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Title: The Essentials of Logic - Being Ten Lectures on Judgment and Inference
Author: Bosanquet, Bernard
Language: English
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THE ESSENTIALS OF LOGIC
being
TEN LECTURES ON JUDGMENT AND INFERENCE
by
BERNARD BOSANQUET
FORMERLY FELLOW OF UNIVERSITY COLLEGE, OXFORD
MACMILLAN AND CO.
LONDON AND NEW YORK
1895
The right of Translation is reserved
Richard Clay & Sons, Limited,
London & Bungay.
Transcriber's Note: Footnotes have been placed under the paragraphs to
which they relate. A few added footnotes and additions to Bosanquet's
footnotes, giving the equivalents of Greek words in the text, are in
square brackets. Bosanquet's marginal notes have been used as
subheadings. Page numbers from the original are in braces {}.
{v}
PREFACE
In this course of lectures I have attempted to carry out, under
the freer conditions of the University Extension system, a purpose
conceived many years ago at Oxford. It was suggested to me by the
answer of a friend, engaged like myself from time to time in teaching
elementary Logic, to the question which I put to him, “What do you aim
at in teaching Logic to beginners? What do you think can reasonably be
hoped for?” “If the men could learn what an Inference is, it would be
something,” was the reply.
The course of lectures which I now publish was projected in the spirit
thus indicated. Though only the two last discourses deal explicitly
with Inference, yet those which precede them contribute, I hope, no
less essentially, to explain the nature of that single development
which in some stages we call Judgment, and in others Inference. So far
as I could see, the attempt to go to the heart of the subject, however
imperfectly executed, was appreciated by the students, and was rewarded
with a serious attention which would not have been commanded by the
trivialities of formal Logic, although more entertaining and less
abstruse.
The details of traditional terminology may be found in Jevons’s
_Elementary Lessons in Logic_ (Macmillan). Those {vi} who desire to
pursue the study more in the sense of the present work, may be referred
above all to Bradley’s _Principles of Logic_, and also to Lotze’s
_Logic_ (E. Tr.), and to Sigwart’s great work on Logic, the English
translation of which, just completed, opens a storehouse of knowledge
and robust good sense to the English student. My own larger _Logic_
expresses _in extenso_ the views which these lectures set out in a
shorter form.
I hope it will be admitted by my critics that this experiment, whether
successful or unsuccessful, was worth making, and that except in the
University Extension system, it could not easily have been made.
Bernard Bosanquet.
London, January 1895.
{vii}
CONTENTS
LECTURE I THE PROBLEM OF LOGIC
1. Difficulty of the Science 1
2. The Problem stated 3
3. World as Idea 4
4. “World” 5
5. The Animal’s World 6
6. The World as “Objective” 7
i. Common sense 8
ii. Common-sense Theory 8
iii. Philosophic Theory 11
7. Our separate “Worlds” 14
8. Subjective Idealism 19
LECTURE II JUDGMENT AS THE CONSCIOUSNESS OF A WORLD
1. Defect of Subjective Idealism 21
2. The World as Knowledge 22
3. Knowledge is in the form of Judgment 23
a. Necessary 23
b. Universal 26
c. Constructive 27
4. The Continuous Affirmation of Waking
Consciousness 33
5. Comparison with World as Will 37
6. Distribution of Attention 40
{viii}
LECTURE III THE RELATION OF LOGIC TO KNOWLEDGE
1. Meaning of “Form” 42
2. Form of Knowledge dependent on Content 49
3. The Relation of Part and Whole as Form
determined by Content 54
4. Nature of Knowledge 58
5. Conclusion 59
LECTURE IV TYPES OF JUDGMENT, AND THE GENERAL
CONDITIONS INVOLVED IN ASSERTION
1. Correspondence between Types of Judgment
and Nature of Objects as Knowledge 61
_a_. Impersonal Judgment 61
_b_. Perceptive Judgment 62
_c_. Proper Names in Judgment 64
_d_. Abstract Judgment 65
2. The General Definition of Judgment 66
i. What is implied in claiming Truth 67
ii. By what means the claim is made 69
iii. The kind of Ideas which can claim Truth 74
_a_. Idea as Psychical Presentation 74
_b_. Idea as Identical Reference 74
LECTURE V THE PROPOSITION AND THE NAME
1. Judgment translated into Language 80
2. Proposition and Sentence 82
3. Difference between Proposition and Judgment 82
4. “Parts of Speech” 85
5. Denotation and Connotation 88
6. Have Proper Names Connotation? 91
7. Inverse Ratio of Connotation and Denotation 94
{ix}
LECTURE VI PARTS OF THE JUDGMENT, AND ITS UNITY
1. Parts of the Judgment 98
2. Copula 99
3. Are Subject and Predicate necessary? 100
4. Two Ideas or Things 101
a. Two Ideas 102
i. Mental Transition 102
ii. Absence of Assertion 103
b. Two Things 104
5. Distinction between Subject and Predicate 107
LECTURE VII THE CATEGORICAL AND THE HYPOTHETICAL
JUDGMENTS
1. Some Criticisms on the ordinary scheme of
Judgment 112
a. Why we need a Scheme 112
b. The Common Scheme 113
2. Which Judgments are Categorical? 116
(1) The “Particular” Judgment 116
a. Natural Meaning 116
b. Limited Meaning 117
(2) “Singular” Judgment 118
(3) “Universal” Judgment 119
(4) “Hypothetical” Judgment 121
(5) “Disjunctive” Judgment 123
LECTURE VIII NEGATION, AND OPPOSITION OF JUDGMENTS
1. Distinction between Contrary and Contradictory
Opposition 126
2. Contrary Negation 128
3. Why use Negation? 130
4. Stage of Significant Negation; Combination
of Contrary and Contradictory 132
5. Negative Judgment expressing Fact 134
6. Operation of the Denied Idea 135
{x}
LECTURE IX INFERENCE AND THE SYLLOGISTIC FORMS
1. Inference in General 137
2. Conditions of the Possibility of Inference 139
3. System the ultimate condition of Inference 140
4. Immediate Inference 141
5. Number of Instances 142
6. Figures of Syllogism, illustrating Progress
from Guess-work to Demonstration 146
LECTURE X INDUCTION, DEDUCTION, AND CAUSATION
1. Induction 151
a. By simple Enumeration 151
b. Enumeration always has a Ground 152
c. Perfect Induction 152
d. System 153
e. Analogy as Step towards System 155
f. Negative Instance 158
g. Classification and Generalisation 159
h. Hypothesis 161
2. Deduction 162
a. Subsumption 163
b. Construction 163
3. Causation 164
4. The Postulate of Knowledge 165
5. Conclusion 166
{1}
LECTURE I THE PROBLEM OF LOGIC
_Difficulty of the science_
1. There is no science more difficult than that on which we are
entering in these lectures. It is worth while to discuss the nature of
this difficulty. It is a question of interest rather than of intricacy.
All sciences have, perhaps, much the same possibilities of broad theory
and subtle analysis. But Logic stands alone in the difficulty with
which the student sustains his persuasion that its point of view is
worth applying.
In most other sciences, even in the philosophical sciences, there
is a continual stimulus to sense-perception, to curiosity, to human
interest. The learner is called upon to dissect animals or plants,
to undertake delicate manipulations with beautifully contrived
instruments, to acquaint himself with the history of nations, with
the genesis of worlds, with strange and novel speculations upon the
nature of space, or with the industry and well-being of various classes
among mankind at the present day. And these elements of novelty, these
stimulations of sense-perception or of practical interest, carry us
forward imperceptibly, and sustain our {2} eagerness to analyse and
combine in theoretic completeness the novel matter thus constantly
impinging upon us.
In Philosophy, and more especially in Logic, we can promise little
or nothing of this kind. The teacher of Philosophy, from Socrates
downwards, has talked about common things, things already familiar
to his hearers. And although he calls upon them to think of these
things in a peculiar way, and from an unaccustomed point of view, yet
it is likely to be felt that he is demanding a new effort, without
supplying a new interest. And it is a common experience, that after a
time the mind rebels against this artificial attitude, which fatigues
without instructing, if we have accustomed ourselves to understand by
instruction the accumulation of new sense-perceptions and the extension
of historical or scientific vision over a wider superficial area.
Now this I cannot help, and I will not disguise. In Philosophy, and
in Logic above all, it must be so. The whole point and meaning of the
study is that in it we re-traverse familiar ground, and survey it by
unfamiliar processes. We do not, except accidentally, so much as widen
our mental horizon. For those who care to understand, to trace the
connecting principles and functions that permeate our intellectual
world, there is indeed an interest of a peculiar kind. But even
experienced students will occasionally feel the strain of attending to
difficult distinctions, entirely without the excitement of novelty in
sense-perception or of a practical bearing upon human life. It is this
that makes Logic probably the hardest of all the sciences.
{3} _The problem stated_
2. We cannot hope to vanquish this difficulty unless we face it boldly
from the first. There are in the old-fashioned Logic-books tricks and
puzzles, fallacies and repartees, which can in some degree be made
amusing; but of these I do not intend to speak. The course by which
alone I can hope honestly to awaken a true logical interest among
any who may be quite unfamiliar with the subject, is to approach the
matter descriptively, and try to set before you fully and fairly what
the problem is which the process of knowledge has to meet. And then
it may be possible to claim a genuine theoretical curiosity--none the
less genuine that it may be tinged with a sympathy for man’s common
birthright of intelligence--for the detailed explanation of the means
by which this problem is solved from day to day. Such an explanation is
the science of Logic.
The problem may be thus introduced. Several of those present have,
I believe, attended a previous course of lectures on Psychology.
They have learned, I presume, to think of the mind as the course of
consciousness, a continuous connected presentation, more or less
emphasising within it various images, and groups of images and ideas,
which may be roughly said to act and re-act upon each other, to cohere
in systems, and to give rise to the perception of self. This course
of consciousness, including certain latent elements, the existence
of which it is necessary to assume, is an individual mind, attached
to a particular body, and so far as we know, not separable from the
actions and affections of that body. What is the connection between
such a course of consciousness in any individual, and the world as
that individual knows and wills it? This is the point at {4} which
Psychology passes into Logic. Psychology treats of the course of ideas
and feelings; Logic of the mental construction of reality. How does the
course of my private ideas and feelings contain in it, for me, a world
of things and persons which are _not merely in my mind_?
_World as Idea_
3. Schopenhauer called his great work, _The World as Will and
Idea_. [1] Leaving out Will for the moment, let us consider the world
“as Idea.”
“‘The world is my idea;’ [2] this is a truth which holds
good for everything that lives and knows, though man alone
can bring it into reflective and abstract consciousness. If
he really does this, he has attained to philosophical wisdom.
It then becomes clear and certain to him that what he knows
is not a sun and an earth, but only an eye that sees a sun,
a hand that feels an earth; that the world which surrounds
him is there only as an idea, _i.e._ only in relation to
something else, the consciousness which is himself. If any
truth can be asserted _a priori_, it is this; for it is the
expression of the most general form of all possible and
thinkable experience: a form which is more general than
time, space, or causality, for they all pre-suppose it.
.....
“No truth, therefore, is more certain, more independent of
all others, and less in need of proof than this, that all that
exists for knowledge, and, therefore, this whole world, is
only object in relation to subject, perception of a perceiver,
in a word, idea. This is obviously true of the past and the
future, as well as of the present, of what is farthest off, as
of {5} what is near; for it is true of time and space
themselves, in which alone these distinctions arise. All that
in any way belongs or can belong to the world is inevitably
thus conditioned through the subject and exists only for the
subject. The world is idea.”
[1] E. Tr. (Trubner, 1883).
[2] Schopenhauer, _op. cit._ beginning.
The world, then, for each of us, exists in the medium of our mind.
It is a sort of building, of which the materials are our ideas and
perceptions.
_The “world”_
4. So much for “idea.” What do we mean by “world”? A succession of
images passing before us, or rather making up our consciousness, like a
dream, is not a world. The term is very expressive; it is a favourite
word in Shakespeare. When the courtier says —
“Hereafter, in a better world than this,
I shall desire more love and knowledge of you,”
he does not mean, as I used to think, “in heaven”; he means in a
better condition of social affairs. In “mad world, mad kings, mad
composition,” the term means more especially the set of political and
family connections within which extraordinary reversals of behaviour
have just taken place. Often we use the expression, with a qualifying
epithet, to indicate some particular sphere of connected action, “the
ecclesiastical world,” “the political world,” and so forth. Always
there seems to be implied the notion of a set of things or persons
bound together by some common quality which enables them to act upon
each other, and to constitute what is technically termed a “whole.”
_The_ “world” _par excellence_, then, ought to mean the one connected
set of things and persons which we all recognise {6} and refer to as
the same, and as including ourselves along with all who use the word in
the same sense.
Then the “world as idea” means no less than this, that the system of
things and persons which surrounds all of us, and which each of us
speaks of and refers to as the same for every one, exists for each of
us as something built up in his own mind--the mind attached to his own
body--and out of the material of his own mind.
_The animal’s world_
5. Let us illustrate this building up by thinking of the world, our
surroundings, as an animal must be aware of it. The lowest beginnings
of sight, for example, give no colour and no shape. An animal in this
stage can, probably, only just take warning if a dark object comes
between him and the light. Therefore he cannot have the ordered visual
image of space definitely stretching away all round him, which is the
primary basis of our idea of a world. He can move, no doubt, but there
is nothing to make us suppose that he records and co-ordinates the
results of his movements into anything like that permanent order of
objects which must be constructed in some way by a human being even
though born blind. Succession, we might say, is much more powerful
with animals than co-existence; but we should have to guard ourselves
against supposing that this was what we mean by succession, that is,
a process definitely recognised as in time, with a connection of some
reasonable kind between its phases. For the most part with animals
out of sight is out of mind; if so, the present is not interpreted,
enlarged, and arranged with reference to what is not present in time
or space by them as it is by us. And therefore the consciousness of a
single system of things, {7} permanent, and distinct from the momentary
presentations of the senses, cannot, in all probability, grow up for
them. If so, they have no real world, but only a dream world, [1]
_i.e._ a world not contrasted with the stream of presentation, nor
taken as the common theatre of all actions and events. This difference
between the world of an animal and that of a human being, is a rough
measure of what man does by mental or intellectual construction in
making his world.
[1] The character of the sensory powers, which are strongest in
many animals, contributes to this conclusion. Mr. F.H. Bradley
is sure that his dog’s system of logic, if he had one, would
run, “What exists smells; what does not smell is nothing.” The
sense of smell can scarcely give rise to the idea of a world of
objects. It has hardly any capacity of structural discernment.
_The world as objective_
6. We have now got the idea of a “world,” as a system of things and
persons connected together, taken to be the same for oneself at
different times and for different minds at the same time, yet existing,
for oneself, in the medium of one’s individual consciousness.
We see at once that we cannot stop here. We have really got a
contradiction. If the parts of our world are connected with each other,
they are not merely dependent upon us, that is, upon the changes of our
consciousness. And we all take them to be independent of us, in the
sense that we do not suppose the presence or absence of our perception
to make any difference to the world except by the continuance or
cessation of our perception of it or of its parts. This is the state
of mind in which we practically live, philosophers and all. I do not
really take notice of any difference in mode of existence between the
wall in front of me, which I see, and the wall behind me, which I {8}
do not see. While you are in this lecture-hall, if you think of your
rooms at home, you think of them as they look, that is, as they would
look if you were there to see them. How else, indeed, could you think
of them? This is practically necessary, and therefore, for practical
purposes, true.
But if you take it as a theory, omitting the hypothetical factor,
“if I was there to see,” you go wrong. You then treat your world
as being, outside your consciousness, the same that it is inside
your consciousness, without allowing for the withdrawal of your
consciousness. You are then on the way to think that the world, _as
you see, hear, and feel it_, is outside your mind, and that the sight,
hearing, feeling, and the ideas born of them, are inside your mind as
a sort of faint and imperfect _copy_ of the world which you then call
“external,” _in the sense of outside the mind_.
_Common sense_
i. The first position was that of common sense. The second is that
of common-sense theory. Common sense is quite justified. It says,
“Things affect each other, but the mere presence and absence of our
perception does not affect them.” For practical purposes we must
treat them as being, when unapprehended by our minds, just the same
as when apprehended by our minds. This is the first idea or rather
postulate--for it is not a theoretical idea--of objectivity. Objective
= “independent of our consciousness for practical purposes.”
_Common-sense theory_
ii. In describing the second position as that of common-sense theory
I do not refer to the doctrine of any regular school of philosophers.
There was a Scotch school of philosophy--the school of Reid in the
eighteenth century--commonly called the common-sense school. I will say
{9} below how I think this school was related to the position which
I am now describing. But my present purpose is to hit off the simple
theory of reality which common-sense people make for themselves when
they reflect. Now this theory, in which we all live except when we make
a special effort, accepts the distinction between things and the mind.
For example, it defines truth as the conformity of ideas to objects.
That means something of this kind: the ideas are inside our heads,
and the objects are outside our heads. If we are to have knowledge,
the objects have to be represented inside our heads, and they get in
through the senses. And then you have two similar forms of the world,
one outside our heads, which is real, and another like it but less
perfect and without solidity or causal power, inside our heads, which
is ideal or mental. This is what I call the common-sense theory of the
Objective. Like common sense, it assumes that there is a world which
the withdrawal of our individual consciousness does not affect, but
which persists and acts all the same. Unlike common sense, it lays down
an assertion as to the nature of this world, viz. that it is, apart
from our consciousness, the same as it is for our consciousness. The
world in consciousness, it assumes, is subjective, the world out of
consciousness is objective, and the former is an imperfect copy of the
latter in a feebler material.
The schools of common-sense philosophy, such as are represented by
Locke and Reid, are not quite so simple-minded as the reflection of
ordinary common sense, because every systematic thinker sees at once
that the question stares him in the face, “If the world outside the
mind is copied {10} by the world inside the mind, how can we ever know
whether the copy conforms to the original?” We are by the hypothesis
inside the mind; whatever has passed through the senses is inside the
mind. We cannot as at present advised get at anything outside the
senses or outside the mind. In face of this question, the common-sense
philosophies have two courses open. They may start from the idea of
things outside the mind, but admit that in passing through the senses
the things are in some partial respects transformed--as for instance,
that they acquire colour, sound, and smell in passing through the
senses--this is what Locke says. Or again, still starting from the idea
of things outside the mind, they may simply assert that perception
is of such a nature that it gives us things as they really are. The
former was the view of Locke, the latter that of Reid. This latter
view obviously might pass into the most extreme idealism, and its
interpretation, if it does not so pass, is exceedingly difficult.
But whatever may have been the view of the historical “common-sense
school,” [1] the common-sense theory which we all make for ourselves
involves a separation between the mind and reality. The objective world
is the world as independent of mind, and independent of mind means
existing and acting outside mind, exactly, or almost exactly, as it
seems to exist and act before the mind.
[1] See Seth, _Scottish Philosophy_ (Blackwood, 1885).
Now this is an absolute _cul-de-sac_. If the objective is that which is
outside perception, the objective is out of our reach, and the world of
our perception can never be objective. This is the pass to which we are
brought by taking {11} common sense as the guide of theory and not as
its material.
_Philosophical theory._
iii. There is no way out but by retracing our steps, and avoiding a
false turn which we took in passing from common sense to common-sense
theory. It was quite true that the world is unaffected by the
withdrawal of my individual perception and consciousness (except in so
far as I acted _qua_ bodily thing in the world); but it does not follow
from this that _if_ it becomes the object of a consciousness in me,
it can be so otherwise than as presented within that consciousness.
We must distinguish between the idea that the objective is outside
consciousness and therefore not in consciousness, and the idea that
the objective can be in the individual consciousness, but identified
with something beyond the individual consciousness. It may be that
consciousness is capable of containing a world, not as a copy of a
ready-made original, but as something which it makes for itself by a
necessary process, and which refers beyond this finite and momentary
consciousness.
According to these ideas, the objective is, shortly stated, whatever
we are obliged to think. This, though it is _in_ our thought, is not
considered merely _as_ our thought, or as a train of images or whole
of presentation in our minds. That is an artificial point of view, the
point of view of psychology, and we must carefully avoid starting from
it. But knowledge refers beyond its mental self, and has no limitation
in time or in kind except its own necessity. Thus, I am forced to
think, by a certain context of ideas and perceptions, that there is
now a fire burning in my study at home. This judgment is not barred
by the fact that my mind, as a {12} function attached to my body, is
here three miles away. The thought is objective for me, so long as I am
obliged to think it. My presence in or absence from the room where the
fire is burning has no effect on the question, except as it furnishes
me with evidence one way or the other. Not only absence in space is no
obstacle, but succession in time is no obstacle. My thought, which _is_
here and now, refers confidently to what has happened in long intervals
of time, if the necessity of consistency obliges it to do so. Thus if
I go back to my room and find the fire out and the room very cold, I
infer without hesitation to certain acts and events which are needed
to explain this state of things. And interpretations or explanations
of this kind make up my world, which is for me in my thought, but is
presented as more than my thought, and cannot be a world at all unless
it is more than in my thought. It is in as far as my thought constructs
and presents a world which is more than my momentary psychical state,
that my thought, and the world as presented to me in it, is objective.
The world is not a set of my ideas, but it is a set of objects and
relations of which I frame an idea, and the existence of which has no
meaning for me except as presented in the idea which 1 frame. We are
not to think of (i) Ideas, and (ii) Things which they represent; the
ideas, taken as parts of a world, _are_ the things.
We begin to see, then, how the nature of knowledge meets the puzzle
which I stated above. How, I asked, can a connected “world,” whose
parts act on one another quite independently of my perception, be in
my individual mind? I answer that it does not follow, because the
world _is for me_ {13} only in my presentation, that my presentation
is the only thing which goes on in the world. “What I am obliged to
think” may represent a real development depending on laws and a system
which is not confined to my individual course of consciousness. The
“objective” in this sense is for Logic an assumption, or rather a fact
to be analysed. We do not attempt to prove its existence, except in the
sense of calling attention to its nature in detail. It will be seen
that “outside the mind” ceases, on this view of objectivity, to have
meaning as regards anything that can be related to us. “Outside” is a
relation of bodies to one another; but everything, about which we can
so much as ask a question, is so far inside the mind, _i.e._ given in
its continuum of presentation or idea.
I will recapitulate the three conceptions of the “objective.”
(1) According to practical “common sense” the objective is independent
of our consciousness in the sense that the presence or absence of our
consciousness makes no difference to the operation of things upon each
other.
(2) According to “common-sense theory” the objective is independent
of our consciousness in the sense that the presence or absence of our
consciousness makes no difference in the mode of being of things (viz.
that the world in consciousness approaches objectivity by resembling or
reproducing a similar and quite objective world outside consciousness).
(3) According to philosophical theory the objective is independent of
our consciousness in the sense that it is what we are constrained to
think in order to make our consciousness consistent with itself. “What
we are constrained to {14} think” is not confined, in its _reference_
to our thought, or to thought at all.
_Our separate worlds._
7. Thus, for the purposes of Logic, we must turn our usual ideas upside
down. We must try to imagine something of this kind. We have all seen
a circular panorama. Each one of us, we must think, is shut up alone
inside such a panorama, which is movable and flexible, and follows him
wherever he goes. The things and persons depicted in it move and act
upon one another; but all this is in the panorama, and not beyond it.
The individual cannot get outside this encircling scenery, and no one
else can get inside it. Apart from it, prior to it, we have no self; it
is indeed the stuff of which oneself is made. Is every one’s panorama
exactly the same? No, they are not exactly the same. They are formed
round different centres, each person differing from all the others
by individual qualities, and by his position towards the points and
processes which determine his picture. For--and here is the remarkable
point--every one of us has painted for himself the picture within
which he is shut up, and he is perpetually painting and re-painting
it, not by copying from some original, but by arranging and completing
confused images and tints that are always appearing magically on his
canvas. Now this magical panorama, from which the individual cannot
escape, and the laws of which are the laws of his experience, is simply
his own mind regarded as a content or a world. His own body and mind,
regarded as things, are within the panorama, just as other people’s
bodies and minds are. The whole world, for each of us, _is_ our course
of consciousness, in so far as this is regarded as a system of objects
which we are obliged to {15} think. Not, in so far as it really _is_
a system, for an onlooker, say for a psychologist. For no doubt
every child’s mind, and every animal’s mind, _is_ a working system
of presentations, which a psychologist may study and analyse from
without. Consciousness is consciousness of a world only in so far as
it _presents_ a system, a whole of objects, acting on one another, and
therefore independent of the presence or absence of the consciousness
which presents them.
I take another very rough metaphor to explain this curious contrast
between my mind as a working system, observable from without, and
belonging to my individual body--distinguishable from the thirty or
forty quite different minds belonging to the thirty or forty persons in
this room--and my mind as a continuum of presentations which includes,
as objects, itself, and all the other minds in the room, and the whole
world so far as I have any conscious relation to it whatever.
All of us are familiar with the appearance of a microscope ready
adjusted for use, with its little lamp, its mirror and illuminating
apparatus under the stage, with a specimen on the stage under the
object-glass, its object-glass and its eye-piece. Any one who
understands the working of a microscope finds this a most suggestive
spectacle. He follows in his imagination the light as it comes from
the lamp to the mirror, through the illuminating lenses, through the
transparent specimen, through perhaps a dozen lenses arranged as an
object-glass within an inch of distance, through the eye-piece and
into the observer’s eye. Give him the parts, lenses, prisms, and
mirrors into his hands, and he will test them all, and tell you exactly
how they work. This {16} scientific onlooker may be compared to the
psychologist looking at another man’s mind. He sees it as a thing among
other things, a working system of parts.
But there is one thing that the mere onlooker cannot see. He cannot
see the object. That can only be seen by looking through the tube.
And every one has felt, I should think, the magical transformation,
suggestive of looking through another man’s eye and mind, which occurs
when you put your eye to the eye-piece of an optical instrument. The
outside world of other objects, the tube, the stage, the mirror, the
bystanders, the external light, all disappear, and you see nothing but
the field of vision and whatever distinctly pictured structure may
be displayed within it. The observer who looks through the tube may
be compared with each one of us as he contemplates his own world of
knowledge and perception. This is a thing that no one else can ever do.
The metaphor, indeed, breaks down, in so far as each of us is able to
observe the history and character of his own mind as an object within
the field of presentation which is before his mind. Of course such a
metaphor must break down at some point. But it remains true that the
mind, while directly observing its field of objects, cannot observe its
own peculiarities, and when turned, as we say, upon itself, is still
observing only a part of itself. It remains true that my mind contains
the whole presented world for me and is merely one among thousands of
similar mind-things for you.
Thus, I repeat, the world for each of us is our course of
consciousness, looked at in that way in which it presents a {17}
systematic, organised picture of inter-acting objects, not in that way
in which it is a stream of ideas and feelings, taking place in our
several heads. In the former point of view it is the world as our idea;
in the latter point of view it is simply the consciousness attached to
our body. We might soon puzzle ourselves with the contradictions which
arise if we fail to distinguish these points of view. In one sense my
mind is in my head, in the other sense my head is in my mind. In the
one sense I am in space, in the other sense space is in me. Just so,
however rough the metaphor, from one point of view the microscope is
one among a host of things seen from the outside; from the other point
of view all that we see is in the microscope, which is itself not seen
at all.
It is in this latter sense that our mental equipment is looked at, when
it is regarded as knowledge; and it is in this sense that it forms a
panorama which absolutely shuts in every one of us into his own circle
of ideas. (It is not implied, we should carefully observe, that his
ideas or experience are in any way secondary to his self, or separable
from it, or an adjective of it.) Then how does it happen that our
separate worlds, the panoramas which we construct, do not contradict
one another?
