the Method
of Difference, the Method of Residues, and the Method of Con
comitant Variations. Among- other defects of his exposition, there
is one that darkens in a special degree the subject of induction.
We shall be able to appreciate the nature of this defect if we
realize that the essence of inductive reasoning lies in the use of
your facts to disprove erroneous theories of causal connexion. It
is, as Mill himself asserts, a process of elimination.'2' The facts
will never show directly that a is the cause of x ; you can only
draw that conclusion, if they show that nothing else is. In order
to show that nothing else is, it is of course in the first place neces
sary that you should know what other circumstances there are
among which the cause might be sought ; you cannot { single out
from among the circumstances which precede or follow a pheno
menon those with which it is really connected by an invariable
law' (to borrow an excellent phrase of Mill's 3) unless you have
ascertained what circumstances do precede or follow it on divers
occasions. But as to do that is no part of the inductive reasoning
which we are now considering, we may for the present neglect it,
or assume it to have been done. The important thing to notice
here is, that you do not discover what is the cause, except by
eliminating the alternatives. Yet it is very often impossible to
do this completely ; nevertheless the nature of your reasoning is
precisely the same, when you are left with the conclusion that
the cause is either a or b or c, as if you had been able to eliminate
I) and c also, and so determine that the cause is a. Moreover, it
makes no difference to the nature of your reasoning, as a process of
advancing to the proof of the cause by the disproof of the alterna
tives, what the principle is to which you appeal in order to disprove
them. You know that nothing is the cause of x which does not
satisfy certain conditions — which is not present whenever x occurs
and absent when it does not, which does not vary or remain constant
as x does so. It is sufficient to be able to show that one of these
conditions is not satisfied by a given circumstance p, in order to
conclude that p is not the cause of x; and which condition it is
does not matter in the least. It is unlikely that in any particular
1 Logic, III. viii. 2 e. g., ib. § 3 init. 8 Ib. § 1 init.
396 AN INTRODUCTION TO LOGIC [CHAP.
investigation every alternative hypothesis which we disprove as
to the cause of the phenomenon that we are studying will be
rejected because it fails to satisfy the same one of these conditions ;
the facts of our experience will probably show us one occurring
where the phenomenon is absent, and the phenomenon occurring
in the absence of another, a third unaffected in quantity or degree
through all the variations of the phenomenon, and so on. All that
is essential to the progress of our enquiry is that we should be able
to show some fact inconsistent with supposing such and such an
alternative to be the cause; then that alternative is eliminated,
and the cause must lie among- the rest.
The essence, then, of these inductive enquiries is the process of
elimination. The reasoning is disjunctive. And the character
of the reasoning is unaffected either by the completeness of the
elimination (i.e. the fact that there are no alternatives left in
the conclusion) or by the ground of elimination used. Yet Mill
has so formulated his c Methods' as to make it appear (a) that
they are only used when the elimination is complete ; ($) that they
are different when the ground of elimination is different. From
this it follows that very few inductive reasonings really conform
to any of them ; but the credit which this part of his work has
obtained, and still more the currency given to the names of his
1 Methods ', in which his doctrine is enshrined, threaten us with a
repetition of the same sort of mischief as arose from supposing that
every argument could be put into the form of a syllogism. Just
as arguments not syllogistic at all were forcibly tortured into the
appearance of it, to the destruction of any proper understanding
of what syllogism really is, and how it differs from other forms
of reasoning, so inductive arguments are now often forced into
a pseudo-conformity with the canon of one of these ' Methods ', to
the utter confusion of the mind. For in the process, we are made
to allege that some circumstance is (say) the only one in which
a number of instances of a particular phenomenon agree, in order
to conclude in accordance with the canon of the 'Method of
Agreement"' that it is therefore the cause of the phenomenon,
when we know perfectly well that it is not the only such cir
cumstance; and as we know that it is not by such assumptions
that we really conclude that circumstance to be the cause, we
are only confused by a Logic which makes it appear that it is.
xx] RULES OF CAUSE AND EFFECT 397
There are passages in Mill's work (as is often the case with him)
which implicitly correct his own error. In speaking- of what he
calls the ' Method of Agreement ', he writes : ' The mode of dis
covering and proving laws of nature, which we have now examined,
proceeds on the following axiom. Whatever circumstance can be
excluded, without prejudice to the phenomenon, or can be absent
notwithstanding its presence, is not connected with it in the way
of causation. The casual circumstances being thus eliminated, if
only one remains, that one is the cause which we are in search of :
if more than one, they either are, or contain among them, the
cause ; and so, mutatis mutandis, of the effect/ l It is plain from
this that I am not the less reasoning in accordance with this
method, because I am only able to say in the conclusion that the
cause of the phenomenon is one or other of several alternatives,
than if I were able to offer a definite solution. Yet this is quite
ignored in what immediately follows : ( As this method proceeds
by comparing different instances to ascertain in what they agree,
I have termed it the Method of Agreement ; and we may adopt
as its regulating principle the following canon/ which Mill
proceeds to enunciate thus : —
' If two or more instances of the phenomenon under investigation
hare only one circumstance in common, the circumstance in which alone
all the instances agree is the cause (or effect) of the given phenomenon.'
Every one who has tried knows how difficult it is to find cases
to which this canon can be applied ; for it is seldom that your
instances have only one circumstance in common. Where such
instances are forthcoming, they are peculiarly instructive to the
investigator ; and therefore Bacon placed them first in his list of
Prerogative Instances (i.e. instances to be consulted first), under the
name of Instantiae Solitariae? But what if your instances have
several circumstances in common ? Are they, therefore, useless to
the investigator? Throughout the organic world it is observed
that species present a number of adaptive structures — that is,
structures fitting them for the conditions under which they have
to live. To the question how this has come about several answers
1 Logic, III. viii. 1 ad Jin.
2 Nov. Org. II. 22, where instances such as are required by Mill's Method
of Agreement and by his Method of Difference are described under this
name. And this is the proper way to treat them — not as instances the use
of which constitutes a distinct method of inductive reasoning.
398 AN INTRODUCTION TO LOGIC [CHAP.
have been suggested; one, the oldest, attributed them to special
design on the part of the Creator : another to the inherited effects
of use and disuse : another to the survival of those individuals who
happened to be born with a body more suited in any respect than
their neighbours' to the conditions of their life, combined with
the elimination of the less fit. Now if it is pointed out that some
adaptive structures, like the horny back of a tortoise or the shell of
a mollusc, cannot be improved by use as a muscle can, one of these
suggestions is overthrown, at least as a complete solution of the
problem ; but it remains doubtful so far whether we are to refer
the structures in question to design or to natural selection : yet
we have certainly made some way in our enquiry, and this argu
ment is part of our inductive reasoning. Mill's canon, however,
is inapplicable to such a case as that, because the tortoise with his
horny back, and the elephant with is powerful trunk for seizing
branches, though both possessing adaptive structures, which may
in both have been developed by natural selection, are not instances
with only one circumstance in common. It is excellent advice to
see in what the instances of your phenomenon agree ; but the
ground of the advice is that you may eliminate the circumstances
in which they differ ; and the principle at the foundation of the
' Method of Agreement ' is not that * the sole invariable antecedent
of a phenomenon is probably its cause V for the ' Method ' is often
employed when there is no sole invariable antecedent ; it is that
"not/ling is the cause of the phenomenon in the absence of which it occurs.
Again, so obvious is the difficulty of finding such instances as
the application of this ' First Canon ' requires, or such as the second,
that of the ' Method of Difference ', requires, that Mill, having
begun by mentioning four methods (of Agreement, of Difference, of
Residues, and of Concomitant Variations), adds a fifth, which he calls
the Joint Method of Agreement and Difference. In order to apply
the ' Method of Difference ', you are to find an instance in which the
phenomenon under investigation occurs, and another in which it
does not, agreeing in every circumstance except one, which last
circumstance is to occur only in the former ; and that will be the
cause (or effect) or an indispensable part of the cause of the pheno
menon. Such instances as these may also not be forthcoming ; and
therefore, under the name of the Joint Method, Mill describes the
1 Jevons, Elementary Lessons, p. 241 (1880).
xx] RULES OF CAUSE AND EFFECT 399
case in which you look for a circumstance about which it can be
said that it is the only one that is neither absent in any instance
where the phenomenon occurs, nor present in any where it does not.1
Here then both grounds of elimination are employed ; but there is
no reason in the world, as a study of his account of his Methods
would show, why he should not have had another Joint Method,
of Difference and Concomitant Variations, or of Agreement and
llesidues, and so forth. An enquiry into the cause of one phenomenon
need not confine itself throughout to one ground of elimination.
For the above reasons it would be well to recognize that Mill
has not formulated four (or five) but one ' Method of Experimental
Enquiry ' — as indeed Bacon might have shown him ; of which the
essence is, that you establish a particular hypothesis about the
cause of a phenomenon, by showing that, consistently with the
nature of the relation of cause and effect, the facts do not permit
you to regard it as the effect of anything else (and mutatis mutandis
if you are enquiring into the effect of anything). It is this which
makes the reasoning merely inductive. If you could show in
accordance with known or accepted scientific principles that the
alleged cause was of a nature to produce the effect ascribed to it,
your reasoning would be deductive ; leaving aside the question how
those scientific principles were ascertained, you would be applying
them to produce a conclusion which you see to be involved in their
truth ; and if we suppose the principles to be of such a nature that
we can see they must be true, then the conclusion will appear
necessary, and a thing that could not conceivably be otherwise.
1 Mill's canon for the ' Joint Method ' is by no means carefully worded
(Logic, III. viii. 4). It would be better if for 'the circumstance in wh'ieh
alone the two sets of instances differ ' we read ' the circumstance in which
alone the second set of instances agrees to differ from the first set '. Note
that Mill represents it as necessary, under the terms of the Joint Method, to
show of every other circumstance than that which is alleged as cause in the
conclusion both that it is absent in some instance where the phenomenon
occurs and that it is present in some instance where it does not. This is
because he develops it as an answer to the objection, that although a circum
stance b is absent in a particular instance of x there is no reason why it
should not cause x on another occasion. The difficulties created by the
so-called Plurality of Causes will be considered later. The point in the
text here is. that it is quite possible, and very common, to show that one
circumstance is not the cause on one ground— say that the phenomenon
occurs without it, and another on another ground — say that it occurs
without the phenomenon, and a third on a third ground — say that it is
variable while the phenomenon is constant, all in the same investigation.
400 AN INTRODUCTION TO LOGIC [CHAP.
Take, for example, the maxim that men hate those who have conferred
a benefit on them.1 We may regard that as, in the first place, an
induction formed from the consideration of many instances of ill
will, which are unaccountable otherwise than on that principle ;
yet so far it remains a thing obscure and unintelligible, a relation
which the facts forbid us to dispute, but in which we see no neces
sity. Now if a man were to say that men hate to feel themselves in
a position of inferiority, and that they do feel themselves in a
position of inferiority to those from whom they have received a benefit,
the maxim follows deductively ; and these principles are not only,
like the original maxim, capable of being inductively supported by
an appeal to experience, but they are also intelligible to us in a way
in which that was not ; it is mercifully untrue to say that they
appear necessary, but they do appear more or less natural. Where,
however, we have to rely purely on induction, there is none of this
' naturalness ' : I stand on my conclusion because ' I can no other ',
and not because I see any intrinsic necessity for it. Necessity there
is, if I am right about my facts, and am to reason in this case
consistently with what I know to be involved in the causal relation ;
but that necessity is not intrinsic; had the facts been otherwise,
and for all I can see they might have been, I should have concluded
otherwise ; and then I should have been just as content to accept
that as I now am to accept this conclusion.
There is an enormous number of general propositions, which we
accept for no better reason than that the facts are inconsistent with
our denying them, and not because in themselves they have any
thing which could have led us to suppose them true, antecedently
to our experience. When it is said that we ought always to follow
experience, it is meant that we ought not to trust our notions of
what seems antecedently fit to be true, or mere guesses as to the
connexions that subsist in nature, but accept only those connexions
which our experience forces us to accept because it is inconsistent
with any alternative. Such reasoning is called a posteriori, because
it starts from the facts, which are conceived as logically dependent
on, or posterior to, their principles, and thence infers the principles
on which they are dependent. Conversely, deductive reasoning is
1 Of course this, like most maxims with regard to human nature, is not
an universal truth : what kind of men hate those who have conferred a benefit
on them would be the next subject for enquiry.
xx] EULES OF CAUSE AND EFFECT 401
often called a priori, because it starts from the principles or conditions,
which are conceived as logically prior to the consequences that
follow from them.1 When a priori reasoning is condemned, it is
not meant that we are never to reason deductively, but only that
we are not to reason from principles that are not warranted by
experience ; at any rate this is the only sense in which the condemna
tion can be justified. But it is an error to suppose that all general
principles are arrived at a posteriori, or by process merely of showing
that facts are not consistent with any other; the Law of the
Uniformity of Nature itself, as we have seen, is not arrived at in
that way, since if we once doubt it, it is impossible to show that
the facts are any more inconsistent with its falsity than with its
truth ; neither are mathematical principles so arrived at : we do not
believe that three times three is nine, because we show successively
that it is not five or ten or any other number except nine. Still it
is true that in the inductive sciences the vast majority of our
generalizations are reached either in this a posteriori manner, or by
the help of deduction from other generalizations so reached. And
it may be well to show by one or two examples how generalizations
that rest merely on induction present as it were a blank wall to our
intelligence, as something at which we cannot help arriving, but
which we can in no way see through or make intrinsically plausible.
Facts show that the excision of the thyroid gland dulls the intelli
gence : could any one see that this must be so ? Explanation may
show that 011 a contribution which the gland, when properly func
tioning, makes to the circulating blood depends the health of the
brain ; but that comes later than the discovery of the effects of
excision; and even so, can we understand the connexion, which
facts establish, between the state of the mind and the health
of the brain? Or take a thing more frequent and familiar. It
sounds perhaps the most natural thing in the world, that we should
see with our eyes, hear with our ears, taste with our palate, and
so forth. Yet for all that we can see a priori, it might just
as well have been the case that we should see with our ears and
hear with our eyes, smell with our palate and taste with our
1 Or, in another sense, illustrated in most mathematical reasoning because
the premisses, without being more general than the conclusion, or giving
the cause why it is true, are not based upon an appeal to facts which might
conceivably have been otherwise : cf. p. 505, n. 2, infra.
402 AN INTRODUCTION TO LOGIC [CHAP.
fingers. Doubtless if we tasted with our fingers, we should not
have to eat in order to taste ; there might be some advantages in
that, and at any rate it is not antecedently inconceivable. It may
be said that the mechanism of the eye, by which light is focused from
many points at once upon the extended surface of the retina, and
the eye is readily turned in any direction, makes it a priori a more
suitable organ of sight than the ear could be ; and it is true that upon
the assumptions that light-sensations are produced by the stimulation
of a nerve, that this stimulation is supplied by wave-motions in the
ether, that distinguishable colours are produced by differences in
the wave-length, and that the arrangement of these colours in the
visual field corresponds to that of the nerve-fibres appropriately
stimulated in the retina, we can find in the eye an excellent
arrangement for securing clear vision. There is nothing, however,
in those assumptions (which have only been proved inductively) that
is any more intelligible to us than if the wave-motions of the
ether stimulated the fibres of the ear; though doubtless our vision
would be less serviceable in the latter case. There is in fact no
psycho-physical correspondence that is at present intelligible to us,
although particular correspondences may be intelligible in the sense
of conforming to more general principles which we have found to
prevail. The same may be said with regard to the properties of
chemical compounds, which are not for the most part intelligible
from a consideration of the properties of their elements ; hence in
saying that they depend upon the composition of the substance we
rely merely upon this, that no other view consists with the facts
which we have observed in our experiments. The largeness of
these two classes of inductive generalizations may perhaps make it
unnecessary to illustrate further what Bacon would call the ' surd
and positive * * character of conclusions resting only on induction ;
but, as showing how the mind desiderates something better, we may
notice the attempt continuously made to conceive chemical as at
bottom only physical processes. In the physical process, the suc
cessive stages do to some extent at least appear to follow necessarily
one out of another ; on their mathematical side, the principles that
connect them are not mere matter of fact, but matter of necessity
which we cannot conceive otherwise. Hence the attraction of
1 De Principiis atque Origlnibus, Ellis and Spedding's ed., III. p. 80.
xx] RULES OF CAUSE AND EFFECT 403
reducing chemical processes to physical terms. It is true that the
appearance of new sensible properties in bodies in virtue of their
physico-chemical composition is not hereby explained; but it is
supposed that they only possess these for us : that the appearance
is subjective, or in other words that while the processes in bodies
themselves are purely physical, we are determined to receive
qualitatively different sensations by different physical stimuli.
There is not much prospect at present of rendering psycho -physical
correspondences really intelligible ; thus there is a temptation to
regard the emergence in a chemical compound of properties which
cannot be seen to have any necessary connexion with the properties
of its elements as only subjective, a fresh case of that psycho-
physical correspondence which we admit that we can only ascertain
and not understand : in order that we may if possible find in the
principles of chemistry itself something intelligible, and not merely
necessary to be admitted. The gain is more apparent than real ;
but the procedure betrays a sense that though it may lead us far
and win us much, induction turns out at last to be the blind alley
of the reason.
We must return, however, from these general considerations upon
the nature of induction to the particular inductive reasoning which
rests upon our knowledge of the requirements of the causal relation.
By and by we shall find that reasoning which is really inductive
enters into processes of a more complex and partially deductive kind.
What we are at present considering is in principle quite simple.
The cause of a phenomenon 1 is to be sought among those circum
stances under which it occurs in the instances that we take. The
causal circumstances are indicated by a process of exhaustive elimina
tion. Those which are not causal can be eliminated because the
facts show that in regard to this phenomenon they do not satisfy
the conditions of a cause. Now the grounds on which we may
eliminate are these ; and each points to some particular requirement
of the causal relation, failure to satisfy which disproves that relation
as between two given phenomena :
1. Nothing is the cause of a phenomenon in the absence of which
it nevertheless occurs.
1 Or mutatis mutandis the effect. I shall not complicate the exposition
by always adding this.
D d 1
404 AN INTRODUCTION TO LOGIC [CHAP.
2. Nothing is the cause of a phenomenon in the presence of which
it nevertheless fails to occur.
3. Nothing is the cause of a phenomenon which varies when it is
constant, or is constant when it varies, or varies in no pro
portionate manner with it.
To these may be added a fourth ground :
4. Nothing is the cause of one phenomenon which is known to be
the cause of a different phenomenon.
This last principle is also, like the others, involved in the general
conception of a reciprocal causal relation ; but in applying it we
appeal not merely to what we observe in the instances of the
phenomenon under investigation, or in the instances where under
more or less similar circumstances the phenomenon does not occur ;
we appeal also to previous generalizations regarding the connexion
of phenomena. These generalizations, however, are used not to
account for the connexion which we are now establishing — it is not
deduced from them ; but merely to exclude alternative explanations
of the present phenomenon, and so force us upon the one which we
finally accept; and so far the reasoning which appeals to such
a ground of elimination is still inductive.1 But it belongs especially
1 On these grounds of elimination Mill's ' Inductive Methods ' severally
repose. The first is the foundation of his 'Method of Agreement', the
second of his ' Method of Difference ', the first and second jointly of his
'Joint Method of Agreement and Difference', the third of tyis 'Method of
Concomitant Variations ', and the fourth of his ' Method of Residues '. All
of them are quite general, and have been stated above in a way which only
holds if in the cause we include everything necessary and nothing superfluous
to the production of the phenomenon in question. The illustrations in the
present chapter are not confined to that, the strictest, sense of cause ; but
the important point involved will be considered later in Chapter xxii, on
Non-reciprocating Causal Relations. Where the cause sought is a non-
reciprocating cause, other principles call to be applied : e. g. we may say
that * where the removal of one of a number of conditions is found to involve
the cessation of a phenomenon, though the other conditions may remain,
but its restoration is not found to involve the restoration of the phenomenon
in the absence of those other conditions, it may be called the cause of the
phenomenon '. ' Cause ' here is clearly only a sine qua non, but for various
reasons the indispensability of some particular condition may be what we
wish to ascertain. Lotze, in Bk. II. c. vii. of his Logic, headed Universal
Inductions from Perception, has paid some attention in § 261 to the formula
tion of principles of this kind, stating what degree of connexion between
two elements C and E can be inferred from what kind of observations with
regard to the circumstances of their occurrence. The section is eminently
worth consulting in reference to the nature of inductive reasoning ; and the
principles in question might all be called Topics of Cause, though some of
them are doubtful ; just as Aristotle recognized Topics which hold true in
application only for the most part. Hume too in Part III. § xv. of his
xx] RULES OF CAUSE AND EFFECT 405
to the later stages of a science, because it presupposes the discovery
of other causal connexions, as a means of prosecuting some present
enquiry.
It is plain that we cannot get to work in the application of these
principles, until we have clearly conceived the phenomenon we are
studying, and ascertained and distinguished the circumstances under
which it occurs (or fails to occur) from one another. And if all
this were done, their application would be an easy matter, as Bacon
imagined he could make it. All symbolic representation of such
inductive arguments by letters of the alphabet, where one letter
stands for the phenomenon investigated, and others for the circum
stances among which its cause is sought, presume these tasks to
have been achieved ; and thus they are apt to convey a totally
false impression of the degree of difficulty attaching to inductive
enquiries.1 The truth is, that inductive reasoning is in form very
Treatise, Of the Understanding (already, like this chapter in Lotze, referred to),
gives a number of Rules by which to judge of Causes and Effects which are
derivative, but highly important, as for example that ' where several different
objects produce the same effect, it must be by means of some quality, which
we discover to be common amongst them 1. But those in the text seem to
be really the ultimate principles, if a reciprocating cause is meant.
1 On the artificial simplification which letters of the alphabet also imply,
cf. Venn's Empirical Logic, c. xvii. pp. 406, 407. If they are to be used at
all, to which I see no objection so long as their limitations are understood,
it is important how we use them. In Mill's use of them, which has been
followed by Jevons, Elementary Lessons in Logic, and by Fowler, Inductive
Logic, and I dare say by others, there are two defects. He uses big letters to
symbolize 'antecedents1 or causes, and the corresponding small letters to
symbolize 'consequents' or effects. Now in the first place he has thus
always an equal number of big and small letters ; but when we are looking
for the cause of some phenomenon x, and seek it among a number of alterna
tives abed..., we have not also before us effects as many as the
alternatives among which the cause of this phenomenon is sought. Only
in symbolizing his ' Method of Residues ' is this feature appropriate ; there
certain circumstances collectively are supposed to be known to be the cause
of a number of effects (or of an effect of a certain quantity or degree), and
out of these we reject, as not the cause of one among the effects, those which
we know to produce the others (or if the question is one of quantity or
degree, we reject those whose total effect we know to differ from what we
have to account for, as not accounting for the remaining component).
Hence separate symbols for the effects (or components of the effect) of the
various circumstances among which the cause of one effect (or component)
is sought, as well as separate symbols for the causes, are required. The
second objection is, that he uses corresponding big and small letters (ABC
followed by a b c, &c.). Now, as Mr. F. H. Bradley points out (Principles of
Logic, p. 339, note *), the letters are intended to symbolize the phenomena as
presented to us before we apply our inductive canons ; and therefore they
ought not to imply, as by this correspondence they do, that the phenomena
themselves, as distinct from the facts of their joint or separate occurrence,
406 AN INTRODUCTION TO LOGIC [CHAP.
simple ; but the discovery of the proper premisses is very hard. As
Hume well observes of the rules he gives ' by which to judge of
causes and effects ', ' All the rules of this nature are very easy in
their invention, but extremely difficult in their application/ 1 It is
easy enough to see that if out of so many alternatives abed. . . z,
the cause of x is not b c d . . . or z, it must be a ; and it is easy
enough to see that if c occurs without x, it is not its cause. But to
show that c occurs without #, and to show some reason for rejecting
b d . . . zy as well, and to discover b c d . . . z, and show that no other
alternatives are possible — all these things are extremely difficult.
Something will be said of these operations in the next chapter.
Here we are concerned with the form of the reasoning, which is of
a disjunctive kind, and may be symbolized thus : —
The cause of x is either a or b or c or d . . . or z
It is not b or c or d . . . or z
/. It is a.
In this argument the minor premiss is proved piecemeal by hypo
thetical arguments that rest upon one or other of the above grounds
of elimination, or ' rules by which to judge of causes and effects'*.
If b were the cause of x} it would be present whenever so is
present
But (in this instance) it is not.
If c were the cause of x, it would be absent whenever x is
absent
But (in that instance) it is not :
and so forth. Or if any one prefers it, he may represent this part
of the argument as a syllogism :
Nothing is the cause of x, in the absence of which x occurs
b is a thing in the absence of which x occurs
Nothing is the cause of #, which varies without relation to it
d varies without relation to x.
It is of course possible that bed ...z may all be eliminated, or
shown not to be the cause of x, by the application of the same
principle or major premiss; in this case the minor of the above
disjunctive argument might be proved en Hoc, and not piecemeal ;
have anything about them that proclaims which is the cause of which. Cf.
also Professor Bosanquet's Logic, II. iv. vol. ii. p. 123.
1 Treatise, Of the Understanding, loc. cit.
xx] RULES OF CAUSE AND EFFECT 407
but this is by no means necessary, and in fact unusual, and does
not affect the nature of the argument. It is, however, the only
case contemplated in Mill's formulation of inductive reasoning. It
is also possible (and this Mill's formulation does not recognize at
all) that we may not be able to prove the whole of the above
minor premiss ; and then our argument will take the form
The cause of x is either a or b or c or d ... or z
It is not c or d . . . or z
.-. It is a or b
or It is not d or z
.-. It is a or I or c . . .
where the degree of uncertainty symbolized as remaining at the
end of our enquiry is greater.
It appears plainly enough in this analysis how all induction rests
on the Uniformity of Nature ; for in proving the minor of the
disjunctive argument a principle is always appealed to, that would
fallto the ground if the Uniformity of Nature were denied. It is
Tiot indeed necessary, in a particular investigation, to assume this
uniformity to extend beyond the department of facts with which
we are dealing; if I am looking for the cause of cancer, it is
enough that cancer should be subject to uniform conditions in its
occurrence ; and I should not be impeded in my research by the
fact that thunderstorms occurred quite capriciously. There is,
however, no ground for assuming cancer to be subject to uniform
conditions in its occurrence which does not apply equally to
thunderstorms, or to anything else that could be mentioned; if
I assume the principle of Uniformity at all, I must logically
assume it altogether; and so, though I may be said to appeal to
it in any particular inductive argument only so far as concerns the
department of nature to which my investigation belongs, I really
assume it universally.1 Nevertheless it is not correct to say that
it is the ultimate major premiss of all inductions 2 ; for that im
plies that an inductive argument is, formally considered, a syllo
gism, and we have seen that it is not. It is indeed impossible
to see how this principle can be made the major premiss of any
inductive argument as a whole, though its particular applications
1 Cf. what Aristotle says of the assumption of the Law of Contradiction
implied in all syllogisms, An. Post. a. xi. 77 a 22-24.
* Mill, Logic, III. iii. § 1 med.
408 AN INTRODUCTION TO LOGIC [CHAP.
may afford the major premiss of an argument by which we prove
any part of the minor in our disjunctive argument. Let us say
that ' Nature is uniform ', or (since we can hardly make a middle
term of ( Nature ', which in the sense of nature as a whole is not
predicable of any particular subject) that f All events in nature
take place in accordance with uniform laws ' ; we may then proceed
to argue that * Cancer is an event in nature ', and therefore that it
takes place in accordance with uniform laws ; but we are thus no
further advanced than we were at the beginning, since so much is
assumed in looking for a cause of it at all. Or if we put our major
premiss in the form * Every relation of cause and effect that is ob
served in any instance between one phenomenon and another holds
good universally ', and then used as our minor ' The relation
between a and a? is a relation of cause and effect between one
phenomenon and another observed in certain instances ', we might
indeed take the formal step of concluding that it holds good uni-,
versally (though that is already implied in calling it a relation of
cause and effect), but the whole question at issue is begged in the
minor premiss ; for what we want to prove is just that a is related
to x as a cause, and not in time only and accidentally. For the
formulation of the reasoning by which that is proved — which is the
inductive reasoning — nothing therefore has been done. And any
other attempt to reduce inductive reasoning to syllogism with the
principle of the Uniformity of Nature as ultimate major premiss
Avill be found equally unsuccessful.
It remains to illustrate by a few examples the truth of the con
tention that inductive conclusions are established disjunctively by
the disproof of alternatives.
1. The power of the chameleon to change colour in accordance
with the colour of its surroundings is well known. But this power
is not confined to the chameleon ; it occurs, for example, also in
certain frogs.1 The question raised is as to the cause of this
change. We have first indeed to show that the change is due in
some way to the colour of the surroundings ; that implies a pre
vious inductive argument ; for so long as it was only noticed that
the frog changed colour from time to time, it would be quite uncer
tain with what that change was connected. Of the suggestions
1 This example is taken from Dr. Vernon's Variation in Animals and
Plants (Internat. Scient. Series), pp. 255 seq.
xx] RULES OF CAUSE AND EFFECT 409
that might occur to a biologist (for we may disregard such as might
occur to a collector of portents ; Livy gravely records as portents
of disaster some facts quite on a par with the statement that ' a frog
changed its colour in broad daylight ', but it would be easy to show
that the phenomenon had occurred at a time of no disaster) — of
the suggestions then that might occur to a biologist we may con
ceive the nature of the animal's food to be one : time of day or
season of year to be another : intensity of sunlight to be a third,
and so on ; but when it was shown that the frog might variously
change its diet, and be of the same colour, and that the change of
colour might take place at any time of the day or year, and in
various degrees of sunlight, these suggestions would be discarded,
and so on until the only reasonable suggestion left was that which
connected the change of colour with the colour of the surroundings.
Of course this conclusion would acquire great strength so soon as
any one noticed the frog in the process of changing colour upon
removal from one ground to another; for thus the alternatives
would be confined to those matters in which a change of conditions
had been just then effected. The preliminary induction implied in
saying that it changes colour according to the colour of the ground
on which it rests need not, however, be further considered ; we wish
to know more precisely what produces the change. Now differently
coloured grounds may vary in temperature as well as in colour ;
but it can be shown experimentally that the colour-reaction is
independent of temperature. Granting then, in the absence of
any other alternative, that it depends on the colour as such, we may
ask in what way the differently coloured rays1 affect the animal.
Lord Lister showed that they affected it through the eyes; for
a specimen of Eana temporaria whose eyes had been removed was
no longer affected by any change in the colour of the surroundings
in which it was placed; thus the alternative, otherwise not un
reasonable, is excluded, that the reaction is somehow determined
through the skin, the principle applied being that no circumstance
in the presence of which the phenomenon fails to occur is its cause.
This conclusion is further confirmed by the fact that in other
species that normally exhibit a similar colour-reaction individuals
have been found, in whom the power of adjustment to the colour
1 To speak strictly, rays are not differently coloured, but of different
wave-lengths.
410 AN INTRODUCTION TO LOGIC [CHAP.
of their surroundings is absent, and that these individuals on
examination have been ascertained to be blind ; but it may still be
asked how the stimulation of the eye by different kinds of light
effects the colour-change. Perhaps there are two alternatives here ;
it might be necessary for the frog to be aware of the colour of its
surroundings, or there might be a reflex mechanism. The latter
is supported by the fact that a blinded frog, after a violent
struggle to escape, changed from dark to light, but in half an hour,
though placed in a bright light, became almost coal-black again.
Here it is shown that a colour-reaction can take place without
awareness of colour ; so that awareness of colour is eliminated from
among the conditions necessary to the production of the reaction,
on the principle that a circumstance in the absence of which the
phenomenon 'nevertheless occurs is not its cause. We must look
then for some circumstance common to the case of a blind frog
changing colour after a violent struggle, and of a normal frog
changing colour with a change of surroundings ; and we may find
this in nervous excitation, for that may be produced by the action
of light upon the eye, and also by the struggle. Until some
other feature common to the two cases was suggested, we should
accept this on the principle just cited ; but it is also supported by
the known physiological function of the nervous system in the
building up of reflexes ; it consists too with the fact that when the
excitement subsided the frog returned to a colour not adapted to its
environment. Yet how can the animal's colour be affected by
different kinds of nerve-stimulation ? There have been found in the
skin of the frog pigment granules of divers colours, so arranged that
different surface effects can be produced by different degrees of
concentration in the granules. The final connexion of the pheno
menon of colour-reaction in the frog with these pigment granules
is indeed rather deductive than inductive ; for the part which
efferent currents from the nerves play in provoking muscular con
tractions and relaxations is already known, and so is the fact that
an afferent nerve- current discharges into an efferent nerve ; and we
have just shown that the colour-reaction is connected with afferent
nerve-stimulations.
2. Let us take next a simpler example, and one in which there is
little or no generalization : for inductive reasoning may be applied to
discover the cause of a single event, as well as of an event of a certain
xx] RULES OF CAUSE AND EFFECT 411
kind ; and it is not necessary to carry the analysis (of which more
in the next chapter) so far as to make a general conclusion possible.
Let a novice notice that his bicycle makes an unpleasant noise in
running, and try to ascertain the cause. We are to suppose a novice,
because any one of any experience may be presumed already to
have arrived by induction at the knowledge that one kind of
noise is made in the chain, and another kind in the bearings ; and
the application of this previously acquired knowledge to a particular
case would be deductive. In this problem the determination of the
alternatives among which the cause is to be sought is tolerably
simple ; for the noise must originate in one or other (or it may be
several) of the non-rigid parts. Say that these are, on the machine
in question, the axle-bearings of either wheel and of the cranks, the
bearings of the head, the pedal-bearings, the clutch, the back
pedalling break, and the saddle-springs. All that the rider has to
do is to ascertain which of these parts may be at rest while the
noise occurs, and which may be in motion without the noise. If
the noise ceases in free-wheeling, it is not produced in the axle-
bearings of either wheel, for they are still running, and that is not
the cause, in the presence of which the phenomenon fails to occur ;
for the same reason it is not in the bearings of the clutch, which is
now running. If it is not produced in ' wobbling ' the head, or
turning sharp corners, he may acquit the bearings of the head on
the same principle. If it occurs in driving with each pedal singly,
it does not arise in either pedal-bearings, because it occurs with
each pedal in turn undriven, and that is not the cause in the absence
of which the phenomenon occurs. Similarly if it occurs without
putting on the back-pedalling break, or when he removes his weight
from the saddle, it does not originate in either of those quarters.
Two alternatives remain : it may be in the crank axle-bearings, or
in some looseness of the clutch when that is caught and driving. As
between these alternatives a decision might be made if he dismounted,
and listened while he whirled the hind wheel round by the pedals ;
here however he would be reasoning deductively from the principle
that sounds are more distinct when you are nearer to their point
of origin. The difficulty of generalizing in such a case arises from
the difficulty of distinguishing the phenomenon investigated from
others that may be like it but have different causes. If the noise
which each part of his bicycle could make were of a distinctive
412 AN INTRODUCTION TO LOGIC [CHAP.
kind easily recognized, a man might very soon determine that such
and such a noise (at least in his bicycle) only originated in such and
such a part ; or if he could note the differences between noises other
wise similar coming from before or behind him, from right or left,
he might then (without having originally known, although he dis
tinguished their quality, from which quarter each kind of noise
came) establish inductively in the way described a generalization
that such and such a noise was produced by something in the front
axle-bearing, and such another by something in the left pedal ;
again, further experience, argued from on similar lines, might show
him that a particular character in a noise was due to want of oil in
a bearing, and another character to a broken ball. But so long as
the phenomenon studied is submitted to no such analysis, it is liable
to be confused with others that are not really the same, and error
would obviously arise if we generalized about it under these circum
stances. Hence one may have to be content with a conclusion that
assigns the cause of it in the particular case. It is, however,
instructive to observe that the same process of elimination among
the members of a disjunction is employed here, as if one were
establishing a general conclusion. For ex liypotliesi the novice
recognizes in the noise no intrinsic character which he knows to be
connected according to any principle with a particular origin ; he has
therefore to fall back upon ascertaining its origin by the indirect
method of showing that among the possible origins to which it can
be ascribed there is none but one to which the facts permit him to
ascribe it consistently with the principles of causation.
3. Professor Weismann's theory of the ' Continuity of the Germ-
Plasm ' is well known. The reproductive cells, whether of a plant
or animal, are different in certain important respects from those
composing other parts and tissues, and called somatic or body-
cells; and in particular of course, whereas the latter, in the process
of increase and division, produce only cells of one kind, such as
compose the part or tissue to which they belong, the former produce
cells of every kind that occurs in the organism, and, in fact, are
capable of reproducing the whole organism and not merely a special
part of it. In so doing they must, of course, reproduce the repro
ductive cells also, in order to provide for the following generation.
Now Weismann holds that the reproductive cell, or germ-plasm,
as it develops, sets aside from the outset a part of itself to serve
xx] RULES OF CAUSE AND EFFECT 413
the purpose of reproduction once more, and that this, which is still
germ-plasm, remains as it were isolated in the developing organism,
and unaffected by the other and heterogeneous parts, or somatoplasm,
which the reproductive cell develops into ; and as this happens in
each generation, there is an absolute continuity of the germ-plasm ;
from which it follows in his view that no characters acquired by
the individual in the course of its lifetime and not congenital can
be transmitted to its offspring ; for a character which is purely an
acquired character arises in the somatoplasm, and the germ-plasm
is from the first secluded from the possibility of being affected
by the somatoplasm. Influences which reach the germ-plasm can
alone modify subsequent generations ; of which the most impor
tant is the fusion of two reproductive cells that takes place in
sexual propagation (for the theory applies only to the metazoa,
which increase by copulation) ; for the germ-plasm of the ovum
blends with another germ-plasm conveying more or less different
heritable tendencies, and a sort of shuffling takes place as a result
of which there arises a new individual resembling precisely neither
parent, but exhibiting those ' spontaneous variations', as Darwin
called them, which form the material for Natural Selection to
work upon. Darwin himself, on the other hand, believed that
' acquired characters' might in certain cases be inherited, and
that it was very difficult to account entirely for the progressive
modification of species in adaptation to their environment, without
allowing the influence of this so-called ' Lamarckian ' factor.1 The
question has formed a subject of protracted controversy among
biologists, and it is not an easy one to settle conclusively on
inductive principles by appeal to evidence, because most facts
admit of being interpreted in either way. One of the most
important investigations into the subject2 is a series of experi
ments on guinea-pigs, conducted during thirty years by Brown-
Sequard and extended by two or three other naturalists ; and it
is claimed that in the course of these experiments certain modi
fications appeared in some of the guinea-pigs, the cause of which
lay in injuries done to the nervous system of their parents.
1 Because Lamarck (1744-1829) Imd propounded a theory which ascribed
the gradual modification of species largely to the inherited and accumulated
effects of use and disuse of organs.
2 The following argument is taken from G. J. Romanes' Darwin and after
Dam-in, vol. II. ch. iv.
414 AN INTRODUCTION TO LOGIC [CHAP.
It was found that epilepsy sometimes appeared in animals born
of parents which had been rendered epileptic by an injury to the
spinal cord or a section of the sciatic nerve. Here was a fact
to be accounted for, and the cause must be sought among' the
circumstances to which the epileptic offspring were exposed.
Brown- Sequard attributed it to the injury done to the parent ;
but nobody professes to see how that could produce the effect, so
that one can only be forced to accept that explanation by default
of anything else to which to attribute it. It might be said that
the epilepsy was due to some congenital defect that had no relation
to the experiment performed on the parents ; but epilepsy is not
otherwise known to occur spontaneously in guinea-pigs, and apart
from any improbability in the concidence, we should expect that
if some congenital modification of the germ-plasm produced
epilepsy in these cases, it would have occurred and produced it in
others. Weismann suggested that it was due not to the injury
to the parent, but to ' some unknown microbe ' which, entering at
the incision whereby the injury was made, both produced the
epilepsy in the parent, and by invading the ova or spermatozoa,
produced it also in the offspring. But against this suggestion we
may urge that, though there may be microbes enough unknown
to us, yet if this microbe of epilepsy in guinea-pigs exist, it would
be likely to seize other opportunities of entering ; the disease,
however, as already mentioned, is not otherwise known to attack
them. And it was also found that the epilepsy might be produced
(and apparently transmitted) without incision, by a blow on the
head with a hammer, in circumstances that preclude the entry of
microbes. To this Weismann rejoined that the shock of the blow
might have ' caused morphological and functional changes in the
centre of the pons and medulla oblongata, identical with those
produced by microbes in other cases ', and so set up the epilepsy ;
but these changes would not penetrate, as microbes may be con
ceived to do, to the ova or spermatozoa, and so the disease in the
offspring occurs without the presence of the cause alleged. More
over, there are cases (though the facts of them are not so clear or
well confirmed) in which other diseases produced by other traumatic
injuries to the parent have reappeared in the offspring; these
diseases were not such as could have been produced by microbes ;
and to suppose, with Weismann, that the shock of the injury caused
xx] RULES OF CAUSE AND EFFECT 415
a general weakness of the nervous system, in consequence of which
the animals would be likely to bear ' weak descendants, and such
as are readily affected by disease ', does not account for the diseases
in the offspring- being of the same sort as those respectively pro
duced in the parents. So far, therefore, the alternative hypotheses
to that which attributes the disease in the offspring to the injury
done the parent seem to be excluded ; but Weismann has a final
argument to urge against the ' Lamarckian ' hypothesis. If the
epilepsy was produced in the parent by the injury inflicted, it
ought not to occur in the offspring in the absence of that injury
in the offspring ; and it would therefore be necessary to show that
the nervous lesion which is the alleged cause of the epilepsy, and
not merely the epilepsy itself, is transmitted. To this Romanes
replies, that it very well may be transmitted ; since even if adequate
examination had been made (which is not the case), there may be
structural injuries in a nerve which are not discernible. Never
theless, he admits that the result of the whole debate is to leave
' the Lamarckian interpretation of Brown-Se'quard's results ' rather
unassailed than proved. The facts alleged are f highly peculiar ',
and hardly sufficient by themselves to furnish ' positive proof of
the transmission of acquired characters '.
This example has been chosen because it illustrates very well how
the inductive proof of a conclusion rests on excluding alternative
explanations. The whole chapter in Romanes' work, from which
it is taken, may be profitably studied from that point of view.1
A further knowledge of facts might enable a biologist to suggest
a cause for the appearance of epilepsy in the second (or later)
generations of guinea-pigs, consistent at once with the facts and
with Weismann's theory of the continuity of the germ-plasm.
But this does not detract from the value of the example as an
illustration of the method of inductive reasoning; indeed, it must
be remembered that such reasoning, if the premisses are false, will
probably involve us in false conclusions. But it must be pointed
out, that in the process of excluding alternative suggestions as to
the cause, it was sometimes necessary to do more than merely
1 Cf. Romanes' own words with reference to another experiment on guinea-
pigs : ' Naturally, therefore, the hypothesis of heredity seems less probable
than that of mere coincidence on the one hand, or of transmitted microbes
on the other. But I hope to have fairly excluded both these alternative explana
tions.'' Darwin and after Darwin, p. 119. (The italics are mine.)
416 AN INTRODUCTION TO LOGIC [CHAP.
appeal to one of the grounds of elimination set down earlier in this
chapter; some deduction of the consequences of accepting- such
alternative was needed, more elaborate than is involved in saying
that, if such were the cause, the epilepsy would appear where it
did not, or not appear where it did. Thus it was argued that the
epilepsy was not to be attributed to a microbe, because other
diseases equally appeared to be transmitted, which a microbe could
not have originated; we cannot be said to be here applying the
simple principle, that that is not the cause of a phenomenon, in
the absence of which it occurs, for these other diseases are not the
same phenomenon as the epilepsy. To make the evidence of these
other diseases serviceable, it had to be shown that there was no
tenable alternative to the Lamarckian interpretation put forward
(in lieu of microbes) in their case ; and the principle involved in
the use of their evidence was this, that if it is necessary to attribute
the reappearance of one kind of disease in offspring to its artificial
production in the parents, it is more reasonable to attribute the
reappearance of another kind of disease (epilepsy) in offspring to
its artificial production in the parents, than to a different sort of
cause of whose presence and operation there is no evidence. This
principle may in turn be said to rest upon the principle that like
effects have causes correspondingly like ; and all rests ultimately
on our understanding of the causal relation ; but in order to see
that facts are inconsistent with the ascription of a given pheno
menon to some particular cause, a more or less extensive hypo
thetical deduction of the consequences that ought to follow if that
were the cause is often necessary. It may be noted, too, in this
example, that some of the steps of the argument are only probable ;
if the entry of a microbe at the incision were the cause of the
epilepsy, it would probably occur in cases of natural injury where,
so far as we can see, the .microbe might equally well enter : accord
ing to the principle that that is not likely to be the cause of the
phenomenon, which is probably present on some occasion when the
phenomenon fails to occur.1 And lastly, Romanes cautiously
1 In the Prior Analytics Aristotle discusses at great length modal syllogisms,
i.e. syllogisms where one or both premisses are problematic or apodeictic ;
showing under what conditions the conclusion will be problematic or apo
deictic. We have here an example of what might be called a modal induc
tion ; the parallelism may be commended to the notice of any who think,
with Mill, that an inductive argument which can be represented in symbols
(like his ' Inductive Methods') is the less formal because it is inductive.
xx] RULES OF CAUSE AND EFFECT 417
concludes that the attribution of epilepsy in the offspring- to its arti
ficial production in the parent is not proved, because the cause may
lie in something hitherto undetected ; and this illustrates what was
maintained earlier in the chapter, that the getting1 of a positive
conclusion, but not the inductive character of the argument, depends
on the completeness of the elimination.
4. Adam Smith, in the Wealth of Nations1, discussing the
inferences which can be drawn from the low money prices of
goods in ancient times, and wishing to show that from the low
prices of goods in general nothing can be inferred as to the wealth
of a country, though much can be inferred from the comparative
prices of different kinds of goods, such as corn and meat, mentions
that it was commonly supposed that the said low money prices of
goods in ancient times were a proof of the poverty and barbarism
of the countries where they prevailed. He uses the following
argument to show that this is not the case, but that they prove
only the barrenness of the mines which then supplied the com
mercial world. First, he says that China is a richer country than
any part of Europe, yet the value of the precious metals is higher
there than anywhere in Europe : now on the principle that that
is not the cause of a phenomenon which does not vary proportion
ately with it, we cannot attribute low money prices to poverty in
the face of lower prices where poverty is less. Next, he admits
that since the discovery of America the wealth of Europe had
increased, and the value of gold and silver diminished ; but he
urges that the two events have scarcely any connexion ; the first
being due to the fall of the feudal system and the growth of public
security, the second to the discovery of more fertile mines. In
support of this way of connecting the facts he points to the case
of Poland. Poland was the most beggarly country in Europe, as
beggarly as before the discovery of America ; yet the money price
of corn (the most important single commodity) had risen equally
there : if poverty were the cause of low money prices, it ought not
to be found where prices were high. On the other hand, Poland
was still feudal, so that her beggarly state was consistent with the
connexion of facts alleged by Adam Smith. Again, Spain and
Portugal were the next most beggarly countries in Europe to
Poland, and prices ought therefore to be low there, if there were
1 Bk. I. c. xi, vol. i. p. 365, 7th ed., 1793.
JOSEPH ji Q
418 AN INTRODUCTION TO LOGIC [CHAP.
the connexion between low money prices and poverty that was
supposed ; but it was not the case ; prices were high ; as might be
expected if they depend on the facility with which the precious
metals are obtained, for, owing to their control of the American
mines, gold and silver were brought more cheaply to Spain and
Portugal than to any other country in Europe. The cause of low
money prices in general, therefore, is not poverty and barbarism,
and may be the barrenness of the mines supplying the commercial
world with gold and silver ; and this has been shown by inductive
reasoning. Adam Smith also offers deductive arguments to show
that it is the latter, and is not the former. It is not the former,
because a poor could not afford to pay as much as a rich country, in
labour and means of subsistence, for such comparative superfluities
as gold and silver ; it is the latter, because the purchasing power
of gold and silver, or the amount of goods for which they will
exchange, depends on what has to be given in order to get them ;
and where the mines are fertile, a less amount of labour and
means of subsistence needs to be supplied in the work of getting
them, than where they are more barren. The logician may distin
guish an inductive from a deductive argument ; but investigators
will gladly use arguments of both kinds to support the same
conclusion.
5. We may conclude with an example drawn from the Poor Law
Commissioners' Report of 1834, with regard to the cause of the
appalling increase of pauperism in England during the early part
of the last century1. The Commissioners who were appointed
to find the cause and to suggest a remedy, attributed the evil to
one principal fact in the situation, viz. that the condition of those
receiving parochial relief had been allowed to become not less
eligible than the lowest condition of men maintaining themselves
by independent labour. In proof of this finding, they pointed out
in the first place that the cause alleged was present in all instances
of the phenomenon to be accounted for. The great increase of
pauperism had dated from 1796. In that year, an Act of 1723,
providing that no one should be entitled to relief who would not
enter the workhouse, had been repealed; and it had become
customary for the parish to assure to all labourers, in their own
homes, a certain weekly sum, varying with the numbers in the
1 v. the Blue-book, esp. pp. 186-216.
xx] RULES OF CAUSE AND EFFECT 419
family and the price of bread. This sum was made up in various
ways; sometimes grants were given in supplementation of wages
(which naturally tended to make farmers and other employers give
a lesser wage, and so interested them in the support of a system
from which they saw more clearly the immediately resulting benefit
than the remoter but far greater evils); sometimes the parish
found work, generally lighter than what was exacted for the same
price by private employers (and this led men to prefer to work for
the parish); sometimes a money-grant without any return of labour
was made to men out of work (who were not, therefore, the more
likely to look for work) ; but in any case, it was made possible for
a man to count upon parish pay, sufficient to maintain him as well
as many independent labourers were maintained, whether or not he
endeavoured to support himself.
The cause alleged, then, was present where the pauperism was
present ; but that was not enough to show that it was the cause.
It might indeed be plausibly argued, from familiar principles of
human nature, that such a method of administering poor-relief
would be likely to increase pauperism faster than it relieved it :
but this deductive reasoning was not, and still is not, sufficiently
convincing to men who, from one motive or another, are attached
to such methods — whether from compassion for the immediate
suffering of those applying for relief, or from desire to get relief
on the easiest terms, or from fear, if relief is less readily given,
that it will become necessary to give higher wages to the labourer.
To bring conviction, it was necessary to show that there was
nothing else to account for the phenomenon. Now several other
causes had been suggested to account for this growth of pauperism.