The answer is, that they _correspond_. It is this conception from
which we must start in Logic. We must learn to regard our separate
worlds of knowledge; as something constructed by definite processes,
and corresponding to each other in consequence of the common nature
of these processes. We know that we begin apart. We begin in fact,
though not conscious of our limits, with feelings and fancies and
unorganised experiences which give us little or no {18} common ground
and power of co-operation with other people. But as the constructive
process advances, the correspondence between our worlds is widened
and deepened, and the greater proportion of what we are obliged to
think is in harmony with what other people are obliged to think. Now
of course this would not be so unless reality, the whole actual system
in which we find ourselves, were self-consistent. But more than that,
it would not be so unless the nature of intelligence were the same in
every mind. It is this common nature of intelligence, together with its
differentiated adaptations to reality, that we have to deal with in
Logic.
Thus the separate worlds, in which we are all shut up, must be
considered as corresponding so far as they are objective, that is, so
far as they approach what we are ultimately obliged to think. I say
“corresponding,” because that is the term which expresses the relation
between systems which represent the same thing by the same rules,
but with different starting-points. Drawings in perspective of the
same building from different points of view are such corresponding
systems; the parts represented answer each to each, but the same part
is near or large in one drawing, and distant and small in another; not,
however, by chance, but as a definite consequence of the same laws.
Our separate worlds may be compared to such drawings: the things in
them are identified by their relations and functions, so that we can
understand each other, _i.e._ make identical references, though my
drawing be taken from the east, and yours from the west. The things do
not look quite the same in our different worlds; besides being taken
from different standpoints, both drawings are imperfect and incorrect.
But so {19} long as we can make out the correspondence, we have a basis
for co-operation and for discussion. Logic shows us the principles and
processes by which, under the given influences, these drawings are
constructed.
_Subjective Idealism_
8. If we merely hold to the doctrine of separate worlds, without
insisting upon their correspondence with each other and with reality,
we fall back into the position of subjective idealism, which is a
natural completion of common-sense theory, when, instead of turning
round to retrace its path, it runs deeper into the _cul-de-sac_. It
is a very obvious reflection, that each of us is shut up within his
own mind, and much easier to grasp than the reason for assuming a
real system which appears differently, though correspondingly, in the
centres of consciousness which are ourselves. We cannot get at anything
but in terms of consciousness; how can we justify the assumption that
our consciousness of a world of objects is rooted in reality, _e.g._,
that objects may rightly be treated as persisting and inter-acting
when our personal consciousness is withdrawn? And if we once doubt
this, then why should we assume that our ideas need be or tend to
be consistent with themselves and each other, as for the time they
apparently are?
Subjective Idealism necessarily arises if the common-sense theory of
two worlds, the real outside the mind, and the ideal, copying it,
within the mind, is pushed to its conclusion. The real, outside the
mind, being inaccessible, falls away. The arguments of this Idealism,
as Hume said, “admit of no answer and produce no conviction.” [1]
But I {20} mention the idea, because I do not think that any one
can really understand the problem of Logic, or indeed of science in
general, without having thoroughly thought himself into the difficulty
of Subjective Idealism. It is necessary to be wholly dissatisfied with
common-sense theory, and with the notion of a ready-made world set up
for us to copy in the mind, before the logical analysis of intellectual
construction can have interest or meaning for us. And to produce this
dissatisfaction is the value of Subjective Idealism.
[1] Vol. iv. p. 176 (ed. of 1854), _Inquiry concerning Human
Understanding_, sect. 12.
{21}
LECTURE II “JUDGMENT” AS THE CONSCIOUSNESS OF A WORLD
_Defect of Subjective Idealism_
1. The last lecture was devoted to explaining the distinction between
the stream of presentations and the world as it is for knowledge.
I ended by calling attention to the theory known as “Subjective
Idealism.” This, I said, has the merit of forcing upon us the question,
“How do we get from mind to reality? How do we get from subjective to
objective?” For we have always to remember that our knowledge _is_
within consciousness, though it may _refer_ outside it.
On the other hand, Subjective Idealism has the _defect_ of confounding
the very distinction which we took so much trouble to make plain. Its
essence lies in ascribing to the world of knowledge properties which
are only true of the stream of presentation. It is quite true that the
actual presentations of this room, which each of us has in his head
at this moment, are all different from each other, and different from
any which we have had before, and shall ever have again. Every minute,
every second, they differ; they are perishing existences, wholly
mental, and each of them when past is irrecoverably gone. That is the
property of a presentation within the course of consciousness. It is a
particular perishing existence.
{22} But Subjective Idealism says, “Because these mental existences are
particular perishing existences, and all knowledge consists in them as
its medium, therefore the object of knowledge is nothing beyond these
mental facts, and is not rooted in a permanent system [1] independent
of our mental connections.” Here we must check the inference, and
reply, “No, it does not follow. The presentations which themselves come
and go may refer to something in common, and through them all we may
become aware of something that is not wholly in any of them.” In other
words, there is in Knowledge no passage _from_ subjective to objective,
but only a development of the objective.
[1] Our estimate of Berkeley’s view must depend on the degree
in which we judge him to have identified the Deity with, or
separated Him from, a permanent and universal system. The
statement in the text applies fairly to Hume.
_The world as_ Knowledge
2. Therefore we say, coming closer to our subject, that “_Knowledge_
is the medium in which our world, _as an interrelated whole_, [1]
exists for us.” This is more than saying that it exists in mind or
presentation, because the mere course of consciousness need not
amount to Knowledge. A world, that is, a system of things acting
on one another, could not exist merely in the course of our ideas.
But _Knowledge_, we said, is the mental construction of reality. It
consists of what we are obliged to assert in thought, and because we
are all obliged to think assertorily according to the same methods,
the results of our thinking form corresponding systems--systems that
correspond alike to each other and to reality. (I may be asked, does
not this agreement of {23} our knowledge depend on the agreement of
the physical stimuli supplied to us by nature, as well as on the
homogeneousness of our intelligences? The answer is, that these
stimuli, or nature, have no priority in Knowledge. Their identity is
merely a case or consequence of the identity of our experience as a
whole. We are regarding nature as a system developed in experience, not
as an unknown somewhat behind it. To suppose that solid or extended
existence somehow comes before and accounts for everything else, is a
form of the common-sense theory we have dismissed. Knowledge and Truth
have their limitations as forms of Reality, but an appeal to solidity
or extension will not furnish the required supplementation.)
[1] The words italicised make a reservation in favour of
feeling, which has its own form of reality, but is not
relational.
_Knowledge is in the form of Judgement_
3. All that we have been saying about Knowledge is summed up in the
sentence, “Knowledge is a judgment, an affirmation.” We need not
trouble ourselves yet about negation. We all know what affirmative
assertion is, and it is near enough for the present to say that all
knowledge is judgment in the sense of affirmative assertion.
I will explain how we sum up all we have said of knowledge by calling
it a judgment.
Judgment or affirmation always implies three properties, though they
are not always recognised.
It is (a) necessary, (b) universal, and (c) constructive.
_Judgment necessary_
(a) Judgment is necessary. In saying this, we express all that we said
about the objectivity of the world in knowledge. “Objective” meant, we
concluded, what we are obliged to think. And judgment is necessary,
because it expresses what we are obliged to think; obliged, that is,
not as we are obliged to feel pain, as an unexplained and {24} isolated
fact, but obliged by a necessity operative within the movement of our
consciousness, though not, of course, theoretically recognised as
necessity in common thinking. Thus, in the simplest phases of Judgment,
necessity does begin to approach the kind of necessity by which we feel
pain or are visited by persistent irrational associations.
We can trace an explicit sense of necessity in any scientific matter,
or in any doubtful and complex matters in which we are aware of our own
reflections. We constantly hear and read such phrases as, “I am unable
to resist the conclusion”; “I am forced to believe”; “I am driven to
think”; “I have no alternative but to suppose.” These are every-day
phrases in controversy and in theoretical discussion. And what they all
mean is just what was insisted on in the last lecture; the objective or
real for us is what we are obliged to think. Given our perceptive state
and our mental equipment, the judgment follows.
In trivial or simple judgments this necessity is harder to observe
within consciousness, and approaches more and more to the mere
constraint exercised upon us by physical reality. In a judgment of
mere sensuous comparison, such as a “colour-match,” the necessity is
not that of an intellectual system, but almost that of a feeling which
we cannot dispel. The chief intellectual labour is here negative, and
consists in precautions to remove all disturbing influences, both
mental and material, so as to let the perception operate freely on the
mind. But yet here _is_ necessity; we never for a moment think that we
can modify the result; our aim is simply to distinguish from all others
the particular strand of necessity by which we desire to be guided.
{25} It is easy for an observer to detect intellectual necessity in
judgment, even where the judging subject is wholly unreflective. If
you contradict an obvious judgment made by an uneducated man, he will
no doubt be quite unable to point out the intellectual necessity
which constrains him to it, _i.e._ to argue in support of it; but he
will be bewildered and probably indignant, which shows that, unknown
to himself, his whole intellectual existence is really impeached by
impeachment of a necessary conclusion from it. Many people cannot see
the difference between impeaching their argument and impeaching their
veracity; and this confusion arises, I presume, from a just feeling
that their whole mind is on its trial in the one case as in the other,
although they do not distinguish between the forms of its action which
are concerned. We are told, indeed, in formal logic, that ordinary
statements of fact do not claim necessity; but this merely arises
from confining necessity to explicit necessity expressed in a special
grammatical form.
But, it may be objected, we do not always feel that every trivial
judgment emanates from and so implicates our whole mental constitution
and equipment. If I say to a friend, “I saw you at Charing Cross
yesterday,” and he says, “No, you could not, for I was out of town,”
then, unless I was very certain indeed, I should admit having made a
mistake, and think no more about the matter. That only means, (1) that
the unity of the mind is not thoroughly complete--there are many more
or less detached systems in the mind, and one of them may not be very
deeply inwrought in the whole intellectual frame; and (2) the necessity
of thought may itself modify the certainty of the fact, _e.g._ I know
that {26} a mistake of identity is quite a common thing, and this
knowledge co-operates with my friend’s denial.
But in any perceptive judgment, however unimportant its immediate
content, if it is clear and persistent, a contradiction is a most
serious thing. There is a well-known form of bewilderment connected
with the judgment of direction; if you forget or do not know of a turn
that you have taken, and come out, for example, on familiar ground from
the North when you think you are coming on it from the South, so that
objects have the reverse position of what you expected, then, supposing
that you cannot explain the contradiction, the result is sometimes
a very grave perplexity; some men are quite unhinged by it for the
moment, and a psychologist in France [1] has given it a new name,
“Vertigo of Direction.” This again shows how your whole intellectual
nature is staked upon the most trifling perception, and if you seem to
be forced to a flat contradiction even in the simplest judgment you are
almost “beside yourself.”
[1] M. Binet. See _Mind_, x. 156.
_Judgment universal_
(b) Judgment is universal. There are different senses of “universal” as
of “necessary.” We are now speaking only in the widest sense, in which
universality is a property of all judgment whatever. If we assume that
all our intellectual natures are the same, then to be universal is a
mere consequence of being necessary. I not only feel that my judgment
is inevitable for me, but I never think of doubting that, given the
same materials, it is obligatory for every other intelligent being.
If some one disagrees with a judgment of mine, I try to put the case
before him as it is in my mind. And I am absolutely sure that if I
could do so, he {27} would be obliged to judge as I do. If it were not
so, we should never think of arguing. We should simply say, “Perhaps
his mind is differently constituted from mine,” as, in fact, with
reference to special sets of dominant ideas, and to special provinces
of experience, we often do say. But these we regard as hindrances,
imperfections, accidents. We do not doubt that the system of reason is
active in him as in us.
And thus, as reason is essentially a system, the universality of
judgment involves something more. We not only think that our judgment
is obligatory upon every one else, in as far as they have the same
materials, but we think that it must be _consistent with_ the
judgments of all other persons, just as much as with our own. If it
is inconsistent with any other judgment, we think that one of the two
must be wrong; that is, we will not admit the possibility that the real
world, as others construct it, is out of harmony with the real world as
we construct it.
Thus knowledge, being judgment, is necessary and universal, and in the
widest sense this is true of all judgments.
_Judgment is constructive_
(c) These are two properties of the Judgment, but they do not tell us
what it is. We shall of course examine its nature more fully in the
later lectures. At present we need only think of it as affirmation.
This may be simply described as “pronouncing the interpretation of our
perceptions to form one system with the data of our perceptions.” We
may at once admit the distinction between _data_ and interpretation to
be only relative. Its relativity is the consequence of the constructed
or so to speak artificial {28} character of our real world. We can get
at no data unqualified by judgment.
We may take as an example our perception of things in space. How
much of what we see is given in present sense-perception? This is a
question to which there is no definite answer. We do not know what
the presentations of vision were like before we had learnt to see as
a fully conscious human being sees. We have no right to assume, that
after we have learned to see in this way the actual sense-presentation
remains the same as it was in a different stage of our visual
education. We can give no precise meaning in the way of a time-limit
to the _presentness_ of perception. But we know this much, that it
takes a long time and many kinds of experience to learn to see as an
educated human being sees, and that this acquired capacity is never at
a stand-still, but is always being extended or diminished according to
the vitality, growth, or atrophy of our apperceptive masses. There is
always a certain element of amplification or interpretation, which by
experience, or attentive introspection we can eliminate from the data,
apparently forced upon us by reality, although these data themselves
are modified through and through both by habitual interpretation,
and by the very defining attention which aims at eliminating all
amplification from them.
But yet the whole of sense-perception has a peculiar quality in being
_present_. Artificial though it is, it yet, relatively speaking,
contains an irreducible datum. It is distinguishable from everything
which is not present. It is pervaded by something which we cannot
reduce to {29} intellectual relation, though if we withdrew from it all
that is relation, the apparent datum would be gone.
Now Knowledge is the affirmation or judgment which identifies the
constructive interpretation of our present perception with the reality
which present perception forces upon us. This is clear enough to begin
with, but will have to be modified below to suit the more circuitous or
mediate types of Judgment.
I take two examples, one from sight and one from sound.
Here is a table. In common language we should all say, “We see that
is a table.” The expression is quite correct, because human seeing
is a judgment. But yet, if you were asked to reduce your perception
to terms of sight pure and simple--I mean of visual sensation--why,
unless you were an analytic psychologist or a very skilful artist,
you would not be able to do it. To speak of one point only, you would
have to eliminate the attribute of depth and distance. That is all, so
far as mere vision is concerned, your theory and your interpretation.
The problem for an artist is to get back, at his high plane of
perceptive power, to what in theory would be the lower plane. He has to
re-translate his perception of a thing in space into a flat coloured
surface. The difference between his flat picture and a real object in
space is a rough measure of the difference made by interpretation or
implication in the datum of sense-perception when we say, judging by
sight only, “That is a table.” All the experiences of touch and motion,
from which we have learned to perceive the solidity of the object, are,
theoretically speaking, put into the judgment by us. They are not given
by the eye alone, although we cannot now {30} separate them from that
which is given by the eye alone. For the artist’s flat picture, which
I used as an illustration, is not a stage in our visual education.
Our visual education has proceeded _pari passu_ with our education by
touch and motion; and we saw objects in space as solids, long before
we reflected that for the eye alone a coloured surface would naturally
appear as flat. [1]
[1] The view that depth is a visual datum in the same sense as
breadth seems to me in flagrant contradiction with experience.
But for our present purpose the question is only one of degree,
as no one maintains, that either depth or breadth are seen
without education as an adult sees them.
But this impossibility of getting at an original datum only shows
how entirely we are right in saying that our world is constructed
by judgment. For the process of interpretative amplification passes
quite continuously from the unconscious to the conscious; and every
definitely expressed judgment, though perfectly homogeneous with the
processes which have qualified its datum, and though it may fall
wholly within the maximum of what in ordinary parlance we should call
a simple given perception, contains an identification of some ideal
element, enlargement, or interpretation, with that relatively given
element which reveals itself through a peculiar quality of presentness
pervading the “given” perception.
In the example “That is a table,” the unity of judgment is so well
shown that the identification becomes almost unreal. In fact, we never
judge except to satisfy an interest and so simple a judgment used as an
example, apart from any context which could explain the need for it,
has an air of unreality. You may hear a child make such a judgment {31}
constantly in the sheer pleasure of recognition. An adult would never
make it explicitly unless in some particular context; but it is made,
as I shall maintain below, by the mere glance of his eye which takes in
the table as a real object in a real world of space. Its appearance to
the eye is in this case the datum, while the interpretation consists in
construing this appearance as a solid individual existence in space.
We will look at an example in which the discrimination of elements is
easier. Take the affirmation, “That is a cab,” assuming it to be made
from merely hearing a sound. In this we can much more nearly separate
the datum or minimum of sense from our enlargement or interpretation
of it, and we know that our interpretation is liable to be wrong;
that is to say, the reality into which we ought to construe the sound
may be some other kind of vehicle, and not a cab. Now compare this
with the affirmation, “That (which I see) is a cab.” This judgment of
sight-perception, though its terms are more inextricably interwoven,
has just the same elements in it as the judgment of sound-perception,
“That (which I hear) is a cab.” In the sound-perception the structure
is quite plain. A particular complex quality in the sound suggests as
its objective explanation, what is perfectly distinguishable from it in
thought, the movement of a cab on a particular kind of pavement. The
quality of the sound, its roughness, loudness, increase and decrease,
all form points of connection with the sound of a cab as we know it,
and with the speed, weight, etc. of such a vehicle. But it is quite
easy to consider the sound in itself apart from its interpretation, and
we sometimes feel the {32} interpretation to be more immediate, and
sometimes more inferential. We sometimes say, “I hear a cab,” just as
we say, “I see one,” but in case of sound we more often perhaps say,
“That sounds like--” such and such a thing, which indicates a doubt,
and the beginning of conscious inference.
Thus we see how continuous is the mental construction of reality.
From our unreflective education in seeing, hearing, and touching, to
the explicit judgment of the trained observer, which in its turn
passes readily into inference, there is no definite break. Once the
idea of reality, or of a world, is applied in practice (I do not say
reflectively grasped), there is no further difficulty in principle
throughout the whole process of its construction.
We may then sum up so far: our knowledge, or our world in knowledge,
exists for us as a judgment, that is, as an affirmation in which our
present perception is amplified by an ideal interpretation which is
identified with it. This interpretation or enlargement claims necessity
or universality, and is therefore objective as our world, _i.e._ is
what we are _obliged_ to think, and what we are _all_ obliged to
think. The whole system in process of construction, viz. our present
perception as extended by interpretation, is what we mean by reality,
only with a reservation in favour of forms of experience which are
not intellectual at all. Every judgment then affirms something to be
real, and therefore affirms reality to be defined, in part, by that
something. Knowledge exists in the form of affirmations about reality.
And our world as existing for us in the medium of knowledge consists,
for us, of a standing affirmation about reality.
{33} _Continuous affirmation of waking consciousness_
4. This standing affirmation about reality may be described in
other words as “the continuous affirmative judgment of the waking
consciousness.” In the common logic-books you will find judgment
treated only as the “proposition,” that is, as an assertion made in
language. That is a very convenient way of treating the judgment,
and is not false, if you remember that the proposition, that is, the
assertory sentence, is rather a translation of the judgment than the
judgment itself. But the judgment expressed in a proposition is always
some one definite assertion, with a limited subject and predicate. We
shall speak of the judgment in this sense--the usual sense--later. But
to-day I want to describe the judgment in a more extended sense, that
is, as co-extensive with the waking human consciousness, so far as
aware of a world.
If Judgment consists in the extension of our perceptions by an
interpretation considered as equally real with their content, it
clearly is not confined to the particular facts and truths which from
time to time we utter in language. And more than this, everything that
we do definitely utter, implies a great deal which is not definitely
uttered. If I say, “I have to catch the train at Sloane Square to go
down to Essex Hall,” I only mention the reality of one train, one
square, and one building. But my assertion shades off into innumerable
facts, the equal reality of which as elements in my world is necessary
to make this judgment intelligible and true. It implies the real
existence of the underground railway, which implies that of London, and
therefore that of the surface of our globe in a certain definite order,
and of the civilised world. It implies the reality of this building and
of the meetings which we hold in it, of the University {34} Extension
system, and of my own life and habits as enabling me to take part in
the work of that system. Only a part of this is in the focus of my
attention as I judge; but the whole is a continuous context, the parts
of which are inseparable; and although I do not affirm the whole of it
in so many words, when I say that I am coming down here by train this
evening, yet if any part of it was not affirmed the rest would, so to
speak, fall to pieces, _i.e._ would lose relations in the absence of
which its meaning would be destroyed. Other detached parts of one’s
life and knowledge may seem to be separable from the content of such
a judgment; but on looking closely we see that this is not the case.
So long as we are awake, our whole world is conceived as real, and
forms for us a single immense affirmation, which hangs from present
perception, and shares its constraining power. My present perception
is the illuminated spot, and shades off gradually into the rest which
forms the background, receiving from this background its organised
systematic individuality, while impressing upon it a relation to
its own sensuous presentness. We have only to reflect, in order to
illustrate this connection, on the way in which the idea of London
forms a determining background for the present perception of this
room, while on the other hand it is perceived by us as real in our
presentation of this room.
And indeed the simplest example of what I am pointing out is the
arrangement of objects and places in space. The visual picture which
each of us forms of this room is certainly an affirmative judgment. It
is a judgment because it consists of ideas affirmed as true of reality.
As we look round, all the distances of the objects and the walls from
{35} each other, and their shapes and position, seem to be imprinted on
our minds without an effort. But really they are conclusions from long
education in the art of seeing and from the experience of the other
senses. They are an enlargement or interpretation of sense-perception,
taken as real, _i.e._ as forming a system which is one with the
content of sense-perception, and touches us through sense-perception,
and therefore they exist for us in the form of Judgment. And, as I
described before, our whole world, both of things in space and of our
own history and circumstances, is also affirmed as the background
implied in this picture. That is to say, it is all connected together,
it is all taken as equally real, and it is all vouched for by its
connection with what is given to us in perception. What do we mean by
saying that the Antipodes are real, and implied in my perception of
this room? We mean that they are an element, necessary to educated
thought, in the same system with which I am in contact at this moment
by sight, touch, and hearing, the system of reality. And though I may
not have explicitly thoughts of them since entering the room till now,
yet, if they were no part of my affirmed system of ideas, my perception
of anything in space would be quite different from what it is.
This sense of necessary connection is confined, I think, to our
_waking_ consciousness. Of course there are degrees between waking and
dreaming; but I should be inclined to set up the presence or absence
of judgment as a very fair test of those degrees. We say that a man
is _awake_ in as far as he is aware (i) of a reality which is not his
mere course of consciousness, and (ii.) of the same reality of which
other {36} people are aware; _i.e._ in as far as he identifies his
present perception with a reality, and that the real reality. It is
said that surprise, _i.e._ the sense of conflict between expectation
and the reality, is absent In dreams, and in a very remarkable passage
Aeschylus identifies the life of the savage in his (imaginary)
primitive state with a dream-life, considered as a life of sensuous
presentation, in which the interpretative judgment of perception was
absent. With extraordinary profoundness, in portraying this all but
animal existence, he strikes out all those relations to the objective
world by which man forms for himself a system that goes beyond the
present, so as to leave the stream of presentation without any
background of organised reality. [1]
[1] I quote from Mrs. Browning’s Translation of the _Prometheus
Bound_, which seems close enough for the present purpose.
“And let me tell you, not as taunting men,
But teaching you the intention of my gifts,
How first, _beholding, they beheld in vain.
And hearing, heard not, but, like shapes in dreams_,
Mixed all things wildly down the tedious time,
Nor knew to build a house against the sun
With wicketed sides, nor any woodwork knew,
But lived, like silly ants, beneath the ground,
In hollow caves unsunned. There came to them
No steadfast sign of winter, nor of spring
Flower-perfumed, nor of summer full of fruit.
But blindly and lawlessly they did all things,
Until I taught them how the stars do rise
And set in mystery, and devised for them
Number, the inducer of philosophies.
The synthesis of letters, and besides,
The artificer of all things, Memory,
That sweet muse-mother.” _Pr_., v. 445, ff.
The expression “seeing saw not, and hearing heard not” appears to
suggest the contrast of presentation and objective perception.
{37} It may be asked, “Why should not a man form for himself a system
which interprets his own perception, but is discrepant from the system
of every one else? Should we in that case count him as awake?” Yes, he
would be awake, but he would be mad. Suppose, being a common man, he
interprets all his perceptions into a system which makes him out to
be King of England; in such a case he cannot be set down as dreaming,
because he is alleging a connection which goes beyond his present
perception, and has, ostensibly, been propounded as an interpretation
of it into a systematic order of things. He has in short _a_ world, but
he has broken away from _the_ world, and therefore we pronounce him
mad. A completely new vision of life may cause a man to be thought mad.
[1]
[1] See Browning’s _Epistle of Karshish_.
The whole world, then, of our waking [1] consciousness may be treated
as a single connected predicate affirmed as an enlargement of present
perception. All that we take to be real is by the mere fact of being so
taken, brought within an affirmative judgment.
[1] I do not mean to say that judgment and consciousness of
a world can be wholly absent in dreams, and often no doubt
they are distinctly present. But in those dreams, in my own
experience the normal ones, which leave behind a mere impression
that unrecognisable images have passed before the mind, judgment
and the sense of reality must surely have all but disappeared. I
am inclined to think that dreams are very much rationalised in
recollection and description.
_Comparison with world as Will_
5. To further illustrate the relation of what, in our permanent
judgment, is distinctly thought, what is dimly thought, and what is
implied, let us look for a moment at what we may call “the world
as will.” This is _not_ the doctrine of Schopenhauer in his work,
_The World as Will and Idea_, {38} although the two conceptions have
something in common. His is a metaphysical doctrine, in which he says
that the fundamental reality of the Universe must be conceived as
Will. We have nothing to do with that. We are speaking merely of what
the world is for us, and for us it is not only a system of reality
but a system of purposes. Our world of will is a permanent factor of
our waking consciousness, just as much as our world of knowledge.
Now our will is made up of a great number of purposes, more or less
connected together, just as our knowledge is made up of a great number
of provinces and regions more or less connected together. And just as
in our knowledge at any moment much is clear, much is dim, much is
implied, and the whole forms a continuous context, so it is with our
purposes.
When, for example, one stands looking at a picture, one’s immediate
conscious purpose is to study the picture. One also entertains dimly or
by force of habit the purpose to remain standing, which is a curious
though common instance of will. We do not attend to the purpose of
walking or standing, yet we only walk or stand (in normal conditions
of mind) as long as we will to do so. If we go to sleep or faint, we
shall fall down. Purpose, like judgment, is confined to the waking
consciousness.
But further; the purpose which one entertains in standing to look at a
picture is not really an isolated pin-point of will. It is uppermost
in the mind at the moment in which we carry it out, but it is only the
uppermost stratum, or perhaps rather the present point attained upon a
definite road, within an intricate formation or network of purposes,
which taken together constitute the world of will. The purpose of
looking {39} at a picture shades off into the more general purpose of
learning to take pleasure in what is good of its kind, which is again
set in a certain place within the conception of our life and the way
in which we desire to spend it, and our purposes throughout every
particular day are fitted into one another, and give a particular
setting and colour to each other, and to each particular day, and week,
and year.
Now less or more of all this may be clearly in the mind when we are
carrying out a particular momentary aim. But it is quite certain that
in a human life the particular momentary aim derives its significance
from this background of other purposes; and, if they were to fall away,
the distinct momentary purpose would change its character and become
quite a feeble and empty thing.
Thus we have, in our world of will, a parallel case which illustrates
the nature of our world of knowledge. There is the clear will to look
at the picture, the dim will to continue standing, and the implied will
to carry out certain general aims, and follow a certain routine or
course of life, which gives the momentary purpose its entire setting
and background.
I have spoken of the will in order to illustrate the judgment, because
the dim and implied elements are perhaps more easy to observe in the
case of the will. Almost all our common waking life is carried on by
actions such as walking and sitting, which we hardly know that we
will, but which we could not do if we did not will them. And also the
greater part of our life is rather within a sphere of will which has
become objective for us in our profession, interests, and ideals, than
a perpetual active choice between {40} alternatives such as brings the
act of volition before us in the most striking way. Just so it is with
judgment. Our speaking and writing is a very small part of our judging,
just as our conscious choice between alternatives [1] is a very small
part of our willing.
[1] I do not for a moment suggest that our “conscious choice” is
ultimately different in kind from our habitual persistence in a
course of life. I only take it as an instance in which we fully
attend to our volition.
_Distribution of Attention_
6. Thus the world of knowledge and the world of will must each of them
be regarded as a _continuum_ for the waking consciousness. Whenever
we are awake, we are judging; whenever we are awake we are willing.
The distribution of attention in these two worlds is very closely
analogous. In both, it is impossible to attend to our whole world at
the same moment. But in both, our world is taken as being a single
connected system; and therefore (i.) attention shades off gradually
from the momentary focus of illumination into less and less intensity
over the other parts of the continuous judgment or purpose; but (ii.)
that which is _in_ the focus of attention depends for its quality upon
that which is less distinctly or not at all in the focus of attention.
And as attention diminishes in intensity, the implication of reality
does not diminish with it. In other words, in spite of the inequality
of attention, the reality of our whole world is implied in the reality
of which at any moment we are distinctly aware. But being distinctly
aware of reality is another name for judgment.
Now the common logical judgments which we shall have to analyse
and classify are simply those parts of this continuous affirmation
of consciousness which are from time {41} to time separately made
distinct. Each of them therefore must be regarded as a partial
expression of the nature of reality, and the subject will always be
Reality in one form, and the predicate reality in another form. The
ultimate and complete judgment would be the whole of Reality predicated
of itself. All our logical judgments are such portions and fragments
of this judgment as we can grasp at the moment. Some of these gather
up in a system whole provinces of reality, others merely enlarge,
interpret, or analyse the content of a very simple sense-perception.
We shall not go far wrong in practice if we start from this judgment
of Perception as the fundamental kind of Judgment. The real subject in
Judgment is always Reality in some particular datum or qualification,
and the tendency of Judgment is always to be a definition of Reality.
We see the parts of Judgment most clearly in such thoughts as “This is
blue”; “This is a flower”; “That light is the rising sun”; “That sound
is the surf on a sandy shore.” In these we can plainly distinguish the
element of presentation and the interpretative construction or analytic
synthesis which is by the judgment identified with it.
{42}
LECTURE III THE RELATION OF LOGIC TO KNOWLEDGE
_Meaning of “Form”_
1. I spoke of the whole world, which we take to be real, as presented
to us in the shape of a continuous judgment. It is the task of Logic
to analyse the structure of this Judgment, the parts of which are
Judgments.
The first thing is then to consider what sort of properties of
Judgments we attend to in Logic. It is commonly said that Logic is a
formal science; that is, that it deals with the form, and not with the
content or matter of knowledge.
This word “form” is always meeting us in philosophy. “Species” is Latin
for form, as εἶδος and ἰδεα [1] are Greek for form. The form of any
object primarily means its appearance, that which the mind can carry
away, while the object as a physical reality, as material, remains
where it was. It need not mean shape as opposed to colour; that is a
narrower usage. The Greek opinion was no doubt rooted in some such
notion as that in knowing or remembering a thing the mind possessed
its form or image without its matter. Thus the form came to stand for
the knowable shape or structure which makes a thing what it is, and by
which we recognise it when we see it. This was its species or its idea,
the “image,” as it is used in the phrase, “Let us make man in our own
image.” So in any work of the hands {43} of man, the form was the shape
given by the workman, and came out of his mind, while the matter was
the stuff or material out of which the thing was made.
[1] [= “eidos” and “idea”. Tr.]
The moment we contemplate a classification of the sciences, we see
that this is a purely relative distinction. There is no matter without
form. If it was in this deep sense without form, it would be without
properties, and so incapable of acting or being acted upon. In a
knife the matter is steel, the form is the shape of the blade. But
the qualities of steel again depend, we must suppose, upon a certain
character and arrangement in its particles, and this is, as Bacon would
have called it, the _form_ of steel. But taken as purely relative,
the distinction is good _prima facie_. Steel has its own form, but
the knife has its form, and the matter steel can take many other
forms besides that of a knife. Marble has its own form, its definable
properties as marble (chemical and mechanical), but in a statue, marble
is the matter, and the form is the shape given by the sculptor.
Now applying this distinction to knowledge in general, we see that
all science is formal, and therefore it is no distinction to say that
Logic is a formal science. Geometry is a formal science; even molecular
physics is a formal science. All science is formal, because all science
consists in tracing out the universal characteristics of things, the
structure that makes them what they are.
The particular “form,” then, with which a science deals is simply the
kind of properties that come under the point of view from which that
science in particular looks at things. But a very general science is
more emphatically formal than {44} a very special science. That is to
say, it deals with properties which are presented in some degree by
everything; and so in every object a great multitude of properties
are disregarded by it, are treated by it as matter and not as form.
In this sense Logic is emphatically “formal,” though not nearly so
formal as it is often supposed to be. The subject-matter of Logic,
then, is Knowledge _qua_ Knowledge, or the form of knowledge; that is,
the properties which are possessed by objects or ideas _in so far as
they are members of the world of knowledge_. And it is quite essential
to distinguish the form of knowledge in this sense from its matter or
content. The “matter” of knowledge is the whole region of facts dealt
with by science and perception. If Logic dealt with this in the way in
which knowledge deals with it, _i.e._ simply as a process of acquiring
and organising experience, then Logic would simply be another name for
the whole range of science, history, and perception. Then there would
be no distinction between logic and science or common sense, and in
trying to ascertain, say, the wave-length of red light, or the cab-fare
from Chelsea to Essex Hall, we should be investigating a logical
problem. But we see at once that this is not what we mean by studying
knowledge as knowledge. Science or common sense aims at a particular
answer to each problem of this kind. Logic aims at understanding
the type and principles both of the problem and of its answer. The
details of the particular answer are the “_matter_ of fact.” The type
and principles which are found in all such particular answers may be
regarded as the form of fact, _i.e._ that which makes the fact a fact
in knowledge.
Jevons appears to me to make a terrible blunder at this {45} point. He
says [1]--“One name which has been given to Logic, namely the Science
of Sciences, very aptly describes the all-extensive power of logical
principles. The cultivators of special branches of knowledge appear
to have been fully aware of the allegiance they owe to the highest
of the sciences, for they have usually given names implying this
allegiance. The very name of Logic occurs as part of nearly all the
names adopted for the sciences, which are often vulgarly called the
‘ologies,’ but are really the ‘logics,’ the ‘o’ being only a connecting
vowel or part of the previous word. Thus geology is logic applied to
explain the formation of the earth’s crust; biology is logic applied
to the phenomena of life; psychology is logic applied to the nature
of the mind; and the same is the case with physiology, entomology,
zoology, teratology, morphology, anthropology, theology, ecclesiology,
thalattology, and the rest. Each science is thus distinctly confessed
to be a special logic. The name of Logic itself is derived from the
common Greek word λόγος, which usually means _word_, or the sign and
outward manifestation of any inward thought. But the same word was
also used to denote the inward thought or reasoning of which words are
the expression, and it is thus probably that later Greek writers on
reasoning were led to call their science ἐπιστήμη λογική, or logical
science, also τέχνη λογική or logical art. [2] The adjective λογική,
being used alone, soon came to be the name of the science, just as
Mathematic, Rhetoric, and other names ending in ‘ic’ were originally
adjectives, but have been converted into substantives.”
[1] _Elementary Lessons_, p. 6.
[2] [= “logos”, “episteme logike”, “techne logike” and “logike”. Tr.]
{46} This account of the connection between the name “Logic” and the
terminations of the names of the sciences appears precisely wrong.
Whatever may have been the exact meaning of the expression “Logic,”
or “Logical curriculum,” [1] or “art,” or “science” when first
employed, there can be no doubt that the word logical had a substantive
reference to that about which the science or teaching in question
was to treat. The term “logic,” therefore, corresponds not to the
syllables “logy” in such a word as “Zoology,” but to the syllables
“Zoo,” which indicate the province of the special science, and not
its character as a science. Zoology means connected discourse (λόγος)
about living creatures. Logic meant a curriculum, or science or art
dealing with connected discourse. The phrase “Science of Sciences,”
rightly interpreted, has the same meaning. It does not mean that Logic
is a Science which comprises all the special sciences, but that Logic
is a Science dealing with those general properties and relations which
all sciences _qua_ sciences have in common, but omitting, as from its
point of view matter and not form, the particular details of content by
which every science answers the particular questions which it asks. It
is wild, and most mischievous, to say that “every science is a special
logic,” or that “biology is Logic applied to the phenomena of life.”
This confusion destroys the whole disinterestedness which is necessary
to true scientific Logic, and causes the logical student always to have
his eye on puzzles, and special methods, and interferences by which he
may teach the student of science how to perform the concrete labour
of research. We quite admit that {47} a looker-on may _sometimes_ see
more of the game, and no wise investigator would contemn _a priori_
the suggestions of a student like Goethe, or Mill, or Lotze, because
their author was not exclusively engaged in the observation of
nature. But all this is secondary. The idea that Logic is a judge of
scientific results, able to pass sentence, in virtue of some general
criterion, upon their validity and invalidity, arises from a deep-lying
misconception of the nature of truth which naturally allies itself with
the above confusion between Logic and the special sciences.
[1] πραγμάτεια [= pragmateia Tr.]. See Prantl, i. 545.
Therefore the relation between content or matter of knowledge, and
the form which is its general characteristic as knowledge, is of
this kind. We can either study the objects of knowledge directly as
we perceive them, or indirectly, as examples of the way in which we
know. As studied for their own sake, they are regarded as the matter
or content in which the general form of knowledge finds individual
realisation. In botany, for instance, we have a large number of actual
plants classified and explained in their relation to one another.
A botanist is interested directly in the affinities and evolution
of these plants, and in the principles of biology which underlie
their history. He pushes his researches further and further into
the individual matters that come to light, without, as a rule, more
than a passing reflection upon the abstract nature of the methods
which he is creating as his work proceeds. He classifies, explains,
observes, experiments, theorises, generalises, to the best of his
power, solely in order to grasp and render intelligible the region of
concrete fact that lies before him. Now while his particular results
and discoveries {48} constitute the “form” or knowable properties of
the plant-world _as the object of botanical science_, the science
which inquires into the general nature of knowledge must treat these
particular results as “mere matter”--as something with which it is
not directly concerned, any more than the art which makes a statue
is primarily and directly concerned with the chemical and mechanical
properties of marble. The “form” or knowable properties with which the
general science of knowledge is directly concerned, consists in those
methods and processes which the man of science, developing the modes
in which common sense naturally works, constructs unconsciously as he
goes along. Thus, not the nature and affinities of the plant-world,
but classification, explanation, observation, experiment, theory, are
the phenomena in virtue of which the organised structure of botanical
science participates in the form of knowledge, and its objects become,
in these respects, objects of logical theory.
Hence some properties and relations of objects, being the form or
knowable structure of the concrete objects as a special department of
nature, correspond to the mere matter, stuff, or content of Knowledge
in general, while other properties and relations of objects, being
their form or knowable structure as entering into a world of reality
displayed to our intelligence, correspond to the form of Knowledge as
treated of by a general inquiry into its characteristics, which we
call Logic. It is just as the qualities or “forms” of the different
metals of which knives can be made are mere matter or irrelevant detail
when we are discussing the general “form” or quality of a good knife,
{49} whatever its material. A reservation on this head appears in the
following section.
_Form of Knowledge dependent on Content_
2. For the form of Knowledge depends in some degree upon its matter.
It is very important to realise this truth; for if Logic is swamped
by being identified with the whole range of special sciences, it is
killed by being emptied of all adaptation to living intelligence. What
is called Formal Logic _par excellence_ in all its shapes, whether
antiquated as in Hamilton’s or Thomson’s Formal Laws of Thought,
or freshly worked out on a symbolic basis as by Boole and others,
has, it appears to me, this initial defect, _when considered as a
general theory of Logic_. As a contribution to such a theory, every
method which will work undoubtedly has its place, and indicates and
depends upon some characteristic of real thought. But in the central
theory itself, and especially in so short an account of it as must
be attempted in these lectures, I should be inclined to condemn all
attempts to employ symbols for anything more than the most passing
illustration of points in logical processes. All such attempts, I must
maintain, share with the old-fashioned laws of Identity, Contradiction,
and Excluded Middle the initial fallacy of representing a judgment
by something which is not and cannot be in any way an adequate
symbol of one. If, in order to get at the pure form of Knowledge,
we restrict ourselves to very abstract characteristics in which all
knowledge appears, very roughly speaking, to agree, and which can be
symbolized for working purposes by combinations of signs which have
not the essential properties of ideal contents, then we have _ab
initio_ substituted for the judgment something which is a very {50}
abstract corollary from the nature of judgment, and may or not for
certain purposes and within certain limits be a fair representative
of it. We cannot and must not exclude from the form of Knowledge its
modifications according to “matter,” and its nature as existing only in
“matter.”
In fact, the peculiar “form” of _everything_ depends in some degree
on its “matter.” A statue in marble is a little differently treated
if it is copied in bronze. A knife is properly made of steel; you
can only make a bad one of iron, or copper, or flint, and you cannot
make one at all of wax. Different matters will more or less take the
same form, but only within certain limits. So it is in Knowledge. The
_nature of objects as Knowledge_--for we _must_ remember that “form”
in our sense is not something put into the “matter,” something alien
or indifferent to it, but is simply its own inmost character revealed
by the structural relations in which it is found capable of standing
[1]--depends on the way in which their parts are connected together.
[1] The example of the marble statue may seem to contradict
this idea; and no doubt the indifference of matter to form is
a question of degree. But the feeling for material is a most
important element in fine art; and in knowledge there is only a
relative distinction between formal and material relations.
Let us compare, for example, the use of number in understanding objects
of different kinds.
Suppose there are four books in a heap on the table. This heap of
books is the object. We desire to conceive it as a whole consisting
of parts. In order to do so we simply _count_ them “one, two, three,
_four_ books.” If one is taken away, there is one less to count; if
one is added, there is one more. But the books themselves, as books,
are not {51} altered by taking away one from them or adding one to
them. They are parts indifferent to each other, forming a heap which is
sufficiently analysed or synthesised by counting its parts.
But now instead of four books in a heap, let us think of the four
sides of a square. Of course we _can_ count them, as we counted the
books; but we have not conceived the nature of the square by counting
its sides. That does not distinguish it from four straight lines drawn
anyhow in space. In order to appreciate what a square is, we must
consider that the sides are _equal_ straight lines, put together in a
particular way so as to make a figure with four right angles; we must
distinguish it from a figure with four equal sides, but its angles not
right angles, and from a four-sided figure with right angles, but with
only its opposite sides equal; and note that if we shorten up one side
into nothing, the square becomes a triangle, with altogether different
properties from those of a square; if we put in another side it becomes
a pentagon, and so on.
These two things, the heap of books and the square, are _prima
facie_ objects of perception. We commonly speak of a diagram on a
blackboard or in a book as “a square” if we have reason to take it
as approximately exact, and as intended for a square. But on looking
closer, we soon see that the “matter,” or individual attributes, of
each of these objects of our apprehension demands a different form of
knowledge from that necessary to the other. The judgment “_This_ heap
of books has four books in it” is a judgment of enumerative perception.
The judgment “_The_ square has four sides” is a judgment of systematic
necessity.
{52} Why did we not keep the two judgments in the same logical shape?
Why did we say “_This_ heap” and “_The_ square”? Why did we not say
“this” in both propositions, or “the” in both propositions? Because
the different “matter” demands this difference of form. Let us try.
“The heap of books has four books in it.” Probably we interpret this
proposition to mean just the same as if we had said “This heap.” That
is owing to the fact that the judgment naturally occurs to us in its
right form. But if we interpret “The heap” on the analogy of our
interpretation of “The square,” our judgment will have become false.
It will have come to mean “Every heap of books has four books in it,”
and a judgment of perception will not bear this enlargement. The
subject is composite, and one, the most essential of its elements, is
destroyed by the change from “this” to “the.”
Let us try again. Let us say “This square has four sides.” That is
not exactly false, but it is ridiculous. Every square must have four
sides, and by saying “this square” we strongly imply that foursidedness
is a relation of which we are aware chiefly, if not exclusively, in
the object attended to in the moment of judging, simply through the
apprehension of that moment. By this implication the form of the
judgment abandons and all but denies the character of systematic
necessity which its content naturally demands. It is like saying, “It
appears to me that in the present instance two and two make four.” The
number of sides in a square, then, is not a mere fact of perception,
while the number of books in a heap is such a fact.
But you may answer by suggesting the case that an {53} uninstructed
person--say a child, with a square figure before him, and having heard
the name square applied to figures generally resembling that figure,
may simply observe the number of sides, without knowing any of the
geometrical properties connected with it; will he not then be right in
saying, “This square has four sides”?
Certainly not. In that case he has no right to call it a square.
It would only be a name he had picked up without knowing what it
meant. All he has the right to say would be, “This object” or “This
figure has four sides.” That would be a consistent judgment of mere
perception, true as far as it went. It is always possible to apprehend
the more complex objects of knowledge in the simpler forms; but then
they are not apprehended adequately, not _as_ complex objects. It is
also possible to apply very complex forms of knowledge to very simple
objects. Most truths that can be laid down quite in the abstract about
a human mind could also be applied in some sense or other to any speck
of protoplasm, or to any pebble on the seashore. And every simple
form of knowledge is always being pushed on, by its own defects and
inconsistencies, in the direction of more complex forms.
So far I have been trying to show that objects are capable of being
different in their nature as knowledge as well as in their individual
properties; and that their different natures as knowledge depend on the
way in which their parts are connected together. We took two objects
of knowledge, and found that the mode of connection between the parts
required two quite different kinds of judgment to express them. Let us
look at the reason of this.
{54} _The relation of Part and Whole_
3. The relation of Part and Whole is a form of the relation of Identity
and Difference. Every Judgment expresses the unity of some parts in a
whole, or of some differences in an Identity. This is the meaning of
“construction” in knowledge. We saw that knowledge exists in judgment
as a construction (taking this to include maintenance) of reality.
The expression whole and parts may be used in a strict or in a lax
sense.
In a strict sense it means a whole of quantity, that is, a whole
considered as made up by the addition of parts of the same kind, as a
foot is made up of twelve inches. In this sense the whole is the sum of
the parts. And even in this sense the whole is represented within every
part by an identity of quality that runs through them all. Otherwise
there would be nothing to earmark them as belonging to the particular
whole or kind of whole in question. Parts of length make up a whole
of length, parts of weight a whole of weight, parts of intensity a
whole of intensity, in so far as a whole of intensity is quantitative,
which is not a perfectly easy question. Wholes like these are “_Sums_”
or “_Totals_”. The relation of whole to part in this sense is a very
simple case of the relation of differences in an identity, but for
that very reason is not the easiest case to appreciate. The relation
is so simple that it is apt to pass unnoticed, and in dealing with
numerical computation we are apt to forget that in application to any
concrete problem the numbers must be numbers of something having a
common quality, and that the nature of this something may affect the
result as related to real fact, though not as a conclusion from pure
{55} numerical premisses. In a whole of pure number the indifference
of parts to whole reaches its maximum. The unit remains absolutely the
same, into whatever total of addition it may enter.
In a whole of differentiated members, such as a square, all this begins
to be different. A side in a square possesses, by the fact of being a
side, very different relations and properties from those of a straight
line conceived in isolation. In this case the whole is not made up
merely by adding the parts together. It is a geometrical whole, and its
parts are combined according to a special form of necessity which is
rooted in the nature of space. Speaking generally, the point is that
parts must occupy certain perfectly definite places as regards each
other. You cannot make a square by merely adding three right angles to
one, nor by taking a given straight line and adding three more equal
straight lines to its length. You must construct in a definite way so
as to fulfil definite conditions. The identity shows itself in the
different elements which make it up, not as a mere repeated quality,
but as a property of contributing, each part in a distinctive way, to
the nature of the whole. Such an identity is not a mere total or sum,
though I imagine that its relations can be fully expressed in terms of
quantity, certain differentiated objects or conceptions being given
(_e.g._ line and angle).
I take a further instance to put a sharp point upon this distinction.
The relation of whole and parts is nowhere more perfect, short of
a living mind, than in a work of art. There is a very fine Turner
landscape now [1] in the “Old {56} Masters” Exhibition at Burlington
House--the picture of the two bridges at Walton-on-Thames. The picture
is full of detail--figures, animals, trees, and a curving river-bed.
But I am told that if one attempts to cut out the smallest appreciable
fragment of all this detail, one will find that it cannot be done
without ruining the whole effect of the picture. That means that the
individual totality is so welded together by the master’s selective
composition, that, according to Aristotle’s definition of a true
“whole,” if any part is modified or removed the total is entirely
altered, “for that of which the presence or absence makes no difference
is no true part of the whole.” [2]
[1] February 1892. [2] _Poetics_, 8
Of course, in saying that the part is thus essential to the whole, it
is implied that the whole reacts upon and transfigures the part. It is
in and by this transformation that its pervading identity makes itself
felt throughout all the elements by which it is constituted. As the
picture would be ruined if a little patch of colour were removed, so
the little patch of colour might be such as to be devoid of all value
if seen on a piece of paper by itself. I will give an extreme instance,
almost amounting to a _tour de force_, from the art of poetry, in
illustration of this principle. We constantly hear and use in daily
life the phrase, “It all comes to the same thing in the end.” Perhaps
in the very commonest speech we use it less fully, omitting the word
“thing”; but the sentence as written above is a perfectly familiar
platitude, with no special import, nor grace of sound or rhythm. Now,
in one of the closing stanzas of Browning’s poem _Any Wife to Any
Husband_, this sentence, only modified {57} by the substitution of “at”
for “in,” forms an entire line. [1] And I think it will generally be
felt that there are few more stately and pathetic passages than this
in modern poetry. Both the rhythm and sonorousness of the whole poem,
and also its burden of ideal feeling, are communicated to the line
in question by the context in which it is framed. Through the rhythm
thus prescribed to it, and through the characteristic emotion which it
contributes to reveal, the “whole” of the poem re-acts upon this part,
and confers upon it a quality which, apart from such a setting, we
should never have dreamed that it was capable of possessing.
[1] In order to remind the reader of the effect of this passage
it is necessary to quote a few lines before and after--
“Re-issue words and looks from the old mint,
Pass them afresh, no matter whose the print,
Image and superscription once they bore!
Re-coin thyself and give it them to spend,--
It all comes to the same thing at the end,
Since mine thou wast, mine art and mine shalt be,
Faithful or faithless, sealing up the sum
Or lavish of my treasure, thou must come
Back to the heart’s place here I keep for thee!”
We are not here concerned with the peculiar “aesthetic” nature of
works of art, which makes them, although rational, nevertheless unique
individuals. I only adduced the above examples to show, in unmistakable
cases, what is actually meant when we speak of “a whole” as constituted
by a pervading identity which exhibits itself in the congruous or
co-operating nature of all the constituent parts. In wholes of a higher
kind than the whole of mere quantity the parts no longer repeat each
other. They are not merely distinct, {58} but different. Yet the common
or continuous nature shows itself within each of them.
The parts of a sum-total, taking them for convenience of summation
as equal parts, may be called units; [1] the parts of an abstract
system, such as a geometrical figure, may be called elements (I cannot
answer for mathematical usage), and the parts of a concrete system, an
aesthetic product, a mind, or a society, might be called members.
[1] A unit of measurement implies in addition that it has been
equated with some accepted standard. If I divide the length of
my room into thirty equal parts, each part is a “unit” in the
sum-total; but I have not measured the room till I have equated
one such part with a known standard, and thus made it into a
unit in the general system of length equations.
But every kind of whole is an identity, and its parts are always
differences within it.
_Nature of Knowledge_
4. It will be well to sum up here what we have learnt of the nature
of knowledge in general, before passing to the definition and
classification of Judgment.
Knowledge is always Judgment. Judgment is constructive, for us, of
the real world. Constructing the real world means interpreting or
amplifying our present perception by what we are obliged to think,
which we take as all belonging to a single system one with itself,
and with what constrains us in sense-perception, and objective in the
sense that its parts act on each other independently of our individual
apprehension, and that we are obliged to think them thus. The process
of construction is always that of exhibiting a whole in its parts,
_i.e._ an identity in its differences; that is to say, it is always
both analytic and synthetic. The objects of knowledge differ in the
mode of relation between their {59} parts and the whole, and thus give
rise to different types of judgment and inference; and this difference
in the form of knowledge is a difference in the content of Logic, which
deals with the objects of experience only from the point of view of
their properties as objects in an intellectual world.
_Conclusion_
5. I hope that these general lectures, which, as I am quite aware, have
anticipated the treatment of many difficult questions which they have
not attempted to solve, have been successful in putting the problem of
Logic before us with some degree of vividness. If this problem were
thoroughly impressed upon our minds, I should say that we had already
gained something definite from this course of study. The points which I
desire to emphasise are two.
(1) I hope that we have learned to realise the world of our knowledge
as a living growth, sustained by the energy of our intelligence; and to
understand that we do not start with a ready-made world in common, but
can only enter upon the inheritance of science and civilisation as the
result of courage, labour, and reasonable perseverance; and further,
that we retain this inheritance just as long as our endurance and
capacity hold out, and no longer.
And (2) I have attempted to make clear that this living growth, our
knowledge, is like the vegetable or animal world in being composed
of infinite minor systems, each and all of which are at bottom the
same function with corresponding parts or elements, modified by
adaption to the environment. So that the task of analysing the form of
judgment bears a certain resemblance to that of analysing the forms
of plants. Just as from the single cell of the undifferentiated Alga,
to {60} the most highly organised flower or tree, we have the same
formation, with its characteristic functions and operations, so from
the undifferentiated judgment, which in linguistic form resembles
an ejaculation or interjection, to the reasonable systems of exact
or philosophical science, we find the same systematic function with
corresponding elements.
But the world of knowledge has a unity which the world of organic
individuals cannot claim; and this whole system of functions is itself,
for our intelligence, approximately a single function or system,
corresponding in structure to each of its individual parts, as though
the plant world or animal world were itself in turn a plant or animal.
We cannot hope to exhaust the shapes taken by the pervading fundamental
function of intelligence. We shall only attempt to understand the
analogies and differences between some few of its leading types.
{61}
LECTURE IV TYPES OF JUDGMENT AND THE GENERAL CONDITIONS
INVOLVED IN ASSERTION
_Correspondence between types of Judgment and nature of objects as
Knowledge_
1. The question of correspondence between the types of Judgment and the
orders of Knowledge was really anticipated in discussing the relation
between the content and the form of knowledge. We saw that the content
or matter and nature known determines on the whole the form or method
of knowledge by which it can be known.