One was the great rise in the price of corn, which had occurred
during, and partly in consequence of, the French war: another
was the increase of population : and another was the introduction
of machinery — a highly unpopular thing at the time, because its
first and mos,t obvious effect was to displace labour; and there
had been agricultural riots directed against the use of machinery
in 1830.
It would not be possible to show that none of these causes had
ever made a man a pauper. But it was possible to show that in
the main the pauperism so widely prevailing (which was so great
a national evil because it prevailed so widely) could not be due
E e 2
420 AN INTRODUCTION TO LOGIC [CHAP.
to them. The Commissioners were able to point to numerous
instances of three kinds, in which the pauperism so prevalent
elsewhere was absent ; in all of them, the cause they alleged was
absent too; but the alternatives which they wished to disprove
were present.
The first class of instances consisted of certain parishes where
what was called a Select Vestry had adopted the plan (still then
lawful, though not since 1796 compulsory) of refusing relief to any
able-bodied labourer except in a workhouse where a full task of work
was exacted. It was their experience that pauperism immediately
and greatly diminished. And naturally ; for when men who had
hitherto been content to take parish pay found they had to work
as hard all the same, they preferred to work for themselves ; with
a motive for independent industry and thrift, they became more
industrious and thrifty; becoming more industrious, they were
better worth employing; and the farmer besides, knowing that
the parish would no longer supplement the inadequate wages by
which he had obtained labourers upon his farm, was compelled, if
, he would still have labourers, to give a better wage.
The second class of instances was furnished not by parishes
which, in removing the cause alleged, had removed the pauperism
which it was alleged to be the cause of ; but in the parishes them
selves where the pauperism existed. It was furnished by what are
called the non- settled labourers, who in all parishes were found to
be more industrious, thrifty, and prosperous, and less pauperized,
than the settled labourers. As the circumstances of two sets of
labourers in one parish are likely to be more nearly alike than
those of labourers in distinct parishes, these constituted what Bacon
calls a prerogative instance ; for all the conditions equally affect
ing settled and non-settled labourers may be excluded, in looking
for the cause of this difference between them, on the principle of
rejecting the circumstances present when the phenomenon is absent.
By a non-settled labourer is meant a labourer living in another
parish than that which is legally bound to support him. If he
becomes a pauper, such a person can be removed to the parish to
which he is legally chargeable ; and to save their own rates, over
seers were always anxious to remove any one they could. To the
labourer, on the other hand, removal was as a rule by no means
welcome ; such labourers, therefore, found that they had to choose
xx] RULES OF CAUSE AND EFFECT 421
between removal, which they did not want, and an effort to main
tain themselves by their own labour ; for if the parish relieved
them at all, they would only get — unlike their settled neighbours
— little relief on hard terms where they were.
The third class of instances was afforded by parishes which had
never adopted the practice, so common since the Act of 1796, of
relieving able-bodied men out of the workhouse ; i. e. they had
never consented to make the condition of the pauper as eligible
as that of independent labourers ; and in them the same extensive
pauperization and increase in the rates, which had occurred else
where, had never happened.
Now in all these three classes of case, the Commissioners' theory
held good ; for when the effect was absent, so was the cause to
which they attributed it. But the same could not be said for the
alternative theories put forward. If it were alleged that non-
settled labourers had smaller families, which is doubtful, yet the
increase of population was not confined to parishes which had
adopted, or banished from those which had abandoned, the practice
rendered permissive by the Act of 1796. The price of corn had
risen, and the introduction of machinery must have had its effects
—whatever they were — in the parishes which had abandoned or
never adopted that practice as much as in the rest, and among the
non-settled as much as among the settled labourers of any parish.
In short, looking to the mass of pauperism, there was no other
circumstance which might be suggested as its cause, that could
not, upon one or other of the plain grounds of elimination so often
referred to, be rejected ; and the Commissioners' cause was left in
possession of the field ; with the additional support derived from
the deductive reasoning that might not have been thought of —
even if it would have carried conviction — by itself. For it often
happens that we can subsequently show that a cause, to which an
effect has been attributed on the grounds that there is nothing
else to which the facts permit us to ascribe it, must, in according
with some accepted principles prevailing in the subject-matter to
which the enquiry belongs l, produce that effect : although, but for
the help which the inductive argument had given us in finding
the cause, the deductive argument would never have occurred to us.
1 i. e. special principles, or ifiiat apxai Cf. supra, p. 359.
CHAPTER XXI
OF OPERATIONS PRELIMINARY TO THE APPLICA
TION OF THE FOREGOING RULES
IT was allowed in the last chapter that it is impossible to
apply the kind of reasoning there analysed until a good deal
of work has already been performed upon the material which
experience offers us. That work is really much harder than the
reasoning that succeeds it; indeed so simple does the reasoning
look when thrown into symbolic form, that it would not be
surprising if any one mistrusted the foregoing account on the mere
ground that induction must be a harder business. A consideration
of the present chapter may reassure him on this point.1
The operations that have to be performed in order that the
foregoing rules, or any other more special rules of the same kind,
may be applied, are difficult to classify in a perfectly satisfactory
manner. Different writers have called attention, and have given
different names, to processes which are sometimes more or less
the same essentially. Moreover, we should make our list shorter
or longer according to the extent to which we considered what
may be called the Methodology of the several sciences. By this
is meant an attempt to give special directions, based partly on
general logical considerations and partly on the nature of the facts
with which it deals, for mastering the special difficulties which
a particular science presents; for example, a mythologist might
be enjoined to adopt the comparative method, and collect, with all
the precautions which the experience of those who know the
difficulty of rightly interpreting the savage mind can suggest,
1 Mill deals with the subject of this chapter for the most part in his Fourth
Book, Of Operations subsidiary to Induction. In the sense that the reasoning-
described in the Third Book cannot be profitably performed till they have
taken place, they may be called subsidiary ; but Induction is perhaps rather
the whole process of eliciting from facts the principles that account for
them than merely the form of reasoning involved therein; and these
operations certainly hold no subordinate place in that process.
PRELIMINARIES OF INDUCTIVE REASONING 423
the myths and customs of many different lands : in biology again
we should probably be told of the importance of obtaining statistics
of a trustworthy kind regarding the mode in which divergences
were distributed on either side of the average or normal in respect
of divers measurable characters in animals and plants : and so
forth. The particular preliminaries, without which inductive
reasoning in each science may have little prospect of success, could
of course only be determined by some one well acquainted with
that science ; though it is quite possible that a man of logical
training, coming fresh to the study of what others have done, may
be the better able for that training to make contributions to the
work of scientific investigation ; still, here as elsewhere, Logic learns
by reflection on the immediate operations of thought about things.
A methodology of the several sciences lies however beyond the
scope of this volume, and would require far greater knowledge than
it has at its command. The list of operations therefore which
follows makes no pretence to go as far as it might, or to embody
the only possible division.
First of all may be placed what has been called the Analysis of
the Given 1 : and this is requisite in two ways,
1. in determining precisely the phenomenon to be studied -}
2. in distinguishing and detecting the various circumstances under
which it occurs, or tinder which it fails to occur when perhaps it might
have been expected.
Long before we consciously seek 'rerum cognoscere causas ',
a beginning has been made in the performance of this analysis :
and the results are embodied in the general names by which men
group and distinguish different objects, attributes, or events. But
there are many distinctions which ordinary language ignores, and
it often gives different names to things which are in some impor
tant respect identical. For ordinary purposes the identity may be
of no account, and yet in a scientific enquiry it may prove funda
mental. For example, to the lawyer hares and rabbits are vermin,
to the sportsman they are game, and to the zoologist they are
rodents ; each of these men for his own purposes is interested in
characters that unite them respectively with quite a different
group of other animals; but there is nothing in their specific
1 Professor Welton's Inductive Logic, c. v.
424 AN INTRODUCTION TO LOGIC [CHAP.
names to indicate their affinities with any one of these groups.
Or again breathing, burning-, and rusting are three processes for
all practical purposes so very different, occurring in such different
connexions and of importance to us in such very different ways,
that they naturally have obtained distinct names ; yet one of the
greatest steps in the history of chemistry was connected with
the discovery that they are, chemically speaking, all processes of
the same kind, viz. the combination in the first two cases of carbon
and in the third of iron with the oxygen of the air.1 These cases
illustrate the way in which it may be necessary to ignore our
customary classification of things, and bring together, upon the
strength of some identity which an analysis may have discovered
in them, things that we have habitually kept quite apart in
thought. It is equally necessary at times to distinguish things
which we have habitually classed together, if we are to make any
progress in the investigation of them. The case of rent furnishes
a good instance. The name is given equally to the sum which
a man pays for the occupation of land, and to that which he pays
for the occupation of a building ; as these are very commonly paid
to the same person, as a lump sum is then charged for the two,
and as the ordinary tenant in search of a dwelling is prepared to
pay so much for accommodation, but indifferent to the question
whether the owner considers his charge to be based on the value
of the house or of the site it stands on, it follows that most of us
find no inconvenience in this double use of the word. The farmer
who has to consider separately what the land he farms is worth to
him per acre, and what the value of the homestead is to him, is
more or less aware of the ambiguity ; but the political economist,
when he comes to consider the causes that determine rents, is
bound to distinguish house-rent and ground-rent by name. Indeed
until that is done, his investigation will make no progress ; for the
two depend upon quite different conditions. The rent of a house,
apart from any special history or sentiment, depends chiefly on the
cost of building another like it, and the current rate of interest
on money in the country at the time ; but land cannot be produced
as it is wanted, and this natural limitation of supply may give to
a particular piece of land, in virtue of its fertility or its situation,,
a rentable value that depends mainly on its superiority in those
1 Cf. pp. 436, 437, infra. Of course the oxygen need not be atmospheric oxygen.
xxi] PRELIMINARIES OF INDUCTIVE REASONING 425
respects over other land which cannot be dispensed with for culti
vation or for building, and only very slightly and remotely, if at
all, upon the circumstances which regulate house-rent.
The process of discovering identities between things in which we
commonly ignore them, and that of discovering differences between
things which we commonly take for the same, very generally involve
one another. We perform as it were a mental re-grouping ; and in
the act of bringing together what we had hitherto only distin
guished we most probably break up or find distinctions in the groups
from which members are brought together. But in a given case
one aspect may be much more prominent than the other ; and
Bacon has observed l that some men have a greater capacity for
the one kind of work than for the other, insisting (like Plato
before him) on the necessity of noting, in the investigation of
nature, both the resemblances and the differences that are ordi
narily overlooked. Analysis is at the bottom of each process, for
until we have distinguished the various characters of things, we
have not discovered the bases on which to compare them. It must
be added however that analysis may be of great importance, yet with
out leading to any act of fresh classification, when we want primarily
to know the circumstances under which a phenomenon occurs.
We have now to some extent considered the nature of the work
involved in the performance of the two tasks above mentioned :
namely, in determining precisely the phenomenon we have to
study, and in distinguishing and detecting the various circum
stances under which it occurs, or under which it fails to occur
when perhaps we should have expected it. It is sufficiently
obvious that without performing them we should hope in vain to
discover causal connexions by way of induction. If we have no
precise or exact conception of the phenomenon to be studied, or
have not (as one might say) duly determined it, we may examine
instances that we ought to ignore, and ignore instances that we
ought to examine. The result of the former error will be that we
shall try to make our theory as to the cause of x consistent with
the facts of the occurrence of a different phenomenon y : and the
result of the latter, that we may be ignorant of facts which might
throw great light upon the cause of x. The necessity of making
a correct enumeration of the circumstances under which a pheno-
1 Nov. Org. I. 55.
426 AN INTRODUCTION TO LOGIC [CHAP.
menon occurs, before asking- with which of them it is causally con
nected, needs no comment ; nor is it less plain that, if the question
is to be answered, we need equally to recognize the circumstances,
where they occur also in the absence of the phenomenon.
But though this work is so necessary, it is impossible to give
any rules for the efficient dispatch of it. Familiarity with a science
may help a man to perform it in the investigations of that science,
teaching him the sort of thing- to look for, and the sort of way
in which to look for it. Yet the sagacity upon which the discovery
of new truth depends does not come to most men even by such
familiarity. The logician's business at any rate, since he cannot
teach them to do it, is to make men realize the part which it plays ;
and one or two further examples may be given with that object.
A research which has been so frequently cited in works on
Induction as to become almost a stock instance will serve this pur
pose — Wells' s Theory of Dew. Dew, as is now pretty generally
known, does not rise but falls : the atmosphere can hold in suspen
sion a certain proportion of water in the form of vapour, but the
amount depends upon the temperature of the atmosphere, and
increases with it. If anything suddenly chills the atmosphere, it
precipitates such a portion of the moisture which it holds as exceeds
the maximum it can hold at the temperature to which it is reduced.
It may be chilled in various ways. One is the contact of a
colder surface, on which the moisture is thereupon precipitated ; and
the rapidity with which the surface of a body gets chilled depends
on various circumstances — partly on its substance, partly on its
texture (rough surfaces, or those with many points, like grass,
radiating heat more rapidly than smooth ones) : another way is
by the inrush of a heavier and colder current : another is by
radiation to the sky, and the degree to which that takes place
depends on the amount of cloud about ; a sheet or other covering
stretched over the ground acting in the same sort of way over
a small area, though with more effect over that area, as the
clouds spread out over the earth. This precipitation of moisture
held in suspension in the air is seen not only when dew falls;
when warmer weather comes after a frost, particularly if accom
panied by rain, the cold surface of a stone wall, if painted or other
wise not porous, drips with the water it has extracted from the air
which its contact chills. In the same way cold spring water poured
xxi] PRELIMINARIES OF INDUCTIVE REASONING 427
into a glass in summer will chill the outside of the glass, so that
water is deposited on it from the air without : and when hot water
is poured into a glass without filling it, and sends its vapour into the
air above, some of this vapour bedews the interior surface of the
glass above the water-level, until this portion of the glass has
acquired by conduction the temperature of that below it. Now our
present business is not with the reasoning by which Wells showed
the deposition of dew to depend upon a relation between the tem
perature of the atmosphere and of the body on which the dew fell,
taken in conjunction with the degree of saturation of the atmo
sphere at the time. But it is plain that he could never have done
this, if he had not taken note of all the above points, the material
and texture of bodies, as affecting their surface-temperature,
the clearness or cloudiness of the nights on which he looked for
dew, the conditions of air and wall when the latter drips with
moisture, and so forth. It would have been in vain to observe
that one body collected more dew and another less, unless their
roughness and smoothness were noted, as well as their substance :
or that on some nights there was heavy dew and none on
others, unless the saturation of the atmosphere were ascertained as
well as its temperature. And similarly, it was necessary that he
should get a right conception of the thing called dew that he
proposed investigating. There are clammy days when everything
grows damp from a moist fog hanging in the air. It would not
have been unnatural to look in this for a phenomenon of the same
nature as dew, and to overlook such things as dripping walls and
moisture-frosted tumblers. Yet the mistake would have put the
enquirer altogether off the scent.
Curative effects of different kinds are exhibited by certain
waters. To the eye many of the waters are indistinguishable ;
and if the palate detects a difference, yet it would not be found
possible to connect efficacy in particular complaints with particular
flavours according to any explicit and invariable rule. It is plain
that no progress can be made unless the various diseases are described
not merely by their more obvious symptoms but by reference to the
physiological character involved : and the water chemically analysed,
so that one may know each separate ingredient, and the different
proportions in which they are present in different cases. Again, the
bacteriological theory of disease would never have been formulated,
428 AN INTRODUCTION TO LOGIC [CHAP.
until the bacteria themselves were found — bodies so small that before
the construction of powerful microscopes their presence was of neces
sity overlooked ; and when one hears of pathologists endeavouring
to isolate the microbe of some particular disease, one realizes how
impossible it is, without the preliminary work of distinguishing the
circumstances, to apply the ' canons of induction ' to any effect.
Or suppose that an enquiry is undertaken not into the physiological
cause of a disease, but into the causes of its dissemination, either
generally or on some particular occasion : let the disease, for
example, be malaria. Malaria was long supposed to be contracted
from the exhalations of the ground; and it was true that many
malarious districts were marshy, and that persons who avoided the
swamps at dusk and dawn seemed less liable to be infected ; but it
was not until it was noticed that such districts were infested with
mosquitoes of a particular species, and it occurred to some one to
connect this circumstance with the communication of the disease,
that false ideas were exposed and the true law of the matter
established.
The last remark suggests a transition to the next preliminary
operation that we may notice — the formation of hypotheses.
Much has been written upon the question whether Logic can lay
down any rules by which the formation of hypotheses should be
controlled; but beyond the somewhat obvious and quite general
consideration that an hypothesis must contain nothing inconsistent
with principles which thought finds necessary, it does not seem that
Logic can be of any more service here than in the performance of
the work of analysis. It would be an illegitimate hypothesis on the
part of a bank clerk confronted with a small discrepancy in his books,,
to suppose that on this occasion two and two made three ; but a petty
theft on the part of the Principal Manager, though very likely a
foolish hypothesis, would not be logically illegitimate. It might
indeed be urged, that the hypothesis of angelic intervention, though
there is nothing inconceivable in the existence of angels, would not
be a legitimate way of proposing to account for an event; and
this may be admitted ; for there is no use in attributing phenomena
to causes whose presence we have no means of ascertaining ; since
such hypotheses can never be brought to the test of facts. It is
obviously more reasonable to go on trying to account for them by
ascertainable natural causes in the hope of being able to connect
xxi] PRELIMINARIES OF INDUCTIVE REASONING 429
them by general principles with other observable phenomena, than
to abandon that hope at the outset and invoke the agency of
beings whose existence cannot be empirically verified ; so that
although we can hardly pronounce it logically inconceivable (how
ever it may be scientifically inadmissible) for the physical order so
to depend on something beyond itself as to make it impossible to
account for a particular natural event by reference solely to other
natural events preceding it, yet we may on logical grounds pronounce
it unscientific : i. e. it is seen to be unscientific not in virtue of any
special knowledge of the particular science to which such hypothesis
belongs, but in virtue of our general appreciation of the aim of
science as such, and of the logical conditions under which that aim
can be realized. An 1 this is perhaps what Mill really had in his
mind when he said l that ' It appears, then, to be a condition of the
most genuinely scientific hypothesis, that it be not destined always
to remain an hypothesis, but be of such a nature as to be either
proved or disproved by comparison with observed facts '. It should
be of such a nature that observable facts, if we could find them,
might prove or disprove it 2 : i. e. it should not appeal to the agency
of causes (like the intervention of an angel 3, or the influence of the
organic type as a whole upon the growth of the individual organ
ism) of whose presence we can have no independent evidence,
and whose nature we are not able so to ascertain as to determine
deductively how they must act if they are present ; for with the
agency of such causes as these any facts are equally compatible ;
and thus they furnish no explanation why the facts are so and not
otherwise. For this reason, as Bacon said, in looking for the
causes of things in nature Deum semper excipimus 4 : and Laplace,
when Napoleon observed to him that there was no mention of God
in his Mecanique Celeste, replied that he had no need of that hypo
thesis. But that an hypothesis should be of such a nature that
observed facts will ultimately either prove or disprove it, and not
merely might ultimately do so, seems a condition quite impossible to
1 Logic, III. xiv. 4.
2 Facts, as we have seen, cannot prove an hypothesis by their agreement
with it, except so far as at the same time they disprove its rivals by their
disagreement.
* Cf. Newman's Parochial and Plain Sermons, vol. ii, Sermon xxix, on The
Feast of S. Michael and all Angels.
4 De Principiis atque Origin-Hits, Ellis and Spedding, III. p. 80.
430 AN INTRODUCTION TO LOGIC [CHAP.
lay down. We cannot tell the future in these matters ; how long-
may an hypothesis be destined to remain an hypothesis without
prejudice to its genuinely scientific character ? The ultimate destruc
tion of life on the earth is assumed by science ; for human minds,
an hypothesis which is not proved or disproved before that date
will always remain an hypothesis. We cannot suppose that its
scientific character, when it is made, is to be estimated by the pro
spect of its truth being- definitely ascertained a few years,, or even
a few myriads of years, earlier or later. Darwin, in the Origin of
Species l} writes as follows : ' As the embryo often shows more or
less plainly the structure of the less modified and ancient progenitor
of the group, we can see why ancient and extinct forms so often
resemble in their adult state the embryos of existing species of the
same class. Agassiz believes this to be a universal law of nature ;
and we may hope hereafter to see the law proved true. It can,
however, be proved true only in those cases in which the ancient
state of the progenitor of the group has not been wholly obliterated,
either by successive variations having supervened at a very early
period of growth, or by such variations having been inherited at
an earlier stage than that at which they first appeared. It should
also be borne in mind, that the law may be true, but yet, owing
to the geological record not extending far enough back in time,
may remain for a long time, or for ever, incapable of demonstra
tion.' But that the rule in question is an universal law is a scientific
hypothesis.
An hypothesis then must be thinkable2, consistently with the
fundamental assumptions of the science which makes it : but we
cannot restrict, within these limits, the freedom of scientific hypo
thesis. What is important is that men should be cautious not in
1 Origin of Species, c. xiv, 6th ed. p. 396. The italics are mine.
2 Lotze would explain this by saying that our hypotheses must conform
to our postulates. He draws a distinction (Logic, § 273) between a postulate
as ' an absolutely necessary assumption, without which the content of the
observation with which we are dealing would contradict the laws of our
thought', and an hypothesis as 'a conjecture, which seeks to fill up the
postulate thus abstractly stated by specifying the concrete causes, forces,
or processes, out of which the given phenomenon really arose in this
particular case, while in other cases maybe the same postulate is to be
satisfied by utterly different though equivalent combinations of forces or
active elements '. It should be added, that in saying that hypotheses must
be thinkable consistently with the fundamental assumptions of the science which
makes it we are enlarging as well as restricting the liberty of the mind in
xxi] PRELIMINARIES OF INDUCTIVE REASONING 431
framing but in testing hypotheses. The publication of every wild
conjecture is undesirable ; but it would be equally undesirable
that a man should never entertain an hypothesis which contem
porary opinion could pronounce wild. Darwin said that he had
framed and abandoned many an hypothesis which he would be
ashamed to avow : he does not imply that he was ashamed to have
framed them. The best control over the licence of the imagination
is exercised by special knowledge. The man who knows most
about any department of nature will see most readily what hypo
theses are foolish in that department, just as in such practical
matters as legislation the best critics of a bill are those who have
experience of the affairs with which it deals.
It is clear that every causal connexion presents itself at the out
set in the light of an hypothesis, to the mind to which it first occurs.
The framing of the hypothesis may sometimes be very simple,
though the proof of it may be very difficult. If we know exactly
what persons were cognizant of a secret which has been betrayed,
it is easy to say that one of them must have betrayed it;
and so far there is no hypothesis ; hypothesis begins so soon
as we ascribe the offence tentatively to any one of them, and
in this there is not the least difficulty ; but a proper test of it
may be impossible. Whereas here, however, all the alternatives
are before us, and in the abstract any one of them would
equally fit the facts, because it is simply a question of connecting
an event x with one of a number of conditions a b c, about
which we do not know enough to say that it might not be con
nected with any one of them : yet commonly it happens that the
facts which an hypothesis has to fit are more or less elaborate;
and then the framing of it is not such a simple matter as the
pairing off of two terms a and x. Take for example the question
of the authorship of the Acts of the Apostles ; if that book must
have been written as it stands by one of the recorded companions
of St. Paul's journeys, it is a simple thing to say that the author
may be Luke, or may be Silas : although it need be by no means
a simple thing to decide between them. But if that is not necessary,
framing them. We restrict it to something which the facts of experience
might test : but the fundamental assumptions of a science may be meta
physically untenable, and we enlarge it to extend to all which these
assumptions cover, however it may be ultimately impossible to think the
facts in terms of them.
432 AN INTRODUCTION TO LOGIC [CHAP.
if the book may be of late date, and contain the work of several
hands, it becomes very difficult to frame an hypothesis which shall do
justice to all the features of it. We have a large number of facts
to co-ordinate; and the assumptions by which we connect them
must all be mutually coherent. Historical criticism presents many
problems, where no hypothesis is free from difficulty ; and though
doubtless a problem must have a solution, yet an ignorance of some
details, and very likely the erroneous accounts that we have received
of others, may leave us permanently unable to find it. And the
penetration and ingenuity of the historian are shown in such cases
in devising as well as in testing hypotheses ; indeed the two opera
tions cannot be kept altogether distinct : for when our knowledge
of the concrete detail of events is considerable, the process of
framing an hypothesis to fit them all is itself a process of testing.
Now what is true in history, where upon the whole l our business
is rather to determine events in conformity with acknowledged
principles than to determine principles in accordance with empiri
cally ascertained events, is true also in science, of whose business
the latter would be the more accurate description. Scientific
hypotheses consist for the most part not in the mere coupling in
the mind, as cause and effect, of two insulated phenomena (if the
epithet may be allowed) : but in the weaving of a large number of
phenomena into a coherent system by means of principles that fit
the facts. In the framing of hypotheses therefore we are called
upon to conceive facts in new ways : and to conceive not simply
that certain facts are connected, but how, or in accordance with
what principle, they are connected. And this often involves
a radical transformation in our way of looking at the facts them
selves ; for a fact is not such an easily ascertainable thing as the
language we sometimes use might seem to imply. In a sense facts
are stubborn : in another sense they are pliant to our thought. They
are stubborn so far as we have rightly apprehended them ; but
what we call fact is largely matter of inference and interpretation,
performed often unconsciously, and often erroneously ; there is room
1 Upon the whole, because the historian has often to rediscover principles —
constitutional, legal, social, or economic ; and history advances by changes
in men's way of conceiving the relations of past facts to one another as well
as by changes in their view of what the facts were. We no longer believe
in William Tell ; but the Patriarchal Theory has also changed our views as
to the relations between the individual and the State in ancient society.
xxi] PRELIMINARIES OF INDUCTIVE REASONING 433
here for re-interpretation, in accordance with the requirements of the
rest of our knowledge, and so far as facts lend themselves to this they
may fairly be called pliant. It would have been called a fact, for
example, in the days before Copernicus (though some of the Greeks
had questioned it) that the sun went round the earth ; but this was
only an interpretation of appearances which we have now been
taught to see to be equally compatible with the fact that the earth
goes round the sun. It would have been called a fact that species are
fixed and immutable ; and it is the case that they breed so true upon
the whole in any one generation as to make that a fairly accurate
statement for practical purposes. Yet we have learnt to see that
this comparative stability is consistent with any degree of modifi
cation over long enough periods of time. These instances will be
enough to show how the familiar facts take on a new appearance
in the light of new theories.
Now some new theories or hypotheses are, as we all know,
more far-reaching in their effects than others; for some are much
more general, and apply to a much larger number and variety of
facts. Their introduction marks an epoch in the progress of science ;
and Whewell attached more importance to the framing of such
hypotheses than to any other of the operations connected with
inductive reasoning. Indeed he held that this step was the induc
tion ; and that the history of the inductive sciences could be re
presented as the preparation, elaboration, and diffusion of successive
hypotheses each more adequate to all the facts of a science than
its predecessors. He did not use the word hypothesis very promi-
I nently in this connexion ; he preferred to speak of conceptions : and
what he called the colligation of facts by means of appropriate concep
tions * was in his view the essence of induction. The new conception,
however, is always an hypothesis as first entertained, and only con
verted into a part of the accepted body of knowledge by its superior
success in co-ordinating facts. This work of ' colligation ' therefore
must not be regarded as something distinct in its nature from the
framing of hypotheses : it is rather a special and important case of
it, where the hypothesis, instead of merely connecting facts in
a more or less familiar way that leaves our view of them very
much what it was before, involves a profound and far-reaching
1 v. Novum Organum Renovatum, Bk. II. c. iv : Philosophy of Discovery,
c. xxii. §§ 1-37.
434 AN INTRODUCTION TO LOGIC [CHAP.
change in our view of the facts themselves. Thus the suggestion
that malaria is communicated by the bite of the Anopheles mos
quito neither altered seriously our notion of the nature of that
insect (though it altered our practical attitude towards it in a way
by no means favourable to the numbers of Anopheles) nor intro
duced any new way of conceiving disease ; for the bacteriological
conception of disease had already been applied to many other fevers.
But the first suggestion that a disease depended on or consisted in
the presence and multiplication of some specific noxious bacillus
in the blood altered profoundly men's view both of what it was,
and of how it was communicable, and of how it might be cured.
In the relation of this ' colligation ' to the more general notion of
framing hypotheses we have an instance of the difficulty of distin
guishing sharply the different operations of thought which logicians
have enumerated as preliminary (though by no means subordinate)
to such application of the rules on which inductive reasoning jests
as we examined in the last chapter.
A somewhat unprofitable controversy arose between Whewell
and Mill as to the part which the ' colligation of facts ' should be
regarded as playing in induction. While Whewell said it was the
induction, Mill said that it was improperly so called. Mill seems to
have been influenced in part by the idea that an induction must end
in establishing a general proposition, whereas it is possible to bind
facts together by a new conception and so place them in a different
light and reinterpret them, without apparently generalizing; he
seems too to have considered that no-thing in the whole process of
thought, by which general conclusions were reached from the
examination of particular facts, ought to be called induction, except
what could be reduced to the form of inference or reasoning : the
rest was all subsidiary to induction. But the operations of thought
preliminary to the application of such rules as inductive reason
ing rests on are not subsidiary in the sense of being of secondary
importance ; and it would perhaps also be better to distinguish in
duction as the whole process from the reasoning employed in it.
We might then agree with Whewell that in induction, i.e. the
whole process of the ' interpretation of nature ', what he called the
' colligation of facts ' is an operation of the very first importance,
demanding higher and more uncommon powers of mind than
inductive reasoning ; while we agree with Mill that it is not the
xxi] PRELIMINARIES OF INDUCTIVE REASONING 435
inferential operation. But if by induction we mean the inferential
operation, then we shall have to say that this ' colligation of facts '
is more momentous in the history of science than induction ; for
most of us, as Bacon rightly said1, would light upon the use of
the methods of inference to which Mill would restrict the name
of induction, by our ordinary intelligence, without their being
formulated for us; but few can originate the new conceptions
that bring order and intelligibility into a mass of facts.
The instance which served to illustrate the dispute will help to
show what this ' colligation ' is. The ancients at first supposed
the planets to move in circles round the earth. When further obser
vation showed that this was not so, they conceived the centre of
the circle in which a planet moved to travel on the circumference
of another circle ; these circles were conceived not as mere imagi
nary paths, but as physical entities actually revolving ; and it was
possible to assign such a radius and rate of revolution to them as
would account for the planet fixed upon the outer circle describing
the path it does. This hypothesis had grown more and more com
plicated, as the mass of observations upon the movements of the
planets had increased ; and though it was capable of application to
the heliocentric no less than the geocentric theory, Kepler sought
for one more satisfactory. After trying a large number of other
curves, and rejecting them on the ground that they did not agree
with the observations, he at last discovered that the planet Mars
the primary subject of his investigations — moved in an elliptical
orbit round the sun, which stood in one of the foci. Now the
ellipse is here the appropriate conception which binds together into
an unity the successive observed positions of the planet Mars. Each
position taken singly must of course necessarily be on the circum
ference of that or any other curve ; for any curve can pass through
any point. But he sought for a curve which would pass through
all the positions ; and he found that in an ellipse. There was
indeed nothing disjunctive in his argument. Other curves were
rejected because disproved by the observations ; but the ellipse was
accepted because the observations agreed with it, and not because
no other curve would satisfy them. If it had suggested itself
sooner, the others would not all have been tried. There are curves
of higher degree, that will equally satisfy the observations, and had
1 Nov. Org. I. 130.
if a
436 AN INTRODUCTION TO LOGIC [CHAP.
they occurred to Kepler, he could perhaps have given no other reason
for preferring- to accept the ellipse than an a priori preference for
the simplest curve that would do so. It is to be noted, however,
that even here the critical matter was the thinking of an ellipse, and
not the testing its agreement with the facts : any one with the
necessary mathematical training could have done that, whenever the
ellipse had been thought of. And so it often is, though not always,
when the appropriate conception is a conception of causal relation : not
always, because sometimes there may be as much difficulty or more
in testing the conception than in thinking of it. To test it, we
may have to deduce its consequences by some intricate mathema
tical calculus, as in the case of the Newtonian theory of gravita
tion; or to devise an experiment in which we may see whether
the theoretical consequences of our conception occur. Great
mathematical power or great ingenuity may be wanted here ; but
the reasoning will be deductive. Yet even so, to introduce the
appropriate conception is much ; new ideas are scarce ; inductive
reasoning, if the material were given all ready prepared, is easy.
An excellent example of the part which a new hypothesis may
play in inductive enquiry is furnished by the Oxygen theory. It is
borrowed from Whewell x, whose works afford many more. It
was for a time supposed that combustible bodies were combus
tible because of the presence in them of a peculiar substance,
that escaped in the process of burning. This hypothetical sub
stance was called phlogiston ; and it was very natural to think
that one could see it escaping into the air wherever a fire was
burning. When it was found that there was one air (or, as we
should now say, gas) in which bodies burnt readily, and another in
which they would not burn at all, it was conceived that air could
only absorb a limited quantity of phlogiston in proportion to its
volume; in the former it was supposed that there was no phlo
giston, and it was called dephlogisticated air ; the latter was sup
posed to be already saturated with all that it could hold, and was
called phlogisticated air accordingly. The phlogiston theory re
ceived a shock when it was discovered that if a body were calcined,
or reduced to ashes, in a closed vessel, the weight of the ashes was
greater than that of the body before it was burnt. This, however,
was explained by supposing phlogiston to be a substance naturally
1 Whewell, Hist. Ind. Sci., vol. iii. Bk. XIV. 11. 4-7.
xxi] PRELIMINARIES OF INDUCTIVE REASONING 437
light, whose escape therefore left a body heavier — a view plausi
ble, perhaps, when we remember how the sparks fly upward, yet
really presenting great difficulties in relation to the theory of gravi
tation. The great French chemist Lavoisier, however, applied a new
conception to the facts : he conceived that, when a body burned,
what happened was not that a substance naturally light escaped
from it into the air, and so left it heavier ; but a substance
naturally heavy was withdrawn from the air and combined with
the burning body ; burning in fact was a process of what we should
call chemical combination ; and Lavoisier supported his theory by
showing that after the calcination of a body in a close vessel the
air in the vessel was lighter by the same amount by which the ashes
were heavier ; this observation perhaps was not conclusive, if the
phlogiston had carried its natural levity into the air ; but the new
way of conceiving the facts accorded far better with the general
theory of gravitation. The substance thus withdrawn from the
air in burning he called oxygen ; and oxygen now took the place
of dephlogisticated air ; while phlogisticated air, instead of being
conceived as saturated with phlogiston, was conceived to be a dif
ferent substance from oxygen, incapable of entering into those
chemical combinations which constituted burning. This substance
was rechristened azote, and afterwards nitrogen. Lavoisier further
showed that oxygen was withdrawn from the air and chemically
combined with other substances not only in burning but also in the
familiar process of breathing, and in the rusting or oxidation of
iron, which could rust in water also because oxygen was present
there as well; and thus his new conception, that burning was
really a process of chemical combination between a substance in the
atmosphere, which he called oxygen, and the substance of the body
burnt, served to throw light equally on processes at first sight quite
remote from burning. In this example, therefore, we have as it
were a ' colligation ' of two kinds : primarily, in so far as a large
number of facts about burning were all rendered consistent with
one another and bound together by the help of this new conception
of what goes on when a body burns ; secondarily, in so far as that
conception was shown to be applicable to other phenomena as well
as burning, and they are therefore brought under the same explana
tion with it. It may be worth while to give one more example of
the transforming and connecting power exercised by a new and
438 AN INTRODUCTION TO LOGIC [CHAP.
appropriate conception upon a multitude of facts, in the biological
theory of Evolution, or the modification of species through natural
descent. We are not for the moment concerned with the question
whether the only agency in determining such modification is Natural
Selection. The theory of Natural Selection, as a theory of the way
in which modifications have, not indeed originated, but been estab
lished when they had once arisen, teaches that in each generation
individuals vary more or less in colour, size, structure, &c., from their
parents ; that some of these variations are useful to their possessors
under the circumstances in which they live ; and that their possessors
will, in the constant struggle for existence going on in the world,
have an advantage over their competitors ; so that those indi
viduals who happen to. possess ' adaptive ' variations will survive
and propagate, while their less fortunate and worse-adapted rivals
will perish ; and thus species are brought into and kept in confor
mity with the conditions under which they have to live. Now
there is not complete agreement among biologists either as to the
extent to which the peculiarities of different species of plant or
animal are adaptive, or as to the extent to which those that are
adaptive can be accounted for by the theory of Natural Selection
alone ; though there is no doubt that the doctrine of Evolution won
its way on the strength of the success of the principle of Natural
Selection in accounting for at any rate a vast number of adaptive
structures, instincts, and colourings. But the doctrine of the Evolu
tion of Species, or their modification by descent, as opposed to their
special creation in immutable form, does not stand or fall with the
view that Natural Selection is its exclusive modus operandi. This
doctrine has brought into intelligible connexion with one another
whole departments of fact. It explains the various and intricate
relations of likeness and unlikeness between different species of the
same genus, different genera of the same family, different families
of the same order, &c. ; it explains why the same structural plan is
observed in many cases where the function of some part of the
structure has been lost or altogether altered : and why it is that where
their life requires the performance of the same function in groups
otherwise very remote morphologically from one another, we find
the function fulfilled by such very different means as are, for
example, the wing of an insect, of a bird, of a bat, and of a flying-
fish. Again, it explains the divers series of fossil forms : and
xxi] PRELIMINARIES OF INDUCTIVE REASONING 439
accords with the facts of embryology, such as that the embryo of
a given vertebrate only gradually develops the more distinctive
specific features, and at an earlier stage is very little distinguishable
from the embryo belonging to a different genus or family ; for the
characters which appeared later in the course of evolution and
supervened as it were upon a simpler structure appear later in the
growth of each subsequent individual of the same more complex type,
and supervene upon the simpler structure there. Again, it explains
the facts of geographical distribution, such as that the degree of
affinity between species is much greater when they inhabit a con
tinuous area, than on either side of a geographical barrier ; and
that the barriers on either side of which the difference is most
marked are not the same for every kind of organism, but are for
each kind those which would offer the most effective obstacle to the
migration of that kind — high mountain ranges in the case of land
animals or fresh-water fish, deep sea in the case of salt-water fish,
and so forth : or such facts again as this, that ' wherever there is
evidence of land areas having been for a long time separated from
other land areas, there we meet with a more or less extraordinary
profusion of unique species, often running up into unique genera V
All these facts, and many others, for which upon the old hypothesis
of the special creation of immutable species it is impossible to
suggest a reason or a motive, fall into line upon the hypothesis of
modification by descent, and are bound together by that conception
as common consequences.
We have now considered some of the most important operations,
without which inductive reasoning would be powerless to advance
inductive science. One or two others may be noticed. It may
seem unnecessary to mention the observation and registration of facts ;
yet that is no small part of the work that has to be performed
before we are in a position to tell what phenomena may be supposed
to stand related to one another as cause and effect. Along with
this goes often what was incidentally referred to on p. 436 2 — the
devising of experiments by which to test whether a phenomenon is
1 Romanes, Darwin and after Darwin, i. 235 et al.
2 The other process, of mathematical calculation, there referred to, falls
rather to be considered later : as belonging to a stage of science in which
deductive reasoning plays a larger part than in the application of the rules
discussed in the last chapter.
440 AN INTRODUCTION TO LOGIC
present or absent, varies or is constant, as should be the case if its
cause is what we take it to be. If it be supposed, for example,
that spirit-rapping is really produced by ' cracking ' the joints, it
will be necessary not only to show that a man can produce such
noises that way, but to devise conditions under which one may be
certain that the joints cannot be 'cracked' without its being
detected, and see whether the ' spirits ' still continue to rap.1 The
collecting and sifting of statistics, and their reduction to tabular
form or curves, is also in many enquiries a necessary preliminary
to the application of the rule that nothing can be the cause of
a varying phenomenon which does not vary proportionately with it.
This is perhaps enough to say upon the present subject. There
are other tasks set to our thought in science, which are of great
importance to its development; but we have been concerned especially
with those that are presupposed in inductive reasoning. The
help afforded to the ' interpretation of nature' by a well-chosen
armoury of technical terms, great' as it is, is not confined to the use
of inductive reasoning. And the work of abstraction has had
account taken of it in what was said of analysis and hypothesis
and the formation of conceptions. By abstraction we mean con
sidering some special feature of the concrete fact, in mental separa
tion from all with which it is combined in its existence. It is
between feature and feature that we strive to trace connexion.
The concrete mass of events changes from moment to moment.
Not until we pick it to pieces are we able to see what it is in one
state of the mass that determines what in another. Every common
term involves some degree of abstraction ; but in science we have
to break up what in daily life we treat as a single matter, and to
consider by itself, or in abstraction, that which had hitherto not
been specially noted and distinguished in the total nature of some
comparatively concrete notion.
1 r. Podmore's History of Modern Spiritualism, i. 184, 185.
CHAPTER XXII
OF NON-RECIPROCATING CAUSAL RELATIONS
IN all that has been so far said with regard to the process of
inductively determining the cause of a phenomenon, it has been
assumed that the cause, whatever it is, reciprocates with the
phenomenon : i. e. that not only does the phenomenon occur
whenever the cause is present, but that the cause must be present
whenever the phenomenon occurs ; so that you may safely argue
from either to the other, as in geometry you may equally infer that
a triangle is equilateral from the fact that it is equiangular, and
that it is equiangular from the fact that it is equilateral.
But we often speak of one thing as being the cause of another,
where this reciprocal relation by no means obtains. We say that
drunkenness causes crime, although many people get drunk without
committing crime, and many people commit crime without getting
drunk. And in some of the examples of inductive reasoning given
in previous chapters, the cause found was not a reciprocating cause.
The appearance of congenital epilepsy in guinea-pigs was shown to
be possibly due to a traumatic injury producing epilepsy in the
parent ; yet it was not alleged that the production of epilepsy by
these means in the parent was always followed by the appearance
of epilepsy in the offspring.
It was said that the inductive proof of the cause of a phenomenon
rested on the definition of cause ; for nothing that does not stand
to the phenomenon in relations that satisfy the definition can be
the cause of it ; and it is by eliminating all alternatives that its
cause is inductively established. Our definition of cause assumed
that it reciprocated with its effect. But if it does not, we clearly
have no right to eliminate whatever fails to reciprocate. The
admission that there are non-reciprocating causal relations may
seem therefore to invalidate reasoning that starts with the assumption
that cause and effect reciprocate.
This difficulty has been postponed till now, partly that the
exposition of the subject might not be unduly complicated : but
442 AN INTRODUCTION TO LOGIC [CHAP.
also, because the causal relation is really, and in its strict sense,
reciprocal, and without understanding that first, we could never
render non-reciprocating1 causal relations intelligible to ourselves.
Properly speaking, to give the cause of anything is to give every
thing necessary, and nothing superfluous, to its existence. Never
theless we should often defeat our ends, if we gave precisely this ;
if our object in seeking the cause of a thing is that we may be
able to produce or prevent it, and if something is necessary to its
existence which is a property of an object otherwise superfluous,
it would be of no use specifying the property necessary unless we
also specified the otherwise superfluous object in which it was
found.1 Even though we have no such practical purpose, so long
as we do not know what object contributes, in the property which
it possesses, the factor necessary to the effect, we can hardly be
said to understand completely the production of the effect. Hearing
at a distance, for example, depends on the transmission of certain
vibrations through an elastic medium ; the necessary elasticity is
a property of the air ; and therefore we can hear at a distance in
the air, while if there is a vacuum interposed between the sounding
(i. e. the vibrating) body and the ear, the transmission of the sound
is prevented. It is true that, except in respect of its elasticity, air
is quite superfluous so far as hearing at a distance is concerned;
not air in the concrete, but that property in abstraction, is one of
the conditions that make up the reciprocating cause of hearing at a
distance. But an elastic medium cannot be just elastic and nothing
else besides.2 We want to know what possessed of the necessary
elasticity is present when we hear at a distance ; nor could any one,
without knowing that, prevent the transmission of sound by removing
the elastic medium ; for he would not know what to remove.
We may pursue this illustration a little further. It might be
shown inductively that the intervening air was the cause of the trans -
1 e. g. it may be the texture of pumice-stone that fits it to remove ink-
stains from the skin ; but it would be of more use to tell a man with inky
fingers to get a piece of pumice-stone, than to give him a description of the
fineness of texture which would render a body capable of making his
fingers clean.
2 It is just the fact that we know no more about the ether than its form
of elasticity which makes it a somewhat unsatisfactory conception ; and led
the late Lord Salisbury, in his Presidential Address to the British Association
at Oxford in 1894, to say of it that it merely 'furnished a nominative case
to the verb to undulate \
xxn] NON-RECIPROCATING CAUSAL RELATIONS 443
mission of sound ; indeed it was shown inductively, by the help of
a well-known experiment. And speaking1 loosely, it is true that
from the presence of air it can be inferred that sound will be
transmitted, and reciprocally, from the transmission of sound, that
air intervenes. Yet neither inference is quite safe. The first is
only true with qualifications : the distance must not be too great in
proportion to the loudness of the sound, and so forth. The second
may be altogether false; for sound can be transmitted through
water, or (with the help of a telephone l) through a vacuum. And
in this case the reason is that the elasticity is provided in some
other way than by means of a continuum of air. We saw that,
except in respect of its elasticity, air was superfluous : but we could
not get the elasticity alone. Now we find that there are other
elastic media which will serve, and the elasticity may be provided
by them. An elastic medium is what is wanted ; but divers things
will supply the want. They are alternatives, and none of them
exclusively reciprocates with the effect; for the effect may be
produced by the help of any one of them, so that the occurrence of
the effect does not prove that any one more than another is producing
it. But their common property of providing an elastic medium
does reciprocate ; sound cannot be transmitted without that.
There is, then, always a reciprocating cause ; but it is not always
most instructive to state only that. And very often that is not
what we want to know. There are several reasons for this.
In the first place, though the object of a science is to discover
strictly universal propositions, and though in most sciences 2 these
involve relations of cause and effect, yet as a science advances, its
problems often take a different form than that of an enquiry after the
cause of a given phenomenon. We may start with some phenomenon
that seems comparatively simple ; and, as we proceed, may find
that it depends upon a number of conditions being combined together,
each of which can be fulfilled in a number of ways, but none of them
without much that is superfluous or irrelevant to the production of
the phenomenon in question ; each is an incident of some concrete
event, or implies the operation of a property of some concrete object,
1 The elasticity of the air is employed also in the telephone : but not
continuously. It is hardly necessary for the present purpose to go into the
detail of the apparatus.
2 Not in any branch of purely mathematical study ; nor again in Logic.
444 AN INTRODUCTION TO LOGIC [CHAP.
like the elasticity of air in the case of the transmission of sound.
To state in abstract form the conditions that must be satisfied,
without indicating the kind of object or event in which such
conditions can be realized, is uninstructive ; for it fails to explain
by what the phenomenon is produced; yet to mention every object
or event in which the conditions might be realized would be an
endless and unprofitable task. Hence we alter the form of our
problem. Looking upon the phenomenon as the complex result
of many conditions, we attempt to determine not what assemblages
of objects or events will produce the result, nor on what properties
or incidents therein it depends ; but what is the principle of action
in different objects or events, in virtue of which some one particular
condition necessary to the production of the phenomenon is realized
in them. For the reciprocating cause of a complex phenomenon
we substitute as the object of our search the principle in accordance
with which a certain kind of object or event acts. Our problem is
better expressed as that of discovering laws of nature, than causes.
For example, we may ask what is the cause of the monsoons — that
is, of the regular and periodic winds that blow steadily in certain
regions for one part of the year in one and for another in the
opposite direction ? If we said that they were due to periodic
alternations in the distribution of atmospheric pressure, it would
not be very instructive ; for we really want to know what events,
happening in those regions, produce these differences. Yet the
events which contribute to determine the deviation and direction of
the monsoons are numerous and variable : the exact combination of
them differs from year to year and from place to place, and produces
corresponding differences in the result. It is better therefore to
take these events, by their kinds, singly : to point out the difference
in power of the sun at any place produced by the varying direct
ness of its rays ; how the sea gives off vapour ; how vapour absorbs
part of the heat of the sun's rays ; how the heated water circulates
with the colder ; how the earth absorbs and retains the heat of the
sun ; how air is expanded by heat ; how the principle of atmospheric
pressure acts under conditions of different expansion ; and so forth.
Then we can see that if a certain combination of events occurs,
a particular complex result must arise ; if the sun travels from over
the sea to over the interior of a continent, we shall find monsoons ;
for the difference between summer and winter temperature will in
xxn] NON-RECIPROCATING CAUSAL RELATIONS 445
the interior be very great, but on the sea, owing to the way in which
the moisture of the air absorbs part of the heat, and the currents
in the water carry away part, it is not so great ; hence as summer
is ending, the air inland will be hotter and have expanded more
than out at sea, as winter is ending it will be colder and have
contracted more ; so that at one time the current of air sets inland
in accordance with the laws of atmospheric pressure, and at another
time it sets shoreward. The principles, or ways of acting, on the
part of the sun according to its altitude, of the earth and sea
respectively under the influence of heat, of air when unequally
expanded, &c., are not exhibited solely in the phenomena of monsoons ;
while the details of those phenomena display the influence of other
principles of action on the part of other objects (e. g. the action of
a mountain-wall on a moisture-laden wind). To give the cause
of monsoons, without deficiency or superfluity, would mean that we
must not mention the sun (because only the heat of its rays is
material) nor the sea (because only its fluidity and its power of
giving off vapour concern us, and a lake, if it was big enough,
would do as well) nor any other of the concrete things which act in
the way required, but only their requisite actions. If we do not go
to this length of abstraction, we shall have to include in our state
ment of the cause elements at least theoretically superfluous ; and
even so, we shall have to choose some particular monsoon, supposing
we are to state everything that goes to produce it. It is clearly
simpler to break up the problem, and look for the principles in
accordance with which objects of a certain kind act under certain
circumstances ; then we can show that the monsoon is only the
complex result of the action of a number of objects under the
particular circumstances of the case, and in accordance with the
principles of action which our ' laws ' express.
This then is one reason why what we want to know is not by any
means always the reciprocating cause of a determinate phenomenon :
the phenomenon under investigation is often highly complex, and
subject to all sorts of variation on the different occasions of its
occurrence, through variation in the objects or events contributing
to its production ; not the whole nature of the objects or events
under whose influence it occurs is relevant to its occurrence, but
only certain particular properties or modes of action ; and it is
possible to formulate severally the principles of action involved,
446 AN INTRODUCTION TO LOGIC [CHAP.
from which the joint result may be seen to follow, where it would
not be possible to assign to the phenomenon any group of concrete
objects or events as cause, about which we could say not only that,
given them, the phenomenon must be given, but also that, given
the phenomenon, they must have been given too. These laws or
principles of action may of course be proved inductively in just the
same way as may a causal connexion between two particular
phenomena a and x. Just as we may argue that a cannot be the
cause of x} if it occurs in the absence of x, or is absent when x occurs,
so we may argue that a law or principle of action cannot be rightly
stated, if consequences should follow from it as thus stated which
do not actually arise, or should not follow, which do arise. Here,
as there, we may have no other reason for accepting a theory than
that the facts are inconsistent with any other that we can devise ;
and then our argument is inductive.
Another reason for the same fact is that for practical purposes
it is generally more important to know what means will produce
a certain result, than by what it has been produced. We cannot
alter the past ; we may control the future. The means prescribed
for the production of a certain result may contain much that is not
relevant precisely to the production of that result ; and as this
irrelevant matter may be different on different occasions, there may
be a choice of means. To have a choice of means is undoubtedly
useful ; but if any of these means is called the cause of the result
in question, the term cause is clearly not used in the strict sense ;
for we may be able to argue forward from the means as cause to
the result as effect j but we cannot argue backward from the
result as effect to this particular means as cause. Yet this may be of
comparatively little consequence, if our interest lies less in being
able to determine by which means the result in question was produced
on a past occasion, than that it will be produced if such and such
means are employed. About a variety of advertised rat-poisons,
all that we should care to know would be that they would rid us
of rats ; and we might endeavour to determine inductively whether
a particular poison was efficacious. But we should be indifferent to
the fact that other poisons might be equally efficacious, and that
rats who died off need not have been killed by this particular
poison ; in other words,, we shall not want to learn the reciprocating
cause of the dying off of rats. Indeed as long as the effect is
xxn] NON-RECIPROCATING CAUSAL RELATIONS 447
stated in such a general way, a reciprocating cause cannot be given.
There are, as Mill observed, many causes of death ; and though he
was referring to men, it is also true of rats. But death is not
altogether the same thing whenever it occurs ; and the doctor or the
coroner knows this. The many different causes of death do not
have altogether the same effects ; if you shoot a man and if
you behead him, the difference in the result is visible ; if you pole-
axe an ox and if you poison him, he is not equally edible. As soon
as we begin to be interested in the particular variety of death pro
duced, we find the number of causes that produce the result in
which we are interested diminish rapidly ; if we carried our in
terest far enough into detail, we might say that for death of
a particular kind there was only one cause possible. But since
much of this detail is quite unimportant, we treat as instances of
the same event events which in some respects are different, and
then say that the same event has divers causes : forgetting that the
differences between these several causes consist partly in irrelevant
circumstances, included in our statement because indissolubly bound
up with what is relevant, but otherwise superfluous to the production
of this event : and partly in circumstances that are represented by
differences in the resulting event, only by differences which we
ignore. Here then, in the fact that our search is often for means
to the production of a phenomenon of a certain general character, to
the precise form of which we may be indifferent, is a second reason
why the causal relations which we seek to establish are often non-
reciprocating.
On the other hand, thirdly, there are cases where it concerns us
more to be able to argue from one phenomenon to another as its
cause, than from the latter to the presence of the former as effect.
For example, there may be alternative symptoms of the same
disease : for the effects of the disease may differ to some extent in
patients of different age, or sex, or race. Here it may be impor
tant to show, that if a certain symptom occurs, that disease must
be present to produce it ; while the fact that the disease may exist
without giving rise to that symptom is a minor matter, and one
which, if we could be certain that some other equally conspicuous
and unambiguous symptom would occur instead, might be called
altogether unimportant. In such a case we shall be anxious to show
a causal connexion between the disease and the symptom in ques-
448 AN INTRODUCTION TO LOGIC [CHAP.
tion, though again the relation will be non-reciprocating; but it
will fail to reciprocate this time, because the so-called cause may
exist without the so-called effect, although the so-called effect
cannot exist without the so-called cause ; whereas in such cases as
were considered in the last paragraph, the so-called cause always
produced the so-called effect, but the so-called effect might exist
without the so-called cause.
Fourthly, our enquiries are often directed to the discovery of the
cause or effect of some singular event — singular, not in the sense of
unusual, but of a single and definite instance : we ask, for example,
what has been the effect of the repeal of the corn laws, or what
was the cause of a particular railway accident, or epidemic. It is
plain that the relation we wish to establish in such cases as these
is a non-reciprocating relation. The repeal of the corn laws was
a measure introduced into a highly complex social and economic
state, and whatever results we can point to depend on much else
besides that measure ; no one would pretend that the same measure
would have produced the same results in other circumstances. It
might be possible here to substitute for the question, what effect
repeal has produced in the United Kingdom, the more scientific
question, in what way corn laws act : the answer to the latter
question might be given in the form of one or more universal pro
positions : but the answer to the former will be a singular judge
ment. For it is practically impossible to specify all the conditions
which have combined with repeal to produce the results in which
the influence of repeal is exhibited ; so that we cannot hope to
establish an universal proposition of the form that repeal of corn laws
produces always under such and such conditions the result which we
ascribe to it in the case of the United Kingdom since 1846. If
a man says therefore that the repeal of the corn laws has increased
the population, or depopulated the country, or crippled the ancient
Universities, or made inevitable a celibate clergy, he is not to be
understood to mean either that it would always produce any one
of these effects, or that they must always be due to a repeal of corn
laws : but only that in the history of the United Kingdom, had
the corn laws remained in force, other things being equal, these
effects would not have occurred in the same degree. So also when
we enquire the cause of a singular effect : it may be known that
the reciprocating cause of small-pox is the presence of a certain
xxii] NON-RECIPROCATING CAUSAL RELATIONS 449
microbe in sufficient strength in the blood ; but if we ask for the
cause of a definite outbreak, something- else than that is wanted.
We want to know what particular precaution has been omitted, by,
taking which this outbreak might have been prevented ; or in what
particular way the infection was conveyed to the neighbourhood.
Thus we might say that the outbreak was due to a tramp sleeping in
a common lodging-house, or to insufficient vaccination ; but it is not
imagined that a tramp suffering from small-pox cannot sleep in any
common lodging-house without an outbreak of small-pox following
in the place ; or that no such outbreak ever occurs unless from that
reason ; while insufficient vaccination, even if no serious outbreak
ever occurred where it could not be alleged, may prevail without
an outbreak following, so long as nothing brings the infection.
Similarly in the case of a railway accident, the question is, what
particular act or omission that some one is responsible for, or what
other unforeseen event, can be alleged, without which on this occasion
there would have been no accident : did a signalman give the wrong
signal, or pull the wrong points ? did an engine-driver disregard
a signal? had a flood washed out the ballast of the line, or a fire
destroyed a wooden bridge ? These and many more are the ' causes '
of railway accidents, though railway accidents occur without them,
and they may occur without accidents following.
In previous chapters we have represented the phenomena between
which it is sought to establish causal relations by letters of the
alphabet. Each of these letters is quite distinct from the rest,
insulated as it were, and discontinuous both with those grouped
with it to indicate contemporaneous phenomena, and with those
placed apart to indicate phenomena preceding or succeeding it ;
and the use of them as symbols tends to suggest that the course
of events is a succession of discontinuous phenomena, which pro
duce each the next in a number of parallel or contemporaneous
series. Nothing could be further from the truth : it is impossible
to conceive the matter thus.1 We have already noted the ambiguity
1 Let nobody object that in such a matter we must ask what experience
teaches, and not what it is possible to conceive. Experience can teach
nothing inconceivable. All thinking is an attempt to make experience
more intelligible, and so far as it is not intelligible, we assume our account
of it to be untrue. It is for this reason that we are always recasting in
thought the appearances which experience presents. The very search for
causal connexions is an example of this operation. It rests on the principle
•SEPH Q g-
450 AN INTRODUCTION TO LOGIC [CHAP.
— the convenient ambiguity — of the term phenomenon ; some ' phe
nomena ' which we isolate and individualize by a name do succeed
one another; but others do not precede or succeed at all, but
endure or persist. Kant said that ' only the permanent can change ' :
we look on events as occurring to things ; permanent things change
their states ; and the permanent thing enters into the earlier and
the later state alike, or persists through them. What that is which
remains unchanged, how we are to conceive it, and how we are to
conceive the junction between its abiding nature and its changing
states — these are very difficult questions. And such deep questions do
not belong to the Logic of Inductive Science. But it is clear that
our alphabetic symbols fail in the first place to represent the per
sistence of anything through change : they are discontinuous in
their series where they symbolize a change which is continuous. And
secondly they are discontinuous within the group that represents
contemporaneous phenomena ; whereas the contemporaneous phe
nomena they represent are not similarly insulated from one another.
What we commonly speak of as single phenomena are bound
together not in independent series unit to successive unit, but by all
sorts of cross ramifications, so that each is what it is in consequence
of conditions which are at the same time conditioning many others
in the most complicated way. To this complication the letters of
the alphabet do no justice. Doubtless if we carry our analysis far
enough, we may find the a which is the reciprocating cause of x :
but a will not in that case as a rule be anything for which we have
any single name ; a long and carefully guarded statement of con
ditions will be what it must signify.
The fact is that in most cases the reciprocating cause of any
thing, if we push our enquiries far enough, emerges as the conditions
that constitute it, and not those that precede it and bring it about.
The reciprocating cause of small-pox is that activity of a specific
that change is only intelligible if it embodies universal principles of change :
but these principles are not presented to our observation. Therefore we
believe that events occurred, which have not fallen within our experience :
as Robinson Crusoe, seeing footprints, concluded that men must have been
to the island whom he had not seen. And if we deny that the events
1 experienced ' are all that occur, on the ground that their succession would
then be without principle and unintelligible, we may equally deny that
history can consist of streams of discontinuous events, even though these
succeeded one another according to the most constant rules, on the ground
that such a succession would be unintelligible.
xxii] NON-RECIPROCATING CAUSAL RELATIONS 451
bacillus in the blood in which small-pox consists : the reci
procating" cause of malarial fever is the corresponding activity of
another bacillus. But in the procession of events by which that
state is brought about there may be one, which — for one reason or
another — it concerns us to single out, and call the cause : and that
will often be a non-reciprocating cause. It need not be so ; it is
possible to find an event, whose happening in a given set of
conditions or to a given subject always gives rise to some definite
new event or state of that subject, and without whose happening
such new event or state of that subject never arises. It is supposed
for example that malaria is always communicated to man by the
bite of the Anopheles mosquito ; there are persons immune to the
bacillus, and therefore the bite of Anopheles is still a non-
reciprocating cause ; but if we knew what state of a subject
precluded immunity, then we could say that the bite of Anopheles
caused malarial fever in any man in that state, and we should have
stated a reciprocating relation ; for no man in that state could be
bitten without getting malaria, nor get malaria without being
bitten. If with Aristotle we call the conditions which constitute
anything informal cause, and the event whose occurrence brings
those conditions into being when they had previously not all of
them existed, the efficient cause1, we may say that the formal cause
reciprocates or is commensurate with the phenomenon (as indeed
anything must which can in any sense be called the definition of it :
and the conditions into which it can be analysed may be called its
definition); while the efficient cause seldom reciprocates. The
event which provides the conditions, or part of the conditions,
constituting the phenomenon, may also be called, in a metaphor
of Bacon's using, the vehicle of the formal cause; the bite of the
Anopheles mosquito is the vehicle of, or conveys, the bacillus in
whose activity malarial fever consists ; the headsman's axe, or
the bullets of the firing party, convey, or are the vehicle of, that
bodily state which we call death.
There are indeed many cases where our ignorance of the con
ditions constitutive of a certain phenomenon compels us to seek
1 Besides the formal and the efficient, Aristotle distinguished the materia'
cause, or matter of which a thing is made, and the final cause, or purpose
of its being. These were all causes in the sense of being necessary to the
existence of what they are the cause of. Cf. e. g. Phys. /3. iii. 194b 16-195a 3.
Gg 2
452 AN INTRODUCTION TO LOGIC [CHAP.
instead for some event indispensable to its occurrence, even though
our scientific interest would be better satisfied by discovering- the
constitutive conditions. And there is one most extensive and
important class of cases where the reciprocating conditions cannot
really be called constitutive of the phenomenon ; it is this class of
cases which made it necessary at the beginning of the last
paragraph to write ' most ' and not ' all '. The former sort may be
readily exemplified in the biological sciences. 'That form of
barrenness/ writes an authority quoted by Romanes1, ' very common
in some districts, which makes heifers become what are called
" bullers " — i. e. irregularly in season, wild, and failing to conceive
— is certainly produced by excess of iron in their drinking water,
and I suspect also by a deficiency of potash in the soil/ Here we
have one and perhaps two causes alleged for an effect, whose nature
we do not understand sufficiently to see how the causes bring it
about, though the facts may prove the connexion. Such a relation
may be called discontinuous — i. e. we do not see how the alleged
cause, by any intelligible procession of events, passes into the effect,
or helps to set up the conditions constitutive of it. We connect one
phenomenon as cause with another as effect, where from our
ignorance of the intimate nature of the effect, and of the subject in
which it is produced, and from the fact that the intervening process of
change is withdrawn from view, the two seem quite heterogeneous.
In Chicago, one is told, there are machines into which you place a
pig at one end, and receive sausages at the other. The pig and the
sausages, to any one who has no conception of the nature of the
machine and what befalls the pig in it, appear in a relation of
sequence without continuity : first the pig exists, and then instead
of it, the sausages ; but we do not see how the one becomes the
other. This somewhat mythical machine may serve to illustrate
how our ignorance of the nature of the process of change connect
ing one event with another may produce apparently discontinuous
causal relations; and such relations are often all that we can at
present hope to discover ; and they are generally, as may easily be
understood, non-reciprocating relations. This case is different from
that mentioned previously on p. 446 ; for there it was our practical
ends which interested us in causes that were non-reciprocating ;
1 J. W. Crompton : i\ Darwin and after Darwin, iii. 170.
xxn] NON-RECIPROCATING CAUSAL RELATIONS 453
here it is due to the limitation of our scientific knowledge that we
have to acquiesce in them.
But in the extensive and important class of cases to which atten
tion must be called next, we find discontinuity even where the causal
relation reciprocates : viz. when the cause is physical and the effect
psychical, or vice versa. It has already been stated that such con
nexions furnish one of the best kinds of example of purely inductive
reasoning, because there is nothing in the nature of a particular
physical process which would lead us to anticipate the particular
psychical state that we find ourselves led by the facts to connect with
it. What may be the true interpretation of this apparent dependence
of psychical states on physical processes, and physical movements
on psychical states, is the hardest question in metaphysics. Mean
while, at the standpoint at which many sciences and all of us in our
ordinary thought are content to stop, we attribute many psychical
events to physical causes, and vice versa. In science indeed the
attribution of physical effects to psychical causes is less common
than that of psychical effects to physical causes ; just because
between the successive events in the physical order there are
prospects of establishing that continuity, which there seems less
hope of establishing in any completeness in the psychical series,
and none of establishing between members of one series and
members of the other, between a motion of matter in the brain and
a sensation or thought or feeling or emotion. The series therefore
whose members do appear capable of continuous and coherent
connexion is often treated as independent, and psychical states
regarded as by-products of particular terms in the physical series ;
although further reflection can easily show that such a statement of
the case, when thought out into its consequences, involves us in hope
less contradiction. We are however at present only concerned with
the interdependence of physical and psychical states as it appears to
exist, and is for many practical purposes rightly treated as existing.
It is supposed that to every distinct state of consciousness there
corresponds some distinct state of the body ; and this bodily state is
not separated from the state of consciousness by any intervening
process, the discovery of which might help us to see how one gives
rise to the other (as drinking water with an excess of iron in it is
separated from the supervening barrenness in a heifer). There is
perhaps no interval of time between them, but the completion of
454 AN INTRODUCTION TO LOGIC [CHAP.
the conditions in which the bodily state consists is eo ipso the pro
duction of the corresponding state of consciousness ; so that some
writers have been led to speak as if the state of consciousness could
be analysed into these bodily conditions, and they really constituted
it. That however, when examined, proves to be nonsense.
Yet though in this field we may hope to find relations that
reciprocate in spite of the discontinuity between the so-called cause
and its effect, there are instances here too where the causal relations
are non-reciprocating ; and of this perhaps the most notable instance
is death. It was explained above, how the many alternative causes
of death are not all of them causes of the same effect ; because
they do not put the body into the same state, although the differ
ences may not concern us. But if we look not to what befalls the
body, but to the result on consciousness — whether we suppose it
to be that the soul is separated from the body, or that it is
destroyed — we can see no difference in that main result correspond
ing to the difference of the means by which it is produced. If the
soul, or individual consciousness, be destroyed at death, there is
of course nothing any longer in which a corresponding difference
can be displayed ; if it be not, we may conceive that as the manner
of a man's death, if it be not absolutely sudden, affects him while he
yet lives — one death being more painful, for example, than another
— so the differences between one death and another are repre
sented by some difference that persists in the experience of the soul
after death, and therefore the effect is not really the same upon the
soul when the physical * cause ' is different. But such a suggestion
is quite un verifiable ; and however that may be, it is well to realize
the peculiarity of the relations which we try to establish between
physical causes and psychical effects ; owing to the heterogeneity
of the two terms, we cannot hope to find an intelligible cause of
the psychical state in the conditions constitutive of the physical
state with which it is connected ; at this point there is discon
tinuity ; and so there may arise an appearance of different causes
producing the same effect which we cannot explain as we explained
it in a purely physical sequence. There we saw that different
series of events might, in their course and as a part of their result,
agree in establishing the same complex of conditions constitutive of
some particular phenomenon, although the difference in the events
occasioned differences in the rest of their result which we ignored.
xxn] NON-RECIPROCATING CAUSAL RELATIONS 455
Here, inasmuch as we cannot see that the different causes establish
conditions that are constitutive of the effect at all, the appear
ance of the same effect when the causes are different cannot be
exhibited as a case where effects different as a whole (in a way
corresponding- to the difference of the causes) agree so far as
concerns the conditions constitutive of the phenomenon we are
investigating.
The term Plurality of Causes T has been used to indicate the fact
that the same phenomenon may have different causes on different
occasions. We have seen that the fact is more apparent than
real : that the alternative ( causes ' of a phenomenon, which make
up the plurality, are none of them causes in the strictest sense,
but rather events which agree so far as the production of the
phenomenon requires, though taken as a whole they are very dif
ferent. It would perhaps be well if there was a term to indicate
the corresponding fact, that the same phenomenon may produce
different effects on different occasions : a fact also more apparent
than real, for such phenomenon cannot be the cause, in the strictest
sense, of any of the alternative effects which it produces. We
might speak in this sense of the Diversity of Effects. In neither
case do cause and effect reciprocate.
Where the cause or effect sought is non-reciprocating, it is
obvious that the rules on which the elimination involved in induc
tive reasoning rests are no longer to be safely trusted. If the same
effect may have divers causes, we cannot say that nothing in the
absence of which a phenomenon occurs can be the cause of it ; it
cannot be its cause in the particular instance in which it is absent ;
but it may be on another occasion. If a small group of plants be
geographically isolated from the main stock, it will diverge, and in
course of time probably give rise to a new species ; but there are
other ways in which a particular group may be prevented from
interbreeding with the main stock (e. g. by flowering at a dif
ferent season), so that new species may arise in the absence of
1 The term was introduced by Mill, who sometimes speaks as if he thought
the Plurality of Causes more than an appearance : as if he thought that, in
the strictest sense of the term cause, the same phenomenon may have
different causes on different occasions. The Plurality of Causes must be
distinguished from the Composition of Causes : which means that a complex
phenomenon, which we call one, may be due to a number of causes acting
together on one occasion. Clearly none of these is the cause in the full
sense, but only part of the cause.
456 AN INTRODUCTION TO LOGIC [CHAP.
geographical isolation ; it would clearly be unsafe to conclude, from
the fact that new species had arisen without geographical isolation,,
that geographical isolation was not a cause of new species arising.
No doubt such an argument would betray insufficient analy
sis : it would overlook the fact that geographical isolation was
not a single factor, but highly complex ; and that one feature
about it — viz. that it prevented interbreeding with the rest of the
stock — characterized also such very different phenomena as differ
ence of flowering-season, or selective sterility.1 However, our
analysis is very commonly incomplete ; and then it is possible, that
by applying the above rule, of eliminating whatever fails to occur
in any instance of the effect, we have eliminated the cause alto
gether : and that if some circumstance is left uneliminated, because
it fails to occur in none of the instances of the phenomena, we take
it to be the cause of what it has really nothing to do with. If
a child were given the same medicine in a variety of jams, and
always had a particular biscuit afterwards, it might very likely
attribute the effects of the medicine to the biscuit. Suppose my
apple-crop fails four years in succession, and that each year it was
' overlooked ' by a woman reputed to have the evil eye : were I to
argue that the failure was not due to insufficient rain, since in the
first year there was plenty — nor to late frosts, for in the last year
there were none — nor to blight, which only occurred once — nor to
high winds, since the third year was singularly quiet, I might
at last attribute the failure of the crop to the ' witch- woman ' over
looking it.
In such a situation it is well to test one's results by the second
rule, that nothing is the cause of a phenomenon, in the presence of
which the phenomenon fails to occur. If the child were frequently
given the same biscuit when it had not been dosed, it would learn
to disconnect the biscuit from the effects of the medicine ; and if
the witch-woman were observed to overlook my orchard in several
years when I subsequently obtained an excellent crop, I might be
cured of my superstition. It is however possible that I might still
hold her responsible for the bad crops, and apply the doctrine of
1 Or 'physiological isolation' — i.e. that certain members of a species x
which happen to exhibit some modification m are more fertile with one
another than with the rest of the species in which this modification has not
appeared. This would prevent swamping by intercrossing, and so, for
breeding purposes, isolate the new variety.
xxii] NON-RECIPROCATING CAUSAL RELATIONS 457
the Diversity of Effects to explain why her action had failed of its
previous result on other occasions. Perhaps I might have had
the crop blessed by a priest, and attribute to that an effect
counteracting- the influence of the evil eye ; or merely say, that
the evil eye cannot be expected always to produce the same
results, when there must be many contributory conditions that are
varying.
There is no remedy against such errors except a wider acquaint
ance with facts, and a closer analysis of them, and a better way of
conceiving them and their connexions. To this end however very
special help is given by experiment. The results of an experiment
are of the same kind with the data of observation — facts, namely,
with which we have to make our theories consistent; and the
inductive reasoning to which the facts contribute premisses is not
altered in character because the facts are obtained experimentally.
But where we can experiment, we can commonly discover facts
which observation would never reveal to us. We can introduce
a factor into conditions carefully prepared, so that we know more
or less accurately what change we make, and in what we make it ;
and then, when we watch the effect, the work of elimination has
more grounds to proceed on. If we are in doubt whether to refer
some phenomenon to a plurality of causes, or to a single circum
stance which, as present in all our instances, they have not so far
enabled us to eliminate, we might resolve the doubt by producing
this circumstance experimentally : should the phenomenon not
follow, we have then shown that, at least in the conditions into
which we introduced it, the factor in question will not produce it.
We may then try one and another out of the plurality of alleged
alternative causes : and if we find each of them producing the
phenomenon, we shall conclude that they are causes of it. We
shall still probably be far from having discovered its precise cause,
without deficiency or superfluity ; but we shall have advanced our
enquiry. The child who attributed to the biscuit the effects of the
medicine could correct its error by experimenting with the biscuit
separately, and the medicated jams separately. And if I could
bring myself to experiment with the evil eye, I might convince
myself that it was innocuous to orchards.
It should be noted that though the Plurality of Causes and the
Diversity of Effects render precarious, when our analysis is imperfect,
458 AN INTRODUCTION TO LOGIC [CHAP,
the application of both the grounds of elimination just cited — viz.
that nothing is the cause of a phenomenon in the absence of which it
occurs, and nothing also, in the presence of which it fails to occur —
yet the amount of error in which we may be involved is not the
same in each case. Should we reject in turn everything, without
which the phenomenon is found to occur, we might reject all its
several causes, and fall back on something whose presence in the
instances we have examined is quite accidental : something alto
gether immaterial to the phenomenon. On the other hand, should
we reject everything, with which the phenomenon is yet found not
to occur, though we might be wrong in concluding that what is
left is the whole cause of the phenomenon, or that the phenomenon
may not have other causes, yet we should be right in concluding
that it was not altogether irrelevant to the production of the pheno
menon. I give a dog cyanide of potassium, and it dies ; assuming
this to be the only fresh circumstance in the case, I cannot con
clude that dogs do not die without taking cyanide of potassium ;
but I can conclude that taking cyanide of potassium contributed
something to the death of this dog, and that the conjunction of
the two events was not merely accidental, as eating the biscuit was
accidental to the child's subsequent experience, or as being ( over
looked' by a witch- woman was accidental to the failure of my
apple-crop. In the former case, where I reject everything in whose
absence the phenomenon occurs, I reject too much : the essential
factor lurks undetected each time in a different ' vehicle ' : each of
these ' vehicles ' is rejected in turn, and the essential facts rejected
with them. In the latter case, where I reject everything in whose
presence the phenomenon fails to occur, I may reject both too
much and too little — perhaps too much, for what I reject, though
insufficient of itself to produce the phenomenon, may contain con
ditions without which it cannot be produced : perhaps too little,
for what is left, while I take it to be essential to the phenomenon,
may still contain more than the essential factor that lurks within it ;
so that other things, in which the same essential factor is con
tained, may equally serve to produce the phenomenon ; yet still I
retain something essential, and do not reject everything which
I need to retain.
This also is to be considered : that in the loose sense of the
term cause which we are now employing, we may either mean
xxn] NON-RECIPROCATING CAUSAL RELATIONS 459
(i) something essential, but by itself insufficient, to the production
of the phenomenon (as when we say that atmospheric pressure is
the cause of water rising in the common pump, though the produc
tion of a vacuum by pumping is necessary too) : or (u^ something^
sufficient, but superfluous in part, to its production (as when we say
that the explosion of a powder magazine under the place where he
is standing is the cause of a man's death) : or (iii) something at
once superfluous in part and insufficient, but containing an element
that is essential (as when we say that the Company Acts are the cause
of a new class of fraudulent actions) : or, where our phenomenon is
the failure or destruction of an effect that depends on the fulfilment of
a number of conditions, in the absence or! any one of which the effect
cannot occur, (iv) something sufficient but not essential to such failure
or destruction (as when we say that a late and severe frost causes the
failure of the fruit crop). Now when by ' cause y we mean (i) some
thing essential but insufficient, it is only part of the real cause ;
and there must be other factors, also essential but singly insuffi
cient ; and it is false to say (1 ) that nothing in the presence of which
the phenomenon fails to occur is its cause in this sense ; though it is
true to say (2) that nothing in the absence of which it occurs is its
cause. Nevertheless when we use the former rule to show that certain
circumstances are not the cause, and therefore that what remains is
so, we use it really to show that such circumstances are not sufficient,
and that what remains is essential : which if we thereupon call the
cause of the phenomenon, we mean to emphasize the fact that it is
essential, but not necessarily to assert that it is sufficient; and
hence, though what we reject or eliminate may have as much right
to be called the cause as what we retain and call so (as being also
essential though not sufficient), we fall into no error in inferring
that what we retain is (or contains) something essential, nor need
we fall into the error of supposing that there is nothing essential in
what we reject. But when by ' cause ' we mean (ii) something
sufficient, but in part superfluous, to the production of the pheno
menon, then on the contrary it is true to say (1) that nothing is the
cause, in the presence of which it fails to occur : but false to say (2)
that nothing is the cause of it, in the absence of which it occurs ; if
a man could be blown to pieces by the explosion of a powder-maga
zine without dying, that would not be, in this sense, the cause of
his death ; but if he may die without being blown to pieces, being
460 AN INTRODUCTION TO LOGIC [CHAP.
blown to pieces may still in this sense be a cause of it. In this
sense (ii) of cause therefore, the second of the above rules or grounds
of elimination is false, and the first true ; while conversely in
sense (i), the first is true, and the second false. But when we are
speaking- of cause in sense (i), the application of what is then the
false rule is less misleading than, in sense (ii), is the applica
tion of the rule which is false for it. We really argue from the
principle that nothing is sufficient, in the presence of which the
phenomenon fails to occur, to the conclusion that something else is
essential. This principle is true. If the something else is there
upon called the cause, in the sense of being essential though insuffi
cient, yet what is eliminated is denied to be cause, in the sense
merely of being insufficient. By means of this discrepancy in the
meaning attached to the term ' cause ' as applied respectively to
what we reject and what we accept, in the case where we wish to
establish that one thing is essential to the production of another,
though not necessarily sufficient, the rule, that nothing in the
presence of which the phenomenon fails to occur is its cause, comes
to seem a safer ground of elimination, than the rule, that nothing
in the absence of which it occurs is its cause, appears to be. But
if the term ' cause ' is interpreted in both with the same strictness
and consistency, there is no justification for discriminating between
them.
[J. S. Mill, who spoke of what he called the Plurality of Causes
as the ' characteristic imperfection of the Method of Agreement ',
said that the Method of Difference was unaffected by it. Clearly
he was wrong. The above argument endeavours to bring out the
truth underlying the exaggeration of his statement. That he was
wrong may be seen further by help of the following considerations.
If x occurs under the circumstances abc9 and not under the circum
stances be, I can infer that be is not sufficient to produce x, and that
a contributed to its production on this occasion ; but I cannot infer
that x could not have been produced without a: pbc might equally
produce it. That a and p can equally produce x (or equally produce
it in be) is an instance of the Plurality of Causes ; and it is the
Plurality of Causes therefore which prevents my inferring univer
sally that x is produced by a, or requires a for its production, and
limits me to the inference that a produces x, at least in be. It will
be said that a and/> must have some common property rt which is
the really essential factor. No doubt ; but, as we have seen, this
is equally the case in any instance of Plurality of Causes; if I
xxn] NON-RECIPROCATING CAUSAL RELATIONS 461
[refuse to infer, in accordance with the ' Method of Agreement',
from the fact that x occurs under the circumstances abc, ade, q/g,
that a is its cause, urging- that for aught I know the cause may be
c in one case, e in the next, and g in the third, I must believe that
c, e, and g contain a common r which is the really essential factor ;
and then a is not the ' only circumstance in common ', for r is
another : just as in the other case a was not the ' only circumstance
of difference ', where x occurred and where it did not, but really r
contained in a was a circumstance of difference as well.
The distinction which Mill draws between the two ' Methods' then
is not altogether sound ; for the appearance of Plurality of Causes
affects the inference which can be drawn in each. But there is this
much truth in it, as was pointed out in the text : that in the ' Method
of Agreement ', where I am eliminating that in the absence of which
the phenomenon occurs, I may unwittingly eliminate the essential
factor : I throw away the baby with the bath, and am left supposing
that a is the cause of x} when a may really have nothing to do with
it, and its presence in each of my instances be a mere accident ; in
the { Method of Difference ', where I eliminate that in the presence
of which the phenomenon fails to occur, though a large part of
a may be superfluous to the occurrence of #, yet it is not altogether
superfluous ; I do not this time connect x with something that has
nothing to do with it. But I am unable to infer a reciprocating
relation between a and x for the same reason that in the former
case I was unable to infer any relation at all — viz. the Plurality of
Causes. And let it not be said that this difficulty would not arise,
if the conditions of the ' Method ' were fulfilled, and a were the
only circumstance of difference where x occurred and where it did
not. For (i) I should still be unable to infer a reciprocating relation :
I could only conclude that a was necessary to the production of x in
be : how much of be was also essential I should not yet have dis
covered. And (ii) — what belongs more particularly to the present
contrast — it is equally the case that if a were the only cir
cumstance of agreement in the instances where x does occur, the
difficulty would not arise. In both cases, if the analysis of the
circumstances were more complete, the Plurality of Causes would
disappear.
Mill seems unconsciously to assume that this analysis is more
complete when we employ his ' Method of Difference ' than when
we employ his ' Method of Agreement '. The reason of his doing so
is probably that experiment uses the ' Method of Difference ' (or
the principle of elimination which it involves), and a completer
analysis is generally obtainable when we can experiment than when
we are confined to the observation of events as they occur in nature :
experiment uses the ' Method of Difference ', because in experi
menting we introduce or remove some particular factor — and that
462 AN INTRODUCTION TO LOGIC [CHAP.
[under circumstances which we have endeavoured to ascertain as
precisely as possible — and watch the result ; and if we are right in
assuming these circumstances to remain otherwise unchanged, we
do approximate to having only the ' one circumstance of difference '
which MilFs canon requires ; in other words, we are really elimi
nating at once and by appeal to a single principle all except this
factor removed or introduced by us ; though it must not be forgotten
that what we eliminate is only shown to be insufficient to the
production of the phenomenon, and may still contain conditions that
are essential though not sufficient: We may note here the reason
why Mill thought the ' Method of Difference ' to be of superior
cogency. The reasoning is clearly no better in it ; but it is easier,
in the case of this ' Method ', to obtain facts of the kind on which
cogency depends, because it is easier to obtain them by experiment,
and this ' Method ' is practically a formulation of one of the com
monest ways in which we reason from the results of experiment.
We may indeed say that the error into which reasoning from an
incomplete analysis of the facts may lead us is greater when our
ground of elimination is that underlying the ' Method of Agree
ment ' than when it is that underlying the ' Method of Difference 3 :
because in the former case we may reject what is essential, and end
by attributing the phenomenon under investigation to something
whose presence is quite accidental ; while in the latter case, we may
rather end by supposing that more is essential to it than really is so.
Yet there is error in both cases, and for the same reason, viz. our in
complete acquaintance with the facts. What Mill however saw was,
that where you can experiment with precision, your acquaintance
with the facts is most complete, and hence the conclusions to be
drawn most cogent. It is just in these cases that the ' Method of
Difference ' as he formulates it is specially applicable ; for it requires
instances where the phenomenon occurs and where it does not occur
with ( only one circumstance of difference '. He overlooked the fact
that the reasoning is just the same, where this condition is not
fulfilled, so long as your ground of elimination is the same — viz. that
nothing in the presence of which the phenomenon fails to occur is
its cause ; and so he attributed to the ' Method ' a superior cogency
which really belongs to the ' prerogative ' nature of the instances
in connexion with which chiefly he considered its use.]
It has been the object of the present chapter in the first place to
acknowledge that the ' Rules by which to judge of causes and
effects', whereon inductive reasoning- depends, are not infallible
where we are dealing with non-reciprocating causal relations : for
they rest on the assumption that one effect has only one cause, and
conversely that the same cause has never any but the same effect ;
xxn] NON-RECIPROCATING CAUSAL RELATIONS 463
and so they furnish no safe guide to the discovery of ' causes ' which
are not the only causes of the effect assigned to them, or of effect^
jwhich are not the only effects that the alleged cause may have.
Its second object has been to show that such non-reciprocating:
causal relations arise from the fact of our including in the cause
more than is necessary, and perhaps also less than is necessary, to
{Reproduction of the effect : or including in the effect less or more
than the cause assigned produces ; i. e. our analysis is not perfect :
we combine with the matters strictly relevant to one another others
irrelevant, but closely bound up with what is relevant : so that there
appears to be a Plurality of Causes for the same effect, or a Diversity
of Effects for the same cause, while really, if we could ' purify ' our
statement of the cause and the effect sufficiently, we should see this
not to be the case. But we admitted that for many purposes, practical
and even scientific, it is causes in the looser sense that we need to
discover — the sense in which the cause includes more than is material
to the production of the effect in question, but a more from which
what is material cannot be dissevered, and so forth. And we saw
that science, when pushing its investigation beyond such a level as
that, tends to substitute for the search for the determinate cause of
some concrete effect the search for laws or principles in accordance
with which things of a certain kind act on one another under specified
conditions.
In illustrating these points, the rules whose guidance we showed
to become unsafe when non-reciprocating relations were in question
were the first two of the rules laid down in the Twentieth Chapter.
But the last two are also liable to mislead us in such cases. These
are, that nothing which is constant when the phenomenon varies, or
varies when it is constant, or varies independently of it, is its
cause: and that nothing which produces a different effect is its
cause. In particular I cannot, because elimination based upon these
rules reveals that x is not independent of a in the instances before
me, infer that x never occurs without a • for p might do as well.
If I find that the faster I run, the hotter I get, and if I know that
the temperature of the atmosphere has not altered, and so forth,
I may infer that running makes me hot ; but not that no one gets
hot without running. If I experiment over a series of years with
a particular manure, and take care to ascertain by ' controlling '
experiments the average crop that I might have expected without
464 AN INTRODUCTION TO LOGIC [CHAP.
its use, I may be led to attribute the excess to the use of the
manure ; but I cannot conclude that a similarly large crop is always
due to the use of it. Errors of that sort would be similar to those
which I might commit in applying the rule that nothing is the
cause of a phenomenon, in the presence of which it fails to occur :
then too I have no right to assume that what I fail to eliminate is
altogether necessary, and that nothing else would serve equally
instead of it. But the danger of eliminating too much, which
besets the application of the rule that nothing is the cause of
a phenomenon, in the absence of which it occurs, does not equally
beset the application of the two rules we are now considering. It
is true that in investigating the cause of a phenomenon that may
vary in quantity or degree, and is due as a whole to a number of
contributory factors, this danger is theoretically possible. The
quantity or degree of the phenomenon might remain constant,
owing to divers complementary variations in the factors, some in
creasing as others decreased; and because the variations masked
one another, I might reject each varying factor in turn, until I had
rejected all the contributory factors, as capable of varying with no
corresponding variation in the phenomenon. But this is not a
probable error. And the fact that the phenomena, to which these
rules are applicable, are chiefly measurable phenomena, is of great
importance in the use of them. Peculiar difficulties no doubt often
beset us in tracing the influence of some particular factor upon
a phenomenon, which varies in magnitude dependency upon the
joint action of a large number of conditions independently variable ;
it is for example exceedingly hard to determine inductively whether
the corn-duty of 1902 influenced the price of bread in Great
Britain. But these difficulties would obviously be altogether in
surmountable if no measurement of the conditions and of their
result were possible. The introduction of the element of quantity
enables us to determine laws which connect a definite amount of
change in one phenomenon with some corresponding amount in
another. Where we can do this, we are already getting clear
of the errors lurking in non-reciprocating causal relations. It still
remains true that we cannot, in virtue of a law which connects with
a change in the condition a a corresponding change in the result #,
argue backwards from the presence of x to that of a. But that
point has been sufficiently exemplified already ; and inasmuch as
xxir] NON-RECIPROCATING CAUSAL RELATIONS 465
some special attention will have to be paid in another connexion 1.
when we are dealing with the importance of quantitative methods
in induction, to the two rules or principles of elimination last
mentioned, it is perhaps unnecessary to say anything further here
upon the care that must be used in arguing from them when the
causal relations which we have it in mind to establish are non-
reciprocating.
1 Cf. infra, c. xxiv, pp. 516-521.
Hh
CHAPTEE XXIII
OF EXPLANATION
To explain anything is to show that it follows from something
either already known, or taken as known, or shown by our explana
tion to be true.1 Explanation is deductive, for it goes from conditions
to their consequences, from principles to that which they involve.
We may explain either a particular fact or a general principle.
There is no fundamental difference between the two undertakings •
but in the explanation of particular facts, particular facts necessarily
figure among the conditions to which we appeal. In all explana
tions, our premisses are ' special ' or ' proper ' or scientific prin
ciples. General logical considerations, such as direct us in the
inductive search for causal relations, account for nothing in par
ticular ; every explanation must be consistent with them, but they
will not themselves explain anything. The explanation of the
facts or derivative laws of any science rests therefore on a scientific
knowledge of the subject-matter of that science.
In an earlier chapter it was pointed out that the first or funda
mental principles of science are themselves insusceptible of scientific
explanation. It does not follow from this that the principles which
at any given time are the most ultimate to which a science appeals
should be insusceptible of explanation ; the Law of Gravitation,
for example, is and has long been a fundamental physical principle,
but various mathematicians have attempted to show that the
behaviour of matter expressed in that law follows necessarily from
some more general principles exhibited also in activities whose prin
ciples we commonly regard as different, like electricity and light.
But the process of explaining must come somewhere to an end,
with principles deducible from nothing prior to themselves.
These principles, as was also pointed out, may possibly appear
1 We may point to facts from which it follows that we must believe a pro
position ; but we do not thereby explain the proposition. It is the thing
believed, and not our believing, which must be shown to follow, if we are to
say that we are finding an explanation.
OF EXPLANATION 467
self-evident when we have reached them ; the First Law of Motion
has often been thought to be a self-evident or necessary truth.
But in most cases, they do not ; and then all that we can say about
them is that nothing so well explains those facts, the study of which
has led us to their enunciation. This however is a pis alter.
It has not infrequently been said that scientific certainty is un
attainable. Jevons urges that the conclusions of Induction are
only probable at the best. The reason is that the principles
which we arrive at as those which explain things are not — at
least as a rule — seen to be necessary; and that we cannot abso
lutely prove that no other principles will explain the facts : just as
in simpler inductive enquiries our confidence in the cause which we
assign to a phenomenon is qualified by the difficulty of being sure
that we have overlooked nothing which might equally, upon the
facts examined, be allowed to be the cause.
Jevons indeed suggests J that the true though impracticable road
to certainty would lie in Complete Enumeration. « Perfect In
duction ' rests on complete enumeration, the ' Imperfect Induction *
of actual scientific procedure does not; and in this he sees the
source of the ' imperfection ' which conclusions only approximately
certain possess. But though we may agree with him that many of
the conclusions accepted in scienee fall short of certainty, we
cannot agree that they would rank higher if they were reached by
complete enumeration ; for in that case they would not be universal
truths at all, in the proper sense, but only truths about the whole
of a limited number of particular facts. Indeed the antithesis of
Perfect and Imperfect Induction is an unfortunate one. It belongs
to a different sense of the term Induction from that which, in the
phrase Imperfect Induction, the term now bears. It is drawn from
the completeness and incompleteness of the enumeration of the par
ticulars on which the Induction rests, and to which its conclusion
refers ; we have seen that if a generalization rests merely on cita
tion of particular facts} without any attempt to establish connexions
of a causal character by analysis and elimination, the citation should
be complete ; though in such cases, the conclusion has not the true
character of an universal proposition. But the reasoning which
infers general truths from the analysis of a limited number of
1 Elementary Lessons, XXV, 'New Edition,' p. 213: Principles of Science,
2nd ed. pp. 146-152.
H h 2,
468 AN INTRODUCTION TO LOGIC [CHAP.
particulars does not rely on enumeration, and is not an operation
of the same kind as that which proceeds by complete enumeration.
Though the one therefore may cite every instance, and the other
not, yet they are not to be contrasted as if they were operations of
the same kind differing1 only in that feature. They are operations
of different kinds ; and their other differences are more fundamental
than the difference in the completeness or incompleteness of the
enumeration they involve. If the one is called perfect because its
enumeration is complete, it must be remembered that it requires
a complete enumeration ; but since the other does not require it, it
is misleading to call it imperfect for not employing it. The im
perfection attaching to the conclusions of inductive science — con
clusions which are said to be reached by ' Imperfect Induction ' —
springs from the defective analysis of the instances cited, not from
failure to cite every instance ; and it is a mistake to suppose that
e Perfect Induction ', if it could be employed — as it is acknowledged
it cannot — would remove the defect of certainty attaching to scien
tific generalizations. For science seeks after the necessary and the
universal, not after the exceptionless.
However, our present concern is less with the reason for the
want of absolute certainty in the principles of scientific
explanation, than with the fact itself. It cannot be denied
that the first principles of science rest for the most part on no
better foundation than this, that no others have been suggested
which explain the facts equally well ; and this is not the same as
saying that no others can be suggested which will do so. And
even if we were satisfied that no others could be suggested, i. e. if
we could be certain that nothing so well explains the facts as the
principles to which we appeal in our explanation, yet if we cannot
see why these principles need have been what we find them to be,
we are still left with something that at once demands to be and
cannot be accounted for.
We shall be wise therefore to recognize these two things about
scientific explanation at the outset, viz. (i) that it often starts
with principles, or truths, or laws, which are neither accounted for
nor in themselves self-evident, but only warranted by the success
with which they account for the facts of our experience : and
(ii) that these principles are not absolutely and irrefragably proved,
so long as any others which might equally well account for the facts
xxin] OF EXPLANATION 469
remain conceivable. But it would be foolish to let these considera
tions engage us in a general and indiscriminate distrust of scientific
principles. Such principles may lack that demonstrable character
which we should like them to have ; and Logic would abandon its
function, if it hesitated, out of respect for the greatness of scientific
achievement, to point this out. But they hold the field ; we are
not entitled to treat them as dogma, which cannot be questioned ;
but we are entitled to say that so long as they remain unshaken,
they should be treated as true.
It may be objected that they are not unshaken ; for the funda
mental concepts of science are unable to resist metaphysical criticism :
the independent existence of matter, the action of one independent
thing on another, the production of a conscious state by a process
in a physical organism, are all unintelligible. And it must be
allowed that the representation of reality which the physical sciences
offer cannot be the ultimate truth. But if the provisional nature of
its metaphysical assumptions be borne in mind (for science does not
really discard, though it sometimes professes contempt for, meta
physics), we may then admit the explanations which it offers within
their limits.
If however we are to accept those principles which best explain
the facts of our experience, we must have some antecedent notion
of what a good explanation is. Now it can certainly be required of
an explanation that it should be self -consistent. But we are not
content with this. There are a number of maxims, which do
actually guide us in theorizing about the laws of nature, pointing
to some more positive ideal than self-consistency. The influence of
these maxims shows that there operates upon scientific minds some
notion of what a rational universe should be, as well as a belief that
the universe is rational, not derived from experience, but controlling
the interpretation of experience. We saw that the principle of the
Uniformity of Nature was an ' anticipation ' of this kind ; but it
does not stand alone in that regard. ( The common notion that he
who would search out the secrets of nature must humbly wait on
experience, obedient to its slightest hint, is/ it has been said1,
1 Presidential Address at the British Association, Cambridge, 1904, by the
Rt. Hon. A. J. Balfour (Times of Aug. 18). He illustrates his statement by
reference to two cases, the persistent belief that the chemical elements will
be found to have a common origin, and the persistent refusal to believe in
470 AN INTRODUCTION TO LOGIC [CHAP.
' but partly true. This may be his ordinary attitude ; but now
and again it happens that observation and experience are not treated
as guides to be meekly followed, but as witnesses to be broken
down in cross-examination. Their plain message is disbelieved,
and the investigating judge does not pause until a confession in
harmony with his preconceived idea has, if possible, been wrung
from their reluctant evidence.' What these preconceived ideas are,
it would be difficult to say precisely ; nor is the question of their
justification an easy one. They have formed the subject of con
siderable discussion on the part of philosophical writers since the
time at least of Leibniz, who perhaps did most to call attention to
them. But one of the most famous has a much higher antiquity.
< Occam's razor ' l — entict, non sunt multiplicandapraeter necessitatem —
is a maxim to which science constantly appeals. It is felt that
there is a presumption in favour of theories which require the
smallest number of ultimate principles : that there is a presumption
in favour of the derivation of the chemical elements from some
common source, or of the reduction of the laws of gravitation,
electricity, light, and heat to a common basis. Again, we are
inclined to believe that the ultimate laws of nature are not only few
but simple. The law of gravitation states that the attraction
between any two bodies varies inversely as the square of the
distance. But it is conceivable that the true relation of the force
of attraction to the distance of the bodies between which it acts
is not so simple ; provided it diverged from the ratio of the inverse
square so slightly that the difference would be less than our obser
vation, with the margin of error to which it is liable, could detect,
such less simple relation would have as much to be said for it, so
far as the facts go, as the simple relation that Newton established.
Yet few would seriously consider its claims. It may be said, and
truly, that there are sound practical reasons for accepting the
simple relation, in preference to any other that has no better claims,
because it renders our calculations much easier ; yet it may be doubted
whether we really regard it as only a more convenient hypothesis.
We should regard it as more likely to be true, and this because
such a simple relation satisfies better our ideal of explanation.
action at a distance. It may however be doubted whether this refusal is as
well justified as that belief by the maxims in question.
1 William of Occam, ob. 1347.
xxin] OF EXPLANATION 471
J. S. MilPs definition of Laws of Nature has been already quoted —
'the fewest and simplest assumptions, which being1 granted, the
whole existing1 order of nature would result '.* In the words ' fewest
and simplest ' are contained perhaps the most important of the
preconceived ideas which we have about the explanation of the facts
of nature.
It is impossible to reduce explanation to any definite formulae.
When nothing1 but a middle term is wanted, to connect with
a subject a predicate empirically found to characterize it, there
it will fall into the form of syllogism.2 But comparatively few
explanations can be expressed in a single syllogism. Where, as
is commonly the case, they trace the complex result of several
principles in some particular combination of circumstances, the
building up of this result in thought can never be expressed syllo-
gistically.
As has been said above, there is no fundamental difference between
explanation of a particular fact and of a general principle. In the
latter case, more abstraction has been performed ; we are explaining
something exemplified in facts that constantly occur, that has been
extricated in thought from varying and irrelevant detail. In the
former also, some amount of abstraction must have taken place ;
but the fact we have thus isolated still retains details that make it
unique. An oculist may explain the common fact that short
sighted persons grow longer-sighted as they grow older, by showing
how clear vision depends on focusing all the rays proceeding to the
eye from each several point precisely upon the surface of the retina ;
in short-sighted persons, the curvature of the lens of the eye is
excessive, and therefore objects have to be nearer than would
normally be necessary, in order that the rays proceeding from any
point in them may be focused on the retina and not in front of it ;
but the curvature of the lens is maintained by certain muscles,
which relax with age, and therefore as years advance, clear vision
of objects is possible at a greater distance. If he were called upon
to explain some unique peculiarity of vision in a particular patient,
the task would still be of the same kind ; but the facts to be taken
into account would partly be facts peculiar to this case, and though
their consequences would be traced according to general principles,
their special combination would make the complex result unique :
1 Logic, III. iv. 1. 2 But cf. infra, p. 487, n. 2.
472 AN INTRODUCTION TO LOGIC [CHAP.
unique however not necessarily, for the same combination might
conceivably recur, but only as a fact within medical experience.
Historical explanation is largely concerned with events in this
sense unique. History has generalizations that admit of explanation
also ; but human affairs are so complex, and our interest in them
extends into so much detail, that the unique occupies a quite
peculiar share of attention in its investigations. And its task
consists largely in making facts intelligible by tracing their develop
ment. For an institution or event, when we come upon it as it
were abruptly, may surprise us : whereas if we know the past, we
may see that its existence or occurrence connects itself with other
facts about the same folk or period in accordance with accepted
principles. The institution of primogeniture for example, according
to which land descends upon the eldest son, is a peculiar institution,
unknown, according to Sir Henry Maine, to the Hellenic, to the
Koman, and apparently to the whole Semitic world; neither did
the Teutonic races when they spread over Western Europe bring it
with them as their ordinary rule of succession. Whence then did
it originate ? for such institutions do not occur at haphazard.