I give a few cases of this correspondence, not professing to complete
the list. We should accustom ourselves to think of these forms as
constituting a progression in the sense that each of them betrays a
reference to an ideal of knowledge which in itself it is unable to
fulfil, and therefore inevitably suggests some further or divergent
form. And the defect by which the forms contradict the ideal, is felt
by us as a defect in their grasp of reality, in their presentation of
real connections.
_“Impersonal” Judgment_
_a_. We think of the judgment as predicating an ideal content of a
subject indicated in present perception. But there are judgments
which scarcely have an immediate subject at all, such as “How hot!”
“Bad!” “It hurts!” In the judgments thus represented the true subject
is some {62} undefined aspect of the given complex presentation. Of
course the words which we use are not an absolutely safe guide to the
judgment--they may be merely an abbreviation. But there are typical
judgments of this kind in which we merely mean to connect some namable
content with that which can only be defined as the focus of attention
at the moment. Such judgments might be called predications of mere
quality. The only link by which they bind their parts into a whole is
a feeling referred to our momentary surroundings. A _mere_ quality, if
not defined or analysed, or a feeling of pleasure or pain, is the sort
of object which can be expressed in such a judgment.
_Perceptive Judgment_
_b_. Then we have the very wide sphere of perceptive judgment, which
we may most conveniently confine to judgments which have in the
subject elements analogous to “This,” “Here,” “Now.” Such particles as
these indicate an effort to distinguish elements within the complex
presented. They have no content beyond the reference to presentation,
and, in “here” and “now,” an implication that the present is taken in
a particular kind of _continuum_. Otherwise they mean nothing more or
other than is meant by pointing with the finger. We may or may not
help out a “subject” of this kind by definite ideas attached to it as
conditions of the judgment. If we do, we are already on the road to a
new form of knowledge, incompatible with the judgment of perception.
For so long as we keep a demonstrative, spatial or temporal, reference
in the thought, the subject of judgment is not cut loose from our
personal focus of presentation. And as the existence of such a focus is
undeniable, we are secure against criticism so far as the {63} content
of the subject is concerned. But if we begin to specify it, we do so at
our peril.
Such judgments as these have been called “Analytic judgments of
sense.” [1] The term is not generally accepted in this meaning, but
is conveniently illustrative of the nature of these judgments. It
is intended to imply that they are a breaking up and reconstruction
of what, in our usual loose way of talking, is said to be given in
sense-perception. They remain on the whole within the complex of “that
which” is presented.
[1] Mr. F.H. Bradley, _Principles of Logic_, p. 48.
From the point of view which we have taken, such judgments are not
confined to what we think it worth while to _say_, but are the essence
of every orderly and objective perception of the world around us. In a
waking human consciousness nothing is unaffirmed.
We have no other term than perception to express the process which is
employed in scientific observation and experiment. But it is plain that
so soon as the judgment that refers to “This” is modified through the
inevitable demand for qualification by exact ideas--“_This_ hurts me,”
“_What_ hurts you?” “This old sprain, at the pace we are walking”--a
conflict of elements has arisen within the judgment. And as commonplace
perception passes into scientific observation, the qualifying ideas, on
which truth and relevancy depend, dwarf the importance of the “this,”
and ultimately oust it altogether. That is a simple case in which
the ideal of knowledge and the nature of reality operate within the
judgment to split asunder its primitive form. The subject as expressed
by a pure demonstrative refuses to {64} take account either of truth,
_i.e._ consistency with knowledge as a whole, or of relevancy, _i.e._
consistency with the relation involved in the particular predication
that may be in question. Our commonplace perception halts between
these two extremes. It deals with the world of individual objects and
persons, which, being already systematised according to our current
observations and interests, has, so long as we keep to its order, a
sufficient degree of truth and relevancy for the needs of daily life.
Thus if I say, “This book will do as a desk to write upon,” the truth
of the qualification “book” (_i.e._ the reality of the subject) is
assumed on the ground of the facility of recognising a well-known
“thing,” while the relevancy of the qualification “book” is not
questioned, because we accept an individual thing as an object of
habitual interest _qua_ individual, and do not demand that whenever it
is named those properties alone should be indicated which are relevant
to the purpose for which it is named. The “thing” is a current coin of
popular thought, and makes common perception workable without straining
after a special relevancy in the subject of every predication. Such
special relevancy leads ultimately to the ideal of _definition_, in
which subject and predicate are adequate to each other and necessarily
connected. A definitory judgment drops the demonstrative and relies
on qualifying ideas alone. It is therefore an abstract universal
Judgment, while the Judgment of Perception, so long as it retains the
demonstrative, is a Singular Judgment.
_Proper names in Judgment_
_c_. But a very curious example of a divergence or half-way house in
Knowledge is that form of the singular Judgment in which the subject is
a proper name. A proper name is {65} designative and not definitory.
It may be described as a generalised demonstrative pronoun--a
demonstrative pronoun which has the same particular reference in the
mouth of every one who uses, it, and beyond the given present of time.
So the reference of a proper name is a good example of what we called
a universal or an identity. That which is referred to by such a name
is a person or thing whose existence is extended in time and its parts
bound together by some continuous quality--an _individual_ person or
thing and the whole of this individuality is referred to in whatever
is affirmed about it. Thus the reference of such a name is universal,
not as including more than one individual, but as including in the
identity of the individual numberless differences--the acts, events,
and relations that make up its history and situation.
What kinds of things are called by Proper Names, and why? This question
is akin to the doctrine of Connotation and Denotation, which will be
discussed in the next lecture. It is a very good problem to think over
beforehand, noting especially the limiting cases, in which either some
_people_ give proper names to things to which other people do not give
them, or some _things_ are given proper names while other things of the
same general kind are not. These judgments, which are both Singular and
Universal, may perhaps be called for distinction’s sake “Individual”
Judgments.
_Abstract Judgment_
_d_. The demonstrative perception may also be replaced by a more or
less complete analysis or definition.
Within this province Definition of a concrete whole is one extreme,
_e.g_. “Human Society is a system of wills”; {66} that of an abstract
whole the other extreme, “12 = 7 + 5.” There are all degrees, between
these two, in the amount of modification which the parts undergo
by belonging to the whole. There are also all sorts of incomplete
definitions, expressing merely the effects of single conditions out of
those which go to make up a whole. These form the abstract universal
judgments of the exact sciences, such as, “If water is heated to 212°
Fahr. under one atmosphere it boils.” In all these cases some idea,
“abstract” as being cut loose from the focus of present perception,
whether abstract or concrete in its content, replaces the demonstrative
of the judgment which is a perception. These are the judgments which in
the ordinary logical classification rank as universal.
_The general definition of Judgment_
2. It was quite right of us to consider some types of judgment
before trying to define it generally. It is hopeless to understand a
definition unless the object to be defined is tolerably familiar. We
have said a great deal about knowledge and about judgment as the organ
or medium of knowledge. Now we want to study particular judgments in
their parts and working, and observe how they perform their function of
constructing reality.
Now, for our purpose, we may take the clearest cases of judgment, viz.
the meanings of propositions.
The distinctive character of Judgment as contrasted with every other
act of mind is that it claims to be true, _i.e._ pre-supposes the
distinction between truth and falsity.
First, we have to consider what is implied in claiming truth.
Secondly, by what means truth is claimed in Judgment.
{67} Thirdly, the nature of the ideas for which alone truth can be
claimed.
_What is implied in claiming truth_
(i.) Claiming truth implies the distinction between truth and falsity.
I do not say, “between truth and falsehood,” because falsehood
includes a lie, and a lie is not _prima facie_, an error or falsity of
knowledge. It is, as may be said of a question, altogether addressed
to another person, and has no existence as a distinct species within
knowledge. Thus a lie is called by Plato “falsehood in words”; the term
“falsehood in the mind” he reserves for ignorance or error, which he
treats as the worst of the two, which from an intellectual point of
view it plainly is.
No distinction between truth and falsity can exist unless, in the act
or state which claims truth, there is a reference to something outside
psychical occurrence in the course of ideas. Falsity or error are
relations that imply existences which, having reality of one kind,
claim in addition to this another kind of reality which they have not.
In fact, all things that are called false, are called so because they
claim a place or property which they do not possess. They must exist,
in order to be false. It is in the non-fulfilment, by their existence,
of some claim or pretension which it suggests, that falsity consists.
And so it is in the fulfilment of such a claim that truth has a
meaning. A false coin exists as a piece of metal; it is false because
it pretends to a place in the monetary system which its properties or
history [1] contradict.
[1] For it is, I suppose, technically false, even if over value,
if not coined by those who have the exclusive legal right to
coin.
As the claim to be true is made by every judgment in its {68} form,
there can be no judgment without some recognition of a difference
between psychical occurrences and the system of reality. That is to
say, there is no judgment unless the judging mind is more or less aware
that it is possible to have an idea which is not in accordance with
reality.
Thus, _if_ an animal has no real world distinct from his train of
mental images, if, that is, and just because, these are his world
directly, and without discord, he cannot judge. The question is, _e.g._
when he seems disappointed, whether the pleasant image [1] simply
disappears and a less pleasant image takes its place, or whether the
erroneous image was distinguished as an element in “a mere idea,” which
could be retained and compared with the systematised perceptions which
force it out, _as_ an idea with reality.
[1] It will be observed that we are not treating the mental
images as being taken for such by the primitive mind. It is just
in as far as they are _not_ yet _taken for such_ that they _are
merely such_. Mr. James says that the first sensation is for the
child the universe (_Psychology_ II. 7). But it is a universe
in which all is equally mere fact, and there is no distinction
of truth and falsehood, or reality and unreality. That can only
come when an existent is found to be a fraud.
We must all of us have seen a dog show signs of pleasure when he
notices preparations for a walk, and then express the extreme of
unhappiness when the walk is not taken at all, or he is left at home.
People interpret these phenomena very carelessly. They say “he thought
that he was going to be taken out.” If he did “_think that_, etc,” then
he made a judgment. This would imply that he distinguishes between the
images suggested to his mind, and the reality of their content as the
future event of going out, and knew that he might have the one without
the other following. But of {69} course it is quite possible that the
dog has no distinct expectation of something different from his present
images, but merely derives pleasure from them, which he expresses, and
suffers and expresses pain when they are replaced by something else. It
is here, no doubt, in the conflict of suggestion and perception, that
judgment originates.
On the other hand, animals, especially domestic animals, do seem to use
the imperative, which perhaps implies that they know what they want,
and have it definitely contrasted with their present ideas as something
to be realised.
However this may be, the claim of truth marks the minimum of Judgment.
There can be no judgment until we distinguish psychical fact from the
reference to Reality. A mere mental fact as such is not true or false.
In other words, there is no judgment unless there is something that,
formally speaking, is capable of being denied. When your dog sees
you go to the front door, he may have an image of hunting a rabbit
suggested to his mind, but so far there is nothing that can be denied.
If he has the image, of course he has. There is nothing that can be
denied until the meaning of this image is treated as a further fact
beyond the image itself, in a system independent of the momentary
consciousness in his mind. _Then_ it is possible to say, “No, the
fact does not correspond to your idea,” _i.e._ what we are ultimately
obliged to think as a system is inconsistent with the idea as you
affirmed it of the same system.
_By what means the claim to truth is made_
(ii.) The first thing then in Judgment is that we must have a world of
reality distinguished from the course of our ideas. Thereupon the claim
to truth is actually made by attaching the meaning of an idea to some
point in the real {70} world. This can only be done where an identity
is recognised between reality and our meaning.
Thus (keeping to the Judgment of Perception) I say, “This table is
made of oak.” This table is given in perception already qualified by
numberless judgments; it is a point in the continuous system or tissue
which we take as reality. Among its qualities it has a certain grain
and colour in the wood. I know the colour and grain of oak-wood, and if
they are the same as those of the table, then the meaning or content
“made of oak” coalesces with this point in reality, and instead of
merely saying, “This table is made of wood that has such and such a
grain and colour,” I am able to say “This table is made of oak-wood.”
This example shows the true distinction between the Logical Subject and
Predicate. The fact is, that the ultimate subject in Judgment is always
Reality. Of course the logical subject may be quite different from
the grammatical subject. Some kinds of words cannot in strict grammar
be made subjects of a sentence, though they can represent a logical
subject quite well: _e.g._ “_Now_ is the time.” “_Here_ is the right
place_.” Adverbs, I suppose, cannot be grammatical subjects. But in
these sentences they stand for the logical subjects, certain points in
the perceptive series.
The true logical subject then is always reality, however much disguised
by qualifications or conditions. The logical predicate is always
the meaning of an idea; and the claim to be true consists in the
affirmation of the meaning as belonging to the tissue of reality at
the point indicated by the subject. The connection is always made by
identity of {71} content at the point where the idea joins the reality,
so that _the judgment always appears as a revelation of something which
is in reality_. It simply develops, accents, or gives accuracy to a
recognised quality of the real. This is easily seen in cases of simple
quality--_e.g._ “This colour is sky-blue.” The colour is given, and the
judgment merely identifies it with sky-blue, and so reveals another
element belonging to its identity, the element of being seen in the sky
on a clear day.
The analysis is not quite so easy when there is a concrete subject like
a person; for how can there be an identity between a person and a fact?
“A.B. passed me in the street this afternoon.” Between what elements is
the identity in this case? It is between him, as an individual whom I
know by sight in other places, and him as he appeared this afternoon in
particular surroundings. His identity already extends through a great
many different particulars of time and place, and this judgment merely
recognises one more particular as included in the same continuous
history. “He in this context belongs to him in a former context.” In
this simple case the operative identity is probably that of my friend’s
personal appearance; but the judgment is not merely about that but
about his whole personality, of which his personal appearance is merely
taken as a sign.
Any assertion which is incredible because the identical quality is
wanting will illustrate the required structure. There is a story
commented on by Thackeray in one of his occasional papers, which
implied that the Duke of Wellington took home note-paper from a club to
which he did not {72} belong. (Thackeray gives the true explanation of
the fact on which the suggestion was founded.) The identity concerned
in this case would be that of character. Can we find an identity
between the character involved in a piece of meanness like that
suggested and the character of the Duke of Wellington? No; and _prima
facie_ therefore the judgment is false. The identity which should bind
it together breaks it in two. But yet, again: supposing the external
evidence to be strong enough, we may have to accept a fact which
conflicts with a man’s character as we conceive it. That is so: in such
a case one kind of identity appears to contradict the other. I may
think that I saw a man with my own eyes, doing something which wholly
contradicts his character as I judge it. Then there is a conflict
between identity in personal appearance and identity in character,
and we have to criticise the two estimates of identity--_i.e._ to
refer them both to our general system of knowledge, and to accept the
connection which can be best adapted to that system.
We have got, then, as the active elements in Judgment a Subject in
Reality, the meaning of an idea, and an identity between them.
Is this enough? Have we the peculiar act of affirmation wherever we
have these conditions?
This is not the question by what elements of language the judgment is
rendered. We shall speak of that in the next lecture. The question is
now, simply, “Is a significant idea, referred to reality, always an
assertion?”
The first answer seems to be that such an idea is always _in_ an
assertion, but need not constitute the whole of an {73} assertion. If
we think of a subject in judgment which is represented by a relative
sentence, it seems clear that any idea which can stand a predicate can
also form a part of a subject. “The exhibition which it is proposed
to hold at Chicago in 1893”--has in effect just the same elements of
meaning, and just the same reference to a point in our world of reality
as if the sentence ran, “It is proposed to hold an exhibition at
Chicago in 1893.” In common parlance we should say, that in the former
case we entertain an idea--or conceive or represent it--while in the
latter case we affirm it.
But if we go on to say that the former kind of sentence as truly
represents the nature of thought as the latter, then it seems that we
are mistaken. Even language does not admit such a clause to the rank of
an independent sentence.
If we insist on considering it in its isolation, we probably eke it
out in thought by an unarticulated affirmation such as that which
constitutes an impersonal judgment; in other words, we affirm it to
belong to reality under some condition which remains unspecified.
Thus the linguistic form of the relative clause, as also the separate
existence of the spoken or written word, produces an illusion which
has governed the greater part of logical theory so far as concerns the
separation between concept and judgment, _i.e._ between entertaining
ideas and affirming them in reality. In our waking life, all thought is
judgment, every idea is referred to reality, and in being so referred,
is ultimately affirmed of reality. The separation of elements in the
texture of Judgment into Subjects and Predicates which, as separated,
are conceived as _possible_ Subjects and Predicates, is therefore
{74} theoretical and ideal, an analysis of a living tissue, not an
enumeration of loose bricks out of which something is about to be built
up.
_The kind of ideas which can claim truth_
(iii.) “Idea” has two principal meanings.
(_a_) A psychical presentation and
(_b_) An identical reference.
This distinction is the same as that between our course of ideas and
our world of knowledge. We must try now to define it more accurately.
(_a_) An idea as a psychical presentation is strictly a particular.
Every moment of consciousness is full of a given complex of
presentation which passes away and can never be repeated without some
difference. For this purpose a representation is just the same as a
presentation; is, in fact, a presentation. Its detail at any given
moment is filled in by the influence of the moment, and it can never
occur again with precisely the same elements of detail as before.
If we use the term “idea” in this sense, as a momentary particular
mental state, it is nonsense to speak of having the same idea twice,
or of referring it to a reality other than our mental life. The idea
in this sense is a psychical image. We cannot illustrate this usage
by any recognisable part of our mental furniture, for every such part
which can be described and indicated by a general name, is something
more than a psychical image. We can only say that that which at any
moment we have in consciousness, when our waking perception encounters
reality, is such an idea, and so too is the image supplied by memory,
when considered simply as a datum, a fact, in our mental history.
(_b_) To get at the other sense of “idea” we should think {75} of the
meaning of a word; a very simple case is that of a proper name. What
is the meaning of “St. Paul’s Cathedral in London”? No two people who
have seen it have carried away precisely the same image of it in their
minds, nor does memory, when it represents the Cathedral to each of
them, supply the same image in every detail and association twice over
to the same person, nor do we for a moment think that such an image
_is_ the Cathedral. [1] Yet we neither doubt that the name _means_
something, and that the same to all those who employ it, nor that it
means the same to each of them at one time that it did at every other
time. The psychical images which formed the first vision of it are dead
and gone for ever, and so, after every occasion on which it has been
remembered, are those in which that memory was evoked. The essence of
the idea does not lie in the peculiarities of any one of their varying
presentations, but in the identical reference that runs through them
all, and to which they all serve as material, and the content of this
reference _is_ the object of our thought.
[1] When we are actually looking at the Cathedral, we say,
“_That is_ the Cathedral.” Does not this mean that we take our
momentary image, to which we point, to be the reality of the
Cathedral? Not precisely so. It is the “that,” not our definite
predication about it, which makes us so confident. The “that” is
identified by our judgment, but goes beyond it.
In order to distinguish and employ this reference it is necessary that
there should be a symbol for it, and so long as it brings us to the
object which is the centre of the entire system, this symbol may vary
within considerable limits.
The commonest and most secure means of reference is {76} the word or
name. [1] So confident are we in the “conventional” or artificially
adapted character of this mark or sign of reference, that we are
inclined to treat it as absolutely unvarying on every occasion of
utterance. But of course it is not unvarying. It differs in sound every
time it is spoken, and in context and appearance every time we see
it in a written shape. Our reliance upon it as identical throughout
depends on the fact that it has a recognisable character to which
its variations are irrelevant, and which practically crushes out
these variations from our attention. Unless we are on the look-out
for mispronunciations or misprints, they do not interfere at all
with our attention to the main reference of words. We know that it
is almost impossible to detect misprints so long as one reads a book
with attention to its meaning. This then is a fair parallel to the
distinction which we are considering between two kinds of ideas. If the
momentary sound or look of a word is analogous to idea as psychical
presentation, “the word” as a permanent possession of our knowledge is
analogous to the idea as a reference to an object in our systematic
world, and is the normal instrument of such a reference.
[1] “A name is a sound which has significance according to
convention,” _i.e._ according to rational agreement.--_Ar. de
Interp_. 16a 19.
But either with the word or without it there may be a symbol of another
kind. Any psychical image that falls within certain limits may appear
as the momentary vehicle of the constant reference to an object. Just
as in recognising the reference of a word we omit to notice the accent
and loudness with which it is pronounced, or the quality of the paper
on which it is printed, just so in recognising the {77} reference of
a psychical image our attention fails to note its momentary context,
colouring, and detail. If it includes something that definitely belongs
to a systematic object in our world of objects, that is enough, unless
counteracted by cross references, to effect the suggestion we require,
and that, and nothing else, arrests our attention for the moment. When
I think of St. Paul’s Cathedral, it may be the west front, or the
dome seen from the outside, or the gallery seen from the inside, that
happens to occur to my mind; and further, that which does occur to me
occurs in a particular form or colouring, dictated by the condition
of my memory and attention at the moment. But these peculiarities are
dwarfed by the meaning, and unless I consider them for psychological
purposes, I do not know that they are there. It is the typical
element only, the element which points to the common reference in
which my interest centres, that forms the content of the idea in this
sense, taken not as a transient feature of the mental complex, but
as definitely suggesting a constant object in our constructed world.
And it suggests this object because it, the typical element, is a
common point that links together the various cases and the various
presentations in which the object is given to us. In this sense it is a
universal or an identity.
How can this conception of a logical idea be applied to a perfectly
simple presentation? It would be impossible so to apply it, but there
does not seem to be such a thing as a simple presentation in the sense
of a presentation that has no connection as a universal with anything
else. In the image of a particular blue colour, we cannot indeed
separate out what makes it blue from what makes it the particular {78}
shade of blue that it is. But nevertheless its blueness makes it a
symbol to us of blue in general, and when so thought of, crushes out of
sight all the visible peculiarities that attend every spatial surface.
We understand perfectly well that the colour is blue, and that in
saying this we have gone beyond the limits of the momentary image, and
have referred something in it as a universal quality to our world of
objects. An idea, in this sense, is both less and more than a psychical
image. It contains less, but stands for more. It includes only what is
central and characteristic in the detail of each mental presentation,
and therefore omits much. But it is not taken as a mental presentation
at all, but as a content belonging to a systematic world of objects
independent of my thought, and therefore stands for something which is
not mere psychical image.
If therefore we are asked to display it as an image, as something
fixed in a permanent outline, however pale or meagre, we cannot do
so. It is not an abstract image, but a concrete habit or tendency. It
can only be displayed in the judgment, that is, in a concrete case
of reference to reality. Apart from this, it is a mere abstraction
of analysis, a tendency to operate in a certain way upon certain
psychical presentations. Psychically speaking, it is when realised in
judgment a process more or less systematic, extending through time, and
dealing with momentary presentations as its material. In other words,
we may describe it as a selective rule, shown by its workings but not
consciously before the mind--for if it were, it would no longer be an
idea, but an idea of an idea.
Every judgment, whether made with language or without, {79} is an
instance of such an idea, which may be called a symbolic idea as
distinct from a psychical image; “symbolic” because the mental units
or images involved are not as such taken as the whole of the object
for which they stand, but are in a secondary sense, as the word in a
primary sense, symbols or vehicles only.
Such ideas can have truth claimed for them, because they have a
reference beyond their mental existence. They point to an object in
a system of permanent objects, and that to which they point may or
may not suit the relation which they claim for it. Therefore the
judgment can only be made by help of symbolic ideas. Mere mental
facts, occurrences in my mental history, taken as such, cannot enter
into judgment. When we judge about them, as in the last sentence,
they are not themselves subject or predicate, but are referred to,
like any other facts, by help of a selective process dealing with our
current mental images of them. We shall not be far wrong then, if in
every judgment, under whatever disguises it may assume, we look for
elements analogous to those which are manifest in the simple perceptive
judgment, “This is green,” or “That is a horse.” The relation between
these and more elaborate forms of affirmation, such as the abstract
judgment of science, has partly been indicated in the earlier portion
of this lecture. The general definition of judgment has therefore
been sufficiently suggested on p. 72. Judgment is the reference of a
significant idea to a subject in reality, by means of an identity of
content between them.
{80}
LECTURE V THE PROPOSITION AND THE NAME
_Judgment translated into language._
1. Judgment expressed in words is a Proposition. _Must_ Judgment be
expressed in words? We have assumed that this need not be so. Mill [1]
says of Inference that “it is an operation which usually takes place
by means of words, and in complicated cases can take place in no other
way.” The same is true of Judgment.
[1] _Logic_ vol. I. c. i., init.
We may say in general that words are not needed, when thinking about
objects by help of pictorial images will do the work demanded of the
mind, _i.e._ when perfectly individualised connections in space and
time are in question. Mr. Stout [1] gives chess-playing as an example.
With the board before him, even an ordinary player does not need words
to describe to himself the move which he is about to make.
[1] In _Mind_, no. 62.
Words are needed when we have to attend to the general plan of any
system, as in thinking about organisms with reference to their type,
or about political relations--about anything, that is, which is not
of such a nature that the members of the idea can be symbolised in
pictorial form. It would be difficult, for example, to comprehend the
respiration of plants under a symbolic picture-idea drawn {81} from the
respiration of the higher animals. The relations which constitute a
common element between the two processes do not include the movements,
feelings, and visible changes in the circulatory fluid from which our
image of animal respiration is chiefly drawn; and we could hardly
frame a pictorial idea that would duly insist on the chemical and
organic conditions on which the common element of the process depends.
In a case of this kind the word is the symbol which enables us to
hold together in a coherent system, though not in a single image, the
relations which make up the content of our thought.
“Words” may be of many different kinds--spoken, written, indicated
by deaf and dumb signs; all of these are derived from the word as
it is in speech, although writing and printing become practically
independent of sound, and we read, like the deaf and dumb alphabet,
directly by the eye. Then there may be any kind of conventional signals
either for letters, words, or sentences, and any kind of cipher or
_memoria technica_ either for private or for general use--in these the
“conventional” nature of language reaches its climax, and the relation
to a natural growth of speech has disappeared. And finally there are
all forms of picture-writing, which need not, so far as its intrinsic
nature goes, have any connection with speech at all, and which seems to
form a direct transition between picture-thinking and thinking through
the written sign.
All these must be considered under the head of language, as a fixed
system or signs for meanings, before we can ultimately pronounce that
we think without words.
Every Judgment, however, can be expressed in words, {82} though not
every Judgment need be so expressed or can readily be so.
_Proposition and sentence._
2. A Judgment expressed in words is a Proposition, which is one kind
of sentence. A command question or wish is a sentence but not a
proposition. A detached relative clause [1] is not even a complete
sentence. The meaning of the imperative and the question seems to
include some act of _will_; the meaning of a proposition is always
given out simply for fact or truth. We need not consider any sentence
that has no meaning at all.
[1] See above, Lect. IV.
_Difference between Proposition and Judgment_
3. Almost all English logicians speak of the Proposition and not of the
Judgment. [1] This does not matter, so long as we are agreed about what
they mean. They must mean the proposition _as understood_, and this is
what we call the judgment.
[1] So Mill, Venn, Jevons, Bain (see his note, p. 80).
In order to make this distinction clear, let us consider the
proposition as it reaches us from without, that is to say, either as
spoken or as written. The words, the parts of such a proposition, as we
hear or read them, are separate and successive either in time alone, or
in time and space. Further, the mere sounds or signs can be mastered
apart from the meaning. You can repeat them or copy them without
understanding them in the least, as _e.g._ in the case of a proposition
in an unknown language. So far, the proposition has not become a
judgment, and I do not suppose that any logician would admit that it
deserved the name even of a proposition. But if not, then we must not
confuse the attributes which it has before it becomes a proposition
with those which it has after.