Maine accounts for it as ' a product of tribal leadership in its decay '.
Chieftaincy is not the same thing as being a landowner ; but some
of the tribal lands were generally the appanage of chieftaincy. So
long as times were warlike, the chieftaincy seems not necessarily to
have gone to the eldest son of the deceased chief; but ' wherever
some degree of internal peace was maintained during tolerably long
periods of time, wherever an approach was made to the formation
of societies of the distinctive modern type, wherever military and
civil institutions began to group themselves round the central
authority of a king, the value of strategical capacity in the humbler
chiefs would diminish, and in the smaller brotherhoods the respect
for purity of blood would have unchecked play. The most natural
object of this respect is he who most directly derives his blood from
the last ruler, and thus the eldest son, even though a minor, comes
to be preferred in the succession to his uncle ; and, in default of
sons, the succession may even devolve on a woman. There are not
a few indications that the transformation of ideas was gradual '.
The custom, Maine thinks, was greatly fixed by Edward Fs decision
in the controversy between Bruce and Baliol ; where the celebrity
of the dispute gave force to the precedent. The rule of primogeni-
XXTII] OF EXPLANATION 473
ture was extended from succession to the lord's demesne to succession
to all the estates of the holder of the signory, however acquired,
and ultimately applied to all the privileged classes throughout
feudalized Europe.1 In a case like this, a knowledge of past facts
enables us to see how a new custom might emerge conformably
to known principles of human nature. There are motives for
allowing the chieftaincy to devolve upon the eldest son, and motives
for conferring it upon the strongest of the near kindred ; when the
latter are weakened by change of circumstance, the former are
likely to prevail. The influence of precedent upon the human
mind is also a familiar principle ; and though it is impossible to
show that in such cases nothing else could have happened (Edward I
for example might have decided differently), yet what did happen
is shown to follow according to accepted principles from the previous
circumstances.
Sciences like Geology or Biology set themselves for the most
part to solve more generalized problems of development: though
to them too some particular fact, apparently in conflict with a
theory, may offer occasion for a detailed historical enquiry. But
the explanation of the occurrence of crystallized rock, common as it
is, is not logically different from what it would be if there were only
one place where it occurred ; and if we set about accounting for
that local and temporal affinity of species which is expressed in
Mr. A. R. Wallace's principle that ' Every species has come into
existence coincident both in space and time with a pre-existing
and closely allied species ',2 we shall not proceed otherwise than
if the affinities of one particular historical group of species were to
be accounted for.
There are other sciences (e. g. Political Economy or Kinematics)
which do not concern themselves with tracing any particular
historical development, yet have to explain the laws manifested
in a succession of events. Here too it may be of the essence
of the explanation to show how one change determines another,
and the new fact thus introduced determines a third, and so forth.
The laws to which we necessarily appeal may be different laws, and
the sequence is explained by resolution into stages, each of which
1 v. Maine's Early Institutions, pp. 197-205, from which the above example
is abridged.
2 Quoted Romanes, Darwin and after Darwin, i. 243.
474 AN INTRODUCTION TO LOGIC [CHAT.
exhibits a general principle, while the special circumstances in
which such a principle is exhibited furnish the occasion for a further
change that exemplifies another.
There are cases where the element of time is one of the most
important of the facts. Many effects depend upon the juxta
position of objects in space, and their juxtaposition depends on
time-conditions. The fortune of a campaign may be decided by
the rapidity of a march, bringing troops upon the field at a critical
moment ; the troops may fight upon the same principles and with
the same degrees of courage all through, but the result is deter
mined by their being there at the time. The working of a
machine would be thrown out by anything that delayed or hastened
the movement of a part with which other moving parts had to
connect ; and the same is of course true as regards the articulated
movements of an animal. The disintegration of mountains is
largely produced by frost succeeding rain ; if rain only succeeded
frost, it would not take place in the same way. Professor Marshall
has called attention, in his Principles of Economics, to the great
importance of the element of time in the working of economic
laws.1
There are however also many results that are to be accounted
for through the concurrent operation of several principles : or rather
— for principles cannot in strictness be said themselves to operate —
through the concurrent operation of several causes, each according
to its own principle. The path of a projectile at any moment
is determined by its own motion, the pull of the earth, and the
resistance of the atmosphere. It is true that at every moment
these forces are producing a new direction and velocity in the
projectile, which forms the basis for an immediate further change ;
and that it is by following the continuous series of these successive
changes that its path is ascertained— a task which the notation of
the calculus alone renders possible. The consideration of any term
in the series of changes as the resultant of simultaneously operating
causes is however different from the consideration of the succession
of one resultant change upon another in the series. And the
explanation of many problems lies in showing the concurrent
operation of different causes, each acting continuously according to
its own law; as opposed to the case just considered, where one
1 e. g. Bk. III. c. iv. § 5, 4th ed. p. 184.
xxm] OF EXPLANATION 475
cause may produce an effect that, by virtue of the conditions with
which its production coincides, then produces a fresh effect in
accordance with a different law. The column of mercury in the
barometer is maintained according- to laws that are all continuously
exemplified, and not first one and then another of them ; the atmo
sphere is always exerting pressure, and in the mercury the pressure is
always equalized in virtue of its nature as a fluid. Economists are
familiar with ( Gresham/s Law ' that bad money drives out good, i. e.
that if in any country the circulating medium is not of uniform
quality, the best is always exported and the worst left behind.
By best is meant that whose intrinsic value bears the highest
proportion to its nominal value ; a sovereign which contains the
proper weight of fine gold being better than one containing less,
and so forth. The explanation of the Law is simple. Government
can make the bad money legal tender for the payment of debts
at home; it cannot compel the foreigner to receive it. For
discharging debts abroad the better money is therefore more
valuable, for discharging debts at home it is no more valuable
than the worse ; it is therefore more profitable to export the good,
and keep the bad money for home purposes; and the desire of
wealth being one of the strongest and most uniform motives in
mankind, what is most profitable is naturally done. Nothing
turns here upon the resolution of a sequence into stages exhibiting
different laws; the derivative law is shown to follow from more
general laws, under the special assemblage of circumstances
described in saying that the circulating medium in a country is
not of uniform quality; but these general laws are exhibited
simultaneously and not successively. That the power of any govern
ment extends to its own subjects only, and that men desire wealth,
are principles more general than Gresham/s Law ; and both apply
to money, which is at once, as legal tender, a matter to which
the power of government applies, and, as medium of exchange,
the equivalent of wealth.
No logical importance attaches to the distinction between
explanations that derive a complex law from simpler laws exempli
fied together, and those that derive it from simpler laws exemplified
successively. Many explanations involve both features. But there
is a difference of more importance between either of these, and that
form of explanation which consists in showing that laws, hitherto
476 AN INTRODUCTION TO LOGIC [CHAP.
regarded as distinct, are really one and the same. Newton showed
that the familiar fact that heavy bodies fall to the earth, and the
equally familiar fact that the planets are retained in their orbits,
were really instances of the same principle, the general Law of
Attraction. Something of the same sort is done when Romanes
brings Natural Selection, and Sexual Selection, and Physiological
Selection, and Geographical Isolation under the general conception
of forms of Isolation preventing free intercrossing among all
the members of a species.1 In cases like these, the derivative
law is not deduced from several more general laws exemplified
together or successively in complex circumstances of a particular
kind ; but a single more general law is shown to be exemplified
in a diversity of circumstances which have hitherto concealed its
identity. This operation is sometimes called subsuniption, as bring
ing several conceptions under one, in the character of instances,
or of subjects of which it can be predicated in common. Yet even
here it is plain that the operation, of tracing the distinctive
peculiarities of the laws explained or subsumed to the special
character of the circumstances in which the same more general
principle is exhibited, is of the same kind as occurs in all other
forms of explanation : only the further synthesis of the consequences
of several laws is lacking.
Explanation, as was said at the beginning of the chapter, is
deductive — deductive, that is, in respect of the reasoning involved
in it. • Yet it has a close relation with the work of Induction, and
the consideration of this will form the subject of the remainder of
the chapter.
Explanation starts, as we have seen, from principles already
known, or taken as known ; and it shows that the matter to be
explained follows as consequence from these. But it is clear that
the reasoning which deduces their consequence from them is un
affected by the nature of our grounds for taking them as true. If
they were nothing more than hypotheses, we might still argue
from them to their consequence as if they were indubitably
certain. Just as we may syllogize in the same way from true
premisses and from false, so it is in any other kind of reasoning.
Moreover, it was pointed out that many at least of the most general
and fundamental of our scientific principles are accepted only
1 Darwin and after Darwin, vol. iii. c. i.
xxm] OF EXPLANATION 477
because they explain the facts of our experience better than any we
can conceive in their stead ; they are therefore, or were at the
outset, hypotheses, used in explanation of facts, and proved by
their relative success in explaining- them. We do not see why they
are true, but only why we must believe them to be true. They
are established inductively, by the facts which they explain, and
the failure of any rival hypothesis ; the facts are explained from
them.
It follows that all the deductive reasoning that enters into an
explanation enters into the inductive proof of an hypothesis which
is shown to explain, and to be the only one that will explain *, the
facts. And many explanations are put forward, which do not
appeal only to principles already known, but have it as their avowed
object to prove one or more of the principles which they employ.
Explanation then figures as an instrument of induction ; and
J. S. Mill spoke accordingly of a ( Deductive Method of Induction ',
and rightly attributed great scientific importance to the process
which he called by that name.
No better instance of this operation can be given than the
familiar instance of the Newtonian theory of gravitation. Sir
Isaac Newton showed that the movements of the heavens could
be explained from two principles or laws — the First Law of
Motion, and the Law of Universal Gravitation. The former is,
that every body preserves its state of rest or uniform rectilinear
motion until it is interfered with by some other body ; according
to the latter, every particle of matter attracts every other particle
with a force that varies directly as the mass and inversely as the
square of the distance. The former had already been established
by Galileo, and Newton took it for granted; but the latter he
proved for the first time by his use of it in explanation.
The theory which bears the name of Ptolemy, though much
older than he, represented the sun, moon, and stars as moving round
the earth ; and originally it was supposed that they moved in circles
with the earth as centre. While the laws of motion were still
1 I add these words, because it is important to realize that an hypothesis
is not really proved by merely explaining the facts. But many hypotheses
are provisionally accepted, which are not proved, on the ground that they
explain the facts, and without the performance of what would often be the
impracticable task of showing that no other hypothesis could equally well
do so.
478 AN INTRODUCTION TO LOGIC [CHAP.
undiscovered, no difficulty was found in their circular motion;
indeed Aristotle supposed it to be naturally incident to the sub
stance of which the heavenly bodies were composed, that their
motion should be circular; for the circle is the perfect figure;
movement in a circle is therefore perfect motion ; perfect motion
belongs naturally to a perfect body ; and the substance of which
the heavens are composed — the quinta essentia, distinct from the
four primary substances, earth, air, fire, and water, that are found
composing this globe — is perfect.1 The only difficulty arose when
it was found that the orbits of the heavenly bodies, other than
the fixed stars, were not perfectly circular ; and that was met by
the hypothesis of epicycles referred to in an earlier chapter.2 The
substitution of the Copernican for the Ptolemaic hypothesis, though
involving a reconstruction of the geometric plan of the heavens,
did not necessarily involve any new dynamics ; Kepler's discovery
that the planetary orbits were elliptical was however a severe
blow to the traditional theory of epicycles, which had already
by that time become highly complicated, in order to make it
square with the observed facts. But when the first law of motion
had been grasped, it was evident that a planet, if left to itself,
would not continue moving in a circle, and returning on its own
track, as Aristotle had thought to be natural to it, and as with
more or less approximation it actually does : but would continue
moving for ever forward with uniform velocity in a straight line.
Circular motion, however uniform,, was now seen to involve an
uniform change of direction for which a dynamical reason was
required. And as the planets were constantly changing direction
towards the sun, a force exerted from or in the direction of the
sun seemed necessary.
Now the greatness of Newton's achievement did not lie in the
conception that the orbital motion of the planets was the resultant
of two forces, the ' impressed force ' (as it is called) which, left to
itself, would carry them forward with constant velocity in a straight
1 According to Aristotle, every body left to itself had a natural motion,
dependent on its own nature : that of the heavens was round a centre, that
of earth and water to a centre, that of air and fire from a centre. The
centre was the centre of this globe, and so (on his view) of the physical uni
verse. Bodies need not be left to their own motion; a stone, for example,
may be thrown towards the sky; but in such case their motion was not
natural, but violent. 2 Supra, c. xxi, p. 435.
xxm] OF EXPLANATION 479
line, and a ' centripetal force ' which, left to itself, would carry
them to the sun. The resolution of curvilinear into rectilinear
motions had been accomplished before him, and the hypothesis
of an attractive force had already been hazarded. It had even
been suggested that such a force might vary inversely as the
square of the distance ; for the area over which it might be con
ceived as spreading in any plane taken through the centre of the
sun varies directly as the square of the distance, and its intensity
might be supposed to decrease as the area increased. Neither was
it Newton who ascertained the facts about the movements of the
planets — no small or easy contribution to the solution of the
problem. But he did two things. He conceived that the force
which deflected the planets into their orbits was the same as that
which made bodies fall to the earth : or, to put it differently, he
identified celestial attraction with terrestrial gravity, and conceived
the earth as continually fa lling out of a straight path towards the
sun, and the moon towards the earth; and he invented a mathe
matical calculus by which he oould work out what were the
theoretical consequences of the principles which he assumed.
Both these steps were of the highest importance. The first
provided data to calculate from ; the second made the calculation
possible. The amount of acceleration produced per second in near
bodies falling to the earth was already known 1 ; from that it could
be estimated what it ought to be for a body so many times
remoter as the moon, or what acceleration a body so many times
more massive than the earth as the sun is ought to produce, if
once a method of performing the calculation could be devised.
With this method Logic is not concerned. Processes of reason
ing are too numerous for Logic to enumerate them all, and those
of mathematics are for the mathematician to appraise ; it is enough
1 Strictly speaking, that acceleration should not be the same at 1,000 feet
from the earth and at 100 feet: and in virtue of atmospheric resistance
a cricket-ball should not fall as far in a given time as a cannon-ball ; but
the theoretical differences would be so small as to escape observation, and
therefore the fact that acceleration is empirically found to be 32 feet per
second for all bodies in the neighbourhood of the earth creates no difficulty.
On the other hand, in the oscillations of a pendulum, which vary in the
plains and in the neighbourhood of mountains, we do find evidence agreeable
to the theory, of the same kind as those minute differences would afford if
we could measure them. The logical bearing of these considerations will
be seen if it is remembered that a theory, though not proved by its con
formity with facts, is disproved by any clearly established unconformity.
480 AN INTRODUCTION TO LOGIC [CHAP.
if the logician can satisfy himself in general regarding the grounds
of mathematical certainty. But assuming the task of deducing
from his principles their theoretical consequences to have been
performed, we may look at the logical character of the reasoning
in which Newton made use of that deduction.
The principal astronomical facts to be accounted for concerned
the movements of the earth and other planets round the sun, and
the movements of the moon round the earth.1 The former body
of facts had been already generalized by Kepler, in his three laws,
(i) that the planets move in ellipses round the sun, with the sun
in one of the foci; (ii) that they describe equal areas in equal
times; (iii) that the cubes of their mean distances vary as the
squares of their periodic times.2 There was also a large body of
recorded observations upon the movements and perturbations of the
moon; and when Newton first worked out his theory, he found
it led him to different results than those actually recorded. He
therefore laid it aside ; and it was only after several years, when
fresh and corrected observations upon the moon's motion were
published, that he returned to it. He then found the theoretical
results agree with the observed facts; but to show this was
not sufficient. He demonstrated further that from any other
hypothesis as to rate of variation in the attractive force results
followed with which the observed facts conflicted ; and thus
showed not only that his theory might be true, but that if the
planetary motions were to be accounted for by help of a theory of
1 Where the planets are mentioned they may be taken to include the
moon, unless the context expressly forbids.
2 Perhaps it should be explained that as a circle is a curve, every point
on which is equidistant from a point within it called the centre, so an
ellipse is a curve, the sum of the distances of every point on which from
two points within it called the foci is equal; that the area described by
a planet in moving from a point a to a point b on
its orbit is the area comprised between the arc, and
the lines joining those points to the centre of the
sun : so that if the planet is nearer the sun, it will
move faster, since if ac, be are shorter, ab must be
longer, to make the area dbc the same ; that the mean
distance of a planet is its average distance from the sun
during its revolution, and its periodic time the period of its revolution, so
that if the cubes of the mean distance vary as the squares of the periodic time,
it follows that a planet whose mean distance from the sun is twice that of
the earth would have a 'year' or period of revolution, whose square was to the
square of one (earth's year) as the cube of two to the cube of one— i.e. that
its period of revolution would = V 8 x the earth's year.
xxm] OF EXPLANATION 481
attraction at all, the law of that attraction must be as he formu
lated it.1
The further confirmations which Newton's Law of Universal
Gravitation has received, from its success in accounting- for other
physical phenomena, need not detain us ; we have to look to the
steps involved in its establishment, and they can be sufficiently
seen in what has been detailed already. First, there was the idea
that the movements of the planets were to be accounted for by
reference to two forces acting on them — the impressed force, and
the force of attraction ; this was not due to Newton. Next, it was
necessary to determine or conjecture the way in which these two
forces severally operated ; so far as the impressed force went, that
had also been in part already done, and it was expressed in the first
law of motion ; the actual velocity of each planet was ascertained
by calculation from astronomical observations, and the velocity
due to the impressed force taken alone was determined by reference
to the actual velocity and the velocity acquired by gravitation.
But the velocity acquired by gravitation, or through the influence
of the attractive force, had to be conjectured; and though the
law of its variation had been suggested before, unless the amount
of its effect between some given masses at some given distance
were known, the law of its variation left the matter quite inde
terminate. The identification of the attractive force with terres
trial gravity thus completed the necessary data; and principles
and facts were now before Newton, sufficient, if a method of
calculation were devised, to enable him to determine what should
be the consequences of his hypothesis. The next step was the
process of calculation. But he had to show, not barely what
the consequences of his hypothesis would be, but that they would
be the same as the observed facts : and moreover, that his was the
only hypothesis1, whose consequences would be the same as the
observed facts.2 The comparison therefore of the facts with
the theoretical results of his and of any other hypothesis was the
step that succeeded the calculation; and having found that they
agreed with his, and with no other, he reasoned thus — Assuming
1 i. e. if it was to embody a simple ratio : cf. pp. 435-436, 470, supra.
2 It was possible to show that no other rate of attraction would give
results conformable to the facts, because the problem was a mathematical
one ; and in mathematics it is easier than elsewhere to prove not only that
if a is true, b is true, but also the converse..
482 AN INTRODUCTION TO LOGIC [CHAP.
that the continual deflexion of the planets from a rectilinear path
is due to an attractive form, their actual motions, if my statement
of the law of attraction is true, would be thus and thus ; if it is
false, they would be otherwise : but they are thus and thus, and
therefore my statement is true.
Now of the steps in this whole logical process, some are not
processes of reasoning at all — the suggested reference of the resultant
motions to those two forces, the suggested identification of one
of the forces with terrestrial gravity, and the comparison of the
theoretical results with the observed facts. Reasoning may have
been employed in establishing the first law of motion; but that
reasoning lies outside the present appeal to it. The reasoning
involved in determining the theoretical results of the action of the
forces assumed is deductive. But the final argument, in which
the agreement of the facts with the results of this hypothesis and
of no other is shown to require the acceptance of this hypothesis,
is inductive. Had the Law of Gravitation been already proved,
we might have said that Newton was merely explaining certain
empirical generalizations about the movements of the planets ; had
it been already proved, the disagreement of its consequences with
the earlier records of the perturbations of the moon would have
led him not to lay aside the theory, but to doubt the observations,
or to assume (as Adams and Leverrier afterwards did for the per
turbations of Uranus) the existence of some other body whose
attraction might account for the discrepancy ; but inasmuch as it
was only now proved by its exclusive success in explaining the
facts, he was arguing inductively to the proof of it.
If we look for a moment at the simpler inductive arguments
which establish the cause of a phenomenon by appeal to ' grounds
of elimination ', we shall find in them too something of this double
character, at once inductive and deductive. The facts appealed to
as showing that a is the cause of x are themselves accounted for by
that hypothesis. If, for example, facts do not allow us to doubt that
malarial fever is conveyed by the bite of the Anopheles mosquito,
then too the power of the Anopheles mosquito to convey malarial
fever accounts for its appearing in persons bitten by that insect. It
is impossible but that, if certain facts are the ratio cognoscendi of
a causal principle, that principle should be the ratio essendi of the
facts. But in these simple arguments there is nothing correspond-
xxm] OF EXPLANATION 483
ing to the deductive reasoning which works out the joint conse
quence, in particular circumstances, of the action of two or more
causes, from a knowledge (or conjecture) of the effect which each of
these causes would produce singly. It is on account of this opera
tion that J. S. Mill gave to reasoning of this kind, even when its
primary object was the inductive establishment of a general
principle, the name of the ' deductive method of induction '.
Such reasoning can only be used where the joint effect of several
causes is calculable from the laws of their separate effects. Where
the joint or complex effect seems totally dissimilar to what any of
the separate effects would be, it cannot be calculated from them in
anticipation; and we rely entirely on the inductive method of
elimination in order to show that such complex effect is to be attri
buted to the action of one particular conjunction of causes rather
than another, without being able to show a priori that it is the
effect they would produce. But into the investigation of any com
plex effect of the other kind, in which the action of the several
causes can be traced as combining to produce it, some measure of
this deductive reasoning will always enter. Most obviously is this
the case in regard to those complex effects which exemplify what
has been called a homogeneous intermixture 1 — i. e. where the
complex phenomenon is quantitative, and there are many factors
determining its quantity, some by way of increase and some of
decrease. The simpler inductive methods are there quite inadequate :
for there need be no two instances of the phenomenon in which its
quantity is the same, nor, if there were, need the combination of
factors be the same ; neither can we infer from the non-occurrence
of the phenomenon, or its presence only in an imperceptible degree,
where the supposed cause is present, that what we had been inclined
1 J. S. Mill gave the name of ' homogeneous intermixture of effects ' to
those cases where the joint effect of several causes acting together is the
sum (or difference) of their separate effects, and differs in quantity only and
not in quality from the effects which the same causes would produce singly ;
this happens, e. g., in the mechanical composition of forces— for which reason
he spoke also of Composition of Causes in such a case. Where the joint
effect differs in quality from the separate effects (and so cannot be calculated
from a knowledge of them) he called it heterogeneous or heteropathic. He
illustrated this from chemical combination, in which the chemical proper
ties of the compound (unlike its weight) are not homogeneous with those of
its constituents, and not deducible from them ; though he quite overlooked
the fact that elements were not the 'cause' of a compound in his usual
sense of that term. Cf. Logic, III. vi.
i i a
484 AN INTRODUCTION TO LOGIC [CHAP.
to ascribe it to does not produce it ; since that cause might be
present, but counteracted by another of contrary effect. Even the
rule that cause and effect must vary concomitantly, and the rule
that no such portion of the effect must be attributed to one among
the factors making up the cause of the whole, as is already accounted
for by other factors, are not sufficient to ensure success in such
enquiries. It is necessary to be able to measure more or less pre
cisely the complex effect, and to know with corresponding precision
the amount of effect that the several supposed causes would pro
duce alone, in order to prove that any particular one among them
cannot be dispensed with, or rejected from being a part cause.
And into this proof a deductive calculation will obviously enter.
In the fiscal controversy, for example, initiated in Great Britain in
1903, it was alleged that the excess in the value of our imports
over that of our exports was due to the crippling of our production
by free-trade ; but this could only be proved by showing that the
difference of value between exports and imports was unaccounted
for, unless we were living on our capital ; and that could not be
shown unless the excess in value of imports were ascertained, which
was attributable to other causes known to assist in producing their
total excess-value — such as the fact that the valuation of our imports
was swollen by the inclusion of the cost of carriage to our ports
(while our exports, being valued before transport, did not receive this
addition) : and by the value of the goods that paid for the service
which the country performs as ocean-carrier, although nothing
appears in the total for exports on that head : and by the value of
the goods that represent payment for the use of British capital
invested abroad, or pensions charged on the Government of India.
The difficulty of determining the amount by which these causes
should make our imports exceed our exports in value rendered it
exceedingly hard to prove, at least on this line of argument, that
we could not be paying out of the year's production for all that we
imported in the year.
To sum up — Explanation considered in itself is deductive : it
consists in showing that particular known facts, or laws, or general
causal connexions, follow from principles already established, in the
circumstances of the case; it establishes therefore nothing new,
except as it makes us understand the reason for that which we had
hitherto only known as a fact. But explanation also enters into
xxm] OF EXPLANATION 485
induction, so far as the principles, from which the facts, or laws, or
general causal connexions, are shown to follow, were not previously
established, but are only now confirmed in showing that the actual
facts, laws, or causal connexions would follow from them and
not from any alternative principles. In such induction there are
four main steps distinguishable : (i) conceiving the several agents,
or causes, at work ; (ii) determining or conjecturing how or accord
ing to what law each of them severally would act; (iii) reasoning
from these premisses to the result which they should produce in
common, as well as to the result which would follow on any rival
hypothesis as to the agents at work, and the several laws of their
operation ; (iv) showing by comparison that the facts agree with
the results deduced from these, and not with the results deduced
from any rival premisses.
Many observations might still be made upon this type of argu
ment — one of the commonest and most important in the sciences.
It might be shown how it may be directed to establish either that
a particular agent produces a certain kind of effect at all, or how
much of that effect, according to its own variations,, it produces : or
that an agent known to produce an effect of a certain kind is one
of the causes contributing to produce that effect on a given occa
sion. The question may be, what causes can produce such an effect,
or which of the causes that can produce it are contributing to pro
duce it now ? We may wish to establish a general principle, or
only some special fact as to the circumstances that are modify
ing the results of that principle in the case before us. It is pos
sible too that the laws of the action of the several agents may some
of them have been previously ascertained and established, while
others are only conjecturally formulated ; or, if the question be as
to the agents contributing to the result in a particular case or class
of cases, the laws of the several actions of them all may have been
established previously. But without dwelling on these points, we
may conclude the chapter with four considerations.
First, the inductive arguments of science display in every dif
ferent degree that combination with deductive reasoning which has
been now analysed. Thus, though we may represent in symbols
the induction whose logical form is a mere disjunctive argument,
and contrast it with this into which the deduction of a complex
result from several premisses so prominently enters, yet in actual
486 AN INTRODUCTION TO LOGIC [CHAP.
practice the contrast is not so sharp ; in few inductive investigations
is the reasoning merely disjunctive ; but the amount of deductive
reasoning that has to be performed before one is in a position to
apply a disjunction, and to say that this hypothesis is true because
the rest can be proved false, varies very greatly in different inves
tigations.
Secondly, to show that the facts agree with the consequences of
our hypothesis is not to prove it true. To show that, is often
called verification; and to mistake verification for proof is to
commit the fallacy of the consequent *, the fallacy of thinking that,
because, if the hypothesis were true, certain facts would follow,
therefore, since those facts are found, the hypothesis is true. It
is the same mistake as that of incomplete elimination, in the
establishment of a simple causal relation : the same as results from
overlooking what was called the Plurality of Causes. A theory
whose consequences conflict with the facts cannot be true ; but so
long as there may be more theories than one giving the same
consequences, the agreement of the facts with one of them
furnishes no ground for choosing between it and the others.
Nevertheless in practice we often have to be content with verifi
cation; or to take our inability to find any other equally satis
factory theory as equivalent to there being none other. In such
matters we must consider what is called the weight of the evidence
for a theory that is not rigorously proved. But no one has shown
how weight of evidence can be mechanically estimated ; the wisest
men, and best acquainted with the matter in hand, are oftenest
right.
Thirdly, there is no logical difference between the reasoning con
tained in explanation, and the inductive reasoning that involves
explanation, except in one point : that the latter infers the truth of
some premiss assumed in the explanation from its success in explain
ing the actual facts and the impossibility of explaining them with
out assuming it. Where this impossibility is not shown, and we
content ourselves with verification — that is, with showing that the
facts consist with the assumption — there the logical difference is
still slighter ; it amounts to this, that in explanation the premisses
are taken as previously known, and in the other case something in
1 Cf. p. 555, infm.
xxm] OF EXPLANATION 487
the premisses is taken as not known previously to its use in the
explanation.1
Fourthly, we may answer here the second of the two questions
raised at the end of c. xvii. Demonstration is explanation from
principles that are self-evident, or necessarily true. If it be said that
in that case very little of what we believe is demonstrated, we must
admit it. We can demonstrate little outside mathematics. But we
have an ideal of demonstration, and it seems to be that ; and it is
not necessarily syllogistic, as Aristotle thought it to be.2
1 J. S. Mill, to whose work the above chapter is not a little indebted
(v. Logic, III. x-xiii), fails to mark sufficiently the difference between
showing that the facts agree with a theory, and showing that the theory
is true. And he does not bring out clearly enough the relation between
what he calls the Deductive Method of Induction (c. xi) and what he calls
the Explanation of Laws of Nature (c. xii). He neither notices how they
differ, nor how closely they agree, though he gives the same investigation
(the Newtonian theory of gravitation) as an example of both of them (xi. 2,
xiii. 1). Moreover, in resolving into three steps his 'Deductive Method of
Induction ', he leaves out the first of the four mentioned on p. 485.
2 Indeed, if syllogism implies the application, to a particular case, of
a general principle known independently, demonstration is never syllogistic ;
for, with complete insight, the necessity which connects the different
elements in a complex fact should be manifest in the case before us, and the
general principle or major premiss is not brought in ab extra, but rather
visible in and extricable from that case (cf. p. 307. supra). This much how
ever Aristotle would probably have admitted ; but most demonstration cannot
even so be put into the form of syllogism, connecting one term with another
through a third by the relation of subject and attribute.
CHAPTER XXIV
OF INDUCTION BY SIMPLE ENUMERATION
AND THE ARGUMENT FROM ANALOGY
THERE are many reasonings which do not prove their conclusion.
It is not merely that we have to use premisses of doubtful certainty ;
for this, though it destroys the strictly demonstrative character of
our knowledge, does not invalidate the reasoning, so long as the
conclusions are what must be drawn, if the premisses are true. We
often draw, and act upon, conclusions, about which we cannot say
even this much, that they must be true if the premisses are. And
in so doing, we often find ourselves right ; nor, if we refused to do
it, could the affairs of life be carried on. Descartes, when he set
himself to examine all which he had hitherto believed, and to doubt
everything which could be doubted, determined with himself that
he would not let this demand for demonstration in things of the
intellect prevent his following the most probable opinion in practical
matters.1 But it is not only in practice that we have to hazard an
assent to conclusions which our premisses do not strictly justify.
Many branches of science would not progress at all, unless we did
the same there. In the first place, by committing ourselves to
a conclusion, and working upon the assumption that it is true, we
may be led to results that will help either to confirm or to overthrow
it ; whereas if we had merely withheld our assent from any con
clusion, because the evidence was inconclusive, we might have
remained indefinitely long possessed only of that inconclusive
evidence. ' Truth/ said Bacon, ' is more readily elicited from error
than from confusion ' 2 ; and perhaps we might add, than from
indecision. Only we must in such cases let our assent be provisional,
and hold our opinion not as demonstrated, but as in default of
a better. The advice of the politician, that a man should make war
with another as with one to whom he may be reconciled, and peace
1 Discours de la Methode, Troisieme Partie.
2 Nov. Org. II. 20.
SIMPLE ENUMERATION AND ANALOGY 489
as with one with whom he may become at variance, may without
suspicion of cynicism be adapted to the assent or dissent with which
we receive conclusions that are based on insufficient evidence. But
secondly, the sciences differ very much in the amount of evidence
which they can hope to obtain for their conclusions. A fairly
rigorous science may be content to use provisionally principles
which are known to be insufficiently proved (and that means really,
not proved at all); but some sciences hardly ever obtain rigorous
proof of their positions, as for example Anthropology ; and yet
much at any rate of their teaching is generally accepted as authori
tative. Aristotle said that it was the business of education to
teach a man to demand rigorous proof of anything according to the
nature of the subject ; for it is as foolish to ask demonstration of
the orator, as to accept plausibilities from the mathematician l ;
and he would have allowed that for this purpose education must
include both a training in f Analytics ' and an acquaintance with
the different kinds of subject-matter to which one's attitude should
be different. It is often said that a man whose studies are too
exclusively mathematical is at sea when he comes to deal with
matters that do not admit of demonstration ; and that contrariwise,
if he is trained only in sciences where rigorous proof is impossible,
he becomes incompetent to see what is required in matters of
a stricter sort.
There are no logical criteria by which to judge the value of such
reasonings, unless what is called the Theory of Probability may
claim to be such a criterion. But the Theory of Probability is
primarily a branch of mathematics; many of the assumptions
which underlie its applications are open to suspicion on logical
grounds ; and its use is at any rate confined to subjects that admit
of quantitative treatment The object of the present chapter how
ever is to consider briefly two kinds of argument, which while being
of this inconclusive character are very common, and have attracted
considerable attention from logical writers accordingly.
Induction by Simple Enumeration consists in arguing that
what is true of several instances of a kind is true universally
1 Eth. Nic. a. i. 1094b 23 Tre7rai8cvp.fvov yap (<TTIV eVi rotrovr
€iri£r)T€iv KaO* fKaarov yevos, e<£' otrov f] TOV npdyfjLaros <f>v<ris firidt \frai' T
yap (fraiveTai }jiadr^iariK.o\) TC TTiOavoXoyovvros drro8fxe<rdai /cat prjTOptKov
490 AN INTRODUCTION TO LOGIC [CHAP.
of that kind. Simple enumeration means mere enumeration; and
such an argument differs from scientific induction in the absence of
any attempt to show that the conclusion drawn is the only conclusion
which the facts in the premisses allow, while it differs from in
duction by complete enumeration in that the conclusion is general,
and refers to more than the instances in the premisses. It should
however be noted here, that induction by complete enumeration, if
the conclusion be understood as a genuinely universal judgement,
and not as an enumerative judgement about all of a limited number
of things, has the character of induction by simple enumeration.
The name of empirical generalization is also given to such argu
ments by simple enumeration.
Bacon's strictures upon this form of reasoning have been already
referred to.1 Regard it as a form of proof, and they are not unde
served. Yet it is still in frequent use, in default of anything better.
It has been inferred that all specific characters in plants and animals
are useful, or adaptive, because so many have been found to be so.
So many { good species ' have become ' bad species ' (i. e. species in
capable of any strict delimitation) in the light of an increased know
ledge of intermediate forms, that it has been inferred that all species,
if we knew their whole history, would do so.2 The familiar
generalization that we are all mortal, though not based solely on
enumeration, draws some of its force thence. Most men's views of
Germans, or Frenchmen, or foreigners generally, rest upon their
observation of a few individuals. The 'four general rules of
geography ', that all rivers are in Thessaly, all mountains in Thrace,
all cities in Asia Minor, and all islands in the Aegaean Sea, are
a caricature of this procedure, drawn from the experience of the
schoolboy beginning Greek History. The history of the theory of
prime numbers furnishes one or two good examples. More than
one formula has been found always to give prime numbers up to
high values, and was assumed to do so universally : x2 + x + 41
worked for every value of x till 40 : 22* + l worked for long, but it
broke down ultimately.3 It is needless to multiply illustrations.
What is the assumption which underlies arguments of this kind ?
It is the old assumption that there are universal connexions in
1 Nov. Org. I. 105. Cf. supra, pp. 352, 364.
2 Romanes, Darwin and after Darwin, ii. 282.
3 v. Jevons, Elementary Lessons, pp. 221-222.
xxiv] SIMPLE ENUMERATION AND ANALOGY 491
nature; and the conjunction of attributes which our instances
present is taken as evidence of a connexion. The arguments are
weak, because the evidence for the connexion is insufficient. If
a b c d, instances of the class xy present the property y, it does not
follow that y is connected with those features on account of which
they are classed together as x. Yet a large number of instances
furnishes some presumption. For some reason must exist, why all
these instances exhibit the same property. If it is not in virtue of
their common character xy it must be in virtue of some other
common feature. When the variety of circumstances is great, under
which the instances are found, and the differences many which they
present along with their identity as #, it is harder to find any other
common features than what are included in classing them as x.
Therefore our confidence in the generalization increases, although
it may still be misplaced. All men are mortal ; for if men need not
die except through the accident of circumstances that are not
involved in being man, is it not strange that no man has avoided
falling in with these circumstances ? There is force in the question.
The number and variety of our observations on the point are such,
that almost everything can be eliminated : almost everything that
has befallen a man, except what is involved in being man, has also
not befallen other men : who therefore ought not to have died, if it
were because of it that men die. Something involved in being
man must therefore surely be the cause of dying.
Induction by Simple Enumeration rests then on an implied
elimination ; but the elimination is half -unconscious, and mostly
incomplete; and therefore the conclusion is of very problematic
value. But where it is felt that the instances do serve to eliminate
a great deal, it is felt that the openings for error are correspondingly
reduced in number, and the conclusion is received with greater con
fidence. General considerations of this kind, however, will not
stand against definite opposing facts ; therefore such an empirical
generalization is at once overthrown by a contradictory instance.1
Neither will they overbear more special considerations drawn from
acquaintance with the subject-matter to which the induction be
longs. Pigmentation is known to be a highly variable property in
many species ; therefore the overwhelming range of instances to
show that all crows are black was felt to be insufficient to give
1 Instantia, eva-rao-is, meant originally a contradictory instance.
492 AN INTRODUCTION TO LOGIC [CHAP.
the conclusion any high degree of value. Again, a difficulty in
conceiving how two properties could be causally connected will
incline us to attach less weight to the fact of their conjunction.
And contrariwise, where the connexion to which the conjunction
points is one which seems conformable with other parts of our
knowledge, we are much more ready to generalize from the con
junction. Many general statements are made about the correlation
of attributes in plants and animals, which rest on simple enumera
tion; but the theory of descent suggests an explanation of the
constancy of such a conjunction; for what was correlated in a
common ancestor might well be correlated universally in the
descendants. We are therefore readier to suppose that attributes
found several times accompanying one another in a species (such
as deafness with white fur and blue eyes in tom-cats, or black
colour with immunity to the evil effects of eating the paint-root in
pigs l) are correlated universally, even though we can see no direct
connexion between them, than we should be if no way of explaining
the constancy of the conjunction presented itself to us.
The argument from Analogy (at least in the usual sense of the
term) is of the same inconclusive character as Induction by Simple
Enumeration ; and like it, rests on the general belief in universal
connexions, and takes a conjunction of attributes as evidence of
their connexion.
Analogy meant originally identity of relation. Four terms,
when the first stands to the second as the third stands to fourth,
were said to be analogous. If the relation is really the same in
either case, then what follows from the relation in one case follows
from it in the other ; provided that it really follows from the
relation and from nothing else. Where the terms are quantities,
or are considered purely on their quantitative side, and the relations
between them are also quantitative, there the reasoning is of course
mathematical in character : analogy in mathematics being more
commonly called proportion. And such reasoning is necessary,
like any other mathematical reasoning. If in respect of weight
a : b : : c : d, and if a weighs twice as much as b, then c must weigh
twice as much as d. So soon however as we connect with the rela
tion c : d, on the ground of its identity with the relation a : b, a
consequence which is not known to depend entirely on that relation,
1 v. Darwin, Origin of Species, c. i, 6th ed. p. 9.
xxiv] SIMPLE ENUMERATION AND ANALOGY 493
our reasoning- ceases to be demonstrative. Suppose that the dis
tance by rail from London to Bristol bears the same relation to the
distance from London to Plymouth as the distance from London to
Darlington bears to the distance from London to Aberdeen : and
that it costs half as much again to send a ton of timber from
London to Plymouth as to Bristol ; we cannot infer that the rate
from London to Aberdeen will be half as much again as it is to
Darlington ; for the rate need not depend entirely on the relative
distance, which is all that is alleged to be the same in the two cases.
There are many relations however which are not relations of
quantity, and hold between terms on other grounds. Here too,
four terms may stand in an analogy : and what follows from the
relation of the first to the second may be inferred to follow from
the relation of the third to the fourth. It might be said that the
relation of his patients to a doctor is the same as that of his
customers to a tradesman, and that therefore as a customer is at
liberty to deal at once with rival tradesmen, so a man may put
himself at once in the hands of several doctors. And if the relations
were the same, the argument would be valid, and indeed in principle
syllogistic ; for the common relation would be a middle term con
necting a certain attribute with a man's position towards his doctor.
' Those who employ the services of others for pay are at liberty to
employ as many in one service as they pay for ' : such might be the
general principle elicited from our practice in shopping, and pro
posed for application to our practice in the care of our health. The
case of patient and doctor is ' subsumed ' under the principle
supposed to be exhibited in the case of customer and tradesman.
Even however if it were not possible to disentangle a general prin
ciple, and reason syllogistically from it, we might use the analogy ;
thinking that there was an identity of relations, and that what is
involved in the relation in the one case must be involved in it in the
other.
Unfortunately however the identity of the relations may be
doubted. Relations are not independent of their terms. Quantitative
relations are no doubt independent of everything except the quanti
tative aspect of their terms, and are on that account usually stated
as between quantities in the abstract. But with other relations it
may be very difficult to abstract, from the concrete nature of the
terms between which they hold, the precise features which involve
494 AN INTRODUCTION TO LOGIC [CHAP.
the relation. Hence we may say that two relations are similar, and
yet doubt whether they are similar in the way that would justify the
inference. They may be partially the same, but the difference may
just invalidate the consequence l ; and reasoning by analogy cannot
then possess the character of necessity.
David Hume held that virtue and vice are not attributes of any
act or agent, but only feelings which an act may arouse in a
spectator ; so that if nobody approved or disapproved my actions,
they could not be called either virtuous or vicious. And one of the
arguments by which he endeavoured to sustain this opinion was as
follows. A parricide, he said, is in the same relation to his father
as is to the parent tree a young oak, which, springing from an acorn
dropped by the parent, grows up and overturns it ; we may search
as we like, but we shall find no vice in this event ; therefore there
can be none in the other, where the relations involved are just the
same ; so that it is not until we look beyond the event to the feel
ings with which other persons regard it, that we can find the
ground for calling it vicious.2 Doubtless there is an analogy here ;
but the relations are not altogether the same ; for the relation of
a parent to a child is spiritual as well as physical, and in the
parricide there is an attitude of the will and the affections which
cannot be ascribed to the oak.
Many arguments from Analogy, in the sense of this loose identity
of relations, have become famous ; and they are a favourite portion
of the orator's resources. How often have not the duties of a colony
to the mother-country been deduced from those which a child owes
to a parent ; the very name of mother-country embodies the ana
logy. Yet it is by no means easy to find the terms which stand
in the same relation. The soil of Britain did not bear the soil of
Australia ; and the present population of Australia are not the de
scendants of the present population of Britain, but of their ancestors.
To whom then does the Commonwealth owe this filial regard, and
why? Doubtless the sentiment has value, and therefore some
justification ; but this argument from analogy will not quite give
account of it. Alexis de Tocqueville again said of colonies, that
they were like fruit which drops off from the tree when it is ripe.
1 Cf. infra, pp. 547-549.
2 Treatise of Human Nature : Of Morals. Part I. § 1. Green and Grose's
ed. vol. ii. p. 243.
xxiv] SIMPLE ENUMERATION AND ANALOGY 495
Here is another analogy, and two of the terms are the same as
in the last. The relation of a colony to the mother-country sug
gests different comparisons to different minds, and very different
consequences : which cannot all of them follow from it. We may
take another instance, where the relations are really closer, and the
argument therefore of more value. To grant that Natural Selection
may be able to do all that is claimed for it, and yet object to it on
the ground that the facts which are accounted for by it may equally
well be ascribed to intelligent design, is, it has been urged, as if
a man were to admit that the Newtonian theory of the solar
system works, and yet were to continue to suppose with Kepler
that each planet is guided on its way by a presiding angel ; if the
latter therefore be irrational, so must the former be.1 Or consider
the following passage 2 : — ' It has been objected to hedonistic sys
tems that pleasure is a mere abstraction, that no one could experi
ence pleasure as such, but only this or that species of pleasure, and
that therefore pleasure is an impossible criterion ' [i. e. it is impossible
to judge what is good by the amount of pleasure which it affords].
'It is true that we experience only particular pleasurable states
which are partially heterogeneous with one another. But this is
no reason why we should be unable to classify them by the amount
of a particular abstract element which is in all of them. No ship
contains abstract wealth as a cargo. Some have tea, some have
butter, some have machinery. But we are quite justified in
arranging those ships, should we find it convenient, in an order
determined by the extent to which their concrete cargoes possess
the abstract attribute of being exchangeable for a number of
sovereigns/ The force of this argument will depend on whether
the particular concrete pleasurable states do stand to the abstract
element of pleasure in the same relation as the concrete cargoes
of ships stand to the abstract element of wealth. Doubtless the
relations are partly the same, for each abstract element is an attri
bute of its concrete subjects. But these are measurable in terms of
their attribute, by the fact of being exchangeable for a definite
number of sovereigns ; and the question is whether there is any
thing that renders the others similarly measurable in terms of
1 Romanes, Darwin and after Darwin, i. 279.
2 McTaggart, Studies in Hegelian Cosmology, § 113.
496 AN INTRODUCTION TO LOGIC [CHAP.
pleasure. On the value of this argument doctors will probably dis
agree : send this again shows how arguments from analogy are
inconclusive.
There is however another sense in which the terms analogy and
argument from analogy are used. The analogy may be any re
semblance between two things, and not merely a resemblance of
the relations in which they respectively stand to two other things ;
and the argument from analogy an argument from some degree of
resemblance to a further resemblance, not an argument from the
consequences of a relation in one case to its consequences in another.
Expressed symbolically the argument hitherto was of the following
type : a is related to b as c is to d • from the relation of a to b such
and such a consequence follows, therefore it follows also from the
relation of c to d. The present argument will run thus : a re
sembles b in certain respects x ; a exhibits the character yy therefore
b will exhibit the character y also. Argument of this type is
exceedingly common.1 ' Just as the flint and bone weapons of rude
races resemble each other much more than they resemble the metal
weapons and the artillery of advanced peoples, so/ says Mr. Andrew
Lang, fthe mental products, the fairy tales, and myths of rude
races have everywhere a strong family resemblance/ 2 It is inferred
here that mental products, which resemble certain material products
in being the work of rude races, will resemble them in the further
point of exhibiting the strong family likeness that is known to
characterize the latter. Or take this instance from Sir Henry
Maine. He is discussing the various devices by which in different
systems of law the lack of a son to perform for a man the funeral
rites can be supplied. We are familiar with adoption. But
adoption in England does not carry the legal consequences of
legitimate sonship. The Hindu codes recognize adoption and
various expedients besides; and the son so obtained has the full
status of a real son, can perform satisfactorily the important cere
monies of the funeral rites, and succeed to property as the real son
would succeed. One of their expedients is known as the Niyoga,
a custom of which the Levirate marriage of the Jews is a particular
case. The widow, or even the wife, of a childless man might bear
1 It was called by Aristotle TrapaSery/ua : cf. Anal. Pri. /3. xxiv, Ehet. a. ii.
1357b 25-36, and p. 501, infra.
2 Custom and Myth, p. 125, ed. 1901 (' The Silver Library').
xxiv] SIMPLE ENUMERATION AND ANALOGY 497
a son to him by some other man of the family, and the son became
his son, and not the natural father's. How did Hindu thought rest
content in so fictitious a relation ? ' All ancient opinion/ says
Maine 1, ' religious or legal, is strongly influenced by analogies,
and the child born through the Niyoga is very like a real son.
Like a real son, he is born of the wife or the widow ; and though
he has not in him the blood of the husband, he has in him the
blood of the husband's race. The blood of the individual cannot
be continued, but the blood of the household flows on. It seems to
me very natural for an ancient authority on customary law to hold
that under such circumstances the family was properly continued,
and for a priest or sacerdotal lawyer to suppose that the funeral
rites would be performed by the son of the widow or of the wife
with a reasonable prospect of ensuring their object/ We may turn
to the exacter sciences, and find this sort of argument from analogy
employed. Before it was known that light travelled in waves, it
was known that sound did so. Light and sound were both capable
of being reflected, and the direction of their reflection obeyed the
same law, that the angle of reflection is equal to the angle of inci
dence. From these facts it was inferred by analogy that light,
like sound, travelled in waves : as was afterwards shown to be the
case. Among the properties of gold was long enumerated fixity,
i. e. that it was incapable of volatilization. As one element after
another was successfully volatilized, it might have been inferred by
analogy that gold could be volatilized too.
We may now compare this with the former type of argument
from analogy ; and afterwards consider their logical value, and
their relation to induction by simple enumeration.
Since analogy properly involves four terms, the latter and looser
but commoner sense of the expression argument from analogy seems
at first sight difficult to account for. Why should a resemblance
which is not a resemblance of relations be called an analogy at all ?
Perhaps the answer is that where the relation is no longer a quanti
tative one, it is apt to be regarded as a property of the subject that
stands in the relation. The quantitative relation of one thing to
another does not affect the intrinsic character of the thing ; but
other relations do. We should not regard it as constituting a
resemblance between a child and a young elephant that one weighed
1 Early Law and Custom, p. 107.
JOSEPH K. k
498 AN INTRODUCTION TO LOGIC [CHAP.
half a hundredweight, and the other half a ton ; but that they both
had mothers (though that is also a resemblance of relations) would
seem to constitute a resemblance. Such a relation rests on and
involves important characters in the thing related of a less purely
relational character than quantitative predicates are. And in this
way the term analogy may well have come to be extended to
resemblances generally, even where the resemblance is not a re
semblance of relations.1
Even in the stricter sense then, the argument from analogy does
not commonly mean the mathematical argument from an identity of
ratio : the relations are only similar, and must be conceived to
involve intrinsic attributes of the things related.2 In considering
the value of the argument therefore we may for the future ignore
the distinction pointed out between the two types of inference to
which the name is given, and may take the second (to which the
first tends to approximate) as fundamental. The argument from
analogy is an argument from a certain degree of ascertained re
semblance between one thing and another (or others) to a further
resemblance ; because a and b are x, and a is y, .-. b is y. What is
the logical value of this argument ?
It is plainly not proof. As Lotze has pointed out 3, there is no
proof by analogy. Many conclusions drawn in this way are after
wards verified; many are found to be false. Arguments from
analogy can often be found pointing to opposite conclusions.
1 I give in a note another possible explanation of the change that has
taken place in the logical use of the term analogy, but one that seems to me
less likely than the foregoing. The ' rule of three ' is in a sense an argument
from analogy. Starting with the conception of an analogy, in the strict
sense, it supplies from three given terms the fourth term which will complete
the analogy. It is therefore an argument from the general conception or
form of analogy to the actual analogy (or complete terms of the analogy)
in a particular case. Now when I argue that because a and b both exhibit
the property x, and a exhibits besides the property y, therefore b will also
exhibit the property y, I may be said to be completing an analogy. The
presence of # in a is to the presence of y in a, as is the presence of x in b to
that of y in b. In this case, the argument would be from the existence of
an analogy to the fourth term of it. But if the looser usage of the term be
interpreted thus, it bears less resemblance to the earlier usage than upon
the interpretation in the text.
2 Metaphysical criticism could easily raise difficulties against the view
that relations as such are extrinsic and attributes intrinsic to their subject.
But we are concerned here rather with a common way of regarding the
matter than with its ultimate tenability ; and I think we do commonly so
regard it.
8 Logic, § 2H.
xxiv] SIMPLE ENUMERATION AND ANALOGY 499
The Parmenides of Plato, a dialogue of his later period, discusses
various difficulties with regard to the relation between the universal
and the particular, which many scholars consider to be criticisms
upon his own ' doctrine of ideas ' as presented in his earlier writings.
One of these is identical with an objection afterwards frequently
urged by Aristotle against the Platonic doctrine as he understood
it.1 It has been suggested that the dialogue incorporates criticisms
which Aristotle had originated as a young man of about 17, when
a pupil in the Academy. Are the points Plato's own, or are they
borrowed from his pupil ? On the one hand it may be said that
when he wrote the Parmenides Plato was too old to revise his system,
as this interpretation of the dialogue conceives that he was doing ;
on the other, that at 17 Aristotle was too young to develop
criticisms so original and profound.
But Kant's chief works, embodying the system which has made
him famous, were written after he was 50; and Berkeley at the
age of 20 was entering in his Commonplace-book important and
original criticisms of Locke.2 One analogy supports the attribution
to Plato, the other that to Aristotle.
If it is not proof, has argument from analogy any value ? Can we
give any rules by which to judge its value in a given case ? Here we
must remember that the argument rests altogether on a belief that
the conjunction we observe discovers to us a connexion ; the presence
of both x and y in the subject a points to such a connexion between
them as will justify our inferring from x to y in the subject b. If
we definitely thought that x and y were irrelevant to one another,
it would be foolish to expect b to exhibit one because it exhibited
the other. But though the argument thus presumes a connexion
between x and y, it makes no pretence of showing that y depends
on x rather than on some other property z in a, not shared with
a by b. There is no elimination. If however there were any
implicit, though not formal, elimination : or again, if there were
anything known to us which seemed to support the hypothesis of
a connexion between x and y : we should attach more weight to the
argument. Hence if the ascertained resemblance between a and b
1 It is true that the argument is already found in shorter form in the
tenth book of the Republic ; Rep. x. 597 C, Farm. 132 D-133 A.
2 Cf. D. G. Ritchie, Plato, pp. 108, 120. I have not reproduced the exact
use which he makes of the analogies.
K k 2,
500 AN INTRODUCTION TO LOGIC [CHAP.
is very great, we may think the argument from analogy stronger.
For there must be something in a to account for the presence of x ;
and if y is not connected with x, we must look for that something
in the remaining nature of a ; but the more we include in x (the
ascertained resemblance), the less there is that falls outside it, and
the fewer therefore the alternatives open to us, to account for the
presence of y in a. Still it must be admitted that so long as we
rely merely on this sort of consideration, it remains to the end as
possible as not that y is unconnected with x, and therefore that y
will not be found in b. Of much more weight is the consideration,
that the connexion between x and y implied in the argument is one
for which our previous knowledge prepares us. The fact that the
angle of reflection is equal to the angle of incidence might well be
supposed due (as indeed it is) to the propagation of sound in waves ;
and if so, we should expect the same fact in the case of light to be
produced by the same cause.
It will be seen that the considerations which must influence us in
determining what weight we are to attach to an argument from
analogy are the same as those by which we must estimate the
value of an induction by simple enumeration. Both point to
a general principle, which if it were true would account for the
facts from which we infer it ; neither proves its truth ; and to try
to prove it must be our next business. Mill rightly says that,
however strong an analogy may be, any competent enquirer will
consider it * as a mere guide-post, pointing out the direction in
which more rigorous investigations should be prosecuted \ And
the same might be said of an empirical generalization. The next
sentences from the same passage of MilFs Logic may well be quoted :
' It is in this last respect that considerations of analogy have the
highest scientific value. The cases in which analogical evidence
affords in itself any very high degree of probability are, as we have
observed, only those in which the resemblance is very close and
extensive ; but there is no analogy, however faint, which may not
be of the utmost value in suggesting experiments or observations
that may lead to more positive conclusions/ 1
How then does argument from analogy differ from induction by
simple enumeration ? In the latter, because a number of instances
of a class x exhibit the attribute y, we infer that all x are y ;
1 III. xx. 3 med.
xxiv] SIMPLE ENUMERATION AND ANALOGY 501
in the former, because two particulars a and b agree in certain
respects #, we infer that y, which is exhibited by a, will be exhibited
by b also. In the latter, from the limited extension of an
attribute over a class, we infer to its extension over the whole class ;
in the former, from a partial agreement between two individuals in
intension, we infer to a further agreement in intension. But the
one passes gradually into the other ; for the former may be called
the application to a particular case of a general principle inferred
in the latter from a larger number of instances than in the former.
This is very plain in an illustration which Aristotle gives of the
' Example' (his name for the argument from analogy). A man
might have inferred that Dionysius of Syracuse designed to make
himself tyrant, when he asked the people for a bodyguard ; for
Pisistratus at Athens asked for a bodyguard, and made himself
tyrant when he got it ; and likewise Theagenes at Meg*ara. Both
these fall under the same general principle, that a man who aims
at a tyranny asks for a bodyguard.1 One of the instances of
argument from analogy given above concerned the volatilization of
gold ; and it might perfectly well be said that it would be contrary
to all analogy for gold to be incapable of a gaseous form. But we
might equally well say that our experience of other elements
warranted the empirical generalization that they could all be
volatilized, and therefore gold must be capable of it. This affinity
between the two processes of inference is however often concealed
by the fact that the points of resemblance in two (or more) subjects,
which form the basis of an inference to a further resemblance, have
not given rise to any special denomination ; there is no general
name by which the subjects can be called on the strength of the
resemblance, and the resemblance may even be one that we recognize
but cannot precisely describe. In the case of gold, we might pick
out the fact of its being an element, as justifying the expectation
that it can be volatilized. In the case of Dionysius, his asking for
a bodyguard is the circumstance that classes him with Pisistratus
and Theagenes, and excites our fear that he aims at a tyranny. But
a weather wise man might be unable to describe what it is in the
appearance of the sky that makes him fear a great storm, though
1 Rhet. a. ii. 1357b 25-36. To make the inference to Dionysius necessary
(it is of course Dionysius I who is meant), the principle would have to be,
that a man who asks for a bodyguard aims at a tyranny ; and that is really
what the suspicious citizen of Syracuse would have had in his mind.
502 AN INTRODUCTION TO LOGIC
lie can say that it was on just such a night as this that some other
storm broke out. The general proposition (the induction as some
would call it), which mediates his inference from that past occasion
to the present, cannot be formulated ; and so he may appear to work
without it, and the affinity between such a process and induction
by simple enumeration may be unobserved. Yet it exists, and, as
has been said, the one process passes imperceptibly into the other,
as the number of instances increases from which the conclusion is
inferred ; though where we cannot formulate a general principle,
we should certainly speak of the argument rather as one from
analogy.
It is of some importance to realize that a general principle is
always involved in such an argument, because it has been contended
that all inference goes really from particulars to particulars.1
There may be psychological processes in which a man's mind passes
direct from a to b, and he predicates of the latter what he was
predicating of the former, without grounding it on anything
recognized to belong to them in common; just as a man who
passes a letter-box in the wall may look round at it to see the
time. Psychologists explain such actions as due to the ' Association
of Ideas'. But this has nothing logical about it, and is not inference.
Any one must admit when questioned, that unless he supposed b to
share with a the conditions on which the presence of y depends, he
could not rationally infer it in b because he found it in a ; and a
process which cannot rationally be performed can hardly be called
a process of reasoning. But that supposition is the supposition
of a general connexion ; and therefore inference from particular to
particular works through an implicit universal principle.
1 Mill, Logic, II. iii. 3, and supra, c. xiv, pp. 278-287 : cf. also Bradley's
criticism, Logic, Bk. II. Pt. ii. c. ii.
CHAPTER XXV
OF MATHEMATICAL REASONING
MATHEMATICS is frequently and rightly called a deductive science.
Yet it has been said to rest on generalizations from experience, and
for this reason to be fundamentally inductive. There are also
certain particular processes of reasoning in mathematics to which
the name inductive is more particularly given.
One of these is just induction by complete enumeration, which
does occur sometimes in mathematics. A proposition may be proved
independently of a right-angled, an obtuse-angled, and an acute-
angled triangle, and therefore enunciated of the triangle universally :
or of the hyperbola, the parabola, and the ellipse, and therefore
enunciated of all conic sections. The formula for the expansion
of a binomial series is proved separately to hold good when the
exponent is a positive integer, negative, and fractional ; and only
therefore asserted to hold good universally. The peculiar nature of
our subject-matter in mathematics enables us to see in each case
that no other alternatives are possible within the genus than those
which we have considered ; and therefore we can be sure that our
induction is 'perfect'. The nature of our subject-matter further
assures us, that it can be by no accident that every species of the
genus exhibits the same property; and therefore our conclusion
is a genuinely universal judgement about the genus, and not
a mere enumerative judgement about its species. We are sure
that a general ground exists, although we have not found the proof
by it. This kind of mathematical induction needs no further
consideration.
The case is different where some proposition is inferred to hold
good universally because it is proved to hold good in one or
two instances. This sort of inference occurs in geometry,
when we prove something about a particular square, or circle, or
triangle, and conclude that it is true of the square, the circle,
or the triangle; and again in algebra, when a formula for the
504 AN INTRODUCTION TO LOGIC [CHAP.
summation or expansion of a series, and such-like, being1 shown
to hold good for certain values of xt is inferred to hold good for
any value. The former kind of procedure is too familiar to need
illustration; of the latter, the simplest illustration is the proof
of the formula for the sum of the first n odd numbers — i.e. of
the odd numbers, beginning with 1, and taken continuously up
to any term that may be chosen. The sum is always n2 • and this
is shown as follows. It is found by addition that the sum of the
first three, four, or five odd numbers is 32, 42, or 52; and then
proved that if the sum of the first n — 1 odd numbers = n— I2,
then the sum of the first n odd numbers must = n2. For the n~ 1th
odd number is 2n—3. Let
Add to each side 2n— 1 (which is the next or nih odd number)
+ 5
If the formula holds for n — 1 places therefore, it holds for n places :
that is, it may always be inferred to hold for one place more than
it has been already shown to hold for. But it was found by
addition to hold (say) for 5 places; therefore it holds for 6;
therefore again for 7, and so on ad infinitum; and therefore
universally.
It is instructive to compare this reasoning with the induction
of the inductive sciences. In one respect it presents the same
problem, viz. What is our warrant for generalization? Yet it
cannot be said that the reasoning is of the same kind.
We saw that in the inductive sciences all generalization rested
on the existence of universal connexions — whether we express that
as the Law of Causation, or the Uniformity of Nature, or in some
other manner. But the particular problem of any inductive enquiry
was to determine what were the conditions with which a deter
minate phenomenon x was connected universally ; and that was
only to be done by an exhaustive process of showing with what,
upon the evidence of the facts, it was not connected universally,
until there was only one alternative left unrejected, which we
were therefore bound to accept. Now it is by no such process of
elimination as this, that we demonstrate the properties of a figure,
or the sum, for any number of terms, of a series. We do not
conclude that the angles of a triangle are equal to two right angles,
xxv] OF MATHEMATICAL REASONING 505
because we have tried and found that there is nothing else to
which they can be equal ; but we see, by means of drawing- a line
through the apex parallel to the base J, that the nature of space
necessarily involves that equality. The geometrician sometimes
appeals to the conclusion of a previous demonstration, without
realizing to himself the reasons for the necessity of that conclusion ;
thus, for example, in proving that the angle in a semicircle is
a right angle, he appeals to the fact that the
three angles of the triangle in which it is
contained are equal to two right angles, and
to the fact that the angles at the base of an
isosceles triangle are equal to one another,
and shows now only that the angle in the
semicircle must therefore necessarily be equal to the other two
angles in the triangle in which it is contained. So far as he thus
appeals to the conclusion of a previous demonstration, and applies
it to the figure before him, he syllogizes; but when he realizes
the necessity of that conclusion, he does not syllogize, but sees
immediately that it is involved in the truth of other space-rela
tions ; and this he finds out by help of drawing the figure. It is
felt that a reductio ad absurdum is a defective proof in geometry
just because we should be able to show that such and such a
proposition is true by direct reference to the conditions which
necessitate it, and not indirectly by the refutation of the con
tradictory. Thus the reasoning proceeds directly from condi
tions to their consequences 2, not as in induction from facts to the
only principles with which they cannot be shown to be incom
patible. And it proceeds by means of our insight (when we
experiment in drawing lines) into the necessary implication of
one fact with another in the system of space-relations. For the
first reason it is deductive ; for the second, its premisses are proper
premisses, Ibicu apyai— geometrical truths which explain other
geometrical truths. It is the same with any process of calculation
1 Or, from the intersection of one side with the base, a line parallel to
the other side.
2 It is true that in mathematics different truths about the system of
spatial or quantitative relations mutually condition one another ; and there
fore the order of demonstration is often indifferent, and condition and
consequence may change places. Still the reasoning is deductive, since our
premisses display to us the rational necessity of the conclusion, and do not
leave it resting on a mere necessity of inference : cf. p. 401, n. 1, supra.
506 AN INTRODUCTION TO LOGIC [CHAP.
in arithmetic or algebra. There too we argue deductively; and
there too our premisses are proper premisses, truths about relations
of quantity which render necessary other relations of quantity.
Nor is there any special difficulty about the f mathematical induc
tion y employed in proving the formula for the summation or
expansion of a series, &c. When we prove that a formula which
holds for n — 1 terms holds for n terms, n represents any number
in just the same way as the circle on a blackboard represents any
circle. Geometrical proofs rest on the intuition of spatial relations,
and algebraic on the intuition of quantitative relations, and so far
the two sciences differ. But that is not more surprising than the
fact that moral philosophy, in which our proofs rest on insight
into relations neither of quantity nor space, differs both from
geometry and from algebra.
Yet we may return to the question, What warrant have we for
generalizing? We must grant that the reasoning by which I
prove that the angle in this semicircle ABC is a right angle, or
that a formula which holds for the sum of the first n — \ odd
numbers holds for the sum of the first n odd numbers, is different
from that by which I prove connexions of cause and effect in the
inductive sciences. Yet why do I conclude that the angle in any
semicircle is a right angle, or that the formula for the sum of the
odd numbers, which holds up to the term next to the n — 1th, holds
up to any next term, when I have only proved it about this semi
circle, and the series up to the next to the n — 1th odd number?
Probably most people's natural impulse would be rather to
express surprise at the question than any sense of difficulty in the
matter. What difference can it make, they would ask, what circle
is taken ? What difference can it make that in proving that what
holds for so many places of odd numbers holds for one place more,
the place you take is represented by n — 1 ? Such counter-questions
would be a very proper rejoinder. But it may be useful to see
what principles they rest on, firmly grasped but perhaps not
consciously formulated.
These principles are, the uniform construction of space, and the
uniform construction of the numerical series. It is because space
relations are unaffected by locality that what I have seen to be
a property of this circle must be a property of any circle ; because
the difference between one odd number and the next is the same
xxv] OF MATHEMATICAL REASONING 507
at every point of the numerical series, that an inference seen to
hold from the n — 1th to the nih place holds for any value of n. If
it were otherwise, I should have to try spaces as I sample cheeses,
with no more reason to believe that a property which I had
demonstrated of the circle on my blackboard would characterize
a circle on the page of this book, than there is to believe that
a flavour found in a cheese bought at Bridgwater will characterize
a cheese bought at Waterford. So also I should have to try
different regions of the numerical series.
But sampling is not altogether an appropriate metaphor; for
when I sample a cheese, I generalize about the whole cheese from
the piece which I taste ; but here I should be unable to perform
any generalization. I should examine a circle, or the odd numbers
up to 157, to know whether that circle has a right angle sub
tended at its circumference by the diameter, or whether the sum
of that series of numbers was 1572. I should not however be able
to take that circle as typical of other circles, nor that series of
numbers as typical of other series. For I could have no more
reason to transfer my demonstration to a second circle, or a series
one place further, than to all circles, and series up to every place.
In fact our belief in the uniformity of space, and in the uniform
formation of the numerical series, stands to mathematical reasoning
as our belief in the uniformity of nature stands to inductive.
Deny them, and in either case no general proposition remains
possible any longer. Nay more ; no demonstration remains possible
even about a particular case. As we could not even prove that
the death of Cleopatra was caused by the poison of an asp, without
assuming that it depended on a cause with which such a kind of
death is connected universally, but could only say that she died
after an asp had bitten her ; so we could not prove that the angle
in any given semicircle was a right angle, but only say that this
semicircle contained a square-looking angle. We rely throughout
on universal connexions between qualitatively identical elements.
An asp, if it is of the same nature, and bites with the same
vehemence a person of the same constitution, must always produce
in him the same effect. And a circle, if it is the same figure,
must have always the same property ; else we cannot even in
a single case assign a definite result to a definite cause, or a definite
property to a definite subject.
503 AN INTRODUCTION TO LOGIC [CHAP.
If there is any difficulty in seeing the parallelism, it arises from
the fact that a circle seems obviously the same figure always.
Circles differ in size and curvature; and triangles have more
differences than circles. But we can easily consider the form of
a circle, in abstraction from its size; or the bare triangularity
of a triangle, in abstraction from the proportions of its sides or
its angles. And when we have in our demonstration proved that
some property follows upon the mere form of a circle, and the
mere three-sided rectilinearity of a triangle, without taking any
thing else about either figure into account, we then know that it
must be true of all circles, or all triangles. In the inductive
sciences our difficulty lies in determining on what conditions,
amidst the complexity of the concrete case before us, a particular
result depends, and what precisely the result is. It is a difficulty
very largely of analysis. No one who had proved that x depended
precisely on a in the case before him would hesitate to generalize
any more than does a geometrician. Indeed he would feel that he
was working with general terms all the time, and proving an universal
connexion rather than a particular one. But so long as his x and a
are not clear-cut and stripped of all irrelevant matter, he cannot
trust a generalization. In mathematics our terms are defined and
precise from the outset l ; our proof shows exactly on what con
ditions a consequence depends ; and we can recognize those condi
tions elsewhere wherever they occur.
We may sum up this part of our discussion as follows. Mathe
matical reasoning postulates in space and in number a system
exhibiting throughout fixed universal principles, as inductive
reasoning postulates it in the course of nature. On that rests the
generality of any conclusion in either case. But the nature of
the reasoning by which mathematics connects spatial or quantitative
conditions with their consequences is quite different from that by
which the physical sciences, so far as they are inductive, connect
physical condition and consequence. The former works by direct
insight into the special nature of its doubtless highly abstract
1 Speaking generally: but of course we may sometimes fail at first to
discover the truly commensurate subject of a predicate ; as if one were to
prove that the external angles of a square were equal to four right angles,
when it is true for any rectilinear figure. Here the number of sides, and
the magnitude of the internal angles, would be falsely included among the
conditions on which the property depends.
xxv] OF MATHEMATICAL REASONING 509
subject-matter ; the latter has no such insight, but looks for terms
that, in face of the facts, will alone satisfy the general conditions of
a causal connexion. In the former, generalization is unnoticecFbecause
it is all-pervading ; for the relevant conditions are distinguished from
the first. In the latter, generalization comes at the end, and attracts
attention as the result of a long effort; for all our task is to
distinguish the relevant from the irrelevant conditions.
There remains one question, which was referred to at the outset
of the chapter. The principles of mathematics have been alleged
to be generalizations from experience, and the science on that account
at bottom inductive.1 It is indeed difficult to see why the same
should not as well be said of the inferences in mathematics.2 Their
demonstrative force arises from the fact that the nature of space or
quantity allows us to see immediately the consequences involved in
certain conditions. But any one who requires repeated experience
to convince him of the truth of a geometrical principle (such as that
two straight lines cannot enclose a space) may just as well require
repeated experience to convince him of the truth of a geometrical
deduction ; we have to do with the mutual implication of spatial
conditions in both cases. And so it is also in the science of pure
quantity. The multiplication table up to 12 x 12 might be said to
contain principles, and the multiplication of 266 x 566 to apply
them ; but whatever reason there is to doubt that 6x6 = 36, there
will be the same reason to doubt whether it follows that 60 x 60 =
3600. However, it will be sufficient if we confine ourselves to the
consideration of the alleged inductive character of the process by
which we ascertain mathematical principles, without attempting to
determine how much would have to be regarded as principles, and
how much as valid consequence.
What is really meant by the allegation is, that whereas every
mathematical principle, such as the axiom of parallels, or 2 + 2 = 4,
is universal, our reason for accepting it as universally true lies in
the fact that we have always found it to hold good in experience.
Two apples and two apples make four apples ; it is the same with cows
or sovereigns, window-panes or waterpots. And whenever we have
seen a straight line falling on two other straight lines and making
the alternate opposite angles measurably equal, we have found — if
1 Mill, Logic, II. v-vii. Cf. Autobiography, p. 226.
a Or for that matter, of any form of inference.
510 AN INTRODUCTION TO LOGIC [CHAP.
we have tried — that however far we produced the two other straight
lines, so long as they continued apparently straight, they remained
at the same measurable distance from one another. All experience
confirms these principles, and none is contrary to them ; so we
accept them as empirical generalizations, possessing, on account of
the extent and variety of the circumstances under which they have
been found to hold good, the same degree of certainty as if they
had been proved by a rigorous elimination of all other hypotheses.
It is really sufficient answer to this view, to recur to what was
said upon a similar attempt to treat the Law of Causation as
empirically established. If the Law of Causation is true, the facts
of our experience help us to determine what are the particular
causal connexions in nature ; if we start by doubting it, the facts
will never bring us any nearer the proof of it. Similarly, if we start
by doubting whether spatial or numerical relations are constant, the
facts will never begin to prove it. Grant that the sum of 2 + 2 is
always the same, and it is worth while to see what it is ; and whatever
countable things we take to reckon with will make no difference.
But question whether it is always the same, and proof that it is so
becomes impossible. For you have no ground for supposing that
if 2 + 2 could sometimes make 5, cases of its occurrence would have
occurred in your experience. Everything becomes problematical; the
frequency of any particular sum of 2 + 2 is quite indeterminate, if
the sum is indeterminate ; and your experience may assure you that
you have never found them making anything else than 4, but
cannot assure you that you are never likely to do so. And so it is
with geometrical principles also. If geometrical relations are not
necessary and universal, we have nothing but a .conjunction of facts
empirically ascertained. In each place and time the conjunction
may be different ; there is no reason to suppose that what occurs
here and now conveys any instruction about the occurrences at
other times and places. If each place and time is loose and inde
pendent, the next may always contradict even the uniform results
of previous experience.
Other lines of refutation are also possible. It might be pointed
out that in point of fact we do not look for confirmation of our
principles to repeated experience; but we interpret experience in
the light of our principles. Two drops of quicksilver + two drops
of quicksilver will make one drop of quicksilver ; but we insist that
xxv] OF MATHEMATICAL REASONING 511
the four drops are there, in a new figure. The angles between the
end-lines and the side-lines of a tennis-court may seem each to be
a right angle, and the sides to be drawn straight ; but if we find
that one end-line is shorter than the other, we say that we know that
the angles cannot be true. It may be said that by this time our
principles are well established, and facts in apparent conflict with
them are therefore reinterpreted so as to be consistent with
them. But facts in apparent conflict must have been frequent
from the beginning. Again, it is hard to see what meaning can
really be attached to the statement that 2 + 2 might conceivably
make 5, or that lines making equal angles with a third straight
line might conceivably remain straight and yet converge ; for such
a thing cannot be represented to thought as possible.
It is of course true that in the application of mathematical
reasoning to what is concrete, our conclusions will only be true if
our premisses were so. If a wheel which I assume to be circular
is not circular, conclusions based on the assumption will prove false.
If I am wrong in my linear measurement of a floor, I shall be
wrong as to the number of square feet of floor-cloth required to
cover it. But that does not shake the certainty and universality
of mathematics ; indeed nothing else would consist therewith.
It is also true that without experience of counting numerable
objects, and of constructing figures in space, I should be unable to
apprehend or understand the truth of mathematical principles.
But this does not make their truth empirical, or my mode of ascer
taining it inductive. For these principles are seen to be intrin
sically necessary as soon as they are understood ; whereas inductive
conclusions are never seen to be intrinsically necessary, but only to
be unavoidable. Nor does further experience add anything to our
assurance, when we have once made the construction or the calcu
lation in which their truth becomes manifest to us ; whereas further
experience of the same conjunction amidst variation of circum
stance is precisely what does add to our assurance of the truth of
an empirical generalization l.
We must conclude that in mathematics there is (or at least should
be 2) no generalization from experience. To suppose mathematical
principles to be such generalizations is like supposing the Law of
Causation to be so. Their universality is the counterpart to the reign
1 Cf. p. 491, supra. 2 Cf. p. 490, supra.
512 AN INTRODUCTION TO LOGIC
of law in physical nature. But the deductive character of mathe
matical science is due to the nature of the subject-matter, and our
peculiar insight into the rational connexion of its parts. What is
implied in our possession of this insight is a metaphysical question
lying beyond our purview.
[The nature of mathematical certainty is a question of far-
reaching metaphysical importance ; and J. S. Mill, in his Auto
biography (loc. cit.), frankly acknowledges that the chief strength
of the opposition to the truth of the Empirical Philosophy had
always seemed to lie here. It was on this account that he sought
to show that mathematical principles in their turn were generaliza
tions from experience. He held the same with regard to logical
principles. It is logically important to see that there can be no
knowledge unless there are truths not empirical — i. e. not open
questions, for a decision on which we must go to the tribunal of
sense-perception or events. And no one will understand the struc
ture of knowledge, who does not see that mathematical principles
are truths of this kind. But it may be asked what their relation
is to logical principles. There are some who have represented
logic as at bottom a branch of mathematics; and others seem
inclined to suppose that mathematics can be reduced to formal
logic. A non-mathematician is not well fitted to discuss these
matters in print ; and the discussion belongs in any case to a more
advanced stage of logical science than this book pretends to attain.
But I ought perhaps to say that I do not understand how either
theory can be true.]
CHAPTER XXVI
OF THE METHODOLOGY OF THE SCIENCES
WE have seen that inferences cannot all be reduced to a small
number of fixed types. They are not all syllogistic, not even all
that are deductive. Their form is not altogether independent of
their matter. All inference, according- to Mr. F. H. Bradley, is a
construction and an intuition.1 The putting together of the pre
misses is the construction, but it is the terms which determine how it
can be effected. The perception of something new to us in the whole
which we have constructed is the intuition ; and if we do not see its
necessity, there is no help for us. But within the unity of this
definition, we may examine any particular type of inference which,
for its frequency or importance, seems to demand our special atten
tion. Syllogism is one of these types ; the disjunctive argu
ment as applied to establish causal connexion is another. The
relation of subject and predicate is one of the commonest which
our thought uses, and therefore inferences based on it are common.
The causal relation is not less important, and the type of inference
used in its establishment equally deserved our study.
We found that this type of inference rested on the conception
or definition of cause.2 We considered very generally what that
conception involved, and how we could satisfy ourselves that we
were right in bringing any particular facts under the conception.
We noticed some of the difficulties which the complexity of nature
places in our way; and some of the cautions which we must
constantly bear in mind in interpreting facts in accordance with the
conception. We found that general truths present themselves to
the mind at first in the form of conjecture or hypothesis, and that
1 Principles of Logic, p. 235. 'The process is a construction and the result
an intuition, while the union of both is logical demonstration.1
2 Not that all disjunctive argument involves that conception ; but only
disjunctive argument applied to the discovery of causes.
JOSEPH L 1
514 AN INTRODUCTION TO LOGIC [CHAP.
often there is no means of testing sucli hypothesis except by first
deducing — it may be by very elaborate reasonings — the conse
quences that should follow in specified circumstances if it were true
and if it were not. But all these matters were discussed and illus
trated in a very general way.
Now different enquiries have their own peculiar difficulties,
arising out of the nature of their subject-matter, and of the
problem which they set. And any rules for dealing with these
peculiar difficulties will constitute rules of method, instructing us how
to set about the task of singling out the laws or causal connexions
from amidst the particular tangle in which the facts are presented
in such science. The consideration of such rules, as distinct from
the use of them, is Methodology ; and so far as herein we consider
how certain general logical requirements are to be satisfied in a
particular case, it is sometimes called Applied Logic.1
To this subject belongs Mill's discussion of the proper method
of studying the moral or social sciences2. He points out how
methods of enquiry appropriate to certain chemical investigations
(to which he therefore gives the name of the Chemical Method)
are inapplicable in dealing with the sciences of human nature.
The chemist, unable in a great degree to predict from his know
ledge of the properties of elements the properties which will
belong to their compounds, has to proceed by experiment con
ducted with every precaution to secure a precise knowledge of the
conditions; and thus discovers the effect of a new condition or
ingredient upon a whole of a certain kind. But we cannot
experiment with society out of a merely speculative curiosity ; the
practical interests involved are too great ; and were that not so, the
thing is impossible. Our material is not under control ; it would
be most instructive to prevent the use of alcohol in England for
a generation, and watch the difference in the amount of pauperism
and crime; but there is no means of performing the experiment,
for to pass a law is not to enforce it. Nor can we ever know
precisely into what conditions we introduce the factor whose effects
we wish to study ; nor can we maintain those conditions unchanged in
all but what is due to the influence of that factor during the course of
1 Cf. Kant, Introduction to Logic, ii. 4(T. K. Abbott's tr., p. 8), who gives
a different sense to the term, but notices this use of it.
2 Logic, VI. vii-x.
xxvi] OF THE METHODOLOGY OF THE SCIENCES 515
our experiment. For these and other reasons, it is hopeless to expect
much light to be thrown upon the laws of social phenomena,
merely by watching what follows in different cases upon the
adoption of the same policy, or by comparing the results of
different policies. There are so many factors which modify one
another ; each effect depends on so many conditions, and each
condition by its presence or absence makes a difference to so many
effects by us regarded as distinct, that it is useless to suppose the
effect of any particular social experiment will stand out sharp and
recognizable amidst its surroundings, or that we could say — Here
is something which could not have occurred but for the measure
we took.
We must have recourse then to deduction. From what we
know of the laws of human nature, we must attempt to determine
the effect which a measure must produce, or the conditions out
of which a given state of society must have arisen. But again the
great complexity of the subject imposes certain restrictions upon us.
We must not expect to be able to' trace any pervading feature
of society to a single motive, as political obedience to fear, or good
government to a system by which the ruler's private interest is
engaged in governing well. And Mill lays stress on one feature in
particular of the method by which the course of human history is to be
explained. Instead of working out first the theoretical consequences
of certain general principles, and then checking ourselves by
comparing our result with the facts, he holds that we should
endeavour first to ascertain empirically the subordinate principles
that manifest themselves in history, and check our formulation
of them by considering whether they are consistent with the more
ultimate laws of human nature and conduct from which in the
last resort they must be derivable. For the facts of every period
are so diverse and manifold, that the former procedure would
probably be a waste of time. We may know the laws of human
nature, but until we know the circumstances of a given state of
society, we cannot tell what result these laws will produce. We
never know them sufficiently for it to be worth our while to
attempt to develop human history a priori, as the astronomer might
attempt to develop a priori the course of a comet or of the tides.
We must be content to confirm such generalizations as we can
frame a posteriori by showing that they present nothing surprising
Lla
516 AN INTRODUCTION TO LOGIC [CHAP.
when they have happened, although we might have been unable
to predict them.1
In the chapter on Non-reciprocating Causal Relations, questions
of methodology were really to some extent discussed. For we were
engaged in considering the difference between the evidence required
to establish a pure causal relation, where nothing irrelevant enters
into the statement either of the cause or of the effect, and a non-
reciprocating relation such as is implied when we speak of a
Plurality of Causes. Now some sciences find it much harder than
others to eliminate the irrelevant; and to them it is specially
important to remember the sort of tests by which the non-reci
procating character of a relation may be detected.
In that chapter, two of the ' Rules by which to judge of Causes
and Effects ' which had been previously enunciated were reconsidered
at some length, and it was shown that, although nothing which
failed to satisfy their conditions could be in the strict sense the
cause of any phenomenon, yet if cause were understood in a looser
sense, as non -reciprocating, it was not safe to make the same
assertion. But of the precautions to be attended to in the applica
tion of the other two Rules little was said.
These rules were, that nothing which varies when a pheno
menon is constant, or is constant when it varies, or varies
independently of it, is its cause ; and that nothing is so whose effect
has already been taken account of in other phenomena. Both
these rules are especially useful where we are dealing with measur
able effects, the total amount of which is dependent on a large
number of conditions ; and the investigations which employ them
have been called ( Methods of Quantitative Induction '.2 It may be
worth while to consider some of the difficulties which beset the use
of them; and that will furnish an example of a methodological
problem ; for a science which deals with measurable phenomena, in
spite of the great advantage which their measurability brings,
generally meets also with some special difficulties, which it needs
particular precautionary measures to surmount.
What is measurable must so far be homogeneous. Sometimes
1 Mill gives to this order of procedure the name of the ' Inverse Deductive,
or Historical Method ' : by which he means the method appropriate to the
study of history. The Historical Method now however commonly means
interpreting present facts in the light of their past history.
3 Jevons, Elementary Lessons in Logic, XXIX.
xxvi] OF THE METHODOLOGY OF THE SCIENCES 517
it is for all practical purposes entirely homogeneous. A gas company
supplies gas by metre ; the gas is measured, and one cubic foot is
practically indistinguishable from any other. Sometimes the homo
geneity is less complete, but there can be no measurement except so
far as it is found. It may be important for a general to know what
percentage of men he is likely to lose by casualties other than in the
field ; these casualties may be of various kinds, and to the individual
soldier it may make a great deal of difference whether he breaks
down through dysentery or fatigue ; but they are all alike in inca
pacitating men for service ; and the general wants a measure of the
extent to which that occurs. A valuer assesses the value of the
personal property of a man deceased ; it consists of pictures,
plate, furniture, horses, stocks and shares, books, and all kinds of
miscellaneous articles ; but so far as these are all exchangeable for
money they have a common property which can be measured in
terms of money.
Now contributions may be made from many sources to any homo
geneous quantity, but when you are merely told what the quantity
is, there is nothing to show of how many parcels, so to say, it is
made up. The total quantity is a sort of unity. Had one parcel
been greater, the total would have been greater ; should one parcel
fluctuate in amount, the total fluctuates; but there is nothing to
show which parcel is fluctuating and which is constant, and the
variation seems to belong to the whole.
It follows that where an effect is quantitative, and there are
a number of contributory factors which, one way or the other,
influence its amount, fluctuations in these do not necessarily stand
out in the result. There is no doubt that overcrowding affects the
death-rate; yet the death-rate in a town may rise while over
crowding has diminished, if other causes operate to increase it
faster than the improvement in housing operates to diminish it.
Hence a hasty application of the rule that nothing is the cause
of a varying phenomenon which does not vary proportionately with
it may lead us into grave mistakes. We might suppose, for instance,
in the last example, that overcrowding had no influence on the
death-rate, because the death-rate seemed to rise and fall inde
pendently. Doubtless it is only seeming; and if the other contri
butory factors could be kept constant, we should find the rise and
fall proportionate. But we cannot keep them constant.
518 AN INTRODUCTION TO LOGIC [CHAP.
And even if we could, we should be exposed to other errors of
interpretation. The death-rate, many as are the causes which
contribute to it, is yet measured as a whole, and treated as one
phenomenon. If all the causes which contribute to it were constant
except one, and that one fluctuated, the whole result might be
attributed to the one circumstance which exhibited proportional
fluctuations with it. In this particular matter, indeed, we know too
much to fall into such an error ; we know that overcrowding is not
the only cause of death. But where our previous knowledge is less,
it is very easy to attribute the whole of a varying effect to the factor
which varies in proportion, instead of only attributing it to the
increase or decrease beyond a fixed amount. The influence of
education upon character is great ; and that is shown by the effects
of giving and withholding it. But we cannot thence infer that it
is all-powerful, or that the whole difference between the criminal
and the good citizen and father is due to comparative defects in the
criminal's upbringing.1
It is clear, then, in the case of a fluctuating effect which is the
complex result of several causes, that though there must no doubt
be a proportionate fluctuation (or constancy) in the cause, yet it is
unsafe to reject from being a cause either a factor which fluctuates
when the effect is constant, or one which is constant when the
effect fluctuates. For we see the effect as a whole ; and the whole
need exhibit no fluctuations proportionate to those of any one part.
The rule of elimination is not false ; and if the separate effects of
each factor were not lost and undistinguished in the total, we should
observe the facts conforming to it. But this not being so, the rule
is unsafe.
The best remedy lies in determining the precise amount of effect
which each factor can produce ; and as each factor may perhaps be
liable to fluctuation, what we need is a principle or law connecting
each degree of its activity with a corresponding quantity of the
effect. This is done, for example, in the Law of Gravitation. And
could we thus calculate the amount of effect which the other causes
at work, at the strength at which they were severally present, were
capable of producing, we might then safely attribute any difference
1 The ' Perfectibilitarians ', like Godwin, at the beginning of the last
century, held very nearly this.
xxvi] OF THE METHODOLOGY OF THE SCIENCES 519
beyond this to some circumstance that fluctuated proportionately
with it.
But in such a procedure we should no longer be appealing- merely
to the principle that the cause of a varying phenomenon must be
something that varies in proportion. We should be invoking also
the fourth of our grounds of elimination, that it can be nothing
whose effect is already accounted for. Only because we have
determined the amount of effect which the other factors can produce
are we entitled to say that the residue is in no part due to them.
And unless we know with fair accuracy what amount of effect may be
justly assigned to other factors present, we cannot upon the strength
of this principle attribute any part to some particular further
factor a. The application of this rule therefore is involved in the
same difficulties as that of the former, through the fact that the
effects of many different causes are compounded and lost in one
total amount
Moreover, so long as all these causes are freely varying, and
masking their separate effects in one total, the determination of the
law of any single cause, much as it would help us to discover the
others, is the very thing that is so difficult. Hence the necessity
of experimenting with each suspected cause singly. It may be
impossible to exclude the influence of any others ; we must endeavour
to keep it constant; or we may employ what is called a controlling
experiment at the same time. We may see what happens both
when a certain factor is introduced, and when it is not, under
circumstances which, though we cannot keep them constant, we
have good reason to believe to be the same in either case. A farmer,
for example, wishes to know whether some new dressing is of any
use to his grass. He cannot remove the other causes which promote
or hinder the growth of grass, and see how large a crop of hay this
dressing could produce alone ; for alone it would produce none at all.
Neither can he control those other causes, so as upon the same field
to use it one year and not the next, and maintain all other factors
the same. But he can select two plots, or series of plots, on which
he has reason to believe that the other causes all operate equally,
and use the dressing on one and not on the other.
But even so, we have not got a great way towards determining
the law of a cause. To show through all that masks it that some
part of an effect is due to a particular cause is not the same as
520 AN INTRODUCTION TO LOGIC [CHAP.
showing how much is due to it : still less as finding- a mathematical
expression that connects definite fluctuations in the one with definite
fluctuations in the other. There are many cases where this last
achievement is impossible, even though the phenomena we study
be quantitative and to some degree measurable; indeed it is impos
sible except in dealing with the physical properties of bodies.
Elsewhere we must be content with a vague much and little. In time
of war, the risk of capture at sea is a great deterrent to neutral
commerce ; but we cannot say precisely how great. The history of
times of plague shows that increased uncertainty of life relaxes the
bonds of custom and morality ; but it would be impossible to give
any measure of the connexion between the two facts, though the
measurability of the facts, in the sense that as the death-rate rises
the frequency of criminal or reckless acts increases, enables us to
establish the connexion. The one fact may be, in mathematical
parlance, a function of the other; but it is not a function of the
other alone; and we cannot so disentangle the many causes and
their complex result as to give precision to the degree in which one
affects the other. Moreover, where the phenomena are more purely
quantitative, the law of variation that connects them is by no means
easy to establish ; for a formula which holds good over a considerable
range of variation may break down beyond those limits. The
coefficient of expansion of a metal, which indicates the rate at which
its bulk increases with successive increments of heat, no longer
applies when the "metal vaporizes. There are what have been
called critical points, at which the change in an effect no longer
observes the same proportion as hitherto to the change in the cause.
Great caution must therefore be observed in formulating any law
upon the evidence of concomitant variation between two phenomena,
even where we are satisfied that we have excluded any variation
due to other causes, and can give a precise measure of the phenomena
in question.
The causes whose effects are merged in a total may not only vary
independently of one another ; some may be intermittent in their
operation. And whether they are continuous or intermittent, they
may be periodic ; and one may have a longer period than another.
There may again be causes which are both intermittent and irregular
in their action, recurring at no definite and periodic intervals.
Yet it is possible to cope with many of the difficulties which these
xxvi] OF THE METHODOLOGY OF THE SCIENCES 521
facts present by taking- averages. No one would expect the rainfall
of one year to agree closely with that of another in the same
locality; the circumstances affecting it are too numerous and
inconstant. But we have no reason to expect that the average
annual rainfall over a considerable period of years should not agree
closely for different periods ; for though in one year there may be
more circumstances that are favourable to rain than in another,
in the next it may be the other way. If, then, the average
rainfall for one considerable period of years were greater than for
another, we should look for some definite reason for the difference :
which we might find perhaps in a difference in the amount of
forest standing in the district at the different dates ; for the
intermittent and irregular causes of whose operation we are aware
would have roughly balanced in the two periods, though not perhaps
in any two single years. Another method is to plot curves. A base
line for example is taken, and perpendiculars drawn to it at equal
intervals for the successive years. On each of these a point is taken
whose height above the base is greater or less in proportion to the
number of inches of rainfall in that year; and a line is drawn
through those points. The line will rise and fall irregularly ; but
it is possible that in spite of these intermediate fluctuations there
may be long-period fluctuations which stand clearly out ; what may
be called the crests and troughs of the curve may be at fairly equal
intervals, though its course is not uniform from trough to crest.
This would indicate the action of some cause having a similar
period ; and if we discovered any factor with a corresponding period
of fluctuation, there would be a strong presumption that it was the
cause.
The profitable use of statistics depends very largely on methods
like these ; but the devices for bringing out their teaching are often
much more elaborate than has been indicated. They belong, how
ever, to the detail of particular sciences rather than to the general
principles of logical method. Enough perhaps has been said to
indicate the misinterpretations of causal relation to which we might
be led, in the case of quantitative phenomena that vary in their
amount, by too hastily applying rules true in themselves to any
unanalysed total effect : as well as the difficulties that beset us in
disentangling the component parts and fluctuations.
A few further and miscellaneous examples of the way in which
522 AN INTRODUCTION TO LOGIC [CHAP.
precepts for the better prosecution of a particular science may be
drawn from general logical principles will serve to conclude this
chapter. It must not be supposed that the subject is at all
adequately treated here; it is only illustrated.
What is called the historical or comparative method has in the
last few generations revolutionized many branches of enquiry. It
is but an application of the general principle of varying the cir
cumstances in order the better to discover the cause of a phenome
non. But of old, enquirers into matters of historic growth, such
as language, or myth, or religion, or legal ideas, were content
to attempt an explanation of the facts of some particular age
or country by observations carried on within that age or country
alone, or if beyond it, only in adjacent ages or countries of the
same type. The historic method looks farther afield. It compares
the institutions of widely different ages, or of peoples who though
contemporaneous stand at widely different levels of civilization and
of thought. In the light of such a comparison, facts may take
on quite a new appearance. Legal or other customs for which
a later age had found a reason in some supposed meaning or utility
which they now possessed are seen to have had a very different
origin, in conditions no longer existing, and ideas no longer enter
tained. Folk-lore is full of such surprises. The custom of throw
ing rice after a married couple as they drive away is sometimes
explained by saying that rice is a symbol of fertility ; Dr. Fraser,
comparing a number of other facts, thinks that the rice was origin
ally intended to lure back the spirit of the bride or bridegroom
to its body; it was supposed that at critical times — and every
thing connected with marriage was critical — the spirit left the body,
in the form of a bird ; the rice would attract it, and if it hovered
about the body it would be more likely to re-enter. Whether
this be the true explanation of the custom or not, only the com
parative method could have suggested it. It is the same with
myth ; the account of the origin of Greek and Roman mythology
popularized by Max Miiller represented it as, in the language of
Dr. Andrew Lang, a disease of language, the pearl in the oyster.1
Names originally designating the attributes of earth or sun or
moon were confused with words of similar sound but different
meaning, and out of these other meanings myths arose. Apollo
1 Custom and Myth, p. 1.
xxvi] OF THE METHODOLOGY OF THE SCIENCES 523
Lykios had no connexion with the wolf ; he was only the Shining-
one; but when that was forgotten, some wolf story would be invented
to account for the name. Such theories are however discredited
when it is found that a myth occurs in forms substantially alike
among widely different peoples, whose languages do not admit of
supposing it to have originated through confusion of similarly
sounding words with different meanings. There is no new prin
ciple in the use of such an argument against the f Sun-myth '
theory of mythology ; we simply say that the theory fails, because
the phenomena it is intended to account for occur where it cannot
be applied. But Aryan mythology is a large subject by itself ; an
enquirer might naturally think that it could be explained without
going to the mythology of African or American savages ; it has
been found that this is not the case; the long descent of man
connects his present with a past very dissimilar, and connects
thereby with one another contemporary forms of civilization wide
apart. Therefore it is important to insist upon studying the pre
sent in the light of history and comparing as extensive a range of
facts as can be gathered together.
We hear sometimes of ' methodological assumptions'. By the
term is meant assumptions made for the sake of getting forward
with the scientific treatment of a subject, but not conceived as neces
sarily true. For example, there is obviously some connexion
between states of mind and states of body. The psychologist,
seeing quite clearly that to suppose the former to be produced by
the latter soon lands him in the most hopeless contradiction, and
ignorant as to the true way of stating the relation between them,
may think the hypothesis of interaction the most convenient assump
tion to make, with a view of increasing and systematizing his
knowledge of the laws which determine the development of the
individual mind; or instead of the hypothesis of interaction (which
conceives mind and body as producing changes in one another) he
may prefer the hypothesis of parallelism, according to which every
mental change has a corresponding bodily change, and vice versa,
but the two series proceed each uninfluenced by the events of the
other. Either hypothesis, if not regarded as true, but only as
facilitating enquiry, would be a methodological assumption. Simi
larly, if he believes in the freedom of the will, the psychologist
may still, as a methodological assumption, accept the doctrine of
524 AN INTRODUCTION TO LOGIC
determinism ; because so far as actions have not any cause suffi
ciently accounting for them in the pre-existing state of the agent,
but spring from the activity of a will acting according to no fixed
laws, it is hopeless to try to explain their occurrence. In his
attempts to do this therefore he will assume what is necessary to
the possibility of doing it, even though he may believe that it
cannot be altogether done.
Lastly, general logical considerations may indicate the weak
places in a particular science at a given time, and thus show what
line of enquiry is logically of most importance to the science in
question. The theory of Natural Selection assumed the existence of
variations, that is, divergences from the parent type in offspring ;
and it assumed these variations to be accidental and non-adaptive.
It concentrated itself at first on the task of showing how great
a degree of adaptation between an organism and its environment
could be brought about, through the operation of the struggle for
existence among individuals varying slightly from type in all
directions ; and how by the accumulation of such small variations
as happened to be favourable in each generation a profound modifi
cation of specific type might ultimately be produced. It was
quite worth while to work this out even upon a basis of assumption
as to certain of the facts. But the pressure of criticism has
directed attention to the question whether variations are all of
them non-adaptive ; and one of the logical requisites of the theory
of Natural Selection is a suitable collection of facts throwing light
upon this point. The facts are not very easy to obtain or estimate ;
but biologists are working at this problem with great assiduity.
A study of the contemporary state of biology from a logical point
of view would have to consider with some care the kind of facts
required on such a point as this, and the sort of instance that would
be crucial1, i. e. decisive against one or other theory.
1 From crux, a sign-post : as directing our choice between two (or more)
theories: v. Bacon, Nov. Org. II. 36. A crucial instance, though it can
disprove, can never prove a theory, except upon the assumption that there
is no other theory with which it agrees. And it is easier to imagine instances
fatal to the view that all variation is non-adaptive than to the view that
adaptive variation sometimes occurs.
CHAPTER XXVII
APPENDIX ON FALLACIES
A FALLACY is an argument which appears to be conclusive when
it is not ; and the chief use of studying fallacies must be that we
may learn to avoid them. Regarding Logic as a science, we might
therefore justly say that we are not called upon to discuss them. The
only way in which their study can help us to understand how our
thought works is by the force of contrast. Show a man an argu
ment which he recognizes to be unsound, show him where the
unsoundness lies, and he may very likely realize more clearly, so
far as they can be formally prescribed, what are the conditions of valid
reasoning. On this account as we went along we contrasted examples
of invalid with examples of valid inference. What more then is
wanted ? for the case is not as it is, for instance, with psychology.