{83} Further, in understanding a proposition, or in construing a
sentence into a proposition (if the sentence only becomes a proposition
when understood), there are many degrees. I read upon a postcard,
“A meeting will be held on Saturday next by the Women’s Liberal
Association, to discuss the taxation of ground-rents.” The meaning of
such a sentence takes time to grasp, and if the words are read aloud
to us, must of necessity be apprehended by degrees. We understand very
quickly that a meeting is to be held next Saturday. This understanding
is already a judgment. It is something quite different from merely
repeating the words which we read. It consists in realising them as
meanings, and bringing these meanings together into a connected idea,
and affirming this idea to belong to our real world. The meanings are
not separate, outside one another, as the words are when we first
hear or read them. They enter into each other, modify each other, and
become parts of an ideal whole. This gradual apprehension of a sentence
recalls to one the boyish amusement of melting down bits of lead in a
ladle. At first the pieces all lie about, rigid and out of contact; but
as they begin to be fused a fluid system is formed in which they give
up their rigidity and independence, and enter into the closest possible
contact, so that their movements and position determine each other. But
still some parts, like words not yet grasped, remain hard and separate,
and it is only when the melting is complete that this isolation is
destroyed, and there are no longer detached fragments, but a fluid body
such that all its parts are in the closest connection with one another.
Thus then in understanding a sentence we have a judgment {84} from the
first. The rest of the process of understanding consists in completing
the content of this judgment by fusing with it the meanings of the
words not yet apprehended; and in the completeness with which this
is effected there will always be great differences of degree between
different minds, and also between the same mind at different times.
Some of us attach a complete and distinct meaning to the words “Women’s
Liberal Association”; some of us do not know, or have forgotten,
exactly what it is, and what are its aims and history. All of us have
some conception of the purpose described as “taxation of ground rents,”
but the phrase conveys a perfectly definite scheme hardly to one in
a thousand readers. Nevertheless, in so far as we have some symbolic
idea which refers to this place or context in the world of objects,
the content of this idea enters into and modifies the total meaning
which in apprehending the sentence before us we affirm of reality. The
heard or written proposition (or sentence, if it is not a proposition
till understood) serves as an instrument by which we build up in our
intellectual world a sort of plan or scheme of connected meanings, and
also, not subsequently but concurrently with this work of building,
affirm the whole content thus being put together to be true of reality.
Then we have what I call a Judgment. It is not that the words are
necessarily forgotten; they, or at least the principal significant
terms, are probably still in the mind as guides and symbols; but yet a
constructive work has been done; a complex experience has been called
up and analysed, and its parts fitted together in a certain definite
order by the operation of universal ideas or meanings, each of which is
a system playing {85} into other systems; and the whole thus realised
has been added as an extension to the significance of the continuous
judgment which forms our waking consciousness. The inconvenience of the
term “proposition” is that it tends to confuse the heard or written
sentence in its separate words with the proposition as apprehended and
intellectually affirmed. And these two things have quite different
characteristics.
_Parts of Speech_
4. Thus we must be very careful how we apply the conception of
“parts of speech.” The grammatical analysis which classifies words
as substantives, adjectives, adverbs, verbs, and the like, is not to
be taken as telling us what words are by themselves, but just the
opposite, viz. what they do when employed in a significant sentence.
They are studied separately for convenience in attending to them, as
we may study the wheels and pistons of an engine; but the work which
gives them their names can only be done when they are together. This
truth is often expressed by saying that “the sentence is the unit
of language,” _i.e._ a word taken by itself cannot have a complete
meaning--unless it is a verb, or used with verbal force, for a verb
is an unanalysed sentence. If any one uses a substantive or adverb by
itself, we think that he has not finished his sentence, and no meaning
is conveyed to our minds. We ask him, “Well, what about it?” The same
is true, as we saw, of a relative clause. If we read in a newspaper
such a clause as this, “The epidemic of influenza, which has appeared
in England for three successive seasons,” followed by a full stop, we
should infer, without hesitation, that some words had dropped out by
accident. Of course such a {86} combination of words would make us
think something, but the meaning which we might ascribe to it would be
conjectural; we should necessarily complete the thought for ourselves
by some affirmation--some relation to reality--while recognising that
no such relation was given in the clause as we read it. Nothing less
than a sentence, or, omitting the wish and the command, nothing less
than a proposition, conveys a meaning in which the mind can acquiesce
as not requiring to be supplemented conjecturally. There are traces in
language that indicate the sentence to have been historically prior to
the word. I question whether the word could be certainly distinguished
within the sentence in early languages that have not been reduced
to writing. The tendency of reflective analysis, as in grammar and
dictionaries, is to give it a more and more, artificial isolation. The
Greeks did not separate their words in writing, and they wrote down
the change in a terminal consonant produced by the initial letter of
the next word, just as if it was within a compound word. Nor had they
really any current term co-extensive with our “word.” Where we should
say “the word ‘horse’” they most commonly use the neuter article
“the” followed by the word in question as if in quotation-marks (”the
‘horse’“). In defining noun and verb, Aristotle has no simple class
name like ”word“ to employ as a common element of the definition, but
uses the curious description ”a portion of discourse, of which no part
has a meaning by itself.“
Of course, single words often stand as signs for propositions. It
is interesting to note the pregnant meaning of a single word in the
mouth of a child. Thus “stool” was {87} used to mean “(1) Where is my
stool? (2) My stool is broken; (3) Lift me on to the stool; (4) Here
is a stool.” [1] There is in this an interesting conflict of form and
meaning, owing to the child of European race having at command only
“parts of speech.” In a less analytical language he might have at
command a sound corresponding to a sentence rather than to a “noun
substantive.”
[1] Preyer, quoted in _Höffding, Psych_., 176.
The verb of inflected languages, [1] such as Greek or Latin, in which
the “nominative case” need not be supplied even by a pronoun, is the
type for us of a sentence not yet broken up.
[1] In German and English, though the verb is inflected, custom
forbids it to stand without the pronoun.
The bearing of this truth on Logic is to make us treat it in two parts
and not in three. We do not treat of Name, Proposition, Syllogism, or
of Concept, Judgment, Inference, but only of the two latter parts. The
name or concept has no reality in living language or living thought,
except when referred to its place in a proposition or judgment. We
ought not to think of propositions as built up by putting words or
names together, but of words or names as distinguished though not
separable elements in propositions. Aristotle takes the simple and
straightforward view. “A term is the element into which a proposition
is broken up, such as subject and predicate.” [1] Of course different
languages separate the parts of the proposition very differently,
{88} and uneducated people hardly separate them at all. Formal Logic
breaks down the grammatical meaning of “name,” so far as to treat as a
“logical name” any complex words that can stand as Subject or Predicate
in a Proposition (_e.g._ a relative clause).
[1] _Anal. prior_., 24b, 16. The opposite view seems to be
expressed in the beginning of the περὶ Ἑρμενείας [= peri
Hermeneias, _de Interpretatione_], that the separate word
corresponds to the separate idea. I have attempted to explain
this as an illusion, p. 73, above.
_Denotation and Connotation_
5. The doctrine of the meaning of names has suffered from their
relation to propositions not being borne in mind. Mill’s discussion [1]
is very sensible, but, as always, very careless of strict system. More
especially it seems a pity to state the question as if it concerned
a division of names into Connotative and Non-connotative; because in
this way we from the first let go of the idea that the meaning of a
name has necessarily two aspects, [2] and we almost bind ourselves to
make out that there are some non-connotative names. It is better to
consider this latter subject on its merits. Mill says that an ordinary
significant name such as “man” “signifies the subjects directly, the
attributes indirectly; it _denotes_ the subjects, and implies or
involves or indicates, or, as we shall say henceforth, _connotes_, the
attributes.” In short, the denotation of a name consists of the things
_to which_ it _ap_plies, the connotation consists of the properties
which it _im_plies. The denotation is made up of individuals and
the connotation of attributes. Denotation is also called Extension,
especially if we are speaking of Concepts rather than of names.
Connotation is then called Intension. In the German writers it is
more usual to say that the Extension or Area (_Umfang_) consists not
of the individuals, but of the species that are contained in {89}
the meaning of a general name. They oppose it to Content (_Inhalt_)
corresponding to our “Connotation.” Thus the “Area” of “rose” would
not be the individual roses in the world, but rather all the species
of rose in the world (_Rosa Canina, Rosa Rubiginosa_, etc.). This
raises a difficulty as to the denotation of a specific name, but
perhaps represents the actual process of thought, in the case of a
generic name, better than that which Mill adopts. The difference is not
important.
[1] _Logic_, Bk. I. c. ii. § 5. Cf. Venn, 174 and 183, and Bain, 48.
[2] See Bradley, p. 155.
Well, then, according to Mill, when we say, “The Marshal Niel is a
yellow rose,” we refer directly to a group of real or possible objects,
and we mean that all these individual objects are yellow roses. The
attributes are only mentioned by the way, or implied. So Dr. Venn says
that the denotation is real, and the connotation is notional.
But there is another side to this question. The objects may be _what
you mean_ but the attributes seem to be _the meaning_, for how can you
(especially on Mill’s theory of the proposition) refer to any objects
except through these attributes, unless indeed you can point to them
with your finger? And so again it seems, especially if we consider
Mill’s account of predication, as if the Connotation were the primary
meaning and the Denotation the secondary meaning. The Connotation
determines the Denotation; and if we “define” the meaning of the name
it is the Connotation that we state. And so Mill tells us two or
three pages further on, that whenever the names given to objects have
properly any meaning, the meaning resides not in what they denote, but
in what they connote. In short, {90} the denotation of a general name
is simply the meaning of its plural, or of its singular, in that sense
in which it implies a plural, while the connotation is the meaning _per
se_, not considered in its instances.
It is clear then that every name has these two kinds of meaning--first,
a content, and then instances, whether possible or actual, of the
content; and the two are obviously inseparable, although they are
distinguishable. Ultimately, indeed, the denotation itself is an
attribute, and so part of the connotation. It is one of the attributes
of man to be a unit in the plurality men, _i.e._ to be “a man.” It
may be said that some names have no plural. If so, these would be
non-denotative rather than non-connotative, but in fact this is not
true. The content of a significant name can always, unless hindered
by a special convention (see below on proper names), be _prima facie_
regarded, in respect of its actual embodiment, as a unit against
other possible units. Granting that there may be an object, which
according to our knowledge can only be real as an isolated case, the
very consideration of it as such a case is enough to distinguish its
existence, whether real or possible, from its content. Thus, as a real
or possible existence, the object is _ipso facto_ considered in the
light of a particular, and as capable of entering into a plurality.
But its nature or content, the meaning of its name, cannot enter
into a plurality. Two _meanings_, two connotations, are alternative
and irreconcilable. Denotation and connotation are thus simply the
particular, or particulars, which embody or are thought of as embodying
a content, and the single or universal content itself.
{91} _Have Proper Names Connotation?_
6. Therefore I think that Mill is wrong, when he goes on, “The only
names of objects which connote nothing are Proper Names, and these
have, strictly speaking, no signification.” [1] If the name has no
signification, for what reason, or by what means, is it attached to a
person or a place? You may say that it is only a conventional mark. But
a mark which has power to select from all objects in the world, and
bring to our minds, a particular absent object, is surely a significant
mark. Granted that it is conventional, yet by what mechanism, and for
what purpose, does the convention operate?
[1] Cf. Venn, 183 ff, and Bradley, 156.
Mill’s point, however, is quite clear. To be told the name of a person
or object does not inform us of his or its attributes. Directly,
it only warns us by what sign the same person or object will be
recognisable in language again. [1] If a name is changed, the new name
tells us nothing different from the old, [2] whereas if an object that
was called vegetable is now called animal, our conception of it is
radically transformed. A name expresses the continued identity of an
object, and this implies only a historical continuity of attributes and
relations, and no constant attribute whatever.
[1] We cannot make it a distinctive mark of proper names that
they recur in different and quite disconnected meanings, because
the words which are used as general names have this same
property. Nor can we say that a proper name is not used in the
same sense of more than one object. Family names and national
names make this plainly untrue. Through these, and names
typically employed, there is a clear gradation from proper to
general names.
[2] The case of marriage may be urged. But a lady’s change of
name does not by itself indicate marriage. It is a mere fact,
which may have various explanations. The change of title (from
“Miss” to “Mrs.”) is more significant, but it is not a change of
name.
{92} Thus a _proper_ name is a contradiction in terms. [1] A name
should have a meaning. But a meaning cannot be proper--that is,
particular. The name-word is therefore like a demonstrative pronoun,
if this were attached, by a special convention, to one identifiable
object only. It acquires meaning, but its meaning is an ever-growing
contradiction with its usage. The meaning is necessarily general, the
usage is _ex hypothesi_ particular.
[1] So, from the complementary point of view, is a _general_
name. A name, it may be urged, _is_ meant to designate a
particular thing or things. And this a name with a true
“meaning” cannot do.
This convention of usage, which prevents a proper name from becoming
general, _i.e._ from being cut loose and used simply for its meaning,
is always on the point of breaking down. [1] Christian names usually
indicate sex; family names, though now with little certainty, descent
and relationship. There are germs of a general meaning within the
several usages of names; while a Solon, a Croesus, a Christian, a
Mahometan, have become purely general names cut loose from all unique
reference. Still in a proper name, as such, we have no right to build
on any general meaning. Recognition is its only purpose; and the law
permits, it has been said, that a man should have one name for Mondays,
Wednesdays, and Fridays, and another for Tuesdays, Thursdays, and
Saturdays. The essence of a name is a reference to unique identity; it
employs meaning only to establish identity.
[1] See note on last page.
What kinds of things have proper names given, then? Always things
_individually_ known to the people who give {93} the name, and
interesting to them for some reason beyond generic or specific
qualities. Pet animals have names, when other animals of the same kind
have not. The peasants throughout England use names, it is said, for
all the fields, although strangers are not usually acquainted with them.
A Proper Name, then, has a connotation, but not a fixed general
connotation. It is attached to a unique individual, and connotes
whatever may be involved in his identity, or is instrumental in
bringing it before the mind.
When we think of history, the importance of proper names becomes
very great. This is the characteristic logical difference between
history and science. “England” and “France” are proper names, names
of individual existences in contact with our world of perception, not
scientific abstractions. Even the words, “1892 A.D.,” are partly of the
nature of a proper name. They say nothing merely general or abstract
about this year; they assign the year a name by counting forwards from
a unique point in the series of years, itself designated by the name
of a historical personage. Everything that is simply distinguished by
its place in the series of events in space and time is in some degree a
proper name. Thus we could not identify the French Revolution by mere
scientific definition. It is known by its proper name, as a unique
event, in a particular place and time. When thus identified it may have
all kinds of general ideas attached to it. It would be hard to show
that “Our earth,” “Our solar system” are not proper names, in virtue of
their uniqueness.
{94} _Inverse ratio of Connotation and Denotation_
7. It has sometimes been said that Connotation is in inverse ratio [1]
to Denotation. Mill explains the fact upon which any such idea
rests. [2] If we arrange things in classes, such that the one class
includes the other--_e.g. Species_ “Buttercup,” _Genus_ “Ranunculus,”
_Order_ “Ranunculaceae,”--of course the genus will contain many species
besides the one mentioned, and the order many genera besides the one
mentioned. The object of the arrangement is that they should do so, and
thus bring out the graduated natural affinities which prevail in the
world. Thus the denotation of the genus-name is larger than that [3] of
the species, and the denotation of the order-name is larger than that
of the genus-name.
[1] See Venn, p. 174, for reference to Hamilton. Venn points out
the fallacy.
[2] _Logic_, Bk. I. ch. vii. § 5.
[3] Or “than the species,” if we take the denotation as made up
of species.
But further, in such an arrangement the genus can contain only the
attributes which are common to all the species, and the order can
contain only the attributes which are common to all the genera; so the
genus-name implies fewer attributes (less connotation) than any one
species-name under it, and the order-name implies fewer attributes
(less connotation) than any one genus-name under it.
That is the fact which suggests the conception of Denotation and
Connotation as varying inversely.
But in any case it would not be right to speak thus mathematically of
an inverse ratio, because there is no meaning in a numerical comparison
of attributes and {95} individuals, and the addition of one attribute
will exclude sometimes more and sometimes fewer individuals. [1]
[1] See Jevons, p. 40.
And there are more important objections to the whole idea of a
corresponding gradation in these two kinds of meaning. The idea
of abstraction thus implied is altogether wrong. The meaning of a
genus-name does not _omit_ the properties in which the species differ.
If it did, it would omit nearly all properties. What happens is that
the genus-idea represents the general plan on which the species are
built, but provides for each of the parts that constitute the whole,
varying in the specific cases within certain limits. Thus in the
Ranunculaceae some species have no petals. But we do not omit the
character “petals” from the genus-idea. We state the general plan
so far as this element is concerned as “Petals five or more; rarely
none.” This is read by a botanist to mean that in some groups the
petals tend to be aborted, and sometimes are actually missing. In a
symbolic representation of the genus-idea such a property may stand as
A, and its various specific forms as A1, A2, A3, etc. There is nothing
to prevent these specific phases approaching and sometimes reaching
zero. No doubt if the classification is pursued in the direction of
“universals” containing fewer and fewer properties, it is possible
to arrive at concepts which appear to have a larger denotation and
a smaller connotation than those “below” them. “Ranunculaceae,”
“Dicotyledons,” “Plants,” “Organisms.”
But this is only because we choose to form our system by that
process of abstraction which consists in leaving out properties.
_E.g._ comparing Frenchmen with men in general, {96} we assume that
“Frenchman” indicates (_a_) all the qualities of humanity as such,
and (_b_) the qualities of French humanity in addition to these. But
is this so in fact? Humanity, considered as a wider, and therefore
as a deeper, idea, may have more content, as well as more area, than
Frenchmanity. We do not really, in thinking of humanity, omit from our
schematic thought all references to qualities of Greek, Jew, English,
and German, and their bearing and interaction upon one another. It is
only that we have been drilled to assume a certain neatness in the
pyramidal arrangement by which we vainly try to reduce the meaning of
a great idea to something that has no system and no inter-relation of
parts, but approaches as near as possible in fixity to the character
of a definite image, though far removed from such a character in the
impossibility of bringing it before the mind.
So we can only say, “the greater the denotation the less the
connotation,” and “_vice versâ_”, in as far as we arrange ideas by
progressive abstraction in the sense of progressive omission. But
it is not the only way of regarding them. Things may develop new
inter-relations as their number increases. Has the community, as Mr.
Bradley asks, less meaning than the individual person? But we must not
consider the community, would be the answer; we must simply consider
the relation of an idea of one individual to any idea that applies
to many individuals. This is simply to rule out those relations that
arise within progressively larger wholes. We can do so, if we think the
exclusion necessary in the interests of logical purity, but it is only
by doing so that we can maintain the traditional view of connotation
and denotation. It is worth while to think out the {97} matter for
ourselves in relation to such familiar ideas as those of man and
animal. It is plain that the idea of “animal” cannot omit all reference
to intelligence, but must in some way allow for the different phases
of this property which run throughout the animal kingdom, and only
find a climax in man. And it is plain also, that even if intelligence
were wholly omitted, this would not leave behind, as in a simple
stratification, properties in which the whole animal kingdom was the
same. Man’s animality is modified throughout in a way corresponding
to his rationality, so that no general idea could be framed including
him and other animals, simply by collecting properties which are
the same and omitting those which are different. The idea of “man”
really becomes richer when considered in the light of a comparison
[1] with the rest of the animal world. Our great systems of natural
classification, representing affinities graduated by descent, are what
give the view which we have criticised a certain objective importance.
But they do not establish it as an exclusive logical doctrine.
[1] If we insist on throwing the whole of this comparison, in
explicit shape, into the complete idea of man, then the progress
to the idea “animal” can add nothing; even so, however, it loses
nothing, but simply becomes the same set of relations, looked
at, so to speak, from the other end.
{98}
LECTURE VI PARTS OF THE JUDGMENT, AND ITS UNITY
_Parts of the Judgment_
1. The result of taking the Judgment as one with the Proposition
has been to assume that its parts were the same as those of the
Proposition; [1] and moreover the same as those of the Proposition in a
very artificial form, viz. as analysed into three separable elements,
“Subject,” “Predicate,” “Copula,” commonly represented in the examples
of the text-books by Substantive, Adjective or Substantive, and the
Verb “is.”
[1] This assumption involves (see Lecture V.) a confusion
between the Proposition as thoroughly understood, and the
Proposition as a series of partially significant sounds or
signs. For obvious reasons, this confusion is very readily made.
For the operation of Formal Logic it is almost necessary to have
these parts, because it is requisite to transpose the terms (as in
Conversion) without changing their meaning, [1] and to get rid of
_tenses_, which do not belong to Scientific Judgment, and are very
troublesome in Formal Inference.
[1] If the “predicate” is a Substantive, this presents no
difficulty; and if it is an Adjective, it can be done by a
little straining of grammar, or the insertion of “thing” or
“things.” With a verb it is more clumsy.
Thus in Formal Logic we prefer the shape of sentence “Gold is lustrous”
to “Gold glitters,” and “The bridge is {99} cracked” to “There is
a crack in the bridge.” And practically all propositions can be
thrown into this shape, which is convenient for comparing them. The
educational value of elementary formal logic consists chiefly, I am
convinced, in the exercise of paraphrasing poetical or rhetorical
assertions into this typical shape, with the least possible sacrifice
of meaning. The commonest mistakes in the work of beginners, within my
experience as a teacher, consist in failures to interpret rightly the
sentence given for analysis.
But this type is not really ultimate. The judgment can be conveyed
without a grammatical subject, and without the verb “is”--indeed
without any grammatical verb at all. On the whole this agrees with
Mill’s view in the chapter “Of Propositions.” [1] He points out (§ 1)
that we really need nothing but the Subject and Predicate, and that the
copula is a mere sign of their connection _as_ Subject and Predicate.
He does not, however, discuss the case in which the grammatical Subject
is absent.
[1] Mill’s _Logic_, Bk. I. ch. iv.
_Copula_
2. In analysing the Judgment as an act of thought we may begin by
dismissing the separate Copula. It has no separate existence in thought
corresponding to its separate place in the typical proposition of
Formal Logic. It has come to be considered separately, because the
abstract verb “is” is used in our languages as a sign of the complete
enunciation. But there is not in the Judgment any separate significant
idea--any third idea--coming in between the Subject and Predicate of
Judgment. We should try to think of the Copula not as a link, separable
and always {100} intrinsically the same, [1] connecting two distinct
things. We should think of it rather as the grip with which the parts
of a single complex whole cohere with one another, differing according
to the nature of the whole and the inter-dependence of its parts. Benno
Erdmann [2] has strikingly expressed this point of view by saying,
that in the Judgment, “The dead ride fast,” the Subject is “the dead,”
the Predicate “fast riding,” _and the Copula “the fast riding of the
dead_.” In other words, the Copula is simply the Judgment considered
exclusively as a cohesion between parts of a complex idea, the
individual connection between which can only be indicated by supplying
the idea of those parts themselves.
[1] In a comic Logic, with pictures, meant to stimulate dull
minds at a University, I have seen the Copula represented as
the coupling-link between two railway carriages. This is an
excellent type of the way in which we should _not_ think of it.
[2] _Logik_, p. 189.
_Are Subject and Predicate necessary?_
3. The explicit Predicate is more necessary than the explicit Subject.
We have spoken of Judgments expressed by one word, “Fire!” “Thieves!”
etc., and also of impersonal Propositions, “It is raining,” “It
is thawing.” These two classes of Judgments show hardly any
explicit Subject at all. But we could not assert anything without
a Predicate--that would be to assert without asserting anything in
particular.
As these Judgments have, roughly speaking, a Predicate and no
Subject, I do not think it convenient to call them, with Dr. Venn,
existential judgments. It is true that they refer to reality, but their
_peculiarity_ is in not referring to a distinct subject. And when used
for definite and complex assertions they become very artificial, _e.g._
“There is a {101} British Constitution by which our liberties are
guaranteed.” Instead of organising the content of the Judgment, such a
form of assertion simply tosses the whole of it into the Predicate in a
single mass.
The question is only one of words; but it appears to me more convenient
to reserve the term Existential judgments for those highly artificial
assertions which actually employ the Predicate “exist” or “existence,”
_e.g._ “Matter exists.” These are at the opposite end of the scale
from those last-mentioned, and are the nearest approach to Judgment
with Subject and no Predicate. That is to say, their Predicate is
the generalised abstract form of predication [1] without any special
content--the kind and degree of existence asserted being understood
from the context.
[1] Expressed in Greek by the word corresponding to “is,” used
with an accent, which does not belong to it in its ordinary use.
He is good = ἄγαθός ἐστι [= agathos esti]; He exists = ἔστι [=
esti Tr.].
Except, however, in the case of these peculiarly abstract and
reflective assertions, it must be laid down that a predicated content
is necessary to judgment, while an _explicit_ subject of predication is
unnecessary.
_Two Ideas of Things_
4. If it is possible, in some cases, to throw the whole content of
judgment into the predicate, this rather disposes us to criticise the
notion that there must be two distinct matters, objects, ideas, or
contents, in every judgment. The notion in question has two forms.
It is thought that the Judgment consists in putting two _ideas_
together, [1] or,
{102} That the Judgment consists in comparing two or
more things. [2]
[1] For this conception, see Hamilton’s _Lectures on Logic_, i.
227, and for a criticism on it. Mill’s _Logic_, Bk. I. ch. v.,
_init_, Dr. Venn seems to incline to Hamilton’s view, but I do
not feel sure that he intends to discuss the question in the
form in which it is referred to in the text. See his _Empirical
Logic_, pp. 210 and 211.
[2] See Jevons, pp. 61-2; and Mill, Bk. I. ch. iii., _init_.;
and ch. iv., _init_.
_Two Ideas_
(_a_) The notion of “two ideas” has two principal difficulties.
_Notion of mental transition pure and simple_
(i.) In its simplest shape the notion of “two ideas” involves the
great blunder which I explained in Lecture IV. It suggests that the
parts of Judgment are separate and successive psychical states, and
that the Judgment consists in a change from the one to the other.
Herbert Spencer, as I understand him, considers every relation to be
apprehended as a mental change or passage from one idea to another.
This view would degrade logical connection into mere psychical
transition. I do not say that there is no psychical transition in
Judgment. I do say that psychical transition is not enough to make a
Judgment. The parts of Judgment, as we saw in the last lecture, do
not succeed one another separately like the parts of a sentence. The
relation between Subject and Predicate is not a relation between mental
states, but is itself the content of a single though continuous mental
state. Mill has rightly touched on this point. “When I say that fire
causes heat, do I mean that my idea of fire causes my idea of heat?”
[1] and so on. The fact is that “Fire-causing-heat” is itself the
single content or meaning represented in my symbolic idea; it is not a
succession of psychical states in my mind, or a passage from the idea
of fire to the idea of causing heat.
[1] _Logic_, Bk. I. ch. V. § I.