To the psychologist few things are more instructive than the study
of marked abnormalities of mental life : just as to the physiologist
diseases reveal much which cannot be seen in health. For psychology
is an empirical science, so far as it is a science at all : it aims at
discovering the principles in accordance with which the various mani
festations of consciousness develop in the life of the individual ; what
these are it is to a large extent unable to anticipate, although the
metaphysician may have his views as to the conditions under which
alone their action — whatever they may be — is possible. Now insanity
is just as much a fact as any normal mental development ; it must
equally admit of explanation ; and doubtless the same principles, in
accordance with which this development proceeds under certain con
ditions normally and to a sane result, are exemplified in the mental
disturbances which other conditions evoke. They are exemplified
too in a more prominent way ; so that such cases furnish what Bacon
called a glaring instance * to assist us towards their discovery. But
it would be absurd to say that the principles of rational thought are
1 Instantiae Ostensivae, or Elucescentiae. Nov. Org. IT. 24.
526 AN INTRODUCTION TO LOGIC [CHAP.
equally exemplified in fallacy as in sound thinking ; and it would
be absurd to hope to discover, in the procedure of a fallacious mind,
the nature of true thinking-. We have said once and again that
Logic analyses the operations of thought which the mind has
already performed about other matters ; but it must not be sup
posed that it is on that account, any more than mathematics, an
empirical science. The mathematician can only recognize the
necessary relations of number or space by the help of some quanti
ties or figures in which he finds them; yet he recognizes their
necessity to be absolute and universal, and the fact that his non-
inathematical friends make mistakes in their mathematical think
ing is not taken by him as evidence that there are really two ways
of thinking about the matter ; he merely says that on such subjects
they cannot really think. So also with Logic. Only in some thought
in which they are found can the necessary relations involved in
thinking be recognized ; but their necessity too is recognized to be
absolute, and we say that those who think differently are incapable
of thinking about how they think. If any one is inclined to
hold otherwise, and to suppose that the laws of our thinking are
psychological laws, exemplified no less in fallacy than in its oppo
site, let him reflect that even in doing so he is bound to assume the
contrary. For he who in that mind sets out to ascertain what the
principles of thought, as a matter of empirical fact, are, will be unable
by rights to know that the thought is valid by which he conducts
that investigation. How then could he have any confidence in its
results ? Yet the fact that he intends to trust them implies that
he assumes the principles of thought, in accordance with which he
conducts the investigation, to be valid, whatever principles the
investigation may report in favour of ; and herein he takes for
granted that he can recognize immediately what rational thought
is, without reference to empirical facts revealed by psychology.
Nevertheless the insertion of a chapter on Fallacies may be
defended. It has tradition in its favour; and without it, the
nomenclature of fallacies — a nomenclature by no means fallen out
of common use — would remain unexplained. There are practical uses
in it also ; and it would be ridiculous to say that because Logic is
a science we may not turn the study of it to advantage in practice.
Familiarity with some of the commonest types of fallacy is no
security that we shall never fall into them ourselves ; still less are
xxvn] APPENDIX ON FALLACIES 527
we bound to fall into them unless we have acquired that familiarity.
But it may help us to avoid them, by helping us more readily to
perceive them. The overtones which a man has never noticed till
they were pointed out to him he may afterwards detect easily for
himself. A flavour in a dish, a line in a picture, whose presence had
gone unobserved, a man may be unable to ignore, if it has been
singled out and presented to him in isolation. So it may be with
a fallacy. There are many whose perception of the unsoundness
of an argument is not unaffected by their belief in the truth or
falsity of its conclusion : they will detect it where they think that
what it proves is false ; but let it be true — still more, let the supposed
truth be precious to them, or familiar — and the same form of argu
ment in its support may pass unchallenged. Yet if we have accus
tomed ourselves to the look, or type, of the fallacy, we are less
likely to be the victims of such an imposition. It is true that, in
the words of Archbishop Whately *, ' After all, indeed, in the prac
tical detection of each individual Fallacy, much must depend on
natural and acquired acuteness ; nor can any rules be given, the
mere learning of which will enable us to apply them with mecha
nical certainty and readiness : but still we shall find that to take
correct general views of the subject, and to be familiarized with
scientific discussions of it, will tend, above all things, to engender
such a habit of mind, as will best fit us for practice/ And, as
Aristotle intimates 2, a man who may be able to detect a fallacy well
enough, if you give him time, by the light of nature, may be placed
at a practical disadvantage by not being able to do it quickly
enough : here the systematic study of fallacies will help him. Nor
is it only in arguing with others that he may reap some benefit from
the study ; it will accrue to him also in the conduct of solitary
thinking.3 It was however chiefly with reference to the conduct
of debate that Aristotle discussed the subject. It was from this
point of view that he observed, that a man might be suspected of
incompetence, who only found fault with an opponent's argument,
and could not show in what the fault consisted.4 It may be added,
that so far as fallacies are referable to recognized types, it is a great
abridgement of criticism to be able to name the types, and refer
a particular fallacy to one of them.
1 Logic, p. 153, 8th ed. 2 Soph. El. xvi. 175a 23.
3 Ib. 175a 9. 4 Ib. 175a 14.
528 AN INTRODUCTION TO LOGIC [CHAP.
These are practical considerations; and it would probably be
found that importance has been attached to the doctrine of fallacies
chiefly by those who have viewed Logic as an instrument for
reasoning. But an use may be found in the doctrine, of a more
theoretical kind. It is intellectually unsatisfactory to see that an
argument is faulty, and not to see precisely why. We desire for
ourselves, no less than we owe to our opponent, an analysis of the
error. Otherwise, and if we can only see it, and not see through it,
the mind, as Aristotle expresses it, is bound, and unable to proceed.1
It is probable that some of the fallacies of which he finds the solu
tion in different ambiguities of language did once constitute a more
serious entanglement than they do to-day. This is partly because,
as others have pointed out, such fallacies generally disappear by
translation into a foreign tongue ; and peoples more familiar than
the Greeks were with a diversity of tongues have a great advantage
in detecting such. It is partly also because an analysis new in his
day is common property in ours ; and many of its results are so
incorporated into the currency of common thought and speech, that
a man whose attention is called to them feels as if he was taught
only what he already knew.
If however we are satisfied that Logic should treat of fallacies,
it is very difficult to be satisfied with any treatment of them.
Truth may have its norms, but error is infinite in its aberrations,
and they cannot be digested in any classification.2 The same incon
clusive argument may often be referred at will to this or that head
of fallacies. ' Since, in any Argument,' says Whately, ( one Premiss
is usually suppressed, it frequently happens, in the case of a Fallacy,
that the hearers are left to the alternative of supplying either
a Premiss which is not true, or else, one which does not prove the
Conclusion. E. g. if a man expatiates on the distress of the country,
and thence argues that the government is tyrannical, we must sup
pose him to assume either that " every distressed country is under
a tyranny7', which is a manifest falsehood, or} merely that " every
country under a tyranny is distressed ", which, however true, proves
nothing, the Middle-Term being undistributed.'3 The assumption
1 Eth.Nic. 17. iii. 1146a24.
2 Cf. de Morgan, Formal Logic, p. 237. 'There is no such thing as a
classification of the ways in which men may arrive at an error : it is much
to be doubted whether there ever can be.'
3 Logic, p. 159, 8th ed.
xxvn] APPENDIX ON FALLACIES 529
of a false premiss is not indeed perhaps to be called a fallacy, as we
shall see presently ; it is at any rate different in its nature from
inconclusive argumentation. But the choice may equally well lie
between two modes of inconclusive argumentation, when we have
to classify a fallacy ; a man who attempts to refute by an enumera
tion of striking instances the proposition that some specific charac
ters in plants and animals are not adaptive might either be charged
with illicit process of the minor term, in drawing an universal
conclusion where his premisses only entitle him to a particular one,
or with what is called Ignoratio Elenchi, in supposing that a par
ticular affirmative refutes a particular negative.1 And not only is
it impossible to make such a classification of fallacies as will
never leave it in doubt to which class a particular example is to be
referred ; if that were all, it might be said that the types were dis
tinct, and the classification so far a good one, although individuals
could not be assigned to their types unambiguously : but it may be
doubted as well, if the types of error can be exhaustively detailed,
and the classification completed.
The reason for this is twofold. In the first place, there may be
arguments so foolish and inconsequent, that they cannot even be
said to simulate cogency ; these cannot be positively characterized,
but must be lumped together by the mere negative mark of incon-
clusiveness. And secondly, there are many fallacies, the detection
of which requires not general logical training, but acquaintance
with a particular scientific subject-matter. The latter point is of
some importance, as connecting with what has been already said
about demonstration.
We have seen that the syllogism cannot sustain the claim once
made in its behalf, of being the type of all valid inference ; but
that there are deductive reasonings — to say nothing of hypothetical
and disjunctive argument — whose validity lies in no conformity
to a scheme exhibitable in the abstract, or symbolically, but rests
for its apprehension upon acquaintance with the nature of the
special subject-matter with which they deal. The readiest illustra
tion of this, but by no means the only one, is furnished by geometry.
Now what is true of valid is equally true of invalid reasonings.
There are many which are not of a sort that can occur in reasoning
1 Cf. Ar., Soph. El. XXIV. 179b 17 ouSei/ 5e K0>\vct rbv avrov \nyov
nd xxxiii. 182b 10.
M HI
530 AN INTRODUCTION TO LOGIC [CHAP.
on every subject-matter, but are bound up with misconceptions
of the special subject-matter in which they occur. This too may
be readily illustrated from geometry. * Lewis Carroll ' devised
a proof that ' a right angle is sometimes equal to an obtuse angle '.
The demonstration was in all other respects unimpeachable, but
vitiated by one — of course intentional — error in the construction of
the figure, in which a line was drawn to one side of a point
which must in fact fall on the other.1 Just as a knowledge of
O
geometry can alone show where this line must fall, so a know
ledge of geometry can alone expose the inconsequence of the
false demonstration. And similar inconsequences occur in every
particular science, which only an understanding of that science can
show to be inconsequences. Thus if it were argued that because
a and b were halves of the same thing, therefore they were halves
of one another, and since a = 4, b must = 2, it is only a perception
of the nature of quantity that reveals (doubtless in this case to the
least mathematical of us) the invalidity of the first, step in the
argument. It is less obvious that among a people who acknowledge
kinship only through the female, a man would inherit not from his
father but from his brother or maternal uncle. Yet a little reflec
tion shows this to be the case, and shows therefore the fallacy of
1 v. the Lewis Can-oil Picture Book, edited by S. Dodgson Collingwood
(London, 1899), pp. 266-267. (GKmusi really fall to the right of C.)
' Let ABCD be a square. Bisect AB at E, and through E draw EF at
right angles to AB, and cutting DC at F. Then DF=FC.
' From C draw CG=CB. Join AG, and bisect it at H, and from // draw
HK at right angles to A G.
'Since AB, AG are not parallel, EF, JTTTare not
B parallel. Therefore they will meet if produced. Pro
duce EF, and let them meet at K. Join KD, KA,
KG and KG.
'The triangles KAH, KGH are equal, because
AH '= HG, HKis common, and the angles at H are
right. Therefore KA = KG.
' The triangles KDF, KCF&re equal, because DF —
FC, FK is common, and the angles at F are right.
Therefore KD = KC, and angle KDC = angle KCD.
' Also DA = CB = CG.
'Hence the triangles KDA, KCG have all their
sides equal. Therefore the angles KDA, KCG are
equal. From these equals take the equal angles KDC, KCD. Therefore the
remainders are equal : i. e. the angle GCD = the angle A DC. But GCD is
an obtuse angle, and ADC is a right angle.
' Therefore an obtuse angle is sometimes = a right angle.
'Q.E. D.1
xxvn] APPENDIX ON FALLACIES 531
arguing-, where female kinship prevails, that because A is in
possession of a property, his son will possess it after him.
Here the detection of the fallacy rests upon our perception of
the system of relationships uniting the members of a society
which takes account only of union by descent through the female
line.
Aristotle, who noticed that every science afforded its own special
opportunities for erroneous inference, gave to those that involved mis
takes in geometry the name of \|/-eu6oypcty>r7/ia, or false construction.1
As an example he gives Hippocrates' method of squaring the circle
by lunules. A lunule is a figure enclosed between arcs of two circles
concave in the same direction. Hippocrates found a rectilinear area
equal to a lunule whose upper arc was a semicircle, and its lower arc
the fourth part of the circumference of another circle ; he then found
another rectilinear area equal to the sum of (a) three equal and
similar lunules whose outer arcs were semicircles, and their inner
arcs the sixth part of the circumference of another circle, and
(b) a semicircle of the same diameter as the three lunules (i. e. of
diameter equal to the chord of the arcs enclosing them) ; and he
supposed that by subtracting from this rectilinear area an area
equal to the three lunules, he could obtain in the remainder a
rectilinear area equal to the semicircle. He overlooked the fact
that because you can find a rectilinear area equal to a lunule of
the former sort, whose inner arc is a quadrant, it does not follow
that you can find one equal to a lunule of the latter sort, whose
inner arc is a sextant ; and in fact a rectilinear area equal to these
three lunules cannot be obtained.2
Now it will indeed be seen that, in this or any other case of
erroneous reasoning dependent on misconceiving the consequences
which follow from given conditions in a special subject-matter, the
error can be expressed in a false proposition. It is false that
because a rectilinear area can be found equal to one of these lunules,
it can be found equal to the other : it is false that things which are
halves of the same thing are halves of another : it is false that, if we
take account only of kinship through the female line, a man will
be in the same line of descent with his father. But we cannot
see that any of these propositions is false, unless we understand
1 Soph. EL ix, xi. 2 v. Poste's ed. of Soph. El., App. F, pp. 245-247.
M m 2
532 AN INTRODUCTION TO LOGIC [CHAP.
something- of the respective subject-matter. They are as it
were false e special principles ', or i8tai ap\a.L It is not desirable
to call every false proposition a fallacy, as e. g. that snakes eat
dust, or that South America is an island ; nor can we extend the
name to every valid argument that uses a false premiss. If the
falsity of the premiss can only be ascertained empirically, there is
error, but not fallacy. If however the falsity of the premiss is to
be ascertained by thinking out the consequences of certain relations,
or conceptions, in the circumstances of a given case, then we are
guilty of fallacy, or defect of reasoning, in overlooking it; and
that is what frequently occurs in the matter of any particular
science.
There are indeed general heads, under which many such fallacies
can be brought. In particular, they very often arise from over
looking some of the special circumstances of the case : from assum
ing that what is true under certain conditions will still be true
when those conditions are in some way modified. Thus, if two
things a and I are equal to the same thing, they are equal to one
another ; from which we may conclude, that if they bear any same
quantitative relation to a third thing, they bear that relation to
each other ; and then it would follow that if they were halves of
the same thing they would be halves of one another. But in fact,
it is onlv when their same relation to a third is one of equality, not
merely when their relation to it is the same, that they bear to one
another the relation borne to it. We shall meet with this type of
fallacy by and by under the name of Secundum Quid. That head
ing embraces a great range of examples. But though we can
detect in them a common character, it is only by understanding
something of the special matter of the argument, that we can see
that the fallacy is being committed in a given case. The type, if
one may say so, is fluid ; the instances are not so far of one form, that
we can separate their common form from the variety of their
matter, and exhibit it symbolically ; nor, though the type admits of
all this diversity, can we subdivide it, and carry our classification
down to infimae species. We recognize that its character differs
in different cases ; but the differences cannot be formulated.
Our task then is one which does not admit of fully satisfactory
performance. Still no doubt it can be better and worse done.
What classification of fallacies are we to adopt ?
xxvn] APPENDIX ON FALLACIES 533
The earliest, and for long the accepted, classification is that of
Aristotle, given in the last book of his Topics, called the Sophistici
Elenchi. It is not free from defects ; and others, some of which
will be referred to, have been propounded. But the subject is
emphatically one upon which some consensus is desirable. If it is
useful to have a nomenclature of fallacies, it is useful to have
a standard nomenclature. And it is remarkable how, even in rival
classifications, many of the Aristotelian species of fallacy still hold
their own. Later writers have given new meanings to the Aristo
telian names in certain cases ; or have invented names for special
forms of some of the Aristotelian fallacies ; or have included in
their list what are not forms of erroneous argument, but sources of
error of a different kind J ; yet it is surprising how little there is
which cannot be brought within Aristotle's list. And if we consider
not the enumeration of types of fallacy, but their classification, it
will appear, I think, that there is no such merit in any alternative
scheme as justifies us in sacrificing the advantage of keeping to the
standard and traditional scheme of Aristotle.
Aristotle divided fallacies into two main groups — fallacies in
1 Thus the fallacy of Accident has practically been identified with
Secundum Quid by many writers : that of Consequent has, e. g. by de Morgan
and Jevons, been explained as 'the simple affirmation of a conclusion which
does not follow from the premisses ' (de Morgan, Formal Logic, p. 267) : divers
forms of lynoratio Elenchi have received special names : Whately has
explicitly included under fallacies, in defiance of his own definition, 'any
false assumption employed as a Premiss' (Logic, 8th ed. p. 168: cf. del',
on p. 153) : Mill includes among fallacies such sources of error as Mai-
observation— i. e. mingling inference with the report of what is perceived
(Logic, V. iv. 5) ; and his lirst great group of fallacies, to which he gives the
title A priori Fallacies, or Fallacies of Simple Inspection, consists of
a number of maxims which he considers erroneous (though it is not equally
clear that they all are so), such as that what is inconceivable cannot be
true, that effects must resemble their causes, that motion can only be
produced by motion, that the same effect must always have the same cause
(V. iii) ; in iv. 1, Fallacies of Simple Inspection are called ' Prejudices, or
presumptions antecedent to and superseding proof, and in ii. 2 they are
called supposed connexions or repugnances between facts, ' admitted, as the
phrase is,' on their own evidence, or as self-evident. Whately (op. cit. p. 208)
speaks of the fallacy of References, i. e. giving references in support of a
statement to passages which do not really bear it out, in the trust that readers
will not look up the references and discover this. Professor William James
gives the name of the Psychologist's Fallacy to the mistake of supposing that
a man who has a given psychical experience knows it, when he has it, to be
all that I as a psychologist know or believe it to be (Principles of Psychology.
vol. i. p. 196). Locke's argumenta ad verecundiam, ad ignorantiam, ad hominem.
which he opposes to an argumentum ad iudicium, might be called heads of
fallacies (Essay, IV. xvii. 19-22).
534 AN INTRODUCTION TO LOGIC [CHAP.
dictione, or napa TTJV Aefiy, arising through ambiguity of language,
and fallacies extra dictionem, or e£co TTJS Aefeco?, which do not have
their source in such ambiguity. Although one of his species of
fallacies extra clictionem — the fallacy of Many Questions — might
perhaps be referred more naturally to the other group, yet the
division, being dichotomous, is sound. It suffers, however, like all
such divisions, from the defect of not positively characterizing one
member.1 Later writers, willing to remedy this defect, called the
fallacies extra clictionem fallacies in re, or material fallacies. But
this introduces a cross-division. For it cannot be said that fallacies
in dictione are independent of the res or matter of the argument.
On the contrary, inasmuch as they arise through giving different
meanings to the same words either in the two premisses, or in
premiss and conclusion, they disappear if we abstract from the
matter of the argument and look only to the form in which it is
cast. The proper antithesis to matter is form ; a fallacy not in the
matter must be in the form : i. e. it must be independent of what
the terms are, and must therefore persist, if symbols be substituted
for the terms, and whatever term be substituted for the symbols.
This cannot be said of the fallacies in dictione.
It is true that Whately gives a somewhat different interpretation
to the expression material fallacy. He divides fallacies into logical
and material. By the former title he means fallacies where the
error lies in the fact that the premisses do not prove the conclusion ;
by the latter, those in which the premisses prove the conclusion, but
either the premisses are false, or such at least as we are not entitled to
assume, or else the conclusion proved is not that which we profess
or are required to establish. He then subdivides logical fallacies into
two groups, according as their defect of proof can be seen in the
mere form of the argument (e. g. in the case of undistributed
middle) or only if we attend to the ambiguity of the terms em
ployed; the former group he calls purely logical, and the latter
semi- logical. Though the nomenclature here is unfortunate (for
according to his own definition of a logical fallacy, those which lie
in ambiguity of language are altogether and not only half logical),
yet the division is sound. It includes however arguments which have
no fault except that their premisses are false ; and it is true that in
1 Cf. supra, pp. 107-109.
xxvn] APPENDIX ON FALLACIES 535
this he follows the words of Aristotle l ; but in the body of his
treatise Aristotle proceeds as if he had not included them. And
the practice of Aristotle appears preferable in this respect ; for false
premisses are certainly incapable of any classification, and the con
sideration of one does not help us to detect another. That, if the
premisses are false, the conclusion is not bound to be true, every one
should certainly realize ; and it is good advice to a disputant to
consider well the truth of the premisses he is asked to grant, or to
a solitary thinker to consider well the truth of what he proposes
to assume and build upon. Nevertheless there seems t'> be a real
difference between a plausible but inconclusive argument^ which we
can see through by clearer and more attentive thinking, and a false
proposition (whether or not plausible), which cannot be exploded by
any more attentive consideration of itself, though it may by reason
ings that are within our power. For this reason the extension of
the term fallacy to cover ' any false assumption employed as
a premiss ' seems undesirable ; the only sort of false proposition to
which it ought to be applied is false canons of reasoning. If this
correction is made, Whately is left with only two kinds of material
fallacy (Petitio Principii and Ignoratio Elenchi), both of which are
in Aristotle's list of fallacies extra dictionem ; and there is no par
ticular advantage in that regrouping of the species enumerated in both
lists, which the adoption of Whately 's principle of division carries
with it. Whately certainly enumerates under the head of purely
logical fallacies those breaches of syllogistic rule with which we
long ago became familiar by the names of: undistributed middle,
qualernio terminoruw, and illicit process of the major or minor term •
and Aristotle makes no mention of these. But that is not because
his classification provides no place for them ; they are clearly fal
lacies extra dictionem. They were omitted because they did not, in
1 Top. a. i. I00b 23 fpia-TiKos & f'o-Ti (TvXXoyto-/i6f 6 CK <}>mvontv(*>v fV5o£<w,
M ovTW 8c, Kai 6 e£ fVSo£o>i> 77 ^atPO/icVai' (i>ti6£<i)i> <f>mv6fji(vos : cf. Soph. El. ii.
165b 7 ept(TTlKO\ 8f (Xo-yot) oi r'n Ttoi/ (0MU|N»ft«MM' eV8d£o>i> pf) OI>T(DI> df o-uXXo-yio-riKoi
ri <t>aiv6n€vot <rv\\oyt<TTiKoi The latter definition excludes unsound arguments
from premisses really endoxical (i. e. probable or supported by opinion, and
allowable in non-scientific discussion) ; but this can hardly be supposed to
be deliberate. The expression twice used in Soph. EL i. (164a 23 on piv ou/
of fifv «Vi crvXXoyioyzot', ot 6' OI>K ovrts SOKOVOI, (jxivepov : 165a 17 fita ptv ovv
lA« /cat €\
OVK &v 8f) might perhaps by itself be more naturally understood to refer
only to fallacious argument*, and not to include arguments that have no fault
except in the falsity of their premisses.
536 AN INTRODUCTION TO LOGIC [CHAP.
Aristotle's view, simulate cogency ; no one who could not detect
these ought to undertake a disputation ; and even a sophist, aiming
only at appearing to confute his adversary and not at truth, would
hardly dare to employ such methods as these. And so it was with
the writers who for many centuries reproduced — often with in
creasing divergence — the Aristotelian doctrine. ' The pure syllogism
and its rules were to them as familiar as the alphabet. The idea of
an absolute and glaring offence against the structure of the syl
logism being supported one moment after it was challenged, would
no more suggest itself to a writer on logic than it would now occur
to a writer on astronomy that an accidental error (which might
happen to any one) of affixing four ciphers instead of five when
multiplying by a hundred thousand would be maintained after
exposure/ l A sophism, or sophistical confutation, as Aristotle
called a fallacy (for he had in mind throughout the conduct of
a disputation, and the methods by which one might attempt to
confute a thesis maintained by an opponent : though these are of
course equally methods of establishing a conclusion that confutes it),
must be at least fyaivoiJitvQs cn;AXoyto-//oj, apparently conclusive ;
these he wished in his treatise to enable the learner to expose 2 ;
but a plain breach of syllogistic rule had not any appearance of
conclusiveness, and enough had already been said in the Prior Ana-
lytics to enable any one to expose that.
We may therefore abide by the Aristotelian division into falla
cies in dictione and extra dictionem. In each member of the division
he enumerates a variety of types. The lists are as follows 3 : —
1 de Morgan, Formal Logic, p. 240.
2 Cf. Soph. EL i. 165a 26 rov dc \l/fvd6fji(vov f nfyavifr iv 8vvaa6ai.
3 Whately, as was observed above, regroups the fallacies here enumerated
to suit his division. It is of course inadmissible to adopt the nomenclature
of his division, and retain Aristotle's grouping, as is done by Jevons in his
Elementary Lessons, XX and XXI. He treats as purely logical fallacies the
four breaches of syllogistic rule above mentioned ; as semi-logical, Aristotle's
six fallacies in dictione ; and as material, Aristotle's seven fallacies extra
dictionem. He does not therefore understand the distinction between
logical and material as Whately does. 'The logical fallacies,' he says, 'are
those which occur in the mere form of the statement. . . . The material
fallacies, on the contrary, arise outside of the mere verbal statement, or as
it is said, extra dictionem ' (p. 170). This is not of course what those words
meant. But clearly Jevons means by a logical fallacy one which can be
detected in the form without consideration of the matter; it should there
fore be capable of illustration in symbols, as his ' purely logical ' fallacies
are. A material fallacy, on the contrary, needs that we should understand
XXVIl]
APPENDIX ON FALLACIES 537
a. Fallacies in dictions, or Trapa ri]v
1. Equivocation, or Trapa TT)Z> 6/
2. Amphiboly, or Trapa Ti]v a
3. Composition, or Trapa TTJV <rvv0eo-iv.
4. Division, or Trapa TTJI;
5. Accent, or Trapa rj]v
6. Figure of speech, or Trapa TO
I. Fallacies extra dictione ni, or efo> TTJS Ae'£ecoj.
1. Accident, or napa TO au/x/Se/SrjKo's.
2. Secundnm Qnid, or Trapa TO aTrAais ?) TTT) Aeyeaflai /cat
3. Ignoratio Elencki, or Trapa TT)I> rou eAey^ou ayvoiav.
4. Petitio Principii, Begging the Question, or ?rapa ro ci
5. A'ow Causa pro Causa, False Cause, or Trapa ro jxrj
ws atrtoi;.
6. Consequent, or Trapa TO kno^vov.
7. Many Questions, or Trapa TO TO bvo epcoT?J/iaTa ei>
the terms for its detection. From this point of view, it is nonsense to speak
of ' semi-logical ' fallacies ; a fallacy either can be detected in symbols or
not : it must either be 'logical ' or not, and cannot be 'semi-logical'. The
fallacies in dictione, which he ranks as ' semi-logical', he ought undoubtedly
to have ranked as ' material '. On the other hand, some of those which he
ranked as ' material'— the fallacy of the Consequent certainly (which
however he misunderstands) and one type of Petitio Principii — can be
exhibited in symbols, and ought to have been enumerated among the
' purely logical '. The fact is that, if the distinctions of logical and material,
and in diclione and extra dictionem, are to be combined in one classification,
they cannot be identified, as Jevons identifies them. We may either start
with the distinction of fallacies into logical and material, according as they
lie in the mere abstract form of the argument, and can be exhibited in
symbols, or not: and then divide the latter into in dictione and extra
dictionem, according as they arise through ambiguity of language, or not ;
but of course those fallacies extra dictionem which are logical in this
sense must be removed from Aristotle's list of fallacies extra dictionem, if
that title is made to indicate a subdivision of material Or else we may
begin by dividing them into fallacies in dictione and extra dictionem, and
treat logical and material as subdivisions of extra dictionem. In the former
case, what Jevons calls semi-logical (= Aristotle's fallacies in dictione) will
enter by this name as a subdivision of material ; in the latter, what he calls
purely logical will enter as a subdivision of extra dictionem. _ Cf. the remarks
in Mr. St. George Stock's Deductive Logic, c. xxx, who points all this out
very clearly in discussing fallacies. It may be added that there may be
in algebra fallacious arguments which use symbols, but are not on that
account logical in the above sense, because the symbols are not logical
symbols, standing for any term, but specifically symbols of quantity.
538 AN INTRODUCTION TO LOGIC [CHAP.
The fallacies in dictione are so many different forms of error that
may arise through the double meanings of language. They differ
according to the character of the ambiguity ; and it may be any
of the three terms which is ambiguous 1. Obviously such arguments
are invalid; and if the different meanings were expressed by
different terms in each case, we should have a plain quaternio termi-
norum, which would impose on nobody. As it is, the shifting of
the meaning may sometimes pass unobserved ; or the identity of
the language seem to afford some proof of identity of meaning ;
and even where it is obvious that we are tricked by the argument,
we may wish to be able to show how.
1. Equivocation is the simplest form of ambiguity, where a single
word is used in divers senses. 'The sick man is well; for men
who have recovered are well, and the sick man has recovered ' 2 ;
here the equivocation is in the minor term, and arises from the fact
that the expression ' the sick man ' may mean either ' the man who
is sick ' or ' the man who was sick \ The following is an old
example : ' Finis rei est illius perfectio : mors est finis vitae : ergo
mors est perfectio vitae ' ; the equivocation in this case lies in the
middle term. Trivial and punning examples of this fallacy, as of
all those that depend on ambiguity of language, will occur to any
one ; but in many cases it is serious and elusive. ' It is the busi
ness of the State to enforce all rights : a judicious charity is right :
therefore it is the business of the State to enforce a judicious
charity/ 'A mistake in point of law/ says Blackstone, 'which
every person of discretion not only may, but is bound and presumed
to know, is in criminal cases no sort of defence ' 3 ; the State must
perhaps presume a knowledge of the law, and so far we are bound
to know it, in the sense of being required under penalty ; but
a criminal action done in ignorance of the law that a man is legally
bound to know is often considered morally discreditable, as if the
knowledge of the law on the matter were a plain moral duty. How
far that is so in a particular case may be a very doubtful question ;
the maxim quoted tends to confuse the moral with the legal obli
gation. In a long and closely reasoned argument, where important
terms have been defined at the outset, it may still be very difficult
1 Many arguments referable to Aristotle's heads of fallacy are not syllogistic.
2 Ar., Soph. EL iv. 165b 39.
3 Quoted by Austin, Jurisprudence, i. 482.
xxvn] APPENDIX ON FALLACIES 539
to hold them throughout to the precise meaning set forth in the
definition ; and so far as this is not done, the fallacy of Equivoca
tion arises. Locke in his Essay l defines ( idea ' as ( whatsoever the
mind perceives in itself, or is the immediate object of perception,
thought, or understanding ' ; but in the course of it he is at times
a victim to the ordinary associations of the word in English, which
contrasts ' my ideas ' with the ' realities '.
2. Amphiboly 2 is ambiguity in a phrase, in which the words are
used uni vocally throughout, but the meaning of the phrase as
a whole changes through change of the construction in which the
words are taken. A traditional example in Latin is ' Quod tangitur
a Socrate, illud sentit : lapis tangitur a Socrate : ergo lapis sentit ' •
in the major premiss, illud is the object of sentit • the conclusion is
drawn as if it had been the subject. So we might say in English :
' Polyphemus what he best loves doth devour : the ram that leads
the flock he loves the best : therefore the ram devours him '. Lawyers
are well aware of the importance of avoiding ambiguity in the
construction of a legal document (though under that head they
would include the ambiguities which Aristotle assigned to Division
and Composition, as well as Amphiboly and Equivocation too).
Whately cites a good example from the rubric at the beginning of
the Form of Service formerly ordered for use on Jan. 30, the anni
versary of the execution of King Charles I : f If this day shall
happen to be Sunday, this Form of Prayer shall be used and the
Fast kept the next Day following ' ; is the form of prayer to be
used on Sunday and the Fast kept on Monday, or are both to be
deferred ? Another famous and deliberate example is in the oracle
which Ennius said was delivered by Apollo to Pyrrhus — ' Aio te,
Aeacida, Romanos vincere posse/ 3 Ambiguous words and construc
tions are still not unfrequently used to deceive by those
' That palter with us in a double sense ;
That keep the word of promise to our ear,
And break it to our hope/
1 Bk. II., c. viii. § 8.
2 The Greek word is ap$i&o\ia, which is said to be an a-narr] nnpa TOV \<',yov,
as distinct from onuwpia, when the ambiguity is in an ovopa (Soph. EL vii.
169a 22). Hence arose the compound d/^t#oXoXoyi«, which became corrupted
into Amphibology, as ci'tiaXoAarpc/n became corrupted into Idolatry. There
seems to be no reason for not saying Amphiboly in English ; Amphibolia is
frequent in Latin (e.g. Crackenthorpe, Aldrichj.
3 Cf. Cic. de Divinatione, ii. 56. Cicero reasonably observes that Apollo
540 AN INTRODUCTION TO LOGIC [CHAP.
3 and 4. Composition and Division are the converse one of the
other. They consist in taking* together in the conclusion (or one
premiss) either words, or objects of thought, which in the premiss
(or the other premiss) were not taken together, or vice versa.
Plato in the Republic1 argues, from the fact that a man can
refuse the thing that he desires, that there must be a principle of
reason as well as of appetite in the soul. For, he says, it is impos
sible to be contrarily affected at the same moment towards the
same object in the same part of oneself (one cannot for example
at once loathe and long for the same object) ; yet a man who is
thirsty and refuses to drink is contrarily affected at the same
moment towards the same object ; he does not therefore refuse
drink on account of the character of his appetites, but because of
his reason; he reckons that to indulge his appetite would inter
fere with the pursuit of some other end which he prefers. Now
a sophist might attack this conclusion as follows : ' Are you
now drinking ? No. Can you now drink ? Yes. Therefore when
you are not doing a thing, you still can do it ? Yes. But if you
can do a thing when you are not doing it, you can desire a thing
when not desiring it ? Yes. And so you can be contrarily
affected in the same part of yourself (your appetitive nature) towards
the same object at the same time/ 2 The fallacy is one of compo
sition. The admission is that a man can when not desiring a
thing desire it, i. e. that when not desiring it, he is capable of
doing so ; this is used as if it meant that he can desire when not
desiring it, i. e. that he is capable of at once desiring and not desir
ing it; the words ' when not desiring it ' are taken, or compounded,
in one case with ' can ' and in the other with ' desire '. If a man
were to argue that three and two are five, and three and two are
odd and even, therefore five is odd and even, and the same number
may thus be both, he would be committing the same fallacy ; when
did not speak in Latin. Cf. Augustine, de Civ. Dei, iii. 17 ' Cui sane de
rerum future eventu consulenti satis urbane Apollo sic ambiguum oraculum
edidit, ut, e duobus quicquid accidisset, ipse divinus haberetur : ait enim,
Dico te Pyrrhe vincere posse Romanos : atque ita sive Pyrrhus a Romanis
sive Romani a Pyrrho vincerentur, securus fatidicus utrumlibet exspectaret
eventum.' Cf. also Henry VI, Part 2, Act i. Sc. 4, 11. 60-65.
1 Rep. iv. 436 A sq.
To dvvaa-dat fj.fj ypdxfrovra ypiicfrftv is an example of fallacy napa rfjv
trvvBiariv in Soph. El. iv. 166a 24. I do not know if the principle involved
was ever brought against Plato's argument.
xxvn] APPENDIX ON FALLACIES 541
it is said that three and two are odd and even, it is true only if
'odd and even' are not taken together, and predicated thus of
three and two, but if ' odd ' is separately referred to three, and
' even ' to two ; but the conclusion is drawn as if they were taken
together. On the other hand, the same argument furnishes an
example of the counter fallacy of taking separately in one premiss
words which were taken together in the other ; for three and two
together are five, but it is separately that they are odd and even,
and separately that in the conclusion each of them is declared to be
both. And the reader will doubtless have observed that the pre
vious example illustrates no less the division from one another
in the conclusion of words that were combined in the premiss than
the combination in the conclusion of words that in the premiss were
divided.
It was said above that in these fallacies either words or objects
of thought are taken in one place in the argument together and in
another separately. Of course the combination or separation of
certain words carries with it that we think differently in either case
of the things signified. But sometimes the illicit combination or
division made in thought is not reflected by taking words together
or apart. If any one were, upon the strength of the text in Gen.
i. 27 — ' So God created man in his own image, in the image of God
created he him ; male and female created he them ' — to argue
that man was originally created bisexual *, and that the present
division into male and female was the result of the Fall, and were
to base on that a condemnation of marriage, he would be guilty of
the fallacy of Composition ; and quite as foolish arguments have
been drawn from the words of Scripture upon such subjects. Now
here the fallacy lies in referring the words ' male ' and < female '
together to each person signified by * them ', instead of referring
1 male ' to one and ' female ' to another. But the point is the same
in the story of the showman who announced that children of both
sexes were admitted free, and then charged admission to boys and
girls alike on the plea that neither of them were children of both
sexes. Yet in the latter case there are no words that are wrongly
taken together ; it is the sexes thought of, to which the showman
pleaded that he had only promised to give free admission when
1 Cf. the fancy in Plato's Symposium, 189 D E.
542 AN INTRODUCTION TO LOGIC [CHAP.
combined. Words like loth and all, which may indicate equally a
distributive and a collective reference to the things signified by the
substantives to which they belong, are specially adapted to facilitate
this fallacy.1 Another and a double example of the fallacy of Com
position, in a business transaction, is afforded by the tale of a
railway enterprise in one of the British Islands. A company is
said to have been formed to build a railway, and to have announced
in its prospectus that a guarantee of 3°/o on the share capital
had been given by the Government, and a guarantee of 2°/o by
the local authority ; and later in the same document to have stated
that a guarantee of 5 °/o had been given by the Government and by
the local authority.
5. The fallacy of Accent meant to Aristotle one arising through
the ambiguity of a word that has different meanings when differ
ently accented. It was perhaps distinguished from Equivocation,
because words differently accented are not strictly the same word.
The Latin writers illustrate it in words which have different mean
ings when their quantity is different ; e. g. ' omne malum est f ugien-
dum, pomum est malum : ergo f ugiendum '. The ambiguity is of
course one which is more likely to occur in what is written than in
what is spoken.2 In English, which does not distinguish words by
tonic accent, the name is generally given to arguments that turn on
a wrong emphasis of some particular word in a sentence ; in which
if the emphasis were placed differently, the meaning might be very
different. The words of the Catechism in the ' Duty towards thy
1 It illustrates how much akin the different fallacies in dictione are, and
how the same example may from different points of view be regarded as
falling under different heads, that any one who likes can call the showman's*
trick, or others where words like all and both figure similarly, fallacies of
Equivocation. Aristotle does not give any such instances under the head of
(rvvtifins or diaipcffis • it has been however done by divers writers, and if we
look to the nature of the thought involved, justly. And the fallacies in
question might have been defined above as arising, when a conclusion is
reached by taking those things together which we are only entitled to take
separately, or vice versa (cf. Crackenthorpe, Logic, ed. quart, p. 353, cum quiz
tib iis coniunctis arguat, quae separation vera sunt, non coniuncta] ; for even
where words are taken together or separately in one part of the argument,
which were intended to be taken separately or together in the other, it is
only as this leads to our so taking what they signify that fallacy results.
But as this is reflected often in a definite combination and division of words,
and as that probably led to the erection of these as particular species of
fallacy based on ambiguous language, it seemed right to make express
mention of such cases in describing them.
2 Ar., Soph. El. iv. 166* 1.
xxvn] APPENDIX ON FALLACIES 543
Neighbour ' — ' to hurt no body by word nor deed ' — have by laying
stress on body been wrested to include the injunction to be kind to
animals.1
6. The fallacy of Figure of Speech arises through the ambiguous
force of some verbal inflexion, which is wrongly alleged to imply in
one case what it really implies in others. If a man were to argue
from the use of such an expression as ( I am resolved what to do', that,
because the passive signifies not action but being acted on, as in
' I am beaten ', ' I am praised/ therefore a man's resolution is not
his own free act, but the result of something done to him, he
would be guilty of this fallacy. Arguments from linguistic usage
of that sort are by no means uncommon or necessarily unsound : as
that the object of sight is not a visual sensation, because you say
that you feel a sensation, but no one would say that he felt a
colour. In this case there is no ambiguous inflexion, which is what
was held to constitute the differentia of the fallacy now under con
sideration. But let a man say that important is a negative notion,
because imperturbable or impenitent is, and we have a case in point.2
J. S. Mill in his Utilitarianism 3 affords an excellent example of
a man misled by this fallacy in a critical point of his argument.
He is trying to prove that the chief good, or one thing desirable, is
pleasure. ' The only proof/ he says, ' capable of being given that
an object is visible, is that people actually see it. The only proof
that a sound is audible, is that people hear it : and so of the other
sources of our experience. In like manner, I apprehend, the sole
evidence it is possible to produce that anything is desirable, is that
1 This example was given me from personal recollection. Not unlike this
fallacy, understood as consisting in basing on a wrong emphasis a conclusion
not intended by the speaker or writer, is the error of inferring from the
stress which a man lays on one element of a truth that he necessarily over
looks another. It might be said to be Hegel's conception of the progress of
speculative thought, that it advances by emphasizing first one and then the
other side of a contrast in such a way that the emphasis on one leads to
overlooking the other : until a new conception is reached which unites the
two. This indeed he considers inevitable in the development of philosophy.
But many writers have been erroneously interpreted, because it was thought
that when they insisted upon one aspect of a truth they intended to deny
Rome other aspect. This error of interpretation however could hardly be
classed with fallacies in dictione, since the misinterpretation does not arise
through the doubtful stress-accentuation of particular words.
a A lady once observed : 4 The question is, is he a postor or an
impostor?'
a p. 52 (Routledge's ed., ' New Universal Library,' p. 66).
544 AN INTRODUCTION TO LOGIC [CHAP.
people do actually desire it/ But visible, audible mean what can
be seen or heard ; whereas Mill is trying to prove that happiness
ought to be desired, or is the thing- worth desiring. Yet the termina
tion -able or -ible must be taken to have the same force in the word
desirable as in audible or visible, if the argument is to have any
force at all ; and the only thing shown is really that men can desire
happiness : which was never in question.
To distinguish the different sources of the ambiguity in the different
fallacies enumerated above is not a matter of first-rate importance ;
but to be alive to the errors into which ambiguities of language may
lead us is so. ' Verba plane vim faciunt intellectui, et omnia turbant/
wrote Bacon.1 Perhaps the disturbance which they caused was in some
respects more serious of old than now. We do not suffer less from the
subtle and unconscious shifting of the meaning of important terms
in a sustained argument ; but some of the more trivial and (as
we should say) obvious ambiguities may have been a more real
puzzle in olden days. ' The genius of uncultivated nations/ says
de Morgan 2, ' leads them to place undue force in the verbal mean
ing of engagements and admissions, independently of the under
standing with which they are made. Jacob kept the blessing
which he obtained by a trick, though it was intended for Esau :
Lycurgus seems to have fairly bound the Spartans to follow his
laws till he returned, though he only intimated a short absence, and
made it eternal : and the Hindoo god who begged for three steps
of land in the shape of a dwarf, and took earth, sea and sky in that
1 Nov. Org. 1. 43. The false ideas about nature generated through language
Bacon called idola fori. These false ideas or idola were classified by him
according as they had their sources in universal properties of human nature,
in idiosyncrasies of the individual, in language, or in false theories of
science and philosophy. The division was not logically perfect, and the
enumeration in each group is doubtless not complete. This illustrates in
a parallel field the difficulties above acknowledged to render a perfect
classification of fallacies impracticable. Bacon himself calls attention to
the parallel that exists between his undertaking and a classification of
fallacies : 'Doctrina enim de idolis similiterse habet ad interpretationem naturae,
sicut doctrina de sophisticis elenchis ad dialeciicam mdgarem ' (I. 40). The
' interpretation of nature ' involved more than reasoning ; it required the
use of the senses in observation, the recording of facts, the formation of
conceptions, or hypothesis, the invention of a nomenclature, &c. There are
obstacles in the way of the successful performance of these operations, no
less than of reasoning. The fallacies of the common Logic waylay us in
the work of reasoning. His idola arise from circumstances that waylay us
in all these tasks.
2 Formal Logic, p. 244.
xxvn] APPENDIX ON FALLACIES 545
of a giant, seems to have been held as claiming no more than was
granted. The great stress laid by Aristotle on so many forms of
verbal deception may have arisen from a remaining tendency
among disputants to be very serious about what we should now call
play upon words/ Just as many people tend to think that in
conduct the claims of veracity are satisfied or broken, according as
the facts can or cannot, by some verbal quibble, be brought within
the four corners of what they said or promised, so with argument
men may think that there is something in it, though the conclusion
turns upon an ambiguity of language. Not but what men are
often also too ready to assume that a controversy is merely verbal
when it is not.
In the enumeration of the fallacies which he recognizes, Aristotle
obviously had before him the practices of disputants in his own
day.1 One man, the ' respondent }, undertook to defend a thesis ;
the other, the * questioner ', attempted to extract admissions from
the respondent which involved the contradiction of his thesis. But
we find that a man might endeavour to discredit his opponent by
confuting him on a side issue ; and that it was a recognized device
to get him to admit something easier to attack than his original
thesis; though when Aristotle wrote, men had learned to reply
to the entrapping question by asking what it had to do with the
original thesis.2 Similarly we are told that answers in the form
of a plain yes or no were less insisted on when he wrote than
formerly ; whereby a bountiful source of unfair confutations was
cut off.3 The questioner is advised also not only to endeavour
to involve the respondent in a contradiction of his own thesis, but
to bring out its inconsistency with what is held by those whose
authority he or others may respect, or by mankind at large, or by the
majority of mankind, or by his own school.4 Nowadays formal
disputation has gone out of fashion. Men still harangue ; and we
understand by a debate a series of set speeches, in which a pro
posal is attacked and defended. Many of the devices which can be
1 Minto, in the first chapter of his Logic, Inductive and Deductive, speaks
as if Aristotle worked out his system of logic as a whole chiefly with the
conduct of disputation in view. He seems to me to have vory much over
stated his case ; but so far as the treatise on Sophistical Confutations ia
concerned, it is true.
2 Soph. El xii. 172b 16-24.
3 Ib. 175b 8-10. Cf. on the fallacy of Many Questions, p. 556, infra.
4 Ib. xv. 174b 19-23.
546 AN INTRODUCTION TO LOGIC [CHAP.
employed to produce the appearance of confuting an adversary are
common to rhetoric and dialectic — to the harangue and to the inter
change of question and answer. But if we were more familiar with
the latter mode of trying an issue, we should perhaps understand
better the scope that exists for some of the sophistical confutations
that Aristotle mentions. Such disputation is seen chiefly to-day in
courts of law, when counsel cross-examines a witness ; and an un
scrupulous counsel can still confuse a timid witness, and discredit
him before the jury, by involving him in contradictions more
apparent than real. And there have been times when matters,
which to-day are submitted to the judgement of the public by
means of speeches to and fro, reported in the newspapers, were
argued by chosen disputants according to fixed rules of debate
before an audience whose verdict, as to which side got the best of
the discussion, was of high practical importance. Not a few con
troversies of that sort were argued during the Reformation, at
Leipsic or at Marburg or at Zurich or elsewhere.
The fallacies in dictione have to some extent become of less im
portance through the decay of the habit of disputation. The
same cannot be said of those extra dictionem.1 These are not united
by any common character, as the others were by springing from
ambiguity in language.
1. The first in the list is the fallacy of Accident. The following
are some of the examples referred by Aristotle to this head : — ( This
dog is yours : this dog is a father : therefore he is your father/
' Do you know Coriscus ? Yes. Do you know the man approach
ing you with his face muffled ? No. But he is Coriscus, and you
said you knew him/ ' Six is few : and thirty-six is six times six :
therefore thirty-six is few/ His solution of the error involved
seems to be this. A thing has divers accidents, i. e. attributes
which are not commensurate with it nor essential to it; what is
predicable of the thing may or may not be predicable of its accidents,
and vice versa.2 Thus the dog is a father, and is yours ; but
it does not follow that the father is yours — that he is yours as
a father, as he is yours as a dog. Coriscus is approaching with his
face muffled; to be a man approaching with his face muffled is
1 Except perhaps ' Many Questions ' ; but cf. infra, p. 557.
2 Soph. EL v. 166h 30-32, xxiv. 179a 27-31.
xxvn] APPENDIX ON FALLACIES 547
an accident of Coriscus; and it does not follow that, because
Coriscus is known, a man approaching with his face muffled is
known to you. It is an accidental way of regarding thirty-six
things, that they are six groups of six things ; and though the
groups are few, the thirty-six are not therefore few. The defect
of the solution offered is, that it does not enable us to distinguish
between those cases in which what is predicated of a thing's acci
dents may be predicated of the thing itself, or vice versa, and those
in which it may not. € This dog is yours, and this dog is property
(or, a spaniel) : therefore he is your property (or, your spaniel) ' :
why is this argument valid and the former one not ? If you say
that the former is invalid because it equates subject and accident L
when they are incommensurate, why do you allow the latter,
which does so just as much ? A term and its definition may be
equated : they are commensurate, and wherever one occurs in
a judgement you may substitute the other without detriment to its
truth. But you cannot extend that rule to terms that have any
less close relation ; in other cases, you may be led into error
by such substitution or you may not ; the rule would not be
infallible.
We learn from Aristotle himself that other solutions than what
he formulated were offered for some of the fallacies referred by him
to the head of Accident 2 ; and as Poste says 3, ' the fallacy per
accidens has been generally misunderstood/ It has been very
commonly expounded in a way that does not really distinguish it
from the fallacy next to be considered, Secundum Quid. Indeed
what has happened is that the notion of the former has been
dropped, being somewhat ill defined, and the name of the latter,
being somewhat clumsy ; so that what to-day is commonly called
Accident is what the Aristotelian tradition called Secundum Quid.
But because the tradition recognized them as two, a distinction
between the direct and the converse form of the latter fallacy was
drawn, which is really quite unsubstantial.
2. The fallacy of Secundum Quid, or — to give the formula in
full — A dicto simpliciter ad dictum secundum quid, from which the
argument a dicto secundum quid ad dictum simpliciter is sometimes
1 The phrase is from Poste's ed. of Soph. El. (v. p. 73) : cf. esp. his remarks
on p. 158, from which the above interpretation and criticism are borrowed.
3 Soph. El. xxiv. 3 Op. cit. p. 158.
N n
548 AN INTRODUCTION TO LOGIC [CHAP.
distinguished as its converse, is one of the subtlest and commonest
sources of error. It consists in using- a principle or proposition
without regard to the circumstances which modify its applicability
in the case or kind of case before us. Water boils at a temperature
of 212° Fahrenheit; therefore boiling water will be hot enough to
cook an egg hard in five minutes : but if we argue thus at an altitude
of 5,000 feet, we shall be disappointed ; for the height, through the
difference in the pressure of the air, qualifies the truth of our
general principle. A proposition may be intended simpliciter or
without qualification ; or it may be intended subject to qualifica
tions and reservations. In the latter alternative, we may proceed to
apply it where the circumstances implied in our qualifications are
not present ; in the former, where there are circumstances present
which qualify its applicability.1 In saying that a proposition may
be intended simpliciter , it was not meant that it is intended as abso
lutely universal ; for the application of a principle true absolutely
universally cannot of itself lead to error, and a respondent brought
to admit a case inconsistent with a principle put forward thus
absolutely would be convicted of having put forward more than he
could sustain. It was meant that it is conceived to hold true
normally, or in any circumstances that the speaker contemplates ;
the fallacy wjiere there is an unfair confutation lies in extending it
beyond those circumstances. But it is not only in disputation that
the fallacy occurs. We are all of us at times guilty of it; we
argue from principles that hold good normally, without even
settling what conditions constitute the normal, or satisfying our
selves that they are present in the case about which we are arguing.