{103} _Absence of assertion_
(ii.) But further, understanding now that the Judgment is composed of
a single ideal content, and is not a transition from one mental state
to another, there is still a difficulty in the conception that its
component elements are nothing but ideas. If the Subject in Judgment is
no more than an ideal content, how, by what means, does the Judgment
claim to be true of Reality? “The Subject cannot belong to the content
or fall within it, for in that case it would be the idea attributed to
itself.” [1] If the Subject were only a part of an ideal content it
would not claim to be true of Reality, and where it _appears_ to be
only an ideal content there is much dispute in what sense the Judgment
does claim to be true of Reality. “Violations of a law of nature are
impossible.” “The three angles of a triangle are equal to two right
angles.” “All trespassers will be prosecuted.” In these Judgments we
should find it hard to make out that the Subjects are real things
corresponding to our ideas. And yet, if they are not, how can the
Judgment attach itself to Reality? This is the difficult question of
the distinction between the categorical and the hypothetical Judgment,
and we shall have to return to it. In the meantime, we must adhere to
our judgment of perception as the true underlying type. The Subject
is here not an idea, but is the given reality, _this_ or _that_, and
the Judgment is not a conjunction of two ideas, but is present reality
qualified by an idea. We say, “It is very hot,” meaning that heat, the
general quality embodied for us in an ideal content, is true of--forms
one tissue with--the surroundings which here and now press upon our
attention. Or again, “This is red,” {104} _i.e._ the content of the
idea red is what my attention selects and emphasises within the mass
of detail presented to it in its own unique focus which the pronoun
“this” simply points out as though with the finger. We shall find such
a structure underlying all the more artificial forms of Judgment.
[1] _Bradley’s Principles of Logic_, p. 14.
_Two Things_
(_b_) Thus it would seem that Jevons and Mill are much nearer the real
point when they say that the proposition has to do with two Things,
or with a Thing and a group of Things. But we must notice in passing
that Mill, [1] after fighting hard against calling them Ideas, takes
our breath away by saying that they are states of consciousness. There
is, of course, a difficulty, which I will not try to deal with now, in
the fact that however much we _refer_ to things, we have nothing to
_work with intellectually_ but our ideas of them, and in some types
of Judgment the reference to real things is difficult to trace. Mill
further emphasises this by showing, that what we assert in ordinary
_general_ Judgment is co-existence of attributes. [2] “Now when we
say, Man is mortal, we mean that wherever these various mental and
physical phenomena (the attributes of man) are all found, then we have
assurance that the other physical and mental phenomenon called death,
will not fail to take place.” That is, no doubt, a very indirect way of
referring to the real things which we call men. Moreover, he treats all
conclusions in geometry and mechanics as hypothetical. [3] All this we
shall have to return to, in order to reconcile it with our doctrine;
which is apparently coincident with {105} Mill’s view in the place
first alluded to, that the subject in Judgment is always reality.
[1] _Logic_, Bk. I. ch. V. § 5. [2] _Ibid_., § 4.
[3] _Ibid_., Bk. II. ch. vi. §§ 3, 4.
But our point at present is only the duality ascribed to the Judgment
by saying that it essentially deals with _two_ things or groups of
things. Jevons even says [1] that every Judgment is a comparison of
two things--though these “things” are really, it would seem, groups
of things. [2] We thus have it impressed upon our minds that there
is one “thing” corresponding to the Subject-word (or clause) of the
Propositional sentence, and another “thing” corresponding to the
Predicate-word (or clause), and that these are somehow separate, like
two railway carriages, till we bring them together by the coupling-link
of the copula. This is a very inconvenient way of looking at the
matter. It is not true that all Judgment is comparison, in the proper
and usual sense of the word. It is not true that Judgment involves two
things; two or more things may be mentioned in a Judgment, but they
cannot correspond respectively to the Subject and Predicate. It is a
real Comparison if you say, “A.B. is taller than C.D.,” but C.D. is
here not a term in the Judgment. The one person, A.B., is qualified by
the ideal content “taller than C.D.,” and the idea of A.B. so qualified
is referred to, or discriminated within, perceptive reality. Comparison
is a rather complex process, and consists in a cross-reference by which
each of two objects is judged according to a standard furnished by the
other; but this complex process is not necessary to all Judgment, and
cannot be expressed with complete convenience in a single Judgment. And
in {106} any case the two objects that enter into the comparison do not
correspond to two essential parts of Judgment.
[1] _Elementary Lessons in Logic_, p. 61. [2] _Ibid_. p. 62.
It is far more simple and true to say that Judgment is always the
analysis _and_ synthesis of elements in some one thing or ideal
content. “Gold is yellow” has not within it, as Jevons says it has, [1]
any direct comparison of gold with other yellow substances. It simply
drags to light the property “yellow” as distinct within the complex of
attributes belonging to gold, while at the same time insisting that
this property--this meaning of an idea--belongs to, is of one piece
with, perceived reality in so far as gold is given in such reality.
The Judgment exhibits the content in its parts. It breaks it up, and
pronounces it to be all of one tissue, by one and the same indivisible
act. We should practically have a much fairer chance of seeing clearly
what Judgment is if we began by considering it as not two things or
two terms — but as one thing or one term drawn out into elements by
discriminating selection. Even if the paradox that every “Thing” is
a Judgment neglects some necessary distinctions, I am convinced that
we shall understand Judgment much more clearly if we do our best to
approach it from this point of view. Whenever we look or listen, and
_notice_ features and qualities in the perceptions that arrest the
eye and ear, we are rapidly and continuously judging. “The fire is
crackling,” “The daylight is waning,” “That bookshelf is not full,”
“The window-curtain is twisted.” In none of these cases is there
any separation other than an intellectual distinction between the
predicated content and the perceived reality. The Judgment is simply
a distinct {107} insistence on a quality within a certain focus of
reality as belonging to that reality. This is the fundamental nature of
Judgment.
[1] _Loc. cit_.
Therefore, to draw our conclusion as to the Unity of the Judgment, it
is not a transition from one mental state to another; the relation of
which it consists is not between ideas in it, but is the content of the
idea which forms it. Judgment is not primarily comparison between two
things; it is a thing or content displayed as possessing some definite
relation or quality within its identity. Every Judgment is the content
of one idea, but you may of course distinguish relations between ideal
elements within this idea. “Fire causes heat” is a single content or
idea, the nature of fire, expanded into one of its properties.
_Distinction between Subject and Predicate_
5. But then, if the whole Judgment is a single content, what is the
difference between Subject and Predicate, and is it necessary to
distinguish Subject from Predicate at all? If _some_ Judgments can be
made without explicit Subjects, cannot _all_ be made in that way?
This suggestion is very useful as carrying on the simplest type of
Judgment throughout the whole theory of Judgment. By a little torture
of expression any Judgment can be thrown into a form in which undefined
Reality is the general subject, and the whole mass of the Judgment
is the Predicate. “William Pitt was a great statesman” = “There was
a great statesman named William Pitt”; “The three angles of every
triangle are equal to two right angles” = “There are figures known as
triangles with their three angles equal to two right angles”; “All
citizens are members of a moral order” = “There is a moral order,
including the {108} relations of citizenship”; “All trespassers will
be prosecuted” = “Here are conditions which ensure the prosecution of
possible trespassers.” Or you might always put a subject, “Reality is
such that”--“Reality is characterised by.”
Thus we see that, as we have said before, in every Judgment the
ultimate subject is Reality, the world in contact with us as we have
already qualified it by previous Judgment. It is a less mistake to
reject the Subject and Predicate in the Judgment altogether, than to
think that they are separate things or ideas, and that in judging you
pass or change from one to the other. Always bear in mind that it is
possible to mass the whole Judgment as a single Predicate directly or
indirectly true of Reality.
Having said this much, to make the Unity of the Judgment unmistakable,
we may now safely distinguish between the Subject and Predicate
in the Judgment. And we shall find the safest clue to be that the
explicit Subject, when there is one, marks the place at which, or the
conditions under which, Reality accepts the Predicate. The natural
Subject is concrete, and the Predicate abstract; the Subject real, and
the Predicate ideal, but pronounced to be real. The reason of this is
that every Judgment is the connection of parts in a whole, and to be
a whole is the characteristic of reality. In other words, the natural
course of thought is to define further what is already in great part
defined, and our real world is that which we have so far defined. The
isolated judgments of the text-books make it very hard to grasp this,
because you seem to begin anywhere for no connected reason at all. But
if we reflect on actual thought, {109} we find that, as Mr. Stout very
cleverly says, we are always developing a “subject” which is in our
minds (in the ordinary sense of a “subject of conversation”), and this
subject is some region or province of the world of reality.
Now the explicit Subject in Judgment or the grammatical Subject in
Proposition does not always set out the full nature of this, but
merely some mark or point in it which we wish to insist upon. So
that we may find in Judgment almost anything serving as explicit
Subject. Thus, as Aristotle said quite plainly and sensibly, it is
natural to say “The horse is white,” but we _may_ have occasion to say
“This white is a horse”; it depends on the way in which the Subject
comes into our minds. [1] Usually the Subject will be what Dr. Venn
calls the heavier term, _i.e._ the term with more connotation. When
there is no difference of concreteness between parts and whole, the
Judgment becomes reversible as in the equation 7 + 5 = 12. There is no
distinction here between Subject and Predicate. The real underlying
unity or Subject is the numerical system.
[1] See Prof. Bain, p. 56, upon the Universe, and Universe of
Discourse, _i.e._ the general subject which you have in your
mind.
Therefore by recognising Subject and Predicate we represent the
organisation of knowledge, and the connection of inherence or
consequence within the content of our knowledge. If we do not
recognise this distinction we throw the whole of Judgment into an
undifferentiated mass of fact, running all assertion into the same
mould, “It is the case that,” etc. One difficulty still remains. If
the relation between Subject and Predicate is within an idea, and
not between ideas--that is, if the whole explicit content, Subject
and {110} Predicate together, can be regarded as predicated of
reality,--why is the act of predication expressed by a verb, _i.e._
a sign of activity within this content? Why is a verb often if not
always the form of predication which connotes Subject and Predicate?
Not because it is a time-word. On the contrary, we want to get rid
of the tense in Logic. The time of a Judgment ought to be determined
only by the special connection between Subject and Predicate, not by
tense, because tense is always subjective, merely relative to the time
of speaking, and is accidental to the content of Judgment. Action
seems nearer to what we want; the _verb_ expresses both action and
predicate. But the _idea_ of action again does not make a predication,
and the verb “is” does not _really indicate_ action. Perhaps it is the
demonstrative element in a finite verb that makes it the vehicle of
predication, _i.e._ in a finite verb you have a meaning referred by a
demonstrative element to something else. Originally the meaning was
always an action; “is” of course meant “breathes.” But now the verb has
lost vitality by wear and tear, and only refers something to something
else. The puzzle is that the Judgment is not referred to us who make
it, but is expressed as if it was accomplished by something outside us.
That puzzle points to the essential feature which we insisted on, viz.
its objectivity; in predication we refer what is mentally our act to a
subject that represents the real world, not to ourselves at all. When
I say “Gladstone comes to London this week,” the verb which expresses
Gladstone’s action also expresses that my real world in his person
accepts the qualification “coming to London this week.” Because of this
objectivity of thought, I attribute to {111} the real world and not to
myself the connection which is presented to my mind, and so it takes
its place as an act of the real world. But I might throw the whole
content into the Predicate by saying, “The ideal content ‘Gladstone
coming to London this week’ is a predication true of Reality.” Thus
though the distinction between Subject and Predicate best exhibits the
living structure of knowledge, we must beware of the notion that two
ideas or two things are needed for Judgment.
{112}
LECTURE VII THE CATEGORICAL AND HYPOTHETICAL CHARACTERS IN
JUDGMENT
_Some criticism on the ordinary scheme_ [1]
1. We will first consider why we want to examine the types of Judgment,
and then what arrangement of them best fulfils our want.
[1] Read Mill, ch. iv. (Bk. I.), on Propositions; Venn,
_Empirical Logic_, ch. ix., x. Cf. _Knowledge and Reality_ pp.
57-8; and Venn, p. 264. Ordinary statement, Jevons, p. 60, ff.;
cf. p. 163.
_Why we need an arrangement_
(_a_) If we attended purely to the propositions in common use, we
should get an unmanageable variety of forms, though the reality of
thought would be fairly represented. We cannot quite do this; we must
try to select the forms which for some reason are the most fundamental
and constant.
On the other hand, it is possible to think simply of what is convenient
in logical combination; and then for working with syllogistic Logic we
get the well-known scheme of four propositions, each with Subject and
Predicate; and for working with symbolic Logic we get the existential
scheme in which Subject and Predicate disappear, and “All S. are P.”
turns into “There exists no S. which is not P.”; or we get Jevons’
Equational Logic, in which “All A is B” stands as A = AB. Now every
Judgment has a great many aspects, {113} being really a very complex
systematic act of mind, and a logical method can be founded on any of
these aspects which is sufficiently constant to stand for the Judgment.
You can take “All men are mortal” to mean “There are no not-mortal
men,” or “Men = some mortals,” or two or three more meanings. The two
former are artificial or formal corollaries from the natural Judgment,
representing it for some purposes but omitting a great part of its
natural meaning. They tell you nothing about a relation of causality
between the content of man and the property mortal, and they destroy
all implication of existence in the Subject man.
What we want is neither to follow _mere_ everyday language, nor be
guided by mere convenience of logical combination. We want to look at
the Judgment on its merits with reference to its power of expressing
the principal kinds of our experience, which in fact are constructed in
the medium of Judgment. The great kingdoms of intellectual experience
are Perception, History, and Science, and of these three, Science,
including Philosophy, is the form towards which all knowledge presses
on, and its judgment must therefore be considered as the most complete
type.
_The common scheme_
(_b_) With this purpose in mind, let us look at the traditional scheme,
omitting the negative Judgments of which we have not yet spoken. We may
dismiss the Indefinite Judgment “Men are mortal” as imperfect by not
being “quantified,” and we have left, as Categorical Judgments, the
Particular Affirmative “Some men are mortal,” the Universal Affirmative
“All men are mortal,” and the Singular Affirmative “Socrates is
mortal.” The Singular Affirmative, however, is not treated of any
further under the old scheme, {114} because in it the Subject is taken
in its full extent, and therefore the Singular Affirmative Judgment is
ranked with the Universal Affirmative. So as Categorical Judgments we
have left the Particular Affirmative and the Universal Affirmative.
Outside the account of the Categorical Judgment we find the
Hypothetical and Disjunctive Judgments touched on as a sort of
Appendix, standing as “Conditional.” The historical reason of this
is, that they were not recognised by Aristotle, and have never been
incorporated in the diagram of judgments employed in traditional Logic.
Then on the ordinary scheme we have--
Categorical. Conditional.
Particular Universal Hypothetical Disjunctive
Judgments. Judgments, Judgments.
including
Singular
Judgments.
The defects of this scheme from our point of view are—
(i.) Our Impersonal and Demonstrative Judgments are omitted. They
_might_ be classed under the particular, which also has an undefined
element in the subject.
(ii.) The Singular Judgment (of which the chief instance is the
judgment with proper name) is rightly classed as Universal, but yet is
wrongly absorbed in the abstract universal, from which it ought to be
distinguished.
(iii.) In the treatment of the Universal Judgment there are two
defects—
(1) The Collective Judgment, resulting from enumeration, {115} direct
or indirect, is not distinguished from the Generic Judgment, resting
on a connection of content or presumption of causality. “All the [1]
papers have been looked over” should be distinguished from “All
triangles have their three angles equal to two right angles.”
[1] “The” as here used indeed practically = “these,” so
that, by our analysis, such a judgment has no claim to rank
as a universal judgment It is difficult to find a plainly
collective judgment which has not some affinity to judgment with
demonstrative pronoun or proper name. A judgment in which “All
M.P.’s” stands as subject, has affinity with the latter.
(2) The nature of the Universal Judgment is not examined with a view
to the distinction between Categorical and Hypothetical. The common
Logic does not go behind the grammatical form, which on this point is
not decisive.
(iv.) The Hypothetical Judgment [1] is said to consist of two
categorical propositions, or to be “_complex_” But of course it is a
simple judgment, _prima facie_ expressing a relation of reason and
consequent. Its parts are not Judgments, for they are not such as to
stand alone.
[1] Bain, p. 85; Jevons, p. 160.
(v.) The Disjunctive Judgment is often (_e.g._ by Mill and Bain) said
to be equivalent to two Hypothetical Judgments. The strange thing
is that both of these writers take the wrong two. [1] If we allow
conversion of a Hypothetical Judgment two are enough, but of course
they must be the two which cannot be got from each other by conversion,
viz. the two beginning, “If A is B ...” and “If A is not B ...”
respectively. If we do not admit conversion we must have all four.
Let the disjunction be, “This signal light is either red or green.”
In order to know this we must know not {116} only that, “If it is
red it is not green” (with its equivalent, “If it is green it is not
red”), but that, “If it is not red it is green” (with its equivalent,
“If it is not green it is red”). The former by itself leaves open the
possibility that it may be not red or green, but blue or yellow; the
latter by itself the possibility that when it is red it may also at
the same time be green. The former secures that the two terms exclude
each other; the latter, that, taken together, they exclude all other
predicates.
[1] Mill, ch. iv.; Bain, p. 86.
In any case, the disjunctive is more than any combination of
Hypotheticals, and really tends to be Categorical, and ought not to be
claimed as Conditional.
_Which are Categorical?_
2. We will now look at these Judgments in order, consider their real
meaning, and also ascertain the limits of the Categorical Judgment,
viz. that which affirms the existence of its Subject, or in other
words, asserts a fact.
_The Particular Judgment_
(i) The Particular Judgment of common Logic, “Some S. is P.,” has
different meanings according as it is understood naturally, or tied
down to be a result of enumeration.
In any case it is an imperfect, unscientific Judgment, in which the
mind cannot rest, because it has an undefined limitation imposed upon
the Subject.
_Its natural meaning_
(_a_) For the natural meaning, take the example, “Some engines can
drag a train at a mile a minute for a long distance.” [1] This does
not _mean_ a certain number of engines, though of course they _are_ a
certain number. It {117} means certain engines of a particular make,
not specified in the Judgment. The Judgment is Categorical, because
the undefined reservation implies a reference to something unanalysed,
but merely touched or presented in experience. If it was a mere idea
it would have to be clear; and if the full description or definition
were inserted, the Judgment would cease to affirm the existence of
the engines in question. _And the Judgment itself challenges this
completion._
[1] To be accurate, the Judgment would demand the insertion of
precise details about train, distance, and other matters. But
this illustrates the point of the text, because the assignment
of such details would naturally extend to the Subject, and then
the “Some” would be displaced.
_A narrower meaning_
(_b_) A more artificial meaning is to take the Judgment as not formed
by imperfect description, but by imperfect enumeration (understanding
it almost wholly in denotation). “Some Conservatives are in favour
of women’s suffrage.” This means or may mean that we have counted a
certain number, large or small, who are so, and we may or may not know
about the others. _Thus understood, the Judgment challenges complete
enumeration_; it contains of course the elements of a fraction--half,
most, nine-tenths of, and so on.
This again is Categorical; not merely because it implies counting, but
because it implies counting units separately given to experience.
The Particular Judgment does not include our Impersonal and
Demonstrative Judgments; they are not classed in the common text-books.
But as referring to perception they too are categorical and assert
facts, whether they have ideas to help out the perceptive reference or
not. And there is no reason against including them under the Particular
Judgment. The assertion, “This engine can drag a train a mile a
minute,” is much the same kind of Judgment as, “Some engines can, etc.”
Either of these would be false {118} if no such engines existed. _These
Judgments are of the essence of perception_. They have the connection
of content and the undefined complex of presentation struggling
together in them. They assert fact.
_Singular Judgment_
(2) The Singular Judgment of the common Logic is pretty much our
Judgment with a proper name, which I call Individual, and which, as we
saw, is in part rightly called universal--because the Subject extends
beyond perception, and the Predicate follows the Subject. But it is
a concrete or individual Universal, not an abstract Universal, and
therefore asserts the existence of its Subject. The reason why it is
taken to assert the reality of its Subject must be, I suppose, that
it _can_ assert this, its Subject being a name for an existence that
has limited reality within the temporal series, and _cannot_ assert
anything else, not having any general fixed content or connotation
which could imply a _general_ connection of Subject and Predicate. The
general connection of content which is so fatal to the asserting of
fact does not exist in this case. We see this in Mill’s instance. “The
summit of Chimborazo is white,” When the Subject is a unique name with
precise connotation, “The centre of gravity of the material universe
is variable,” then we are passing into the abstract Universal, and I
think we may take such a Judgment perhaps as one of the best examples
of a conjunction of categorical and hypothetical meaning, _i.e._ of
a connection of content ascribed to a Subject affirmed to exist. But
usually one meaning or the other is uppermost.
These Judgments, called Singular or Individual, correspond to the
region of history or narrative. The realities {119} with which they
deal have their definite position in a single system of time and space,
and this is often made emphatic by the use of tenses. But these change
with the date relative to the speaker, so that a Judgment with real
tense must once have been false, or must become false by lapse of
time. Thus the Judgment of fact may be not absolutely true. Nothing is
genuinely true which a change of date can make false. The permanently
true time-relations between Subject and Predicate are determined by
their content, and the copula is not a tense, but a mere sign of
affirmation. The Singular as Categorical is sharply distinguished from
the Abstract Universal, with which common Logic classes it.
_Universal Judgment_
(3) Down to this point the judgment states a _fact_. When we come to
the ordinary universal affirmative, we see at once that it may express
very different meanings. In its natural meaning it strongly _implies_
that its Subject has a particular existence within the series of time
and space, but hardly asserts it.
_Import of Propositions_
Mill, for example, says “the objects are no longer individually
designated, they are pointed out only by their attributes;” “most of
them not known individually at all.” That means that the explicit
Subject is not made of individuals. The natural meaning is disputed; I
incline to think with Venn, that the Subject is naturally taken _more_
in Denotation (not solely, which is unmeaning), and the Predicate
_more_ in connotation. But clearly in literal form the Subject is
simply a significant idea, and its existence in things or events is
not affirmed though it may be strongly implied. Hamilton [1] {120}
says quite calmly--“‘Rainy weather is wet weather’ is a Categorical
Proposition; ‘If it rains it will be wet’ is Hypothetical.” Between
the two I can see no distinction of meaning at all. [2] If indeed we
take the Universal Affirmative in the pure sense of aggregate formed
by enumeration, and therefore finite, it _may_ be said that we assert
the existence of the individuals composing it; but this is a very
unreal view of the meaning of the Judgment (though suggested by its
customary form), and even then it would be hard to prove that we
continue to think of the Subject as individuals. This reference to
a finite aggregate makes the _Collective Judgment_ or _Judgment of
Allness_. It cannot really exist in the case of a class like man, of
unknown extension, and is confined, at its widest, to such cases as
“All present Members of Parliament have to take a line on the Irish
question.” This _might_ be Categorical, but need not be so.
[1] _Lectures_, vol, iii. p. 327.
[2] Contrast Jevons, _Elementary Logic_, p. 163.
Otherwise, the Universal Affirmative of common Logic is literally
Hypothetical, though in some cases it may strongly imply the assertion
of reality. Dr. Venn has discussed this question. [1] He says the
implication of existence is much stronger with a single-word Subject
than with a many-worded Subject; _i.e._ perhaps with a natural than
with an artificial conception. But in any case, the expressed bond with
perception is lost, and in pure form the Subject is a mere abstract
idea, so that the relations of content entirely predominate over the
implication of existence.
[1] _Empirical Logic_, pp. 258-9.
Thus the Universal Affirmative in its full meaning fairly {121}
represents the sciences of classification, combining a subordinate
meaning of Allness or numerical totality with a primary meaning of
connotation of attributes or presumed causality. When we say “All the
Buttercup family have an inferior corolla,” of course we mean that
there is a reason for this. Often we omit the term all, as in “Heat
is a mode of motion.” In doing this we wipe out the last trace of a
reference to individual objects, and we pass to the pure hypothetical
form which absolutely neglects the existence of objects.
_“Hypothetical” Judgment_
(4) The simplest type of this Judgment is, if A is B it is C. This
Judgment corresponds to abstract science, but it is only making
explicit what was implied in the Universal Affirmative. That
expressed a presumption of causality, this expresses a clear Reason
and Consequent or scientific necessity. The point of this form is
(i.) that it drops all reference to individual objects, (ii.) that
it challenges you to explain how the Subject-content is tied to the
Predicate-content. “Water boils at 212°,” is a statement we should
generally pass in so-called Categorical form, because it does not
challenge any great accuracy of connection. But “If water boils, it
is at a temperature of 212°,” puts us upon asking, “Is the condition
adequate?” and we see at once that we must at least say, “If water
boils _under pressure of one atmosphere_, it is at a temperature of
212°,” or else the judgment is untrue. Of course we may apply the form
rightly or wrongly, as you may fill up your census paper rightly or
wrongly. We can only say that it calls upon you to put in an adequate
condition. Therefore I rather object to the form “If A is, B is,”
because it adds very little to the so-called Categorical shape.
{122} We have now to ask how the Hypothetical Judgment connects its
content with reality, _i.e._ how it is a Judgment at all? And the same
explanation must apply to so-called Categorical Judgments, which can be
thrown into this form without change of meaning.
The point from which the explanation starts is taking hypothesis as
supposition. This is much more true, I think, than connecting it with
_doubt_. In Dr. Venn’s _Empirical Logic_ the connection of Hypothetical
Judgment and doubt to my mind disfigures the whole treatment of the
Scientific Judgment. Supposition is distinct from affirmation--that
is true--but just because it is distinct from affirmation, it cannot
indicate doubt. It probably arose out of doubt, but as a method of
science it does not imply doubt, but only the accurate limitation of
attention. What doubt is there when we judge “If equals be added to
equals, the wholes are equal”? We are attending to one particular
thread of the nexus.
Hypothetical Judgment, then, is Judgment that starts from a
supposition. Every supposition is made upon a certain basis of
Reality. Take as an extreme case, “If you ask permission of A.B., he
will refuse it.” This is a supposition and its result, on the basis
of the known character of A.B. And the full judgment is “A.B. is of
such a character, that, supposing you ask him for permission, etc.”
The Hypothetical Judgment may be true, as an assertion about A.B.’s
character, though you may never ask.
Here, then, is the clue to the analysis of _all Abstract Judgments_,
Like Perceptive Judgment, they affirm something of Reality, but they
do this indirectly and not directly. {123} Underlying them there is
the implied Categorical Judgment, “Reality has a character, such
that, supposing so and so, the consequence will be so and so.” And
if this implied assertion is true, then the Hypothetical Judgment is
true, although its terms may be not only unreal, but impossible. “If
a microscopic object-lens with a focal length of 1/100 in. were used,
its magnifying power with an A eye-piece would be so many diameters.”
This is a mere matter of calculation, and is unquestionably true,
depending upon the effects of refraction upon the optical image. But I
do not suppose that such an object-lens could be made, or used. Does
such a Judgment, although true, express a _fact_? No, I should say not,
although common usage varies. I remember a _Pall Mall_ leading article
which said, “It is an absolute fact, that, if Mr. Gladstone had not
done something--the Government would have committed--some iniquity
or other.” Is this what we call a fact? We observe that the content
actually mentioned was never real at all. The implied connection
with reality is “There existed in reality a condition of things
(unspecified) in which _if_ Mr. Gladstone, etc., etc.” Are mathematical
truths facts, and in what sense? Abstract truth need not, and perhaps
cannot express fact, but implies fact indirectly.
_Disjunctive Judgment_
(5) The Disjunctive Judgment “A is either B or C,” is again not
a judgment of doubt but a mode of Knowledge, It may be taken as
numerical; then it gives rise to the statement of Chances. But in its
perfect form it is appropriate to the exposition of a content as a
system, and it may be taken as returning to the Categorical Judgment,
and combining it with the Hypothetical, because its {124} content is
naturally taken as an individual, being necessarily concrete.
The peculiar point of the Disjunctive is that it makes negation
positively significant.
“This signal light shows either red or green.” Here we have the
categorical element, “This signal light shows some colour,” and on the
top of this the two Hypothetical Judgments, “If it shows red it does
not show green,” “If it does not show red it does show green.” You
cannot make it up out of the two Hypothetical Judgments alone; they do
not give you the assertion that “it shows some colour.” [1]
[1] The example in the text, chosen for its simplicity, may
be objected to as involving perceptive concreteness by the
pronoun “this.” You can have a disjunction, it may be said,
dealing with “the triangle” as such; and why should this be
more “Categorical” than the assertion that the triangle has
its angles = three right angles? Still, it might be replied,
the development of a single nature into a number of precise
and necessary alternatives, always gives it an implication of
self-completeness.
Does this state a fact? I think it implies a fact much more distinctly
than the hypothetical does, but of course it is a question whether an
alternative can be called a fact. It seems a precise expression of
some kinds of reality, but it is not a solid single momentary fact.
It is very appropriate to the objects of philosophy as the higher
concrete science, which are conceived as systems of facts bearing
definite relations to each other; _e.g._ “Society is a structure of
individual characters, having positions which are not interchangeable.”
Taken all as a mass, they are conjunctively connected, but taken in
distinguishable relations they are disjunctively related. A human
being as such has some position and no other, and this is ultimately
determined by {125} the nature of the social whole to which he
belongs. He is if this, nothing else, and if nothing else, then this.
A more artificial example, which illustrates the degree in which
actual abstract knowledge and purpose can be embodied by man in
machinery, is the interlocking system of points and signals at a great
railway station. I suppose that the essence of such a system lies in
arrangements for necessarily closing every track to all but one at a
time of any tracks which cross it or converge into it. The track X
receives trains from A, B, C, D; if the entrance for those from A is
open, B, C, and D are _ipso facto_ closed; if A, B, and C are closed,
D is open, and so on. This is a disjunction consciously and purposely
incorporated in material fact, and differs from a Disjunctive Judgment
only in so far as existence necessarily differs from discursive thought.
The disjunction seems to complete the system of judgments, including
all the others in itself, and it is wrong in principle to distinguish,
_e.g._ between a hypothetical and categorical disjunction, or to
consider how a disjunction can be denied. For disjunction in itself
implies a kind of individuality which is beyond mere fact and mere
abstract truth, though allied to both; and all intelligible negation
is under, not of, a disjunction. Negation of a disjunction would
mean throwing aside the whole of some definite group of thoughts as
fallacious, and going back to begin again with a judgment of the
simplest kind. It amounts to saying, “None of your distinctions touch
the point; you must begin afresh.”
{126}
LECTURE VIII NEGATION, AND OPPOSITION OF JUDGMENTS
_Distinction between Contrary and Contradictory opposition_ [1]
1. The only important point in the traditional diagram of opposition
of Judgments is the distinction between contrary and contradictory
opposition, the opposition, that is, between A and E, and the
opposition between A and O, or E and I.
[1] Read Bain, pp. 55-6, on “Negative Names and the Universe
of the Proposition,” also on “Negative Propositions,” p. 83
ff.; Venn, _Empirical Logic_, pp. 214--217; Jevons, _Elementary
Logic_, ix., on “Opposition of Propositions”; Mill, ch. iv. § 2.
In _Contrary_ Opposition the one Judgment not only denies the other,
but goes on to deny or assert something more besides. The mere
grammatical shape “No man is mortal” conceals this, but we easily see
that it says more than is necessary to deny the other, “All men are
mortal.”
In _Contradictory_ Opposition, the one Judgment does absolutely nothing
more than is involved in destroying the other.
The _Contrary_ Negation has the advantage in positive, or at least in
definite import.
The _Contradictory_ or pure Negation has the advantage in the
exhaustive disjunction which it involves.
This is plain if we reflect that Contrary Negation only {127} rests on
the Law of Contradiction, “X is not both A and not A.”
_Ordinary Diagram of Opposition of Judgments_.
[The diagram has diagonal lines, not represented here, from corner A to
corner O, and from corner E to corner I, each labelled “Contradictory
Opposition”. Tr.]
A E
Contrary Opposition.
Sub-contrary Opposition.
I O
A = Universal Affirmative. All men are mortal.
E = Universal Negative. No men are mortal.
I = Particular Affirmative. Some men are mortal.
O = Particular Negative. Some men are not mortal.
Sub-contrary Opposition has no real meaning; the judgments so opposed
are compatible.
It is not _true_ both that “All M.P.’s are wise,” _and_ that “No
M.P.’s are wise,” but both may be false; while Contradictory Negation
implies the Law of Excluded Third or excluded Middle, “X is either
A or not A,” the principle of disjunction, or rather, the simplest
case of it. It is not {128} _false_ both that “All M.P.’s are wise”
and that “Some M.P.’s are not wise.” The point is, then, on the one
hand, that in Contradiction you can go from falsehood to truth, [1]
while in Contrariety you can only go from truth to falsehood; but also
that in Contradiction the Affirmative and Negative are not at all on
a level in meaning, while in Contrariety they are much more nearly
so. Then if we leave out the relations of mere plurality, of All and
Some, which enable you to get contrary negation in pure negative form
in the common Logic, we may say generally that in contrary negation
something is asserted, and in contradictory negation taken quite
literally nothing is asserted, but we have a “bare denial,” a predicate
is merely removed. In actual thought this cannot be quite realised,
because a bare denial is really meaningless, and we always have in our
mind some subject or universe of discourse within which the denial is
construed definitely. But this definite construing is not justified by
the bare form of contradiction, which consists simply in destroying a
predication and not replacing it by another. In as far as you replace
it by another, defined or undefined, you are going forward towards
contrary negation.
[1] _I.e._ Contradictory alternatives are exhaustive.
_Contrary Negation_
2. Thus, Contrary Negation in its essence is affirmation with a
negative intention, and we may take as a type of it in this wider
sense the affirmation of a positive character with the intention of
denying another positive character. _E.g._ when you deny “This is a
right-angled triangle” by asserting “This is an equilateral triangle,”
you have typical contrary negation. It is not really safe to speak of
contraries except with reference to _judgments_, intended to deny each
{129} other; but it is common to speak of species of the same genus as
contraries or opposites, because the same thing cannot be both. [1]
[1] Bain, p. 55 ff.
We must therefore distinguish _contrary_ from _different_. Of course
the same thing or content has many different qualities, and even
combines qualities that we are apt to call contrary or opposite. But
as Plato was fond of pointing out, a thing cannot have different or
opposing qualities in the same relation, that is to say, belonging to
the same subject under the same condition. The same thing may be blue
in one part of it and green in another, and the same part of it may be
blue by daylight and green by candlelight. But the same surface cannot
be blue and green at once by the same light to the same eye looking in
the same direction. _Different_ qualities become _contrary_ when they
claim to stand in the same relation to the same subject. Right-angled
triangles and equilateral triangles do not deny each other if we leave
them in peace side by side. They are then merely different species of
the same genus, or different combinations of the same angular space.
But if you say, “This triangle is right-angled,” and I say “It is
equilateral,” then they deny each other, and become true contraries.
Then the _meaning_ of denial is always of the nature of _contrary_
denial. As we always speak and think within a general subject or
universe of discourse, it follows that every denial substitutes some
affirmation for the judgment which it denies. The only judgments in
which this is not the case are those called by an unmeaning tradition
Infinite Judgments, _i.e._ judgments in which the negative predicate
{130} includes every determination which has applicability to the
Subject. This is because the attribute denied has no applicability
to the Subject, and therefore all that has applicability is
undiscriminatingly affirmed, in other words, the judgment has no
meaning. “Virtue is not-square.” This suggests no definite positive
quality applicable to virtue, and therefore is idle. You may safely
analyse a significant negative judgment, “A is not B” as = “A is not B
but C,” or as = “A is X, which excludes B.” For X may be undetermined,
“a colour not red.” But then if the meaning is always affirmative or
positive, why do we ever use the negative form?
_Why use Negation?_
3. In the first place, we use it because it indicates exclusion,
and without it we cannot distinguish between mere differents on the
one hand and contraries on the other. If you ask me, “Are you going
to Victoria, London Chatham and Dover station?” and I answer, “I am
going to Victoria, London Brighton and South Coast,” that will not be
satisfactory to you, unless you happen to know beforehand that these
stations are so arranged that if you are at one you are not at the
other. They might be a single station used by different companies, and
called indifferently by the name of either. To make it clear that the
suggestion and the answer are incompatible, I must say, “I am _not_
going to Victoria, London Chatham and Dover,” and I may add or not add,
“I _am_ going to Victoria, London Brighton and South Coast.” That tells
you that the one predicate excludes the other, and that is the first
reason why we use the generalised form of exclusion, _i.e._ negation.
But in the second place, it can give us more, and something absolutely
necessary to our knowledge, and that is not {131} merely exclusion, but
exhaustion. In literal form negation is absolutely exhaustive, that is
to say, contradictory. The Judgment “A is not B” forms an exhaustive
alternative to the Judgment “A is B,” so that no third case beyond
these two is possible, and therefore you can argue from the falsehood
of either to the truth of the other. Now this form is potentially of
immense value for knowledge, and all disjunction consists in applying
it; but as it stands in the abstract it is worthless, because it is
an empty form. “A is red or not-red.” If either of these is false the
other is true. But what do you gain by this? You are not entitled to
put any positive meaning upon not-red; if you do so you slide into mere
contrary negation, and the inference from falsehood becomes a fallacy.
Make an argument, “The soul is red or not-red.” “It is not-red ∴ it is
some other colour than red.” The argument is futile. We have construed
“not-red” as a positive contrary, and that being so, the disjunction is
no longer exhaustive. We had no right to say that the soul is either
red or some other colour; the law of Excluded Middle does not warrant
that.
I pause to say that the proof of the exhaustiveness of negation, _i.e._
that two negatives make an affirmative--that if A is not not-B, it
follows that A is B--is a disputed problem, the problem known as double
negation. How do you know that what is not not-red must be red? I take
the law of Excluded Middle simply as a definition of the bare form
of denial, or the distinction between this and not-this; “not-this”
being the bare abstraction of the other than this. Others say that
every negation presupposes an affirmation; so “A is not-B” presupposes
the affirmation “A is B,” and {132} if you knock down the negative,
the original affirmative is left standing. Sigwart and B. Erdmann say
this. I think it monstrous. I do not believe that you must find an
affirmative standing before you can deny.
_Stage of Significant Negation. Combination of Contrary and
Contradictory_
4. Well, then, the point we have reached is this. What we mean in
denial is always the contrary, something positive. What we say
in denial--in other words, the literal form which we use--always
approaches the contradictory, _i.e._ is pure exclusion. The Contrary
of the diagram denies more than it need, but still its form is that
of exclusion. Now we have seen that in denial, as used in common
speech, we get the benefit of _both affirmation and exclusion_, but in
accurate thought we want to do much more than this; we want to get the
whole benefit of the negative form--that is, to get a positive meaning
together with not only exclusion, but exhaustion.
I will put the three cases in one example, beginning with mere
affirmations of different facts.
_Different Affirmations_
(1) “He goes by this train to-day.” “He goes by that train to-morrow.”
This conjunction, as simply stated, gives no inference from the truth
or falsehood of either statement to the truth or falsehood of the other.
_Contrary Opposition, exclusive_
(2) “He goes by this train,” and “He goes by that train,” with a
meaning equivalent to “No, he goes by that.” If it is true that in
the sense suggested by the context he goes by this train, then it is
not true that he goes by the other, and if it is true, in the sense
explained, that he goes by the other, then he does not go by this. Each
excludes the other, but both may be excluded by a third alternative.
If it is _not_ true that he goes by this {133} train--nothing follows.
There may be any number of trains he might go by, or he might give up
going; _i.e._ your Universe of discourse, your implicit meaning is
not expressly limited. If it is _not_ true to say, “No, he goes by
that”--taking the whole meaning together, and not separating its parts,
for this combination is essential to the “contrary”--nothing follows as
to the truth of the other statement. He may not be going at all, or may
be going by some third train, or by road.
_Combined Contrary and Contradictory Negation_
But if you limit your Universe, or general subject, then you can
combine the value of contrary and contradictory negation. Then you say,
(3) “He goes either by this train or by that.” Then you can infer not
only from “He goes by this train,” that “He does not go by that,” but
from “He does not go by this train” to “He does go by that.”
The alternative between “A is B” and “A is not-B” remains exhaustive,
but not-B has been given a positive value, _because we have limited
the possibilities by definite knowledge_. The processes of accurate
thinking and observation aim almost entirely at giving a positive value
C to not-B, and a positive value B to not-C, under a disjunction,
because it is then that you define exactly where and within what
conditions C which is not B passes into B which is not C. Take the
disjunction, “Sound is either musical or noise.” If the successive
vibrations are of a uniform period it is musical sound; if they are of
irregular periods it is noise. This is a disjunction which assumes the
form,
A is either B or C. That is to say, If it is B it is not C. If it is
not B it is C.
{134} Therefore I think that all “determination is negation”--of
course, however, not bare negation, but significant negation; the
essence of it consists in correcting and confirming our judgment of
the nature of a positive phenomenon by showing that _just when_ its
condition ceases, _just then_ something else begins, and when you have
exhausted the whole operation of the system of conditions in question,
so that from any one phase of their effects you can read off what _it_
is not but the _others_ are, then you have almost all the knowledge
we can get. The “_Just-not_” is the important point, and this is only
given by a positive negation within a definite system. You want to
explain or define the case in which A becomes B. You want observation
of not-B; but almost the whole world is formally or barely not-B, so
that you are lost in chaos. What you must do is to find the point
within A, where A1 which is B passes into A2 which is C, and that will
give you the _just-not-B_ which is the valuable negative instance.
_Negative judgment expressing fact_
5. You will find it said that a Negative Judgment cannot express fact;
_e.g._ that a Judgment of Perception cannot be negative. This is worth
reflecting upon; I hope that what has been said makes clear how far it
is true. The bare form of Negation is not adequate to fact; it contains
mere emptiness or ignorance; we nowhere in our perception come upon a
mere “not-something.” No doubt negation is in this way more subjective
than affirmation. But then as it fills up in meaning, the denial
becomes more and more on a level with the affirmation, till at last
in systematic knowledge both become double-edged--every affirmative
denies, and every negative affirms. When a man who is both a {135}
musician and a physicist says, “this compound tone A is a discord Y,”
he knows exactly how much of a discord, what ratio of vibration makes
it so much of a discord, how much it would have to change to become a
concord (X which is not Y), and what change in the vibration ratio from
a1 to a2 would be needed to make it a concord. To such knowledge as
this, the accurate negation is just as expressive as the affirmation,
and it does not matter whether he says “A is Y,” or “A is by so much
not X.” It becomes, as Venn says, all but impossible to distinguish the
affirmation from the negation. No doubt affirmative terms come in at
this stage, though the meaning is negative. Observe in this connection
how we sometimes use the nearest word we can think of, knowing that the
negative gives the positive indirectly--“He was, I won’t say insolent,”
meaning _just not_ or “_all but_” insolent; or again, “That was not
right,” rather than saying bluntly “wrong.”
_Operation of the denied idea_
6. Every significant negation “A is not B” can be analysed as “A is X
which excludes B.” Of course X may not be a distinct C; _e.g._ we may
be able to see that A is not red, but we may not be able to make out
for certain what colour it is; then the colour X is “an unknown colour
which excludes red.”
How does the rejected idea operate in Judgment? I suppose it operates
by suggesting a Judgment which as you make it destroys some of its
own characteristics. It is really an expression of the confirmatory
negative instance or “just-not.” _Just_ when two parallel straight
lines swing so that they can meet, _just_ then the two interior angles
begin to be less than two right angles, which tells us that the {136}
straight lines are ceasing to be parallel. Just in as much as two
straight lines begin to enclose a space we become aware that one or
other of them is not straight, so that A in turning from Y to X turns
_pari passu_ from A1 to A2, and we are therefore justified in saying
that A, when it is Y, cannot be X.
This lecture may pave the way for Induction, by giving some idea of the
importance of the negative instance which Bacon preached so assiduously.
In a real system of science the conceptions are negative towards each
other merely as defining each other. One of them is not in itself
more negative than another. Such a conception, _e.g._, is that of a
triangle compared with two parallel straight lines which are cut by
a third line. If the parallels are swung so as to meet, they become
a triangle which gains in its third angle what the parallels lose on
the two interior angles, and the total of two right angles remains
the same. Thus in saying that parallels cut by a third straight line
cannot form a triangle, and that the three angles of a triangle are
equal to two right angles, we are expressing the frontier which is at
once the demarcation between two sets of geometrical relations, and the
positive grasp or connection of the one with the other. The negation is
no bar to a positive continuity in the organism of the science, but is
essential to defining its nature and constituent elements. This is the
bearing of significant negation when fully developed.
{137}
LECTURE IX INFERENCE AND THE SYLLOGISTIC FORMS
_Inference in general_ [1]
1. The Problem of Inference is something of a paradox. Inference
consists in asserting as fact or truth, on the ground of certain given
facts or truths, something which is not included in those data. We
have not got inference unless the conclusion, (i.) is necessary from
the premisses, and (ii.) goes beyond the premisses. To put the paradox
quite roughly--we have not got inference unless the conclusion is (i.)
in the premisses, and (ii.) outside the premisses. This is the problem
which exercises Mill so much in the chapter, “Function and Value of the
Syllogism.” We should notice especially his § 7, “the universal type
of the reasoning process.” The point of it is to make the justice of
inference depend upon relations of content, which are judged of by what
he calls induction. That is quite right, but the question still returns
upon us, “What kind of relations of content must we have, in order to
realise the paradox of Inference?” This the “type of inference” rather
shirks. See Mill’s remarks when he is brought face to face with {138}
Induction, Bk. III. ch. f. § 2. An Inference, as he there recognises,
either does not hold at all, or it holds “in all cases of a certain
description,” _i.e._, it depends on universals.
[1] Read for Lectures IX. and X., Mill, Bk. II ch. i., ii.,
iii.; Bk. III. ch. i. and ii. at least; Venn, ch. xiv., xv.;
Jevons, _Lessons_ xv. and xxiv.; De Morgan’s _Budget of
Paradoxes_.
I ought to warn you at once that though we may have novelty in the
conclusion of Inference (as in multiplication of large numbers),
the necessity is more essential than the novelty. In fact, much of
Inference consists in demonstrating the _connection_ of matters that
as _facts_ are pretty familiar. Of course, however, they are always
modified in the process, and in that sense there is always novelty. You
obtain the most vital idea of Inference by starting from the conclusion
as a suggestion, or even as an observation, and asking yourself how it
is proved, or explained, and treating the whole process as a single
mediate judgment, _i.e._ a reasoned affirmation. Take the observation,
“The tide at new and full moon is exceptionally high.” In scientific
inference this is filled out by a middle term. We may profitably think
of the “middle term,” as the copula or grip which holds the conclusion
together, made explicit and definitely stated. Thus the judgment pulls
out like a telescope, exhibiting fresh parts within it, as it passes
into inference. “The tide at new and full moon, _being at these times
the lunar tide plus the solar tide_, is exceptionally high.” This is
the sort of inference which is really commonest in science. Such an
inference would no doubt give us the conclusion if we did not know it
by observation, but it happens in many cases that we do know it by
observation, and what the inference gives us is the connection, which
of course may enable us to correct the observation.
{139} _Conditions of the possibility of Inference_
2. In the strictest formal sense there can be no inference from
particulars to particulars. When there seems to be such inference, it
is merely that the ground of inference is not mentioned, sometimes
because it is obvious, sometimes because it is not clearly specified
in the mind. Suppose we say, “Morley and Harcourt will go for
Disestablishment, and I think, therefore, that Gladstone will.” I do
not _express_ any connecting link, merely because every one sees at
once that I am inferring from the intentions of some Liberal leaders to
those of another. If the terms are really particulars, “X is A, Y is B,
Z is C,” one is helpless; they do not point to anything further at all;
there is no bridge from one to the other.
Inference cannot possibly take place except through the medium of an
identity or universal which acts as a bridge from one case or relation
to another. If each particular was shut up within itself as in the
letters taken as an instance just now, you could never get from one
which is given to another which is not given, or to a connection not
given between two which are given.
Take the simplest conceivable case, which hardly amounts to Inference,
that of producing a given straight line. How is it that this is
possible? Because the direction of the straight line is universal and
self-identical as against possible directions in space, and it acts as
a rule which carries you beyond the given portion of it. This might
fairly be called an “immediate inference.” So I presume that any curve
can be constructed out of a sufficient portion of the curve, although,
except with a circle, this is more than repeating the same line over
again. The content has a nature which {140} is capable of prescribing
its own continuation. A curve is not a direction; a truth which is a
puzzle to the non-mathematician--it is a law of continuous change of
direction.
_System the ultimate condition of Inference_
3. _Ultimately_ the condition of inference is always a system. And
it will help us in getting a vital notion of inference if we think,
to begin with, of the interdependence of relations in space--in
geometrical figures, or, to take a commonplace example, in the
adjustment of a Chinese puzzle or a dissected map. Or any of the
propositions about the properties of triangles are a good example.
How can one property or attribute determine another, so that you can
say, “Given this, there must be that”? This can only be answered by
pointing to the nature of a whole with parts, or a system, which just
means this, a group of relations or properties or things so held
together by a common nature that you can judge from some of them what
the others must be. Not all systems admit of precise calculation and
demonstration, but wherever there is inference at all there is at
least an identity of content which may be more or less developed into
a precise relation between parts. For example, we cannot construct
geometrically the life and character of an individual man; we can argue
from his character to some extent, but the connection of facts in his
personal identity is all that we can infer for certain; and even this
involves a certain context of facts, as in circumstantial evidence.
Yet this simplest linking together of occurrences by personal identity
is enough to give very startling inferences. Thackeray’s story of the
priest is a good instance of inference from mere identity. “An old
abbé, talking among a party of intimate friends, happened {141} to say,
‘A priest has strange experiences; why, ladies, my first penitent was
a murderer.’ Upon this, the principal nobleman of the neighbourhood
enters the room. ‘Ah, Abbé, here you are; do you know, ladies, I was
the Abbé’s first penitent, and I promise you my confession astonished
him!’” Here the inference depends solely on individual identity, which
is, as we saw, a kind of universal.
But in this case was there really an inference? Does not the conclusion
fall inside the premisses? It must in one sense fall inside the
premisses, or it is not true. But it does not fall inside them until we
have brought them into contact by their point of identity and melted
them down into the same judgment. I admit that these inferences from
individual identity, assuming the terms not to be ambiguous, are only
just within the line of rational inference, but, as we see in this
case, they bring together the parts of a very extended universal. What
_is_ the lower limit of inference?
_Immediate Inference_
4. In the doctrine of _immediate Inference_ common Logic treats of
Conversion and the Opposition of judgments.
Is a mere transposition of Subject and Predicate, where the truth
of the new judgment follows from that of the old, an inference? It
is a matter of degree. [1] Does it give anything new? “The Queen
is a woman.” “A woman is the Queen.” If we make a real difference
between the implications of a Subject and a Predicate, we seem to get
something new; but it is a point of little interest. {142} Comparison
or Recognition are more like immediate inferences. Comparison means
that we do not let ourselves perceive freely, but take a particular
content as the means of apperception of another content, _i.e._ as
the medium through which we look at it. I do not merely look at the
second, but I look at it with the first in my mind. And so far I may
be said to infer, without the form of proof, from data of perception
to a relation between them. “You are taller than me,” is a result
obtained by considering your height from the point of view of mine, or
_vice versâ_. Recognition is somewhat similar. It is more than a mere
perception, because it implies reproduction of elements not given,
and an identification with them. I recognise this man _as_ so-and-so,
_i.e._ I see he is identical with the person who did so-and-so. It is
a judgment, but it goes beyond the primary judgment, “He is such and
such,” and is really inferred from it. It is a matter of degree. Almost
every Judgment can be broken up into elements, and recognition fades
gradually into cognition--we “recognise” an example of a law, a right,
a duty, an authority; not that we knew _it_, the special case, before,
but that in analysing it we find a principle which commands our assent,
and with which we identify the particular instance before us.
[1] The collective or general judgment, as commonly explained,
cannot be converted “simply,” because the predicate is “wider”
than the subject, and the same rule is accepted for the relation
of consequent to antecedent. The aim of science, it might almost
be said, is to get beyond the kind of judgment to which this
rule applies.
_Number of Instances_
5. The difference between guess-work and demonstration rests on the
difference between a detached quality or relation striking enough to
suggest something to us, and a system thoroughly known in its parts as
depending on one another. This is so even in recognising an individual
person; it is necessary to know that the quality by which you recognise
him is one that no one else possesses, or else {143} it is guess-work.
Still more is this the case in attempting a scientific connection.
All scientific connection is really by system as between the parts
of the content. A quality is often forced on our attention by being
repeated a great many times in some particular kind of occurrence, but
as long as we do not know its _causal_ connection with the properties
and relations involved in the occurrence it is only guess-work to
treat them as essentially connected. This is a matter very easy to
confuse, and very important. It is easy to confuse, because a number
of instances does help us really in inference, as it always insensibly
gives us an immense command of content; that is to say, without knowing
it we correct and enlarge our idea of the probable connection a little
with every instance. So the connection between the properties that
strike us becomes much larger and also more correct than it is to
people who have only seen a few instances. But this is because the
instances are all a little different, and so correct each other, and
show transitions from more obvious forms to less obvious forms of the
properties in question which lead us up to a true understanding of
them. If the instances were all exactly the same they would not help
us in this way, but our guess would still be a guess, however many
instances might have suggested it.
I remember that a great many years ago I hardly believed in the
stone-age tools being really tools made by men. I had only seen a few
bad specimens, one or two of which I still think were just accidentally
broken flints which an old country clergyman took for stone-age tools.
This was to me then a mere guess, viz. that the cutting shape proved
{144} the flints to have been made by men. And obviously, if I had seen
hundreds of specimens no better than these, I should have treated it as
a mere guess all the same. But I happened to go to Salisbury, and there
I saw the famous Blackmore Museum, where there are not only hundreds
of specimens, but specimens arranged in series from the most beautiful
knives and arrow-heads to the rudest. There one’s eye caught the common
look of them at once, the better specimens helping one to interpret the
worse, and the guess was almost turned into a demonstration, because
one’s eyes were opened to the sort of handwork which these things
exhibit, and to the way in which they are chipped and flaked.
Now this very important operation of number of examples, in helping the
mind to an explanation, is always being confused with the effect of
mere repetition of examples, which does not help you to an explanation,
_i.e._ a repetition in which one tells you no more than another.
But these mere repetitions operate _prima facie_ in a different
way, viz. by making you think there is an _unknown_ cause in favour
of the combination of properties which recurs, and lead up to the
old-fashioned perfect Induction and the doctrine of chances, and not to
demonstration. [1]
[1] Ultimately the calculus of chances may be said to rest on
the same principle as Induction, in so far as the repetition of
examples derives its force from the (unspecified) variety of
contexts through which this repetition shows a certain result
to be persistent. But in such a calculus the presumption from
recurrence in such a variety of contexts is only estimated, and
not analysed.