Freedom is good, and therefore it is supposed that every community
should have free institutions, though perhaps there are some races
only fit for a very moderate degree of c freedom '. A man should
be allowed to do what he will with his own ; and that is often
urged as a conclusive argument against any interference either with
his disposition of his property, or his education of his children.
Paris did nothing wrong in carrying off Helen, for her father
left her free to choose her husband ; but the freedom allowed her
extended only to her first choice, like the authority of her father.2
1 Cf. Dicey, Law and Opinion in England, p. 487, on the extension of
principles to fresh cases in 'judge-made law'. Cf. also Ar., Eth. Nic. e. x. 4,
1187" 14-19.
2 Ar., Rhet. |3. xxiv. 14011' 34, quoted by Poste, p. 117.
xxvn] APPENDIX ON FALLACIES 549
There are trivial examples of this as of any other fallacy, as that
if it be maintained that an Ethiopian is black, it is contradictory
to say he has white teeth J ; ' Few men die over eighty : I am over
eighty : therefore I shall probably not die/ 2 But there is no fallacy
more insidious than that of treating a statement which for many
purposes is true as if it were true always and without qualification.3
3. Ignoratio Elenchi means proving another conclusion than what
is wanted. The name does not literally mean that, but ' ignorance
of confutation '. But the business of any one undertaking to con
fute a statement is to prove the contradictory ; and if I prove
anything else, I show that I do not know what confutation requires.
Of course every fallacious confutation shows that I am ignorant of,
or ignore, what is required.4 But other fallacies have other defects ;
in this, the argumentation may be perfectly sound, and the sole
defect lie in the fact that the conclusion proved does not confute
the thesis maintained. Or — since it makes no difference whether
we regard a man as undertaking to confute one thesis or to sustain
another contradictory to it — we may say that the fallacy lies in
proving what is not the precise conclusion which we are called upon
to prove. Against a minister who proposes to put a small duty on
corn to-day it is no sufficient answer to prove that the people are
much more prosperous under free trade than in the days when corn
stood at 60 or 80 shillings a quarter ; against a free-trader it is no
sufficient answer to prove that foreign nations injure us by their
tariffs. Subterfuges of that kind are however so frequent a resource
of the orator, that it is hardly necessary to illustrate them. Every
reader of Plato's Apology will remember how Socrates refused to
appeal to his judges with tears and entreaties, or to bring his wife
and children into court to excite their commiseration ; for his part
1 Soph. EL v. 167a 11.
2 The fallacy here lies in referring to men over eighty a proposition which
is only true of men'simpliciter, viz. that few of them die over eighty. Solutions
however are possible, which would bring the argument under other heads.
3 The qualification may consist either in the presence of conditions not
contemplated in making the statement, or in the absence of some that were
contemplated (or at least that ought to have been contemplated). To argue
that because it is wrong to kill, a man should not fight for his country, is
a case of the former sort ; to argue that because wine is pernicious, there
fore its use should be forbidden (cf. de Morgan, Formal Logic, p. 251), of
the latter. The former would be called the direct, and the latter the con
verse fallacy. But it is clear that there is no difference in principle between
them.
4 Cf. Soph. EL vi. 168a 17sq.
550 AN INTRODUCTION TO LOGIC [CHAP.
was to persuade them, if he could do it, of his innocence and not of
his sufferings.1
Such appeals as Socrates declined to make are sometimes called
the argumentum ad misericordiam, arguments addressed to show that
a man is unfortunate and deserves pity, when it ought to be shown
that he is innocent, or has the law on his side. Other favourite
forms of irrelevant conclusion have also received special names.
The best known is the argumentum ad hominem, in which, being called
upon to confute an allegation, I prove something instead about the
person who maintains it. The politician who attacks an opponent's
measures by showing that they are inconsistent with his former
opinions commits this fallacy ; it is the same if I condemn Home
Rule for Ireland on the ground that Parnell was an adulterer. But
the argumentum ad hominem need not be altogether irrelevant.
A barrister who meets the testimony of a hostile witness by proving
that the witness is a notorious thief, though he does less well than
if he could disprove his evidence directly, may reasonably be con
sidered to have shaken it ; for a man's character bears on his credi
bility. And sometimes we may be content to prove against those
who attack us, not that our conduct is right, but that it accords
with the principles which they profess or act upon. Christ replied
to those who censured him for healing on the Sabbath, by asking
which of them, if his ox or his ass had fallen into a ditch, would
not pull it out on the Sabbath day.2 Their practice was sufficient to
justify him to them, whatever were the true theory of our duties
on the Sabbath. And Aristotle answers the Platonists, who held
all vice to be involuntary, by showing that they could not discrimi
nate in that respect between vice and virtue ; there was no more
reason for calling one involuntary than the other ; virtue, however,
they called voluntary ; and whatever be the true state of the case,
their position at least was not sustainable.3
4. The nature of Petitio Principii is better expressed in the
English name, Begging the Question.4 It consists in assuming
1 Apol 34 C, 35 B C. 2 Luke xiv. 1-6.
3 Eih. Nic. y. vii. 1114a 31-t>25.
* Gk. TO cv apxy Aa/i/3ai/eiv, TO (£ ap^rjs aiTfiadai, to assume or ask for the
admission of the very thing propounded for debate at the outset— the
Trp6fi\r)fjLa. The word petitio belongs to the terminology of disputation,
where the questioner sought his premisses in the admissions of the respondent.
He had no right to ask the respondent to admit the direct contradictory of
xxvn] APPENDIX ON FALLACIES 551
what is to be proved, in order to prove it. To do this within the
compass of a single syllogism — assuming in the premisses the very
thing to be proved, and not merely some thing which depends on
that for its proof — is only possible by the use of synonyms.
If I argue that C is A because B is A and C is B, and if the middle
term B is identical either with the major or the minor, then I use
the proposition to prove itself ; for let B be the same as A : then,
by substituting A for B in the minor premiss, I get ' C is A ' as
a premiss ; or let B be the same as C : then by substituting C for
B in the major premiss, I again get ' C is A f as a premiss ; and in
either case therefore the conclusion is among the premisses. Thus
let the syllogism be that to give to beggars is right, because charity
is a virtue; so far as charity is taken to include giving to beggars,
we have no business to assume that it is a virtue ; for the question
whether it is a virtue and the question whether it is right are the
same question : to call it a virtue is to call it right. Here the
major premiss, that virtue is right, is a tautology, and the minor
contains the petitio. On the other hand, if I defend legacy duties
by saying that property passing by will ought to be taxed, I beg
the question in the major; for a legacy duty is a tax on property
passing by will, and to say that such property should be taxed is
only to assert in other words the justice of a legacy duty.1
But the fallacy is generally committed less abruptly. The premiss
his thesis ; let the thesis, for instance, be that the Pope cannot remit the
temporal punishment of sin in Purgatory : the opponent may not ask the
respondent to admit that he can. If by some verbal disguise he gets the
respondent to admit it, it is only a sophistical confutation ; the respondent
did not see what he was granting, and would have refused to grant it if he
had seen — not because it led to the contradictory of his thesis, for a man is
often fairly refuted by showing that he cannot reasonably deny something
which does that : but because it was the contradictory of it. It is quite fair
to try to get a man to admit a general principle, and then to show that his
thesis is inconsistent with it, provided that the general principle does not
really require the disproof of his thesis in order to its own establishment.
Hence the term principium is a mistranslation. The fallacy lies in begging
for the admission not of a principle to be applied to the determination of
the matter, but of the very matter, in question. As occurring in a book or
speech, where a man puts forward his own premisses, and has not to get
them by the admission of a respondent, it consists in assuming among the
premisses either the conclusion itself which a show is made of proving, or
something more or less directly depending thereon. Cf. Mansel's Aldrich,
App. E.
1 It is also possible to beg the question when the conclusion is negative,
but then only in the major premiss ; and to beg it in other figures than the
first (for details see Poste, Soph. EL, App. A). Cf. also supra, p. 538, n. 1.
552 AN INTRODUCTION TO LOGIC [CHAP.
unduly assumed is generally not the conclusion itself differently
expressed, but something- which can only be proved by means
of the conclusion ; and arguing thus is often called arguing in
a circle. If I argued that early Teutonic societies were originally
held together by kinship, because all societies were so held together
originally1, I might be accused of arguing in a circle; for the
major premiss, it might be said, is only arrived at by enumera
tion ; early Teutonic societies have to be examined in order to
show that it is true. Of course to show that the generalization
was not enumerative would be to rebut the accusation ; but,
as we saw in discussing ' the view that all syllogism is petitio
principii, every syllogism whose major premiss is an enumerative
judgement is so.2 The circle is fairly manifest in such cases ;
but in others it may often escape the notice of its author.
' There are certain people/ says Dr. M°Taggart 3, ' who look on all
punishment, as essentially degrading. They do not, in their saner
moods, deny that there may be cases in which it is necessary. But
they think, if any one requires punishment, *he proves himself to be
uninfluenced by moral motives, and only to be governed by fear. . . .
They look on all punishment as implying deep degradation in
some one, — if it is justified, the offender must be little better than
a brute ; if it is not justified, the brutality is in the person who
inflicts it. This reasoning appears to travel in a circle. Punish
ment, they say, is degrading, therefore it can work no moral
improvement. But this begs the question. For if punishment
could work a moral improvement, it would not degrade but elevate.
The humanitarian argument alternately proves that punishment
can only intimidate because it is brutalizing, and that it is brutal
izing because it can only intimidate/ Romanes finds an example
of petitio in an argument of Huxley's, adduced to show that all
specific characters are adaptive.4 ' Every variety which is selected
into a species is favoured and preserved in consequence of being, in
some one or more respects, better adapted to its surroundings than
its rivals. In other words, every species which exists, exists in
1 For the general statement see Sir Henry Maine, Early Institutions, p. 64.
2 p. 282, supra.
8 Studies in Hegelian Cosmology, § 142. By punishment here is meant
' the infliction of pain on a person because he has done wrong ' (§ 137). And
it is of corporal punishment that we most often hear this view expressed.
4 Dancin and after Darwin, ii. 307.
xxvn] APPENDIX ON FALLACIES 553
virtue of adaptation, and whatever accounts for that adaptation
accounts for the existence of the species/ Here the fallacy lies in
substituting-, for ' every variety which is selected ', ' every species
which exists ' ; the statement in the first clause is true for every
variety which is selected, since selection means the survival of those
best adapted to the conditions of life. But the question is whether
every species which exists has originated by 'selection'. One
more instance may be cited, from a work on the squaring- of the
circle, called The Nut to Crack, by James Smith.1 Smith held the
ratio of circumference to diameter to be 3J, and proved it thus :
' I think you will not dare to dispute my right to this hypothesis,
when I can prove by means of it that every other value of TT will
lead to the grossest absurdities ; unless indeed you are prepared to
dispute the right of Euclid to adopt a false line hypothetically, for
the purpose of a reductio ad absurdum demonstration, in pure
geometry/ That is, he argued first that if 3J be the right
ratio, all other ratios are wrong ; and then, that because all other
ratios are wrong, 3J is the right ratio. And he conceived that he
had established his conclusion by a reductio ad alsurdum — by
showing that the denial of his thesis led to absurdity. But the
absurdity, in such an argument, ought to be ascertained indepen
dently, whereas here it rests upon the assumption of the truth of
what it is used to prove.
5. The fallacy of False Cause is incident to the reductio ad
absurdum. That argument disproves a thesis by showing that the
assumption of its truth leads to absurd or impossible consequences,
or proves one by showing the same for the assumption of its
falsity.2 In False Cause, the thesis alleged to be discredited is not
really responsible for the absurd or impossible consequences, which
would follow equally from the other premisses, whether that were
affirmed or denied. ' It is ridiculous to suppose that the world can
be flat ; for a flat world would be infinite, and an infinite world
could not be circumnavigated, as this has been/ Here the suppo
sition inconsistent with the fact of the circumnavigation of the
world is not that the world is flat, but that it is infinite ; it might
1 Cf. de Morgan. Budget of Paradoxes, p. 327.
2 James Smith argued, not that ' if A is false, B will be true : but B is
false, /. A is true ' ; but ' if A is true, B will be false— (as to which nothing
was known)—.*. A is true'.
554 AN INTRODUCTION TO LOGIC [CHAP.
be flat and still circumnavigable, if it were finite ; the thesis of its
flatness is therefore unfairly discredited.
From a passage in the Prior Analytics it would seem that Aris
totle regarded this fallacy as of frequent occurrence.1 But the fact
that later writers have largely given a different meaning to the name
suggests that it is not really a prominent type. It is often iden
tified with the fallacy Post hoc, ergo propter hoc : i. e., supposing
that one event is due to another, merely because it occurred after
it ; as the countryman is said to have declared that the building of
Tenterden Steeple was the cause of Goodwin Sands, because the
sands only appeared after the steeple was built. Such, as Bacon
truly says, is the origin of almost every superstition — of men's astro
logical fancies, and their fancies about omens or dreams. The story
which he quotes may well be repeated in his own words. c Itaque
recte respondit ille, qui, cum suspensa tabula in templo ei monstra-
retur eorum qui vota solverant, quod naufragii periculo elapsi sint,
atque interrogando premeretur, anne turn quidem deorum numen
agnosceret, quaesivit denuo, At ubi sunt ill'i depicti qui post vota
nuncupata perierint ? ' 2
Inferences of this kind are undoubtedly both frequent and falla
cious ; and Post hoc, propter hoc is a type or locus of fallacies in the
same sort of way as those enumerated by Aristotle. That is, it is
a general or dialectical principle — a principle applicable in divers
sciences, and not exclusively appropriate in any : and it is a false
principle, the application of which is as likely to lead to error as to
truth. Nor is it peculiar to this fallacy, that it can be expressed
as a false principle. Equivocation proceeds on the false principle
that a word is always used with the same meaning : Accident, on
the principle that whatever is predicated of a thing may be pre
dicated of its attribute, and vice versa : Secundum Quid, on the
principle that what is true with certain qualifications is also true
without them. And the fact that these different types of fallacious
inference severally depend on a false, or misleading, principle is
1 Anal. Pri. /3. xvii. 65a 38 TO 8e prj irapa TOVTO trvpfiaivfiv TO ^revdos, 6
TroAXoKir ev rots \6yois ei<a0ap.fv Xfyciv, /c.r.X. Cf. Poste's Soph. EL, App. B,
on this passage.
2 Nov. Org. I. 46. Bacon cites the story in illustration of one of the
' Idola Tribus ', the tendency to overlook or despise facts which do not agree
with an opinion which we have once adopted. J. S. Mill would call this
the fallacy of Non-observation (System of Logic, V. iv).
xxvn] APPENDIX ON FALLACIES 555
what was meant by calling them loci of fallacy.1 But the locus
Post hoc, propter hoc is not quite the same as that of Non causa pro
causa : in other words, the type is a little different. In False Cause
we are dealing with the logical sequence of premisses and conclu
sion ; the fallacy lies in connecting the conclusion with a particular
premiss which might, so far as getting the conclusion is concerned,
have been equally well included or omitted ; and because the con
clusion is false, we erroneously infer this premiss to be false also.
In Post hoc, ergo propter hoc we are dealing with the temporal rela
tion of cause and effect ; the fallacy lies in connecting the effect
with a particular event which might equally well have happened
or not happened, so far as the effect in question is concerned ; and
we erroneously suppose that the effect, which did occur, occurred
because of that event. But if any one likes to use the name False
Cause as equivalent to Post hoc, propter hoc, there is not much harm
done ; for the fallacy which Aristotle meant is not one that we have
much occasion to speak of.
6. It is otherwise with the fallacy of the Consequent, which some
modern writers have also misunderstood.2 For this is one of the
very commonest, and we have already had occasion to notice it
in discussing inductive reasoning.3 It consists in supposing that
a condition and its consequent are convertible : that you may argue
from the consequent to the condition, no less than vice versa. If
a religion can elevate the soul, it can survive persecution : hence it
is argued that because it has survived persecution, such and such
a religion must elevate the soul; or perhaps (for we may follow
Aristotle 4 in including under the name both the forms of fallacy
1 The Sophistici Elenchi is the concluding book of Aristotle's Topics.
2 e. g. de Morgan, Formal Logic, p. 267 ; Jevons, Elementary Lessons, p. 181.
3 p. 486, supra.
* Cf. Soph. EL XXVlii. 181a 27 Trap* 6 /cat 6 rov MfXiVo-ou \6yos' el yap TO
ycyovbs e^ft "PX*JV> T° ay«"7T°" a^iol pf} f\fiv' ®CTT> " ayfvrjros 6 ovpavoy, *at
anetpos. TO fi* ov< earn** avaira\iv yap f) aKo\ovdr](Tis ('with this accords the
argument of Melissus ; for he thinks that if what is generated has a beginning,
what is ungenerated has not ; so that if the heaven is ungenerated, it is also
infinite. But this is not so ; for the sequence is the other way ') ; i. e. from
' A is B' you cannot infer 'not-^l is not-B', but only contrariwise, ' not-B is
not- A' It appears by the same chapter that Aristotle would bring the
illicit, viz. simple, conversion of an universal affirmative judgement under
the same heading. This illustrates the close parallelism between the modi
ponens and tollens in hypothetical, and Barbara and Camestres in syllogistic
reasoning (cf. pp. 312-315, supra). But that Aristotle did not identify them
might perhaps be inferred from the fact that he does not include Undistributed
Middle and Illicit Process of the Major in his list of sophistical confutations,
556 AN INTRODUCTION TO LOGIC [CHAP.
to which hypothetical reasoning is liable) that because it is in
capable of elevating the soul, it will succumb to persecution. Such
fallacies are committed whenever a theory is assumed to be true for
no better reason than that the facts exist, which should result if it
were true — i. e. whenever verification is mistak en for proof 1 ;
and whenever the refutation of an argument advanced in support
of a theory is supposed by itself to be fatal to the theory. If it
can be shown that no other theory accounts for the facts, or that
no other argument can be advanced in support of the theory,
then the matter is different ; but without some reason to believe
this, such inferences are worth nothing. Nevertheless, they are
inferences which we are all very apt to make.2
7. There remains lastly the fallacy of Many Questions. This
consists in putting questions in such a form that any single answer
involves more than one admission. If one admission be true and
another false, and the respondent is pressed for a single answer,
he is exposed to the risk of confutation, whatever answer he
makes. < The execution of Mary Queen of Scots was brutal and
sacrilegious — was it, or was it not ? ' If it was brutal but not
sacrilegious, what is a man to answer? He will be accused by
saying no of denying the brutality, by saying yes of affirming
the sacrilege. Sometimes, instead of submitting two problems for
decision together, the question appears to submit only one ; but
that is one which would not arise except on the assumption of
a certain answer to another : and so the respondent again cannot
answer it without committing himself to more than he intended, or
on a matter which has not been definitely submitted to him. Of
this sort is the famous enquiry, ' Have you left off beating your
while he does include, under the name of the fallacy of the Consequent,
the corresponding though not identical errors which may be committed in
hypothetical reasoning. It may be noted that such inferences would only
not be fallacious where condition and consequent reciprocated — a relation
which corresponds to that of commensurate terms in an universal affirmative
judgement. Hence Aristotle says that the fallacy of the Consequent is
a case of that of Accident (Soph. EL vi. 168b 27). Under it in turn might be
brought Post hoc, propter hoc. If Goodwin Sands were caused by building
Tenterden Steeple, they would have appeared, as they did, so soon as the
steeple was built ; but they might equally have done so, if the building of
the steeple had nothing to do with their appearance.
1 Cf. p. 486, supra.
2 This fallacy is ' logical ', or formal ; it can be expressed in symbols. So
can an argument in a circle sometimes be ; e. g. if it is of the form 'A is B,
B is C .-. A is C: and B is C because A is C and B is A '.
xxvn] APPENDIX ON FALLACIES 557
mother ? ', as well as any question that asks for the reason of what
has not been admitted to be true. It is often recounted how
Charles II asked the members of the Royal Society why a live fish
placed in a bowl already full of water did not cause it to overflow,
whereas a dead fish did so ; and how they gave various ingenious
reasons for a difference which did not exist. If one were to enquire
why a protective system encourages the industry of the country
which adopts it, the fallacy would be the same ; there would perhaps
be some dispute as to whether it is fallacious to ask how dowsers
are made aware by their feelings of the presence of subterranean
waters. It may be said that a respondent is always able to give
an answer which will save him from any misconstruction ; to the
question ' Have you left off beating your mother ? ' the answer ' no '
might seem to be an admission of the practice ; but why should not
a man reply 'I never began it ' ? To this it may be rejoined, first,
that in the old disputations, and in some situations, such as the
witness-box, to-day, a man might be more or less precluded from
' explaining himself ', and required to give a ' plain answer ' to
a question which does not admit of it. With the use of the fallacy
under this sort of duress may be compared the custom of ' tacking '
in the American legislature. The President of the United States
can veto bills, and does veto them freely ; but he can only veto
a bill as a whole. It is therefore not uncommon for the legislature
to tack on to a bill which the President feels bound to let pass a
clause containing a measure to which it is known that he objects ;
so that if he assents, he allows what he disapproves of, and if he
dissents, he disallows what he approves.1 But secondly, even
where no unfair duress is employed, the practice of presupposing
a certain answer to one question in the form of putting another
throws the respondent off his guard, and makes him apt to admit
without considering it what, if it had been explicitly submitted to
his consideration, he might have doubted or denied.
The fallacy therefore is not a trivial one ; such questions are
a real source of error, when we put them to ourselves : of unfair
confutation, when we put them to others. But it is doubtful
whether it is a fallacy extra dictionem. For the ambiguity or
unavoidable falsehood which must in some cases attach to the
answer is a consequence of the way in which the question is
1 Bryce's American Commonwealth.
558 AN INTRODUCTION TO LOGIC
worded ; and the same may be said of the acquiescence in false
assumptions, into which in other cases we are entrapped.
The foregoing- remarks have been directed to explain what are
the types of fallacy which have been traditionally distinguished,
and are still many of them very commonly referred to by name.
The types are not all equally distinct, frequent, or important ; but
the original meaning of each name has been given as far as pos
sible, because nothing but misunderstanding can result when
different writers employ such terminology each in his own mean
ing, and there did not for the most part seem sufficient reason to
prefer any later interpretation for a standard. In a few cases later
interpretations which have much to be said for them have been
given as well. No doubt Fallacy is a subject on which successive
generations to some extent need a new treatise : not because the
principles change, but because the fields change in which they are
most prolific. Many suggestive illustrations of the dominion
which fallacy holds in important subjects of contemporary thought
may be found in the pages of Whately, Mill, or de Morgan,
to which reference has already several times been made.
INDEX
Abscissio Infiniti, 112-13.
Abstraction, its place in Induction,
440, 471.
Accent, fallacy of, 542.
Accident, as a Head of Predicables,
61 sq. : separable and inseparable,
94-5 : fallacy of, 533 n. 1, 546, 554.
Accidental judgements, 190.
Aldrich, H., his Logic cited, on def. of
Modality, 183 : form of Barbara Cela-
rent, 261 n. 3, 539 n. 2.
Amphiboly, fallacy of, 539.
Ampliative judgements, 185, 189.
Analogy, argument from, 492 sq. :
origin of modern sense of, 497, 498
n. 1 : no proof by, 498 : how related
to Induction by Simple Enumera
tion, 500-2 : involves a general prin
ciple, 502.
Analysis in Induction, 423-6, 456-7.
Analytic judgements, 185-90.
Apelt, Professor O., on Aristotle's
Categories, cited, 39 n. 1.
Apodeictic judgements, 173-6, 182.
A posteriori reasoning, 400-3.
Appellatio, 140 n. 1.
A priori reasoning, 401.
Arbor Porphyriana, 115-17.
Arguing in a circle, 552.
Argumentum ad hominem, 533 n. 1,
550 : ad misericordiam, 550.
Aristotle, his definition of a term,
13 n. 2 : of a name, 137 : of syllogism,
224 : on of-iajw^ia and avvuvvfja, 21 : on
ovo/j,a aupiGTov, 30 : on the Categories,
c. iii pass. : on Matter, 41 : on the
Predicable, c. iv pass. : on the four
elements, 86 : on Definition, 114 — cf.
s. v. 'Definition': on irapuvvfjia, 118
n. 1 : on Modality, 184 n. 1 : on
modal syllogisms, 416 n. 1 : on the
Quantification of the Predicate, 200
n. 1 : on indirect conclusions ( = the
so-called fourth figure) in syllogism,
234 n. 1, 258-62, 305 : not the author
of the Dictum de Omni, 274 n. 1, 282 :
on eK0e<m, 296 : 011 hypothetical
reasoning and the av\\oyt<r^s (£
vTToQffffojs, 316 n. 1 : on Enthymeme,
323 n. 1 : on the inductive syllogism,
351-2 : on Induction in the modern
sense, 363 : on the establishment of
i, 359-63 : on tSiat and Koival apxai,
360 n. 1 : on irapdStiypa ( = argument
from analogy), 496, 501 : on fallacies,
c. xxvii pass. : his division of fallacies,
533-4 : his logical writings, 282 n. 1,
348 : his Topics, 361-3 : distinction of
formal, material, final and efficient
causes, 451 : theory of motion, 478 :
demonstration always syllogistic, 487.
Cf. also 32 n. 1, 59 nn. 1, 2, 61 n. 2,
62 n. 1, 66, 68 n. 3, 73, 77 n. 1, 81,
87 n. 1, 98 n. 1, 100, 105, 111, 121,
127, 150 n. 1, 155 n. 1, 207 n. 1, 224
237, 239 n. 1, 240, 283 n. 2, 285 n. 2,
288 n. 2, 302 n. 1, 314 n. 2, 325 n. 3,
350 nn. 1-4, 351 n. 1, 365 n. 2, 378 n. 1,
407 n. 1, 416 n. 1, 489, 548 n. 1.
Assertoric judgements, 169, 171-3.
Association of ideas, 502.
Augmentative judgements, 185, 189.
Austin, J., Jurisprudence, quoted, 538.
Averroes on Fig. 4 of syllogism, 258.
Bacon, Francis, Lord Verulam.quoted,
248 n. 1, 342, 345, 352, 364-6, 397, 402,
425, 429, 435 n. 1, 451, 488 n. 2, 490,
524 n. 1, 525 n. 1, 544 n. 1. 554.
Bain, Alexander, cited, 122 n. 2, 275 n.,
298 n. 1.
Balfour, Rt. Hon. A. J., quoted,
469 n. 1.
Barbara Celarent, history of, 244 n. 1 :
form of in Petrus Hispanus, ib. : in
Aldrich, &c., 261 n. 3, 262.
Begging the question, 550.
Boethius, 53 n. 2, 321 n. 1.
Bosanquet, Prof. B., cited, 125 n. 1,
138, 152 n. 1, 158 n. 1, 406 n. 1.
Bradley, Mr. F. H., cited, 10 n. 1, 29
n. 1,54 n. 1,125 n. l,130n.l, 152 n. 1,
156 n. 2, 157 n. 1, 158 n. 1, 166, 205
n. 1, 209 n. 1, 217 n. 2, 227, 229, 368
n. 1, 405 n. 1, 502 n. 1, 513 n. 1.
Bryce, Rt. Hon. J., American Common
wealth, cited, 557 n. 1.
Buridanus, Joannes, on nomina connota-
tiva, 140 : on Modality, 184 n. 1.
Categorematic words, 14.
Categories, Aristotle's doctrine of,
c. iii : its relation to Kant's, 48sq.,227.
Causation, Law of, c. xix pass. : in-
560
INDEX
volves uniformity, 371-2, 374-6, 378 :
assumed in physical science, 371, 504 :
with what right assumed, 390 : cannot
be proved inductively, 386-90, 510:
grounds of elimination furnished by,
403 : laws of, to be discovered, 372.
Cause, meaning of, 371, 376, 459-60 :
why investigated, 443-9 : non-recipro
cating, c. xxii : Aristotle's doctrine
of, 451 n. 1 : continuity of with effect,
450 : apparent discontinuity i n certain
cases, 452-4 : composition of causes,
483 n. 1 : plurality of causes, 455 sq.,
486, 516 : problem of, how related to
doctrine of the Predicables, 64-7.
Certainty in science, why hard to ob
tain, 467.
Change, impliessomething permanent,
450 : continuity of, ib.
Class, meaning of inclusion in a, 69-71.
Classification, 101 sq. : its relation to
Logical Division, 118-20.
Collective judgements, 156 : c. terms.
26-7.
Colligation of facts, 433 sq.
Commensurate terms, 58, 89-90.
Comparative Method, the, 522.
Composition of Causes, 483 n. 1 :
fallacy of c., 540.
Concept, its nature, 16-18, 55-7 : alone
definable, 67.
Conditional judgement, 321 n. 1 : c.
principles in science, 381-6.
Conjunctive judgement and inference,
321 n. 1.
Connotation and Denotation of terms,
131 sq. : no terms non-connotative,
132 : history of word connotare, 140-2.
Consequent, fallacy of, 486, 555.
Contradiction, Law of, 360 n. 1.
Contradictory judgements. 205.
Contraposition of propositions, 215-17.
Contrary judgements, 205 : terms, ib.
n. 1.
Conversion of propositions, 210 :
simple c., 210 : c. per accidens, 211 :
c.,by negation, 215 : whether a process
of inference, 217-23.
Cook Wilson, Prof. J., cited, 42 n. 2.
Copula, nature of the, 145-53.
Crackenthorpe, R., Logica, cited, 34, 93
n. 2, 261 n. 1, 539 n. 2, 542 n. 1.
Crucial instance, 524.
Darwin, C., quoted, 430, 492 n. 1.
Deduction, meaning of the word, 350
n. 1, 365: contrasted with Induction,
368, 505.
Definition, 59, 72 sq. : nominal, 77 sq.:
rules of, c. v.
Demonstration, 349, 487.
de Morgan, A., Formal Logic, cited, 32
n. 1, 528 n. 2, 533 n. 1, 536 n. 1, 544,
549 n. 3, 555 n. 2, 558 : Budget of
Paradoxes, 553 n. 1.
Denotation of terms, 131 sq.
Derivative laws, 381.
Descartes, R., quoted, 488 n. 1.
Designations, 19, 21.
Development, the meaning of, 73-4.
Dialectical reasoning, 359-61.
Dichotomy, 106 sq.
Dictum de Omni et Nullo, 274, ib.
n. 1, 285.
Differentia, 60, 67 sq. : constitutive
and divisive, 115.
Dilemma, 330-7 : destructive d. may
be simple, 332-4.
Disjunctive judgement, 166-8 : d.
reasoning, 317-21 : in induction, 366,
396, 406.
Distribution of terms, 192-7 : in syllo
gism, 247-54.
Diversity of effects, 455 sq.
Division, Logical, rules of, 101 sq. :
stops with inflmae species, 116: cross-d.,
104: Physical D. (= Partition), 117:
Metaphysical D., 117 : fallacy of D.,
540.
Downam, G., Comment, in Petr. Eami
Dial, cited, 327 n. 3.
Elimination, its place in induction,
395, 456-8 : grounds of, 403.
Empedocles, 86.
Empirical facts, 355 : e. generalization,
490.
Enthymeme, 323-6 : Aristotelian sense
of, 323 n. 1.
Enumeration, Simple, Induction by,
489 sq.
Enumerative judgements, 156.
Epicheirema, 325.
Episyllogism, 325.
Equipollency of propositions, 214 n. 1.
Equivocation, fallacy of, 538, 554.
Essence, 77 sq., 355 : in geometry,
82 sq. : nominal e., 77-8, 280.
Essential judgements, 185, 190.
Exceptive judgements, 190.
Excluded Middle, Law of, 29 n. 1.
Exclusiva, Bacon's, 365.
Exclusive judgements, 190.
Experiment, importance of to induc
tive reasoning, 439, 457 : in some
enquiries impossible, 514.
Explanation, c. xxiii : not possible
from 'common principles', 466: of
particular facts and of laws, the same
in kind, 466, 471 : examples of, 472-
84 : as sub.sumption, 476 : deductive
and inductive reasoning in, 476 sq.
INDEX
561
Explicative judgements, 185, 189.
Exponibilia, 191.
Exposition or eieOtais, 296.
Extension of terms, 121 and c. vi pass.
Fallacies, c. xxvii : reasons for dis
cussing in a treatise on Logic, 525-8 :
difficulty of classifying, 528-33: defini
tion of, 525, 535 : in dictione and extra
dictionem, 534, 537-8 : logical and
material, 534.
False Cause, fallacy of, 553.
Figure of Speech, fallacy of, 543.
Figure of syllogism, what, 233 :
Galenian, or fourth, f., 235, 257-61 :
determination of moods of first f.,
242-5 : do. of the several f., and their
rules, 254-7, 262-3.
*Form and Matter contrasted, 75-6 :
I of thought, 4 sq., 143 n. 1, 166, 213,
~223, 338-9 : species as form, 73, 75.
Forms, Bacon's doctrine of, 364-5.
Fowler, T., his use of symbols in
representing inductive arguments,
405 n. 1.
Fry, Sir Edward, quoted, 337.
Fundamentum Divisionis, 72, 104.
Galenian figure of syllogism, 235,
257-61.
Genus, 59, 67 sq. : should be an unity,
ib. : distinguished from class, 69-71 :
summum, subalternum and proximum g.,
102.
Geometry, distinction of definition
and property in, 82 sq. : cf. s. v.
'Mathematics'.
Grote, J., Exploratio Philosophica, quoted,
55 n. 1.
Hamilton, Sir William, cited, 122 n. 2,
245 n., 262 n., 325 n. 2, 327 n. 2.
Heeel, G. W. F., cited, 47, 285 n. 1.
Herschell, Sir John, cited, 367.
Hippocrates, his attempt to square the
circle, 531.
Historical Method, the, 522.
History and Science contrasted, 63,
218, 432, 472-3.
Hobbes, Thomas, his def. of a name, 15,
137 : thought all inference syllogism,
229 n. 1 : Nominalism of, 278.
Hume, David, cited, 367, 376, 404 n. 1,
406, 494.
Hypothesis, its place in induction,
428-39 : not to be restricted by Logic,
430.
Hypothetical judgement, 163-8 : h.
reasoning, 308-11, 321 n. 1 : do., not
reducible to syllogism, 312-17.
Identity, Law of, 378.
Ignoratio Elenchi, fallacy of, 535, 549.
Immediate inference, meaning of
term, 209 : processes of, c. x : how
far really inference, 217-23.
Individuation, Principle of, 43, 67,
75-7, 117, 131.
Induction, c. xviii pass. : meaning of
word, 350 : confusion in use of, 367 :
Perfect !.( = !. by Complete Enumera
tion), 352, 363 : confusion in contrast
of Perfect with Imperfect I., 467-8 :
the I. of the inductive sciences assumes
universal connexions in nature, 371 :
deductive reasoning often involved
in, 476 sq. : in dealing with a com
plex effect, 484-5 •: examples of, 408-
21, 426-8, 436-9, 442-5, 452 3 (cf. 63
n. 1) : I. by Simple Enumeration,
489 sq. : its relation to argument
from Analogy, 500-2 : its occurrence
in mathematics, 503: Mathematical
I., 503-4 : its relation to the I. of the
inductive sciences, 504-9.
Inductive Methods, Mill's so-called,
394-9 ; their basis, 404 n. 1:1.
reasoning, preliminaries necessary
to, c. xxi.
Inference, general nature of, 209 :
Bradley 's def. of, 513 : Immediate I.,
210 sq. : validity of any i. self-
evident, 241, 316 n. 1: i. not all
syllogistic, 229, 272-3, 338 : a priori
and a posteriori i., 400-3, 515 : i. not
from particulars to particulars, 502.
Infinite terms, 30, 112, 220: i. judge
ments, 162 n. 1, 191.
Instantia, original meaning of, 491
n. 1 : crucis, 524 n. 1 : ostensiva, 525
n. 1 : prerogativa, 366 n. 2 : solitaria,
397 n. 2.
Intermixture of Effects, homogeneous
and heteropathic, 483 n. 1.
James, Prof. W., Principles of Psychology,
cited, 383 n. 1, 533 n. 1.
Jevons, W, S., cited, 13 n. 2, 109.
119, 122 n. 2, 214 n. 1, 356 n. 1, 368
n. 1, 370 n. 1, 398 n. 1, 405 n. 1,
467, 490 n. 2, 516 n. 2, 536 n. 3.
Judgement, the true unit of thought,
12 : nature and forms of, c. vii :
properly expressed by the indicative,
144 : the copula in, 145 sq. : logical,
grammatical and metaphysical subject
of, distinguished, 150: distinction of j.
according to Quantity, 154-61 : do.
Quality, 161-3 : do. Relation, 163-8 :
do. Modality, 168-85 : enumerative or
collective, and universal j., distin
guished, 158: modal particulars, 180:
O O
562
INDEX
infinite j , 163 n. 1 : analytic and syn
thetic, essential and accidental, verbal
and real j. , 1 85-90 : exceptive and exclu
sive j., 190 : exponiblej., 191 : opposition
of j., 205 8: conversion, permutation
and contraposition of j., 210-23: a j.
does not assert agreement or disagree
ment between its terms, 248 n. 1.
Kant, I., his doctrine of Categories,
47 sq. : on analytic and synthetic
judgements, 185-90 : his canon of
syllogism, 286 : on change, 450 : on
Applied Logic, 514 n. 1.
Kepler, J., his hypothesis of elliptic
orbits, 435: the 'three laws of, 480,
495. >.
Knowledge ' of acquaintance ' and
' kn. about ', 55.
Lambert of Auxerre, 258 n. 2.
Lambert, J. H., Neues Organon, on Fig. 2
of syllogism, 292 n. 1.
Lang, Dr. Andrew, Custom and Myth,
quoted, 496, 522.
Laplace, P. S., Marquis de, quoted, 429.
Lavoisier, A. L., oxygen-theory of, 437.
Laws of nature, 358, 380 : precautions
necessary in formulating. 516 sq. :
their character, 384-5 : conditional,
unconditional and derivative, 380-2.
Leibniz, G. W. von, cited, 158 n. 1, 328,
470.
'Lewis Carroll,' quoted, 288 n. 1,
530 n. 1.
Locke, John, quoted, 3, 78, 233 n. 1,
248 n. 1, 280, ib.n.2, 288 n. 3, 533 n. 1.
Logic, defined, c. i, cf. 169 : how far
formal, 4-7, 143 n. 1, 165, 214:
not an art, 8-9 : false antithesis be
tween L. of Consistency and L. of
Truth, 230-1, 342 : Deductive and
Inductive, wrongly opposed, 343 n. 2,
368-9 : relation of progress in, to
progress of science, 342-7 : Inductive
L., history of, 366-7 : Applied L., 514.
Lotze, H., cited, 368 n. 1, 370 n. 1,
387 n. 1, 404 n. 1, 430 n. 2, 498 n. 3.
M^Taggart, Dr. E., Studies in Hegelian
Cosmology, quoted, 495, 552.
Maine, Sir Henry, quoted, 472, 497,
552 n. 1.
Major term, why so called, 235 9 : m.
premiss, how far surviving in com
plete knowledge, 307, 487 n. 2.
Mansel, H. L., Prolegomena Logica,
quoted, 165 : ed. of Aldrich's Logic, do.,
274 n. 1, 325 n. 3, 333, 336 n. 2,
550 n. 4.
Many Questions, fallacy of, 545 n. 3,
646 n. 1, 556.
Marshall, Prof. A., quoted, 474.
Mathematics, reasoning of, 366, c. xxv :
employs syllogism when ?, 307 : its
principles not generalizations from
experience, 509-12.
Matter, Aristotle's conception of, 41 :
genus the matter of its species, 73 :
not the principium individuationis,
76.
Measurement, importance of in induc
tion, 464, 516.
Mellone, Dr. S. H., quoted, 110 n. I.
Methodology of science, 422-3, c. xxvi.
Michael Psellus, 184 n. 1, 245 n.
Mill, James, quoted, 20, 141.
Mill, John Stuart, 11 : on adjectival
terms, 25 : on Definition, 68 n. 1 : on
Cause, 100, 376-9 : on Connotation
and Denotation, 131 sq. : on Modality,
184 n. 1 : on Syllogism, 279 n. 1 : on
' nota notae ', 285 n. 2 : on the evidence
of mathematical principles, 356 n. 1,
509 n. 1, 512 : on Laws of Nature, 880
n. 1, 471 : his attempt to prove the
Uniformity of Nature, 386 n. 1: his < In
ductive Methods ', 394-9, 460-2 : are in
reality one, 399 : their basis, 404 n. 1 :
canon for ' Joint Method ' defective,
399 n. 1 : his < Deductive Method of In
duction', 477, 483, 487 n. 1 : on Hypo
thesis, 429 : on Argument from Ana
logy, 500: on Colligation of Facts, 434 :
on Plurality of Causes, 455, 460-2 : view
that inference is from particulars to
particulars, 502 : on the Logic of
the Moral Sciences, 342, 514-16: on
Fallacies, 533 n. 1, 554 n. 2, 558:
Utilitarianism, quoted, 543. Cf. also
217, 231, 342, 370, 407 n. 2, 416 n. 1,
421 n. 1, 447.
Minor term, why so called, 235-8.
Minto, W., Logic, Inductive and Deduc
tive, cited, 142, 333 n. 1, 344, 545 n. 1.
Mixed modes, 79 n. 1.
Modality, Kant's category of, 52 : m.
of judgements, 168-85.
Modus ponens, 308 : tollens, 310 :
ponendo tollens, 318 : how far valid,
319-20 : tollendo ponens, 318.
Mood of syllogism, 239-40, 254-7 :
indirect, in Fig. 1, 245-6.
Necessity in judgement, 175 : in causal
relations, 376-9.
Negation, nature of, 161-3 : conver
sion by, 215.
Nettleship, R. L., Philosophical Remains.
cited, 125 n. 1, 127.
Newton, Sir Isaac, his history of gravi
tation, 477 sq.
Nominalism, 20, 41, 56, 93, 278.
INDEX
563
Nota Notae, principle of, 285.
Obversion. = Permutation, q.v.
Occam, William of, on nomina conno-
tativa, 140-2 : his 'razor', 470.
Opposition of judgements, 205-8.
Paronymous terms, 118.
Per accidens predication (opp. to
per se\ 36.
Permutation of propositions, 214 :
whether inference, 220-3.
Per se predication (opp. to per accidens",
36.
Petitio Principii, fallacy of, 550 : cf.
278, 535.
Petrus Hispanus, 244 n. 1.
Petrus Mantuanus, 261 n. 1.
Phenomenon, meanings of, 394 n. 1.
Philoponus, Joannes, quoted, 4 n. 1.
Plato, on the four elements, 86 : on
negation, 162 : on judgement, 170
n. 1 : quoted also 127, 343, 499, 540
n. 2, 541 n. 1, 549.
Plurality of Causes, 455 sq., 486, 516:
Mill on, 460-2.
Podmore, F, History of Modern Spiritua
lism, quoted, 440 n. 1.
Poincare, Mons. H., quoted, 384 n. 1,
385 n. 1.
Polysyllogism, 327.
Poor Law Commission, 1834, Report
of, quoted, 418-21.
Porphyry, his list of Predicables, 53
n. 2, 92-6: arbor Porphyriana, 115-17,
122 n. 1.
Port Royal Logic, quoted, 324 n. 1.
Poste, E., ed. of Sophistici Elenchi,
quoted, 394 n. 2, 531 n. 2, 547 nn. 2, 3,
551 n. 1, 554 n. 1.
Post hoc, propter hoc, fallacy of, 554.
Prantl, Carl, Geschichte der Logik, cited,
14 n. 2, 140, 184 n. 1, 244 n. 1, 258
nn. 1, 2, 260 n. 1, 261 n. 1, 346 n. 2.
Predicables, doctrine of, c. iv : Aristo
telian and Porphyrian lists, 53, 92-6 :
its relation to the question of the
meaning of ' cause ', 64-7 : Aristotle's
proof that his list is exhaustive, 111.
Premiss, what, 230, 232 : major and
minor, 232 : major in Fig. 1, 286, 307,
487 n. 2.
Prerogative instance, 366 n. 1.
Principium Individuationis, 76-7 : cf.
67, 117, 131.
Principles, ' common ' and ' special ',
359-61, 505, 532 : * common ' do not
explain, 466.
Problematic judgements, 176-82.
Proper names, 19, 34 : have connota
tion, 136-9 : indefinable, 138.
Property, 61 : its relation to Di-fini-
tion, 77 sq. : fourfold division of. «.)<).
Proposition, secundi and tertii adiacenttx,
147 n. 1 : cf. s.v. 'Judgement'.
Prosyllogism, 325.
irpuTfpov <f>vff(i and n. f/fiiv, 73, 354 n. •">.
Pseudographema, 531.
Quality of judgements, 161-3.
Quantification of the Predicate, 198-
204.
Quantity of judgements, 154.
Batio cognoscendi and r. essendi, 172,
291, 300, 466.
Realism, 41, 56, 93.
Reasoning, probable, 416, 488-9 : of
Mathematics, 503 : cf. s. r. ' Infer
ence '.
Reduction of syllogisms, c. xiii : un
called for, 290 sq., 306.
Relation, distinction of judgements
according to, 163-8.
Ritchie, D. G., Plato, quoted, 499 n. 2.
Romanes, J. G., Darwin and after
Darwin, quoted, 413 sq., 415 n. 1, 439
n. 1, 452, 473 n. 2, 476 n. 1, 490 n. 2,
552 n. 4.
Salisbury, Lord, quoted, 442 n. 2.
Science and History contrasted, 03,
218, 432, 472-3.
Sanderson, T., Compendium Artis Logicac,
cited, 14 n. 2, 214 n. 1.
Second Intentions, 8, 17.
Secundum quid, fallacy of, 533 n. 1,
547, 554.
Shyreswood, William, 244 n. 1.
Sigwart, Chr., Logic, cited, 152 n. 3.
Singular judgements, 154: for what
purposes ranked with universal j., 192.
Smith, Adam, Wealth of Nations, quoted,
417-18.
Sorites, 326-30 : Goclenian s., 327 n. 2.
Species as Head of Predicables, 92 :
s. infima and subalterna, 93 n. 2, 102 :
constituent s., 102.
Spencer, Herbert, 74, 360.
Spinoza, 162.
Stapper, R., on the Summidae Logicales
of Petrus Hispanus, 245 n.
Stock, St. G., Deductive Logic, cited, 29
n. 2, 537 n.
Subaltern judgements, 205 : s. moods,
262.
Subcontrary judgements, 205.
Subject, logical, grammatical and
metaphysical, 150.
Substances, first and second, 40-3.
Subsumption, 286, 307, 369 n. 2, 476,
493.
564
INDEX
Suppositio of names, 14, 140 : s.
materialise 14.
Syllogism, Aristotle's definition of,
225 : problem of, 229 : nomenclature
of, 230-40 : figures of, 233-5 : rnoods
of, 239-40 : their determination, 254-
7 : Fig. 1, moods of, 241-4 : do., in
direct, 245-6 : rules of, 247-54 : reduc
tion of imperfect moods of, c. xiii, 290
sq. : do., indirect, 269 : charged with
petitioprincipii, 278 : Fig. 1 of scientific,
283 : proposed principles of, c. xiv :
Fig. 2, 290-5 : Fig. 3, 295-301, 370
n. 1 : fourth or Galenian figure of.
257-61, 301-6 : in mathematics, when
used, 307 : Aristotle's ov\\oyianos
(£ viro&taecas, 317 n. : Inductive s.,
351-2 : Modal s., 416 n. 1.
Symbols in representing inductive
reasoning, errors in use of, 405 n. 1 :
inadequacy of, 449-50.
Syncategorematic words, 14.
Synthetic judgements, 185-90.
Term and word, distinguished, 13 :
derivation of, 13 n. 2 : mixed t., 14 :
how defined, 15-16 : abstract and con
crete t., 18, 21-3 : singular and common
or general, 18-19 : attributive, 24-6 :
collective, 26-7 : absolute and relative,
27-8 : positive, negative and priva
tive, 28-34 : infinite and indefinite,
30, 220 : univocal, equivocal and ana
logous, 34 : commensurate, 58 : inten
sion and extension of t., 121, c. vi
pass. : connotation and denotation of,
131 sq. : no t. non-connotative,
132 : absolute and connotative, 140 :
contrary, 205 n. 1 : contradictory, ib. :
major, minor and middle, in syllo
gism, 232-3, 235-9.
Thompson, Archbishop, Laivs of Thought,
cited, 122 n. 2, 204 n. 1, 223 n. 1.
Topics, what, 361 : t. of Cause, 394 :
Aristotle's treatise of that name, 358-
63.
Trendelenberg, F. A., cited, 47, 325 n. 3.
Unconditional principles in science,
383-6.
Uniformity of Nature, meaning of,
372-3: cannot be proved inductively, j
386-90, 469: importance of, in in
ductive science, 392-4, 407 : cf. also
s.r. ' Causation'.
Universe of Discourse, 32 n. 1, 148 n.l.
Venn, J., Empirical Logic, quoted, 405 n. 1.
Verification of a theory, not proof,
486, 556.
Vernon, Dr. H. M., Variation in Animals
and Plants, quoted, 408-10.
Wallace, Dr. A. E,, quoted, 473.
Wallis, J., Logic, cited, 216 n. 1, 222 n. 2.
Watts, Isaac, Logic, cited, 99, 261 n. 3.
Welton, Prof. J., Inductive Logic, cited,
368 n. 1, 423 n. 1.
Whately, Archbishop, Logic, quoted,
140, 275 n., 527, 528, 533 n. 1, 534-6,
558.
Whewell, W., quoted, 367: on Colliga
tion of Facts, 433-9.
Wollaston, W., Religion of Nature. de
lineated, cited, 144 n. 1.
Xenocrates on Aristotle's Categories,
38 n. 1.
Zabarella, Cardinal, on Fig. 4 of syl
logism, 258-9 : on Dictum de Omni.
274 n. 4 : on reduction of hypothetical
reasoning to syllogism, 312 n. 1.
Oxford: Printed at the Clarendon Press, by HORACE HART, M.A.
CLARENDON PRESS BOOKS
HISTORY
Archaeology, etc of the East
A History of Fine Art in India and Ceylon. By v. A.
SMITH. 4to, with .5 coloured plates and 381 other illustrations. £3 3s. net.
Chinese Porcelain. By Hsiang Yuan-P'ien. Translated and annotated
by S. W. BUSHELL. With 83 plates by W. GRICCS. Royal 4to. £21 net.
The T'aO ShllO. Translated by S. W. BUSHELL. 8vo. Hs.net.
Ancient Khotan. Report of Archaeological explorations in Chinese-
Turkestan carried out and described under the orders of H.M. Indian Govern
ment by Sir AUREL STEIN. Vol. I. Text, with descriptive list of antiques,
72 illustrations in the text, and appendices. Vol. II. 119 collotype and other
illustrations and a map. 2 vols. 4to. £5 5s. net.
Catalogue Of the Coins in the Indian Museum, Calcutta. (Published
for the Trustees of the Indian Museum.) Royal 8vo, with collotype plates.
Vol. I, by V. A. SMITH, 30s. net ; or in parts (prices on application). Vol. II,
by H. N. WRIGHT (the first section of Part II by Sir J. BOURDILLON), 30s. net.
Vol. Ill, by H. N. WRIGHT, 40s. net.
Stories of the High Priests of Memphis, the Sethon of
Herodotus, and the Demotic Tales of Khamnas. By F. LL. GRIFFITH. With
Portfolio containing seven facsimiles. Royal 8vo. £2 7s. 6d. net.
Meroe. The City of the Ethiopians. By J. GARSTANG, A. H.
SAYCE, and F. LL. GRIFFITH. With 74 plates. Demy 4to. 31s. 6d. net.
Christian Antiquities in the Nile Valley. By SOMERS CLARKE.
With many illustrations. 4to. £1 18s. net.
Ancient Coptic Churches of Egypt. By A. J.BUTLER. 2w. 8vo. sos.
The Arab Conquest of Egypt. By A. J. BUTLER. 8vo. ies. net
The Treaty of Misr in Tabari. By A. J. BITLER. 8vo. 5s. net.
Baghdad during the Abbasid Caliphate, from contemporary
sources. By G. LE STRANGE. With eight plans. 8vo. 16s.net.
The Cities and Bishoprics of Phrygia. By w. M. RAMSAY.
Royal 8vo. Vol. I, Part I. The Lycos Valley and South- Western Phrygia.
18s. net Vol. I, Part II. West and West Central Phrygia. £1 Is. net
Byzantine Art and Archaeology. By o. M. DALTOV. With 457
illustrations. Royal 8vo. Cloth, 38s. net ; morocco back, 4-2s. net.
Early European History
Bronze Age Pottery of Great Britain and Ireland. By
the Hon. J. ABERCROMBY. With 110 plates, of which 98 are collotypes.
2 vols. Royal 4to. £3 3s. net.
The Stone and Bronze Ages in Italy and Sicily. By
T. E. PEET. 8vo, illustrated. 16s. net.
Ancient Britain and the Invasions of Julius Caesar. By
T. RICE HOLMES. 8vo. 21s. net.
The Romanization of Roman Britain. By F. HAVERFIELD.
8vo, with 7 plates. 3s. (id. net.
A Manual of Ancient History. ByG.RAwuxsov. ended. 8vo. us.
European History
Historical Atlas of Modern Europe, from the Decline of the
Roman Empire. 90 maps, with letterpress to each : the maps printed by
W. & A. K. JOHNSTON, Ltd., and the whole edited by R. L. POOLE.
In one volume, imperial 4to, half-persian, £5 15s. 6d. net; or in selected
sets — British Empire, etc, at various prices from 30s. to 35s. net each ;
or in single maps, Is. 6d. net each. Prospectus on application.
Finlay's History of Greece from B.C. 146 to A.D. 1864. A new edition,
revised by the Author, and edited by H. F. TOZER. 7 vols. 8vo. 63s. net.
Italy and her Invaders (A.D. 376-814). With plates and maps. Eight
volumes. 8vo. By T. HODGKIN. Vols. I-IV in the second edition.
I-II. Visigothic, Hunnish, Vandal Invasions ; Herulian Mutiny. £2 2s.
II1-IV. The Ostrogothic Invasion. The Imperial Restoration. £1 16s.
V-VI. The Lombard Invasion, and the Lombard Kingdom. £1 16s.
VII-VIII. Prankish Invasions, and the Prankish Empire. £1 4s.
Dalmatia, the Quarnero, and Istria ; with Cettigne and Grado.
By T. G. JACKSON. Three vols. With plates and illustrations. 8vo. 31s. 6d. net.
The Islands of the Aegean. By H. F. TOZER. Crown 8vo. 8s. ed.
Caesar's Conquest of Gaul. By T. RICE HOLMES. Second edition,
revised throughout and largely rewritten. 8vo. With map and 8 plans. 24s. n.
Genealogical Tables illustrative of Modern History. By H. B.
GEORGE. Fourth (1904) edition. Oblong 4to, boards. 7s. 6d. net.
The Life and Times of James the First of Aragon. By
F. D. SWIFT. 8vo. 12s. 6d.
Gdmara's Annals of Charles V. Spanish Text and English
translation by R. B. MERRIMAN. Hvo. 12s. 6d. net.
Documents of the Continental Reformation. Edited by
B. J. KIDD. Cr. 8vo. 12s. 6d. net,
A History Of France. By G. W. KITCHIN. Cr. 8vo ; revised, VoL I
(to 1453); Vols. II (1624), III (1795), 10s. 6d. each.
De Tocqueville's L'Ancien Regime et la Revolution.
Edited, with introductions and notes, by G. W. HEADLAM. Crown 8vo. 6s.
Speeches of the Statesmen and Orators of the French
Revolution. Ed. H. MORSE STEPHENS. Two vols. Crown 8vo. £1 Is. net.
Documents of the French Revolution, 1789-1791. By
L. G. WICKHAM LEGG. Crown 8vo. Two volumes. 12s. net.
Napoleonic Statesmanship : Germany. By H. A. L. FISHER.
8vo, with maps. 12s. 6d. net.
. Six lectures by H. A. L. FISHER. 8vo. 3s. 6d, net.
' MOSCOW Expedition, ed. H. B. GEORGE. Cr. 8vos 6 maps. 5s.
The Oxford Text-books of European History.
Crown 8vo, with maps. Each 4s. 6d.
Mediaeval Europe. 1095-1254. By KENNETH BELL.
The Renaissance & the Reformation. 1494-ieio. ByE.M.TANNER.
The Fall of the Old Order. 1763-1815. By I. L. PLUNKET.
From Metternich to Bismarck. 1815-1878. By L. CECIL JANE.
English History : Sources
Baedae Opera Historica, edited by C. PLUMMER. Two volumes.
Crown 8vo, leather back. £1 Is. net.
Asser's Life of Alfred, with the Annals of St. Neot,
edited by W. H. STEVENSON. Crown 8vo. 12s. net.
The Alfred Jewel, an historical essay. With illustrations and a map,
by J. EARLE. Small 4to, buckram. 12s. 6d. net
Two of the Saxon Chronicles Parallel ; with supplementary
extracts from the others. A Revised Text, edited by C. PLUMMER and
J. EARLE. Two volumes. Crown 8vo. Vol. I. Text, appendices, and
glossary. 10s. 6d. net. Vol. II. Introduction, notes, and index. 10s. 6d. net.
The Saxon Chronicles (787-1001 A. D.). Crown 8 vo, stiff covers. 3s.
Handbook to the Land- Charters. By J. EARLE. Crown 8vo. IGS.
The Crawford Collection of early Charters and Documents, now in
the Bodleian Library. Edited by A. S. NAPIER and W. H. STEVENSON.
Small 4to, cloth. 12s. net.
The Chronicle of John of Worcester, ins-iuo. Edited by
J. R. H. WEAVER. Crown 4to. 7s. 6d. net.
DialogUS de ScaCCariO. Edited by A. HUGHES, C. G. CRUMP, and
C. JOHNSON, with introduction and notes. 8vo. 12s. 6d. net.
PaSSio et Miracula Beati Olaui. Edited from the Twelfth-century
MS by F. METCALFE. Small 4to. 6s.
The Song Of LeweS. Edited from the MS, with introduction and
notes, by C. L. KINGSFORD. Extra fcap 8vo. 5s.
Chronicon Galfridi le Baker de Swynebroke, edited by sir
E. MAUNDE THOMPSON, K.C.B. Small 4to, 18s. ; cloth, gilt top, £1 Is.
Life of the Black Prince. (See p. 29.)
The First English Life of Henry V. Edited from the MS. by
C. L. KINGSFORD. 8vo. 8s. 6d. net.
Chronicles of London. Edited, with introduction and notes, by
C. L. KINGSFORD. 8vo. 10s. 6d. net.
SlX Town Chronicles of England. Now printed for the first
time. Edited from the MSS by R. FLENLEY. 8vo. 7s. (id. net.
GaSCoigne's Theological Dictionary (' Liber Veritatum'): selected
passages, illustrating the condition of Church and State, 1403-1458. With
an introduction by J. E. THOROLD ROGERS. Small 4to. 10s. 6d.
Fortescue's Governance of England. A revised text, edited,
with introduction, etc, by C. PLUMMER. 8vo, leather back. 12s. 6d. net.
S tOW's Survey of London. Edited by C. L. KINGSFORD. 8vo, 2 vols.,
with a folding map of London in 1600 (by EMERY WALKER and H. W. CRIBB)
and other illustrations. 30s. net.
The Protests of the Lords, from 1624 to 1874 ; with introductions.
By J. E. THOROLD ROGERS. In three volumes. 8vo. £2 2s.
Historical Evidence. By H. B. GEORGE. Crown 8vo. 3s.
3
Clarendon Press Series of Charters, Statutes, etc
From the earliest times to 1307. By Bishop STUBBS.
Select Charters and other illustrations of English Constitutional History.
Eighth edition. Crown 8vo. 8s. 6d.
From 1558 to 1625. By G. W. PROTHERO.
Select Statutes and other Constitutional Documents of
the Reigns of Elizabeth and James I. Third edition.
Crown 8vo. 10s. 6d.
From 1625 to 1660. By S. R. GARDINER.
The Constitutional Documents of the Puritan Revolu
tion. Third edition. Crown 8vo. 10s. 6d.
Tudor and Stuart Proclamations, 1485-1714. Calendared
by ROBERT STEELE under the direction of the Earl of CRAWFORD, K.T. Royal
Ito, two volumes. £5 5s. net.
Calendar Of Charters & Rolls in the Bodleian Library. 8vo. 31s. 6d. n.
Calendar of the Clarendon State Papers preserved in the
Bodleian Library. In three volumes. 1869-76.
Vol. I. From 1523 to January 1649. 8vo. 18s. net. Vol. II. From 1649
to 1654. 8vo. 16s. net. Vol. III. From 1655 to 1657. 8vo. 14s. net.
Hakluyt's Principal Navigations. (See p. 12.)
Aubrey's ' Brief Lives,' set down between the Years 1669 and 1696.
Edited from the Author's MSS by A. CLARK. Two volumes. 8vo. £1 5s.
Whitelock's Memorials. (1625-1660.) 4vois. 8vo. £i ios.
Ludlow's Memoirs. (1625-1672.) Ed. C. H. FIRTH. 2 vols. 8vo. £1 16s.
Luttrell's Diary. (1678-17H.) Six volumes. 8vo. £1 10s. net.
Burnet's History of James II. 8vo. 9s. ed. net.
Life of Sir M. Hale, with Fell's Life of Dr. Hammond. 8vo. 2s. 6d. net.
Memoirs of James and William, Dukes of Hamilton. 8vo. 7s. 6d. net.
Burnet's History of My Own Time. A new edition, based on
that of M. J. ROUTH, by OSMUND AIRY. Two vols., each 12s. 6d. net
Supplement, derived from Burnet's Memoirs, Autobiography, etc, all
hitherto unpublished. Edited by H. C. FOXCROFT, 1902. 8vo. 16s. net.
The Whitefoord Papers. (1739-1810.) Ed.w.A.s.HEwiNs. 8vo. i2s.ed.
History of Oxford
A complete list of the Publications of the Oxford Historical Society
can be obtained from Mr. FROWDE, and see p. 22.
Manuscript Materials relating to the History of Oxford ;
contained in the catalogues of the Oxford libraries. By F. MADAN. 8vo. 7s. 6d.
Oxford Books. By F. MADAN. 8vo. Two volumes, 36s. net. Also sepa
rately ,Vol. I (The Early Oxford Press) 18s. n. , Vol. II (Oxford Literature) 25s. n.
Bibliography
Cotton's Typographical Gazetteer. Hrst Series. 8vo. i2s.6d.net
Bishop Stubbs's and Professor Freeman's Books
The Constitutional History of England. ByW.SiunBs. Library
edition. 3 vols. DemySvo. £2 8s. Also in :i vols., crown 8vo, 12s. each.
Seventeen Lectures on the Study of Mediaeval and Modern History,
1867-1884. By the same. Ed. 3, 1900. Cr. 8vo, 8s. 6d.
History of the Norman Conquest of England ; its Causes
and Results. By E. A. FREEMAN. Vols. I, II and V (English edition) are
out of print. Vols. Ill and IV. £1 Is. each. Vol. VI (Index). 10s. 6d.
A Short History of the Norman Conquest of England.
Third edition. By the same. Extra fcap 8vo. 2s. 6d.
The Reign of William RufuS. By the same. 2 vols. 8vo. £1 16s.
School Books
A School History Of England. By C. R. L. FLETCHER and RUD-
YARD KIPLING. Ed. 2 revised. Crown 8vo, cloth, with 1 1 coloured and 12 black
and white illustrations by H. J. FORD, and 7 maps. Is. 8d. ; bound in French
morocco, 2s. 8d. An Edition de luxe, with additional illustrations, 4to,
7s. 6d. net. Containing many new and original poems by Mr. RUDYARD KIPLING.
Teacher's Companion to the above. By C. R.L.FLETCHER. Cr.Svo. Is.n.
Historical Wall Pictures. By H. J. FORD. Enlarged from the
illustrations in A School History of Enyland. Unmounted 4s. 6d. net each ;
16s. net the set of 4. (Published by Mr. Frowde.)
School History Of England. By O. M. EDWARDS, R. S. RAIT, and
others. Second edition (1911), to the death of Edward VII. With maps.
Crown 8vo, 3s. 6d. ; also in 2 vols. (Vol. I to 1603, Vol. II to 1910), each 2s.
Companion to English History (Middle Ages). Edited by F. P.
BARNARD. With 97 illustrations. Crown 8vo. 8s. 6d. net.
The Story of England. For Junior Forms. ByM.O.DAvis. Crown 8vo,
with 16 maps. 3s. Also in parts, I to James I, II to Victoria, each Is. 9d.
A History of England for Indian Students. By V.A. SMITH. Cr.Svo. 3s.
Perspective History Chart. By E. A. G. LAMBORN. 8s. 6d. net.
Oxford County Histories
Crown 8vo, illustrated, each Is. 6d. net. ' (In superior bindings, 2s. 6d. net.)
Berkshire, by E. A. G. LAMBORN. Cheshire, by C. E. KELSEV.
Durham, by F. s. EDEN. Essex, by w. H. WESTON. Glou
cestershire, by W. H. WESTON. Hampshire, by F. CLARKE.
Oxfordshire, by H. A. LIDDELL. Shropshire, by T. AUDEN.
East Riding of Yorkshire. By J. L. BROCKBA*K.
The Making of London. By Sir LAURENCE GOMME. Cr.Svo. 3s. 6d. net.
Leeds and its Neighbourhood. By A. c. PRICE. Cr. 8vo. 3s. t>u
Southampton. By F. J. C. HEARNSHAW and F. CLARKE. Crown 8vo. 2s. net.
Bucks Biographies. By Lady VERNEY. Crown 8vo. 2s. 6d. net.
Also, for junior pupils, illustrated, each Is.
Stories from the History of Berkshire. By E. A. G. LA.MBORX.
Stories from the History of Oxfordshire. By JOHN IKVIXC.
Special Periods and Biographies
Ancient Britain and Julius Caesar. ByT. RICE HOLMES. 8vo. 2is.n.
Life and Times of Alfred the Great. ByC.Pm»iMEH. 8vo. 5s.net.
The Domesday Boroughs. By ADOLPHUS BALLARD. 8vo. 10s. 6d. net.
Villainage in England. By P. VINO&RADOFF. 8vo. 16s. net.
English Society in theXlthCentury.Byp.ViNOGRADOFF.svo.iGs.n.
Oxford Studies in Social and Legal History. Edited by
PAUL VINOGRADOFF. 8vo. 12s. 6d. net each volume. Vol. I. English
Monasteries on the Eve of the Dissolution. By ALEXANDER SAVIXE.
Patronage under the Later Empire. By F. DE ZULUETA. Vol. II. Types of
Manorial Structure. By F. M. STENTON. Customary Rents. By N. NEILSON.
Vol. III. St. -Andre of Bordeaux. By E. C. LODGE. Poor Law in a Warwick
shire Village. By A. W. ASHBY.
The Gild Merchant : By C. Gross. Two volumes. 8vo. £1 4s.
The Exchequer in the 12th Century. ByR. L.POOLE. 8vo.
Ireland under the Normans, 1169-1716. By G. H.
2 vols. 8vo. With two maps. 21s. net.
The Welsh Wars of Edward I ; By j. E. MORRIS. 8vo. 9s. 6d. net.
The Great Revolt Of 1381. By C.OMAN. 8vo. 8s. 6d. net.
Lancaster and York. (A.D. 1399-U85.) By Sir J. H. RAMSAY. Two
volumes. 8vo, with Index, £1 17s. 6d. Index separately, Is. 6d.
The King's Council in the Middle Ages. By J. F. BALD*™.
[In the press.]
The Rise and Fall of the High Commission. By R. G.
USHER. [In the press.]
Life and Letters of Thomas Cromwell. By R. B. MERRIMAM.
In two volumes. 8vo. 18s. net.
Anglo-Roman Relations, 1558-1 565. ByC.G.BAYNE. [inthe press.
Sir Walter Ralegh, a Biography, by W. STEBBING. Post 8vo. 6s. net
Sir Henry Wotton. By L. PEARSALL SMITH. 8vo. 2 vols. 25s. net.
Edward Hyde, Earl of Clarendon. By c. H. FIRTH. 8vo. is. net.
Anglo-Dutch Rivalry, 1600-1653. By G. EDMTJNDSON. 8vo. 6s. n.
A History of England, principally in the Seventeenth Century. By
L. VON RANKE. Six volumes. 8vo. £3 3s. net. Index separately, Is.
The Journal of John Stevens. Thewarinlreland,1689-91. Edited
by R. H. MURRAY. 8vo. 10s. 6d. net.
The Works Of John Arbllthnot. ByG.A.Amnsx. 8vo. 15s. net.
Great Britain and Hanover. By A. w. WARD. Crown 8vo. 5s.
Henry Fox, Lord Holland. By T. w. RIKER. 2 w. 8vo. 2is. net.
Lord Chatham as an Orator. By H. M. BUTLER. 8vo. 2s. net.
British Statesmen of the Great War, 1793-1814. By
the Hon. J. W. FORTESCUE. 8vo. 7s. 6d. net.
6
History of the Peninsular War. By c. OMAN. TO be completed
in six volumes, 8vo, with many maps, plans, and portraits. Already published :
Vol.1. 1807-1809, to Corunna. Vol.11. 1809, to Talavera. Vol. III. !«<>«»-
10, to Torres Vedras. Vol. IV. 1810 1811, to Tarragona. Us. net each.
Memoir of Admiral Garden, written by himself, 18:>0. Edited by
C. T. ATKINSON. 8vo. 10s. 6d. net.
Progress of Japan, 1853-1871. ByJ.H.GuBBixs. 8vo. ios. 6d. P.
Anglo-Chinese Commerce and Diplomacy : mainly in the
nineteenth century. By A. J. SARGENT. 12s. 6d. net.
Frederick York Powell. By OLIVER ELTON. 2 vols. 8vo. 21s. net.
David Binning Moni'O. By J. COOK WILSOK. 8vo. 2s. net.
F. W. Maitland. Two lectures by A. L. SMITH. 8vo. 2s. 6d. net.
Henry Birkhead. By J. w. MACK AIL. 8vo. is. net.
AVilliam Markham. By Sir CLEMENTS MARKHAM, K.C.B. 8vo. 5s.net.
John Bui'doil Sanderson. By Lady BURDOV SANDERSON. Edited
by J. S. and E. S. HALDANE. 8vo. 10s. 6d. net.
Historical Portraits
Historical Portraits. Chosen by EMERY WALKER. Crown Ho. Vol.1,
1400-1600; Lives by C. R. L. FLETCHER. 8s. 6d. net. Vol. II, 1600-1700;
Lives by C. R. L. FLETCHER and H. B. BUTLER, introduction by C. 1
BELL. 10s. 6d. net. Portraits separately, in envelope, 4s. 6d. net, 6s. net.
Constitutions of the Empire
Law and Custom of the Constitution. By Sir w. R. ANSO*.
In two volumes. 8vo. Vol. I. Parliament. Fourth edition. 1909 Re
issue revised, 1911. 12s. (id. net. Vol. II. The Crown. Third edition.
Part I, 1907. 10s. 6d. net. Part II, 1908. 8s. 6d. net.
Lord Durham's lleport on British North America. Edited
by Sir C P LUCAS, K.C.B. 8vo. 3 vols. £1 5s. net or, Vol. I (Introduction),
7s. 6d. net; Vol. II, 10s. 6d. net; Vol. Ill, 10s. 6d. net.
Federations aild Unions within the British Empire. By H.E.EGERT.KV.
8vo. 8s. 6d. net.
Responsible Government in the Dominions. ByA. B. KEITH.
3 vols. 8vo. £2 2s. net.
The Union Of S. Africa. By Hon. R. H. BRAND (1909). 8vo. 6s. n.
Political Unions. By H. A. L. FISHER. 8vo. Is. net.
The Government Of India, being a Digest of the Statute Law relating
thereto, with historical introduction and illustrative documents. By Sir C P.
ILBERT, K. C.S.I. Second edition, 1907, with a supplementary chapter (1
on the Indian Councils Act of 1909 (also separately, Is net) 11s. 6d. net.
Second supplementary chapter (191-2) on the Coronation Durbar and
sequences. [In the press. |
Second Chambers. By J. A. R. MARRIOTT. 8vo. 5s. net.
English Political Institutions. By J. A. R. MARRIOTT. Cr. 8vo.
4s. 6d.
Greater Rome and Greater Britain. By sir c. P. LUCAS. 8vo.
3s. 6d. net.
History and Geography of America
and the British Dominions
For other Geographical books, see page 59 ; for Legal and Constitutional
works, see pages 55 and 63.
History of the New World called America. By E. J. PAYNE.
Vol. I. 8vo. 18s. Bk. I. The Discovery. Bk. II, Part I. Aboriginal America.
Vol. II. 8vo. 14s. Bk. II, Part II. Aboriginal America (concluded).
A History of Canada, 1763-1812. By sir c. P. LUCAS, K.C.B.
8vo. With eight maps. 12s. 6d. net.
The Canadian War of 1812. By SirC. P. LUCAS, K.C.B. 8vo.
With eight maps. 12s. 6d. net.
Historical Geography of the British Colonies. By Sir c. P.
LUCAS, K.C.B. Crown 8vo.
Introduction. New edition by H. E. EGERTON. 1903. (Origin and
growth of the Colonies.) 8 maps. 3s. 6d. In cheaper binding, 2s. 6d.
Vol. I. The Mediterranean and Eastern Colonies.
With 13 maps. Second edition, revised by R. E. STUBBS. 1906. 5s.
Vol. II. The West Indian Colonies, with twelve
maps. Second edition, revised by C. ATCHLEY, I.S.O. 1905. 7s. 6d.
Vol. III. West Africa. Third edition, revised to 1913, by
A. B. KEITH. [In the press.]
Vol. IV. South Africa. New edition, 1913.
Part I. History before the War. [In the press.]
Part II. Recent History. [In preparation.]
Part III. Geography. ^Revised by A. B. KEITH. [In the press.]
Vol. V. Canada, Part I. 6s. Part II, by H. E. EGERTON. 4s. 6d.
Part III (Geographical) 4s. 6d., and Part IV, Newfoundland, by J. D.
ROGERS. 4s. 6d.
Vol. VI. Australasia. By J. D. ROGERS. 1907. With 22 maps.
7s. 6d. Also Part I, Historical, 4s. 6d. Part II, Geographical, 3s. 6d.
History of the Dominion of Canada. By W. P. GRESWELL. Crown 8vo. 7s. 6d.
Geography of Canada and Newfoundland. By the same. 1891. Cr. 8vo. 6s.
Geography of South Africa. By the same. With maps. 1892. Cr. 8vo. 7s. 6d.
TheStudy of Colonial History. AlecturebyH.E. EGERTON. 8vo. Is. n.
Historical Atlas. Europe and her Colonies. 27 maps. 35s. net.
Cornewall-Lewis on the Government of Dependencies.
Edited by Sir C. P. LUCAS, K.C.B. 8vo. 12s. net.
Sierra Leone : a bibliography. By H. c. LUKACH. 8vo, with intro
ductory essay and maps. 8s. 6d. net.
Political Unions. By H. A. L. FISHER. 8vo. is. net.
Greater Rome and Greater Britain. By Sir c. P. LUCAS, svo.
3s. 6d. net.
8
India
The Imperial Gazetteer of India. New edition, igos. The
entire work in 26 vols., cloth £5 net, morocco back £6 6s. net. The i vols.
of ' The Indian Empire ' separately, cloth 6s. net each, morocco back
7s. 6d. net; Atlas, cloth 15s. net, morocco back 17s. 6d. net; the remaining
21 vols., cloth £4 4s. net, morocco back £5 5s. net.
Vol. 1. Descriptive. Vol. V-XXIV. Alphabetical Gazetteer.
Vol. II. Historical. Vol. XXV. Index.
Vol. III. Economic. Vol. XXVI. Atlas.
Vol. IV. Administrative. Each volume contains a map of India.
Reprints from the Imperial Gazetteer.
A sketch of the Flora of British India. By Sir JOSEPH HOOKER. 8vo. Is. net.
The Indian Army. A sketch of its History and Organization. 8vo. Is. net.
Of India edited by SirW. W. HUNTER.
Crown 8vo. 2s. 6d. net each.
Babar. S. LANE-POOLE.
Albuquerque. H. MORSE STEPHENS.
Akbar. Colonel MALLESON.
Aurangzib. S. LANE-POOLE.
Dupleix. Colonel MALLESON.
Clive. Colonel MALLESON.
Hastings. Captain L. J. TROTTER.
Sindhia. H. G. KEENE.
Cornwallis. W. S. SETON-KARR.
Haidar All and Tipu Sultan.
L. B. BOWRING.
Wellesley. W. H. HUTTON.
The Marquess of Hastings. Major
(Also a special Indian Edition.)
Amherst. ANNE T. RITCHIE and
R. EVANS.
Bentinck. D. C. BOULGER.
Auckland. Captain L. J. TROTTER.
Hardinge. Viscount HARDING E.
Ranjit Singh. Sir L. GRIFFIN.
Dalhousie. Sir W. W. HUNTER.
Thomason. Sir R. TEMPLE.
Colvin. Sir A. COLVIN.
Henry Lawrence. Lt.-Gen. J. J.
MCL,EOD INNES.
Clyde and Strathnairn. Major-
Gen. Sir O. T. BURNE.
ROSS-OF-BLADENSBURG. Canning. Sir H. S. CUNNINGHAM.
Elphinstone. J. S. COTTON. Lawrence. Sir C. AITCHISON.
Munro. J. BRADSHAW. Mayo. Sir W. W. HUNTER.
Asoka. By V. A. SMITH. Second edition, 1909. 3s. 6d. net
Sketches Of Rulers Of India. Abridged from the Rulers of India
by G. D. OSWELL. Vol. I, The Mutiny and After ; Vol. II, The Company's
Governors ; Vol. Ill, The Governors-General ; Vol. IV, The Princes of India.
Crown 8vo. 2s. net each. Also in two vols., 7s. 6d. net ; or each 4s. net.
Macaulay's Clive and Warren Hastings, with introductions and
notes by V. A. SMITH. 2s. each.
A Brief History of the Indian Peoples. By Sir w. w. HUNTER.
Revised up to 1903 by W. H. HUTTON. Eighty- ninth thousand. 3s. 6d.
The Oxford Student's History of India. By v. A. SMITH.
Crown 8vo. Third Edition. With 7 maps and 11 other illustrations. 2s. 6d.
The Oxford India Reader. Authorized selections from the Imperial
Gazetteer of India. By W. BELL. Cr. Svo, illustrated. 2s. 6d.
A Primer of Hinduism. By J. N. FARUUHAR. Crown Svo. 2s.6d.net.
Dubois' Hindu Manners. Translated and edited by H. K. BEAU-
CHAMP. Third edition. Crown Svo. 6s. net. On India Paper, 7s. 6d. net
9
India (continued)
The Government Of India, being a digest of the Statute Law relating
thereto; with historical introduction and illustrative documents. By Sir
C. P. ILBERT. Second edition, 1907, with a supplementary chapter (1910)
^ ^ on the Indian Councils Act of 1909 (also separately, Is. net). 11s. 6d. net.
The Early History of India from GOO B. c. to the Muhammadan Con
quest, including the invasion of Alexander the Great. By V. A. SMITH. 8vo.
With maps, plans, and other illustrations. Second edition. 14s. net.
The English Factories in India: By W.FOSTER. Med.8vo. (Published
under the patronage of His Majesty's Secretary of State for India in Council.)
<> Vols., 1618-21, 1622-3, 1624-9, 1630-33, 1634-36, 1637-41. 12s. 6d. net each.
(The six previous volumes (Vol. II is out of print) of Letters to the East India
Company from its Servants in the East (1602-1617). 15s. each volume.)
Court Minutes of the East India Company. By E. B.
SAINSBURY. Introduction by W. FOSTER. Med. 8vo. 12s. 6d. net each.
Three Vols., 1635-39, 1640-43, 1644-49.
The Court Minutes previous to 1635 have been calendared in the Calendars
of State Papers, East Indies, published by the Public Record Office.
Wellesley's Despatches, Treaties, and other Papers relating to his
Government of India. Selection edited by S. J. OWEN. 8vo. £1 4s.
Wellington's Despatches, Treaties, and other Papers relating to
India. Selection edited by S. J. OWEN. 8vo. £1 4s.
Hastings and the Rohilla War. By Sir J. STRACHEY. 8vo. I Os. 6d,
GEOGRAPHY
Historical Atlas of Modern Europe. (See P. 50.)
Economic Atlas. By J. G. BARTHOLOMEW. Introduction by L. W. LYDE.
Ed. 2, 4to, with over 180 coloured maps. 3s. 6d. net. School edition, 2s. 6d. n.
School Atlas. Physical and Political. By J. G. BARTHOLOMEW. 4to,
with 3-? coloured plates and 42 diagrams. Is. net.
The Dawn Of Modern Geography. By C. R. BEAZLEY. In three
volumes. £2 15s. net. Vol. 1 (to A.D. 900). Not sold separately. Vol. II
(A.D. 900-1260). 15s. net. Vol. III. 20s. net.
Regions Of the World. Ed.H.J.MACKiNDER. Med.Svo. 7s.6d.n.pervol.
Britain and the British Seas. Ed. 2. By H. J. MACKINDER.
Central Europe. By JOHN PARTSCH. Nearer East. By
D. G. HOGARTH. North America. By I. RUSSELL. India. By
Sir THOMAS HOLDICH. The Far East. By ARCHIBALD LITTLE.
:• rentiers: Romanes Lecture (1907) byEarlCuRzoNorKEDLESTON. 8vo. 2s. n.
The Face Of the Earth. By EDUARD SUESS. (See p. 92.)
Peaks and Pleasant Pastures. By CLAUD SCHUSTER. 8vo, with
5 maps. 7s. 6d. net.
Relations of Geography and History. By H. B. GEORGE. With
two maps. Crown 8vo. Fourth edition. 4s. 6d.
Geography for Schools. By A. HUGHES. Crown 8vo. 2s. 6d.
The Maryborough Country. By H. C. BRENTNALL and C. C. CARTER.
Cr. 8vo. 2s. 6d. net.
The Oxford Geographies
Edited by A. J. HEKHERTSON. Crown Svo.
The Preliminary Geography. Ed. 2, 72 maps, is.6d.
'The Junior Geography. Ed. 4, revised, 166 maps and diagrams, 2s.
With Principles of Geography, 3s. With Questions (by F. M. Kirk), and
Statistical Appendix (by E. G. R. Taylor), 2s. (id. With both, 3s. (id.
Quests, and Stat. App. separately, Is.
The Senior Geography. Ed. 3, 117 maps and diagrams, 2s. 6d. With
Physiographical Introduction, 3s. 6d. With Questions (by F. M. KIRK), and
Statistical Appendix (by E. G. R. TAYLOR), 3s. With both, 4s. Quests, and
Sfcat. App. separately, Is.
Physiographical Introduction to Geography. Ed. 2.' is. 6d.
The Clarendon Geography. By F.D. HERBERTSON. 2vois. VOLLSS.
Separately: Parti, Principles of Geography ; Part II, British Isles ; Part III,
Europe, Is. 4d. each. Vol. II. In preparation.
The Elementary Geographies. By F. D. HERBERTSON. I, Ed. 2:
Physiography. Is. II : In and About our Islands. Is. Ill : Europe. Is.
IV : Asia. Is. 6d. V : North America. Is. 6d. VI : The Three Southern
Continents. Is. 9d. VII : The British Isles. Is. 9d.
A Geography of Ireland. By o. J. R. HOWARTH. 2s. 6d.
Australia. In its physiographic and economic aspects. ByT.G.TAYLOR. 3s.6d.
The British Empire. By R. L. THOMPSON. 2s. 6d.
The Upper Thames Country and the Severn- A von Plain.
By N. E. MACMUNN. [In the press.]
Elementary Geography of Scotland. By M. NEWBIGIV.
Practical Geography. ByJ. F.UNSTEAD. 2s. 6d. 2 Parts, Is. Gd. each.
Commercial Geography. By O. J. R. HOWARTH. [In the press.]
An Introduction to Plant Geography. By M. E. HARRY.
The Oxford Wall Maps
Edited by A. J. HERBERTSON. Drawn by B. V. DARBISHIRE.
Prospectus on application.
British Isles : Physical Features ; do. with physical names ; do. with
routes ; Geology ; Rainfall. Five maps, 60 x 40, scale 1 : 1,000,000.
Continents (Europe, Asia, Africa, N. America, S. America, Australasia) :
Physical Features ; do. with physical names ; do. with political names ; Rain
fall ; Vegetation. Thirty maps, 60 x 40 (except Asia, 60 x 60), scale, Europe
and Australasia, 1 : 5,000,000, others 1 : 7,500,000.
World : Physical Features ; Structure ; Thermal Regions ; Pressure and
Winds ; Rainfall ; Vegetation ; Natural Regions ; Political. Eight maps,
40 x 60, scale 1 : 33,300,000.
Price per map : Unmounted 7s. net ; mounted on cloth to fold 8s. 6d. net ;
on cloth and rollers (varnished or unvarnished) 10s. 6d. net, except Asia, 10s. 6d.
net, 12s. 6d. net, 15s. net.
In Sets (prices net) : British Isles, Europe, Africa, N. America, S. America,
Australasia, each in five maps, 32s. 6d., 40s., 50s. Asia, 50s., 60s., 72s. 6d.
World, the eight maps, 55s., 65s., 80s. Physical Features of the eight maps,
with or without names, or with political names (the British Isles with routes),
57s. 6d., 70s., 85s. Rainfall, the eight maps, 57s. 6d., 70s., 85s. Vegetation,
the seven maps, 50s., 60s., 75s.
The Oxford Charts and Outline Maps. Prices : id. net each;
9d. net foi 12 of one kind, Is. 4d. net for 25 of one kind.
ii
Anthropology
Transactions of the Third (1908) International Congress
for the History of Religions. Royal 8vo. 2 vois. 25s. net.
Anthropological Essays presented to Sir EDWARD BURNETT TYLOR in
honour of his seventy-fifth birthday. Imperial 8vo. 21s. net.
The Evolution of Culture, and other Essays, by the late
Lieut.-Gen. A. LANE-FOX PITT-RIVERS; edited by J. L. MYRES, with an
Introduction by H. BALFOUR. 8vo, with 21 plates, 7s. 6d. net.
Bronze Age Pottery of Great Britain and Ireland. By
the Hon. J. ABEHCHOMBY. With 110 plates, of which 98 are collotypes.
2 volumes. Royal 4to. £3 3s. net.
The Stone and Bronze Ages in Italy and Sicily. By
T. E. PEET. 8vo, illustrated. 16s. net.
Anthropology and the Classics. Six lectures by A. EVANS,
A. LANG, G. G. A. MURRAY, F. B. JEVONS, J. L. MYRES, W. W. FOWLER.
Edited by R. K. MARETT. 8vo. Illustrated. 6s. net.
The Ancient Races of the Thebaid : an anthropometrical study.
By ARTHUR THOMSON and D. RANDALL-MAC!VER. Imperial 4to, with 6 collo
types, 6 lithographic charts, and many other illustrations. 42s. net.
The Earliest Inhabitants of Abydos. (A cranioiogical study.)
By D. RANDALL-MAC!VER. Portfolio. 10s. 6d. net.
Folk-Memory. By WALTER JOHNSON. 8vo. Illustrated. 12s. 6d. net
Celtic Folklore: Welsh and Manx. By J.RHYS. 2 vois. 8vo. £i is.
Studies in the Arthurian Legend. By J. RHYS. 8vo. i2s. ed.
Iceland and the Faroes. By N. ANNANDALE. With an appendix
on the Celtic Pony, by F. H. A. MARSHALL. Crown 8vo. 4s. 6d. net.
The MelanesianS, studies in their Anthropology and Folk-Lore. By
R. H. CODRINGTON. 8vo. 16s. net.
The Melanesian Languages. By R.H. CODRINGTON. 8vo. i8s.net.
The Masai, their Language and Folk-lore. By A. c. HOLLIS.
With introduction by Sir CHARLES ELIOT. 8vo. Illustrated. 14s. net.
The Nandi, their Language and Folk-lore. By A. c. HOLLIS.
With introduction by Sir CHARLES ELIOT. 8vo. Illustrated. 16s. net,
The Suk, their Language and Folk-lore. By M. w. H. BEECH.
With introduction by Sir CHARLES ELIOT. 8vo. Illustrated. 12s. 6d. net.
Hausa Folk-Lore Customs, Proverbs, etc. With notes
collected by R. S. RATTRAY. 8vo. [In the press.]
Bushman Paintings. Copied by M. H. TOXGUE, and printed in colour.
With a preface by H. BALFOUR. In a box, £3 3s. net.
LAW
Jurisprudence
Bentham's Fragment on Government. Edited by F. c.
MONTAGUE. 8vo. 7s. 6d.
Bentham's Introduction to the Principles of Morals and
Legislation. Second edition. Crown 8vo. 6s. 6d.
Studies in History and Jurisprudence. By the Right Hon.
JAMES BRYCE. 1901. Two volumes. 8vo. £1 5s. net.
The Elements Of Jurisprudence. By T. E. HOLLAND. Eleventh
edition. 1910. 8vo. 10s. 6d. net.
Elements Of Law, considered with reference to General Jurisprudence.
By Sir W. MARKBY, K.C.I.E. Sixth edition revised, 1905. 8vo. 12s. 6d.
Roman Law
Imperatoris lustiniani Institutionum Libri Quattuor ;
with introductions, commentary, and translation, by J. B. MOYLE. Two
volumes. 8vo. Vol. I (fifth edition, 1912), Its. net ; Vol. II, Translation
(fourth edition, 1906), 5s. net.
The Institutes Of Justinian, edited as a recension of the Institutes
of Gaius. By T. E. HOLLAND. Second edition. Extra fcap 8vo. 5s.
Select Titles from the Digest of Justinian. By T. E. HOLLAND
and C. L. SHADWELL. 8vo. 14s.
Also, sold in parts, in paper covers : Part I. Introductory Titles. 2s. 6d.
Part II. Family Law. Is. Part III. Property Law. 2s. 6d. Part IV.
Law of Obligations. No. 1. 3s. 6d. No. 2. 4s. 6d.
Gai Institutionum luris Civilis Commentarii Quattuor :
with a translation and commentary by the late E. POSTE. Fourth edition.
Revised and enlarged by E. A. WHIT-TUCK, with an historical introduction
by A. H. J. GREENIDGE. 8vo. 16s. net.
Institutes Of Roman Law, by R. SOHM. Translated by J. C.
LEDLIE : introductory essay by E. GRUEBER. Ed. 8. 1907. 8vo. 1
Infamia ; its place in Roman Public and Private Law. By A. H. J.
GREENIDGE. 8vo. 10s. 6d.
Legal Procedure in Cicero's Time. By A. H. J. GREENIDGE. 8vo.
£2 2s. net.
Roman LaWS and Charters. Translated, with Introduction and
notes, by E. G. HARDY. 8vo. Being Sic Roman Law (19
Spanish Charters and other Documents bound together 10s. 6d. net; also
separately, Three Spanish Charters, paper covers, 5s. net.
Problems of the Roman Criminal Law. By J. L. s
DAVIDSON. 2 vols. Med. 8vo. IHs. net.
Contract of Sale in the Civil Law. By J. B. MOYLE. 8vo. los.ed.
Trichotomy in Roman Law. By H. GOUDY. 8vo. 4s. net.
The Principles of German Civil Law. By ERNEST J. SCHUSTER.
1907. 8vo. 12s. 6d. net
'3
English Law
Law and Custom of the Constitution. By sir w. R.
In two volumes. 8vo.
Vol. I. Parliament. Fourth edition. 1909. Reissue revised, 1911.
12s. 6d. net.
Vol.11. The Crown. Third edition. Parti, 1907. 10s.6d.net. Part II
1908. 8s. 6d. net.
Principles of the English Law of Contract, and of Agency in
its relation to Contract. By Sir W. R. ANSON. Thirteenth edition, 191-2 by
M. L. GWYER. 8vo. 10s. net.
Legislative Methods and Forms. By Sir c. P. ILBERT, K.C.S.I.
1901. 8vo. 16s.
Modern Land Law. By E. JENKS. 8vo. iss.
Essay on Possession in the Common Law. By sir F.
POLLOCK and Sir R. S. WRIGHT. 8vo. 8s. 6d.
Outline of the Law of Property. By T. RALEIGH. 8vo. TS. 6d.
Cases illustrating the Principles of the Law of Torts.
By F. R. Y. RADCLIFFE and J. C. MILES. 8vo. 1904. 12s. 6d. net.
The Law Of Copyright (1911). By G.S.ROBERTSON. 8vo. 10s. 6d. net.
Law in Daily Life. By RUD. VON JHERING. Translated with Notes
^ and Additions by H. GOUDY. Crown 8vo. 3s. 6d. net.
The Management of Private Affairs. By JOSEPH KING, F. T. R.
BlGHAM, M. L. GWYER, EDWIN CANNAN, J. S. C. BRIDGE, A. M. LATTER.
Crown 8vo. 2s. 6d. net.
Constitutional Documents
Select Charters and other Illustrations of English Constitutional History,
from the earliest times to Edward I. Arranged and edited by W. STUBBS.
Eighth edition. 1900. Crown 8vo. 8s. 6d.
Select Statutes and other Constitutional Documents,
illustrative of the reigns of Elizabeth and James I. Edited by G. W.
PROTHERO. Third edition. Crown 8vo. 10s. 6d.
Constitutional Documents of the Puritan Revolution, selected and
edited by S. R. GARDINER. Third edition. Crown 8vo. 10s. 6d.
Calendar of Charters and Rolls, containing those preserved in the
Bodleian Library. 8vo. £1 11s. 6d. net.
Handbook to the Land- Charters, and other Saxonic Documents.
By J. EARLE. Crown 8vo. 16s.
Fortescue's Difference between an Absolute and a Limited
Monarchy. Text revised and edited, with introduction, etc, by C.
PLUMMER. 8vo, leather back, 12s. 6d. net.
Villainage in England. By P. VINOGRADOFF. 8vo. 16s. net
Welsh Mediaeval Law : the Laws of Howel the Good. Text,
translation, etc, by A. W. WADE EVANS. Crown 8vo. 8s. 6d. net.
International Law
International Law. By W. E. HALL. Sixth edition by J. B. ATLAY.
1909. 8vo. £1 Is. net.
Treatise on the Foreign Powers and Jurisdiction of the
British Crown. By W. E. HALL. 8vo. 10s. 6d.
The European Concert in the Eastern Question, a collection
of treaties and other public acts. Ed. by T. E. HOLLAND. 1885. 8vo. Hs. 6d.
Studies in International Law. By T.E. HOLLAND. 1898. 8vo. ics.ed.
The LaWS Of War On Land. By T. E. HOLLAND. 1908. 8vo. 6s.net.
Gentilis Alberici de lure Belli Libri Tres edidit T. E.
HOLLAND. 1877. Small quarto, half morocco. £1 Is.
The Law of Nations. By Sir T. Twiss. Part I. In time of peace.
New edition, revised and enlarged. 8vo. 15s.
Pacific Blockade. By A. E. HOGAN. 1908. 8vo. 6s. net.
The Progress of International Law and Arbitration. By
Sir H. ERLE RICHARDS. 8vo. Is. net.
Sovereignty OVei' the Air. By Sir H. ERLE RICHARDS. 8vo. Is. 6d.n.
Colonial and Indian Law (see also p. 55)
British Rule and Jurisdiction beyond the Seas. By the late
Sir H. JENKYXS, K.C.B., with a preface by Sir C. P. ILBERT. 1902. 8vo, 15s. n.
Cornewall-Lewis's Essay on the Government of Depen
dencies. Edited by Sir C. P. LUCAS, K.C.B. 8vo. 12s. net.
An Introduction to Hindu and Mahommedan Law tor
the use of students. 1906. By Sir W. MARKBY, K.C.I. E. 6s.net.
Land-Revenue and Tenure in British India. By B. H.
BADEN-POWELL, C.I.E. With map. Second edition, revised by Sir Thos. W.
HOLDERXESS, K.C.S.I. (1907). With an Appendix (Dec., 1913;. Cr. 8vo. 5s. net.
Land-Systems Of British India, being a manual of the Land-
Tenures, and of the systems of Land-Revenue administration. By the same.
Three volumes. 8vo, with map. £3 3s.
Anglo-Indian Codes, by WHITLEY STOKES. 8vo.
Vol. I. Substantive Law. £1 10s. Vol. II. Adjective Law. £1 15s.
1st supplement, 2s. 6d. 2nd supplement, to 1891, 4s. 6d. In one voL, 6s. 6d.
The Indian Evidence Act, with notes by Sir w. MARKBY, K.C.I.E.
8vo. 3s. 6d. net (published by Mr. Frowde).
Corps de Droit Ottoman : un Recueil des Codes, Lois, Reglements,
Onlonnances et Actes les plus importants du Droit Inte>ieur, et d'Etudes sur
le Droit Coutumier de TEmpire Ottoman. Par GEORGE ^i OUNG. ]
vols. 8vo. Cloth, £4 14s. 6d. net ; paper covers, £4 4s. net. Parts I ( V ols.
I-III) and II (Vols. IV-VII) can be obtained separately; price per part,
in cloth, £2 17s. 6d. net, in paper covers, £2 1 2s. 6d. net.
'5
Political Science and Economy
For Bryce's Studies and other books on general jurisprudence and political
science, see p. 61.
The Greek Commonwealth. Politics and Economics in Fifth-
Century Athens. By A. E. ZIMMERN. 8vo. 8s. 6d. net.
Industrial Organization in the 16th and 17th Centuries.
By G. UNWIN. 8vo. 7s. 6d. net.
Relations of the Advanced and Backward Races of
Mankind, the Romanes Lecture for 1902. By J. BRYCE. 8vo. 2s. net.
Cornewall-Lewis's Remarks on the Use and Abuse
of SOme Political Terms. New edition, with introduction by
T. RALEIGH. Crown 8vo, paper, 3s. 6d. ; cloth, 4s. 6d.
Adam Smith's Lectures on Justice, Police, Revenue, and Arms.
Edited with introduction and notes by E. CANNAN. 8vo. 10s. 6d. net.
BluntSChll's Theory of the State. Translated from the sixth
German edition. Third edition. 1901. Crown 8vo. 8s. 6d. net.
Second Chambers. By J. A. R. MARRIOTT. 8vo. 5s. net.
English Political Institutions. By J. A. R. MARRIOTT. Cr.Svo. 4s. 6d.
Political Unions. By H. A. L. FISHER. 8vo. Is. net.
Biological Analogies in History : the Romanes Lecture for 1910.
By THEODORE ROOSEVELT. 8vo. 2s. net.
A Geometrical Political Economy. By H. CUNYNGHAME, C.B.
Crown 8vo. 2s. 6d. net.
The Elements of Railway Economics. By w. M. ACWORTH.
Crown 8vo. Third impression. 2s. net.
Elementary Political Economy. By E. CANNAN. Third edition.
Extra fcap 8vo, Is. net.
Elementary Politics. By Sir T. RALEIGH. Sixth edition revised. Extra
fcap 8vo, stiff covers, Is. net.
The Study of Economic History. By L. L. PRICE, is. net.
Economic Documents
RlCardo's Letters tO MalthuS (1810-1823). Edited by J. BONAR.
8vo. 7s. 6d. Letters to Trower and others ( 1 8 1 1 - 1 823). Edited
by J. BONAR and J. H. HOLLANDER. 8vo. 7s. 6d.
Lloyd's Prices of Corn in Oxford, isss-isso. 8vo. 3s. 6d. net.
First Nine Years of the Bank of England. By J. E. THOROLD
ROGERS. 8vo. 8s. 6d.
History of Agriculture
The History of Agriculture and Prices in England,
A.D. 1259-1793. By J. E. THOROLD ROGERS. 8vo. Vols. I and II (1259-1400).
84s. net. Vols. Ill and IV (1401-1582). 32s. net. Vols. V and VI (1583-1702).
32s. net. Vol. VII. In two Parts (1702-1793). 32s. net.
History of English Agriculture. ByW.H.R.CuRTLER. Cr.8vo.6s.ed.n.
The Disappearance of the Small Landowner. By A. H.
JOHNSON. Crown 8vo. 5s. net.
,6
0
BINDING SECT. MAR 91970
SEP
Live Music Archive
Librivox Free Audio
Metropolitan Museum
Cleveland Museum of Art
Internet Arcade
Console Living Room
Books to Borrow
Open Library
TV News
Understanding 9/11