On the road from guess-work to demonstration, and generally assisted
by great experience, we have _skilful_ {145} guess-work, the first
stage of discovery. This depends on the capacity for hitting upon
qualities which _are_ connected by causation, though the connection
remains to be proved. So a countryman or a sailor gets to judge of
the weather; it is not merely that he has seen so many instances, but
he has been taught by a great variety of instances to recognise the
essential points, and has formed probably a much more complex judgment
than he can put into words. So again a doctor or a nurse can see how
ill a patient is, though it does not follow that they could always say
why this appearance goes with this degree of illness. In proportion
as you merely _presume_ a causal connection, it is guess-work or pure
discovery. In as far as you can _analyse_ a causal connection it is
demonstration or proof; and for Logic, discovery cannot be treated
apart from proof, except as skilful guess-work. _In as far as_ there
is ground for the guess, so far it approaches to proof; _in as far as_
there is no ground, it gives nothing for Logic to get hold of--is mere
caprice. A good scientific guess really depends on a shrewd eye for the
essential points. I am not mathematician enough to give the history
of the discovery of Neptune by Leverrier and Adams, “calculating a
planet into existence by enormous heaps of algebra,” [1] but it must
have begun as a guess, I should suppose it was suggested before Adams
and Leverrier took it up, on the ground of the anomalous movements of
Uranus indicating an attraction unaccounted for by the known solar
system. And I suppose that this guess would gradually grow into
demonstration as it became clear that nothing but a new planet would
explain the anomalies of {146} the orbit of Uranus. And at last the
calculators were able to tell the telescopist almost exactly where
to look for the unknown planet. The proof in this case preceded the
observation or discovery by perception, and this makes it a very
dramatic example; but if the observation had come earlier, it would not
I suppose have dispensed with the precise proof of Neptune’s effect on
Uranus, though it might have made it easier.
[1] De Morgan, _Budget of Paradoxes_, p. 53.
_Figures of Syllogism_
6. In illustration of this progress from guess-work to science, [1]
I will give an example of the three Aristotelian figures of the
Syllogism. I omit the fourth. I assume that the heavier term, or the
term most like a “thing,” is fitted to be the Subject, and the term
more like an attribute to be the Predicate. The syllogistic rules
depend practically on the fact that common Logic, following common
speech and thought, treats the Predicate as wider than the Subject,
which corresponds to Mill’s view (also the common scientific view),
that the same effect may have several alternative causes (not a
compound cause, but different possible causes), and that consequent
is wider than antecedent. [2] It is this assumption that prevents
affirmative propositions from being simply convertible, _i.e._ prevents
“All men are mortal” from being identical with “All mortals are men,”
and but for it there would be no difference of figure at all, as there
is not for inference by equation.
[1] Cf. Plato’s _Republic_, Bk. VI., end. [2] See p. 141, note.
This progression is here merely meant to illustrate the universal or
systematic connection of particulars in process of disengaging itself.
But I do _not_ say that the first {147} figure with a major premise is
a natural form for all arguments.
I take the scheme of the first three figures from Jevons, and suggest
their meaning as follows:--
X denotes the major term.
Y denotes the middle term.
Z denotes the minor term.
1st Fig. 2nd Fig. 3rd Fig.
Major Premise YX XY YX
Minor Premise ZY ZY YZ
Conclusion ZX ZX ZX
Fig. 3. _An observation and a guess._
Yesterday it rained in the evening.
All yesterday the smoke tended to sink.
∴ The smoke sinking ( may be ) a sign of rain.
( is sometimes )
The conclusion cannot be general in this figure, because nothing
general has been said in the premisses about the subject of the
conclusion. So it is very suitable for a mere suggested connection
given in a single content--that of the time “yesterday,” implying
moreover that both the points in question have something to do with the
state of the atmosphere on that single day.
Fig. 2. _A tentative justification_.
Smoke that goes downwards is heavier than air
Particles of moisture are heavier than air.
∴ Particles of moisture may be in the descending smoke.
A universal conclusion in this figure would be formally bad. But we
do not care for that, because we only mean it to be tentative, and we
do not draw a universal affirmative {148} conclusion. We express its
badness by querying it, or by saying “may be.” The reason why it is
formally bad is that nothing general has been said in the premisses
about the middle term or reason, so that it is possible that the two
Subjects do not touch each other within it, _i.e._ that the suggested
special cause, moisture, is not connected with the special effect, the
sinking of the smoke. The general reason “heavier than air” may include
both special suggested cause and special suggested effect without their
touching. Smoke and moisture may both sink in air, but for different
and unconnected reasons. Still, when a special cause is suggested which
is probably present in part, and which would act in the way required
by the general character of the effect, there is a certain probability
that it _is_ the operative cause, subject to further analysis; and
the argument has substantive value, though bad in form. The only good
arguments in this figure have negative conclusions, _e.g._--
Smoke that is heavier than air goes downwards.
Smoke on dry days does not go downwards.
∴ Smoke on dry days is not heavier than air.
This conclusion _is_ formal, because the negative throws the second
Subject altogether outside the Predicate, and so outside the first
Subject. The one content always has a characteristic which can never
attach to the other, and consequently it is clear that some genuine
underlying difference keeps them apart. Such an inference would
corroborate the suggestion previously obtained that the presence of
moisture was the active cause of the descending smoke on days when rain
was coming.
Fig. 1. _A completely reasoned judgment_.
{149}
All particles that sink in the air in damp weather more
than in dry, are loaded with moisture when they sink.
Smoke that descends before rain is an example of particles
that sink in the air in damp weather more than in dry.
∴ Smoke that descends before rain is loaded with moisture
when it descends (and therefore its sinking is not
accidentally a sign of rain, but is really connected with
the cause of rain).
The major premise belongs only to this figure. In the other it is mere
tradition to call it so, and their two premisses are the same in kind,
and contribute equally to the conclusion, and for that reason the
affirmative conclusion was not general or not formal. If your general
conclusion is to follow by mere form, you must show your principle
as explicitly covering your conclusion. But if you do this, then of
course you are charged with begging the question. And, in a sense,
that is what you mean to do, when you set out to make your argument
complete by its mere form. If you have _bonâ fide_ to construct a
combination of your data, you cannot predict whether the conclusion
will take this form or that form. Using a major premise meant, “We
have got a principle that covers the conclusion, and so explains the
case before us.” Granting that the major premise involves the minor
premise and conclusion, that is just the reason why it is imperative
to express them. The meaning of the Syllogism is that it analyses the
whole actual thought; the fault is to suppose that novelty is the
point of inference. The Syllogism shows you how you must understand
either premise in order that it may cover {150} the conclusion. Or,
starting from the conclusion as a current popular belief, or as an
isolated observation or suggestion by an individual observer (and this
is practically the way in which our science on any subject as a rule
takes its rise), the characteristic process through the three stages
described above consists in first noting the given circumstances under
which, according to the _prima facie_ belief or observation, the
conjunction in question takes place (“yesterday,” _i.e._ “in the state
of the atmosphere yesterday”); secondly in analysing or considering
those given circumstances, to find within them something which looks
like a general property, a law, or causal operation, which may attach
the conjunction in question to the systematic whole of our experience
(the presence of something heavier than air in the atmosphere); and
thirdly, in the exhibition of this ground or reason as a principle, in
the light of which the primary belief or observation (probably a good
deal modified) becomes a part of our systematic intelligible world.
{151}
LECTURE X INDUCTION, DEDUCTION, AND CAUSATION
_Induction_ [1]
1. Induction has always meant some process that starts from instances;
the Greek word for it is used by Aristotle both in his own Logic and
in describing the method of Socrates. It meant either “bringing up
instance after instance,” or “carrying the hearer on by instances.” And
still in speaking of Induction we think of some process that consists
in doing something with a number of instances. But we find that this
notion really breaks down, and the contradiction between Mill and other
writers (Jevons, ch. i.) shows exactly how it breaks down. The question
is whether one experiment will establish an inductive truth. We will
review the meanings of the term, and show how they change.
[1] Read N. Lockyer’s _Elements of Astronomy_; Abney’s _Colour
Measurement_; Introduction to _Bain on Induction_; Jevons’s
_Elementary Lessons on “Observation and Experiment”_ p. 228, and
on _Induction_, p. 214 (about Mill).
_Induction by simple Enumeration_
(_a_) Induction by simple enumeration was what Bacon was always
attacking, and saying, quite rightly, that it was not scientific. It is
the method which I stated in the Third Figure of the syllogism, almost
a conversational method; the mere beginning of observation. “I am sure
the influenza is a serious illness; all my friends who have had it have
been dreadfully pulled down.”
{152}
A B C have been seriously ill.
ABC have had influenza.
∴ Influenza is a serious illness.
Now this popular kind of inference, as Bacon says, “Precarie concludit,
et periculo exponitur ab instantia contradictoria.” Suppose you come
across one slight case of influenza, the conclusion is upset. This
type of reasoning really appeals to two quite opposite principles;
one the principle of counting, which leads up to statistics and the
old-fashioned perfect Induction or the theory of chance, the other the
principle of scientific system.
_Enumeration always has a ground_
(_b_) In counting, we do not think of the reason why we count, but
there always is a reason, which is given in the nature of the whole
whose parts we are counting. If I count the members of this audience,
it is because I want to know how many units the whole audience consists
of. I do not ask why each unit is there; counting is different from
scientific analysis; but yet the connection between whole and part is
present in _my reason for counting_. So really, though I only say,
“One, two, three, four, etc.,” each unit demands a judgment, “This is
one member--that makes two members, that makes three members,” etc.
Counting is the construction of a total of units sharing a common
nature; measurement is a form of counting in which the units are also
referred to some other standard besides the whole in question, _e.g._
the standard pound or inch.
_Perfect Induction_
(_c_) _Mere_ counting or “enumeration” only helps you in induction by
comparison with some other numerical result, and, if imperfect, only to
the extent of suggesting that there {153} is a common cause or there is
not a common cause. _E.g._ if you throw a six with one die fifty times
running, you infer that the die is probably loaded. This is because
you compare the result with that which you expect if the die is fair,
viz. a six once in every six throws. You infer that there is a special
cause favouring one side. The principle is that ignorance is impartial.
If you know no reason for one case more than another, you take them
as equal fractions of reality; if results are not equal fractions
of reality, you infer a special reason favouring one case. [1] Pure
counting cannot help you in Induction in any way but this. _Perfect
Induction_ simply means that the total is limited and the limit is
reached; you have counted 100 per cent, of the possible cases, and the
chance becomes certainty. The result is a mere collective judgment.
[1] See Lecture IX, p. 144, note.
_System_
(_d_) The principle of scientific system is quite a different thing.
Essentially, it has nothing to do with number or with a generalised
conclusion. It is merely this, “What is once true is always true, and
what is not true never was true.” The aim of scientific induction is
to find out “What _is_ true,” _i.e._ what is consistent with the given
system. We never doubt this principle; if we did we could have no
science. If observation contradicts our best-established scientific
laws, and we cannot suppose an error in the observation, we must
infer that the law was wrongly, _i.e._ untruly stated. Therefore, as
Mill says, one case is enough, _if_ you can find the truth about it.
People object that you cannot make a whole science out of one case,
and therefore you must have a number of instances. That is a {154}
_practical_ point to be borne in mind, but it has no real scientific
meaning. “Instance” cannot be defined except as one observation, which
is a purely accidental limitation. The point is, that you use your
instances not by counting cases of given terms, but by ascertaining
what the terms really are (_i.e._ modifying them), and what is their
real connection. This is the simple secret of Mill’s struggle to base
scientific Induction, on Induction by simple Enumeration; the latter is
not the evidence, but the beginning of eliciting the evidence--so that
the Scientific Induction is far more certain than that on which Mill
bases it. Aristotle’s statement is the clearest and profoundest that
has ever been made. [1]
“Nor is it possible to obtain scientific knowledge by way
sense-perception. For even if sense-perception reveals a certain
character in its object, yet we necessarily perceive _this_, _here_,
and _now_. The universal, which is throughout all, it is impossible to
perceive; for it is not a this-now; if it had been it would not have
been universal, for what is always and everywhere we call universal.
Since then demonstration (science) is universal, and such elements it
is impossible to perceive by sense, it is plain that we cannot obtain
scientific knowledge by way of sense. But it is clear that even if we
had been able to perceive by sense [_e.g._ by measurement] that the
three angles of a triangle are equal to two right angles, we should
still have had to search for a demonstration, and should not, as some
say, have known it scientifically (without one); for we necessarily
perceive in particular cases only, but science comes by knowing the
universal. Wherefore if we could have been on the moon, and seen the
earth coming between it and the {155} sun, we should not (by that mere
perception) have _known_ the cause of the eclipse. Not but what by
seeing this frequently happen we should have grasped the universal,
and obtained a demonstration; for the universal becomes evident out
of a plurality of particulars, and the universal is valuable because
it reveals the cause;” and again, [2] “And that the search of science
is for the middle term is made plain in those cases in which the
middle term is perceptible to sense. For we search where we have had
no perception,--as for the reason (or middle term) of an eclipse,--to
know if there is a reason or not. But if we had been upon the moon, we
should not have had to inquire if the process (of an eclipse as such,
and not some other kind of darkness) takes place, or for what reason,
but both would have been plain at once. The perception would have been,
‘The earth is now coming between,’ carrying with it the obvious fact,
‘The moon is now suffering an eclipse,’ and _out of this_ the universal
(connection) would have arisen.”
[1] Aristotle, _An. Post._ 87, b. 28. [2] _Ibid._ 90, a. 24.
_Analogy_
(_e_) I showed you a method on the way to this in the shape of
Aristotle’s second figure, which we may call _analogy_. The plain sign
of it is, that you give up counting the instances and begin to weigh
them, so that the attributes which are predicates fall into the middle
term or reason. In the former inference about influenza we did not
suppose that you had any idea _why_ influenza was a serious illness;
but in analogy there is some suggestion of this kind, so that the
connection is examined into. Here at once you begin to get suggested
explanations and confirmation from the {156} system of knowledge. You
cannot have analogy by merely counting attributes.
I begin from _Enumerative Suggestion_ drawn from observation of
Butterflies.
1. Three species of genus _x_ closely resemble three species of _y_.
2. The species of _x_ would be protected by resembling _y_ (because _y_
is distasteful to birds).
∴ The resemblance may be a “protective resemblance,” _i.e._ a
resemblance brought about by survival of those thus protected.
On this there naturally follows _Analogy_.
1. Protective resemblances naturally increase through series of species
from slighter to closer resemblances.
2. The resemblances in question increase in genus _x_ through series of
species from slighter to closer resemblance to _y_.
∴ The resemblances in question show important signs of being protective
resemblances.
When we get thus far, a single syllogism will not really represent
the argument. It can only analyse with convenience a single step in
inference. But now we have connected the reason of the resemblances
with the whole doctrine of natural selection, the gradual approximation
of the species is most striking, and we could set up a corroborative
analogy on the basis of every feature and detail of these resemblances,
the tendency of which would be to show that no cause or combination of
causes other than that suggested is likely to account for the observed
resemblances.
{157} I give a confirmatory negative analogy.
1. No protective resemblance can grow up where there is no initial
tendency to resemblance.
2. The non-resembling species in the genus _x_ show no initial tendency
towards _y_.
∴ The non-resemblances observed are such as could not produce
protective resemblances. This is a formally bad argument from two
negative premisses justified by its positive meaning, which implies
that _just where_ the alleged effect ceases, the alleged cause ceases
too.
If you look at the case in the Natural History Museum [1] you see the
normal Pierinae down one side, not approaching Euploinae. They are the
positive examples, negatively confirming the explanation of those which
do approach Euploinae. These latter all start from some form which
varied slightly, by accident we presume, towards Euploinae, and then
this partially resembling series splits into three sets, each leading
up to a different and complete protective resemblance.
[1] These cases in the entrance-hall of the Natural History
Museum at South Kensington afford excellent practical
illustrations of Inductive Method. I strongly urge the London
student to try his hand at formulating them.
I said _mere_ number was no help in scientific Induction. But do not
these three sets of resemblances make a stronger proof than any one
would? Yes, because we need a presumption against accident. You would
not want this if you could unveil what really happens in one case,
but as infinite conditions are operative in such matters, and it is
impossible to experiment accurately, [1] this cannot be done; {158}
and it might be said that _one_ such resemblance was an accident,
_i.e._ that it was owing to causes independent of the protection. But
as the cases become more numerous it becomes more improbable that
different circumstances produce the same effect, which would then be
a mere coincidence, in so many different cases. If, however, we knew
by positive and negative analysis what circumstance did produce the
effect, this confirmation would be useless.
[1] Ultimately, no experiments are absolutely accurate. There is
always an unexhausted background in which unsuspected causes of
error may be latent.
_Negative Instance_
(_f_) In order to show _exactly_ what circumstance produces a given
effect, a system must be brought to bear on the phenomenon through
negation. The only test of truth is that it is that which enables you
to organise your thought and perception.
The first means of doing this is Observation, then Experiment, then
Classification and Hypothesis, which takes us into Deduction.
Observation is inaccurate, until you begin to distinguish what is
connected from what is not connected. When you do this, you are very
near experiment, the use of which is to introduce perfectly definite
and measurable changes into what you are observing. [1] There is no
absolute distinction between observation and experiment. Looking at a
tissue through a microscope is observation; putting on a polariscope,
though it changes the _image_ altogether, is observation; if you
warm the stage, or put an acid on the object, that, I suppose, is
experiment, because you interfere with the object {159} itself. What
should we say, for example, as to spectroscopic analysis of the Sun’s
corona?
[1] Jevons, _loc. cit_., esp. quot. from Herschel (p. 234).
The moment you begin accurate observation you get a negative with
positive value, which is really the converse by negation of your
positive observation, a1 is b1; b2 (which is _just_ not-b1) is a2
(which is _just_ not-a1). Thus the two may be represented as the same
judgment in positive and negative forms, which confirm one another.
“Yellow is a compound of red and green”--in Experiment, “if, and as far
as you take away the red or the green you destroy the yellow.” That
describes an experiment with the colour-box. I have inverted the order
in the conversions in compliance with the rule of common Logic, that
Predicate is wider than Subject; but in accurate matter it is a false
rule, and very inconvenient. The common rule means that a man who is
drowned is dead, but a man who is dead need not have been drowned; but
of course if he has the signs of death by drowning then he has been
drowned.
_Classification and Generalisation_
(_g_) _Classification_ is a consequence of all systematic theory; it
is not a separate method of science. It is merely the arrangement
of positive contents negatively related. No doubt where we have a
kind of family relations between individuals classification is more
prominent, and in the theory of continuous matter or operation, where
individualities are not remarkable--_e.g._ in geometry--it is less
prominent. But both are always there--classification and theory.
Classification which expresses no theory is worthless, except that
intended for convenient reference, such as alphabetical classification.
Under classification I may say a word on generalisation. {160} The
common idea of inference from many cases, because they are many, to
all cases of the same kind, is quite without justification. The only
genuine and fundamental law of generalisation is “Once true always
true.” But this might fail to suffice for our practical purposes,
because it might save its truth by abstraction. Let us take the
example, “Water is made of oxygen and hydrogen.” If that is true once,
it is always true _in the same sense_. If you find some fluid of a
different composition which you are inclined to call water, then you
must identify or distinguish the two, and this is a mere question of
classification. _Practically_, however, we could not get on unless our
knowledge had some degree of _exhaustiveness_, _i.e._ unless we knew
roughly that most of _what we take for water_ will have the alleged
properties. But no Induction or analysis, however accurate, can assure
us against confusion and error, viz. assure us that everything we take
to be water will be made of oxygen and hydrogen, nor that water will
always be found on the earth. I call this accurate analysis, which
_may_ be made in a single instance only, and is the only perfectly
scientific generalisation, generalisation by mere determination. Its
classification is hypothetical, _i.e._ in it the individuals are merely
possible individuals.
But this passes into another kind of generalisation, which may be
called generalisation by concrete system, as when we attach scientific
analysis to some extensive individual reality, _e.g._ to the solar
system or the race of man. Then our judgments have a place in the
real world, and our classification is categorical classification. The
generalisation in this case does not follow from the judgment being
extended {161} over a great plurality of possible similar subjects, but
from the subject to which it applies having as an organised totality
a large place in the world; _e.g._ “The human race alone gives moral
interest to the history of bur planet.” These judgments come by making
explicit the reality which underlies such hypothetical judgments as
“all men are capable of morality.” It means that we actually venture to
assign a place in the universe to the system we are speaking of. Then,
though it is an individual, and unique, its name has a meaning, and is
not a mere proper name. The solar system is good instance. Judgments
about it or parts of it are universal but not purely hypothetical,
and as our knowledge of this kind increases it becomes even a little
exhaustive.
_Generalisation by mere likeness or analogy_, on the other hand, is
precarious. It is what popular theory has in its mind in speaking of
Induction, viz. a conclusion from a truth to judgments concerning all
similar cases, _e.g._ from “Water is made of Oxygen and Hydrogen” to
“All liquids which we choose to take for water are made of Oxygen and
Hydrogen.” No scientific method can possibly give us this result. In as
far as it has value it depends upon our guessing rightly by analogy.
It may be replied, “that the signs of recognition are set down in
the law or truth.” Well, if they are certain, generalisation by mere
determination is enough; if they are doubtful, no induction can warrant
your judgment of them in particular cases. Practically, of course, we
get them right pretty often, although wrong very often.
_Hypothesis_
(_h_) Hypothesis is merely supposition; it consists in suggesting a
fact as if it were real, when it is the only way of {162} completing
given facts into a consistent system. If the hypothesis is proved that
is a demonstration. It has been said that “Facts are only familiar
theories.” If a bell rings in the house, I say unhesitatingly, “Some
one rang that bell.” Once in ten years it may be rung, not by a person,
but by some mechanical accident, in which case the “some one” is a
hypothesis, but one always treats it as a fact. The only proof of a
hypothesis is its being the only one that will fit the facts, _i.e._
make our system of reality relatively self-consistent. We believe many
things we can never verify by perception, _e.g._ the existence of the
centre of the earth, or that you have an idea in your minds; and if we
go to ultimate analysis, perception itself involves hypothesis, and
_a fortiori_ all experiment involves hypothesis. Every experimental
interference with nature involves some supposition as to a possible
connection which it is intended to confirm or disprove.
_Deduction_
2. Classification and hypothesis bring us into Deduction, which is not
really a separate kind of inference from Induction, but is a name given
to science when it becomes systematic, so that it goes from the whole
to the parts, and not from the parts to the whole. In Induction you are
finding out the system piecemeal, in Deduction you already have the
clue; but the system, and the system only, is the ground of inference
in both. Induction is tentative because we do not know the system
completely. Their relation may be fairly represented by the relation
of the first figure of the Syllogism to the second and third. The
difference is merely that in deduction we are sure of having knowledge
which covers the whole system. If a man observed, “The difference
{163} between the dark blood in the veins and the bright blood in the
arteries calls for explanation,” that is the beginning of Induction. If
a man states the circulation of the blood as an explanation, that is
Deduction. Really Induction is only a popular name for such Inference
as deals with numbers of instances. Mill’s experimental methods do
not depend upon number of instances, but only upon content; they
presuppose the instances already broken up into conditions A, B, C, and
consequents a, b, c.
I must distinguish subsumption and construction as two forms of
deduction. Only the former _properly_ employs Syllogism in the first
figure.
_Subsumption_
(_a_) Subsumption is argument by subject and attribute; _i.e._ when
we do not know the system so as to construct the detail,--_e.g._ a
man’s character,--and can only state _in_ what individual system the
details occur. Then we _really want_ the major premise to lay down the
properties of the system, and all deduction _can_ therefore be employed
with a major premise, _e.g._ a mathematical argument might ultimately
take the form, “_space is such that_ two parallels cannot meet.”
_Construction_
But (_b_) when the nature of the subject is very obvious, and
the combinations in it very definite, then the major premise is
superfluous, and adds nothing to the elements of the combination.
“A to right of B, B to right of C.
∴ A to right of C.”
This is clear, but it is not formal; as a syllogism it has four terms.
It is simply a construction in a series of which the nature is obvious.
And if you insert a major premise it would be, “What is to the right
of anything is to the right {164} of that which the former is to the
right of,” and that is simply the nature of the series implied in the
inference stated in an abstract form. “Inference is a construction
followed by an intuition.” [1] The construction, I think, however,
must be a stage of the intuition. I am therefore inclined to suggest
that a factor of general insight into principle is neglected in this
definition, from which much may undoubtedly be learned.
[1] Bradley, _Principles of Logic_, p. 235.
_Causation_
3. I have said very little about causation. The fact is, that in
Logic the cause necessarily fades away into the reason, that is, the
explanation. If we follow Mill’s account, we see how this takes place.
I will put the stages very briefly.
_Cause_
(_a_) We start, no doubt, by thinking of a cause as a real event in
time, the priority of which is the condition of another event, the
effect. Pull the trigger--cause--and the gun goes off--effect.
_Complete conditions_
(_b_) The moment we look closer at it, we see that this will not
do, and we begin to say with Mill, that the cause is the antecedent
which includes _all_ the conditions of the effect. The plurality of
alternative causes breaks down, through the conditions defining the
effect. Pull the trigger?--yes, but the cartridge must be in its place,
the striker must be straight, the cap must be in order, the powder must
be dry and chemically fit, and so on, and so on, till it becomes pretty
clear that the cause is a system of circumstances which include the
effect.
_Law_
(_c_) But then our troubles are not ended. Only the essential and
invariable conditions enter into the cause, if the {165} cause is
invariable. This begins to cut away the particular circumstances of
the case. You need not use the trigger, nor even the cap; you may
ignite powder in many ways. You may have many kinds of explosives. All
that is essential is to have an explosion of a certain force and not
too great rapidity. Then you will get this paradox. What is merely
essential to the effect, is always something less than any combination
of real “things” which will produce the effect, because every real
thing has many properties irrelevant to this particular effect. So,
_if the cause means something real_, as a material object is real, it
cannot be invariable and essential. If it is not something real, and
is essential, it fines down into a reason or law--the antecedent in a
hypothetical judgment.
_Ground, or real system with known laws_
(_d_) We can only escape this by identifying both cause and reason
with the complete ground; that is, the nature of a system of reality
within which the cause and effect both lie. But even then, though the
ground is _real_, it is not antecedent in time. We see, indeed, that
the conditions of an effect must be continuous through the effect. If
the process were taken as cut in two at any point, its connection would
be destroyed. If _a_ cause and _b_ effect were really detached events,
what difference could it make if, instead of _a_, _c_ preceded _b_?
_Postulate of Knowledge_
4. The postulate of Knowledge, then, is very badly stated as
Uniformity of Nature. That was due to the vulgar notion of Inductive
“generalisation.” It must be stated in two parts: first, “Once true
always true;” and secondly, “Our truth is enough for us,” that is, it
covers enough of the universe for our practical and theoretical needs.
The {166} two parts may be put together by saying, “The universe is a
rational system,” taking rational to mean not only of such a nature
that it can be known by intelligence, but further of such a nature that
it can be known and handled by our intelligence.
_Conclusion_
5. These lectures have been unavoidably descriptive rather than
thorough, and yet, as I warned you, descriptive of properties which
are in a sense not at all new, but quite familiar, and even trite. You
will not feel, at first, that the full interest which I claimed for
the science of knowledge, really attaches to these dry relations of
abstract thought. You will get no permanent good unless you carry the
study forward for yourselves, and use these ideas as a clue to find
your bearings in the great world of knowledge.
And I would give you one hint about this. _I_ do not suggest that you
should neglect philosophy but yet you should remember that philosophy
can tell you no new facts, and can make no discoveries. All that it
can tell you is the significant connection of what you already know.
And if you know little or nothing, philosophy has little or nothing to
tell you. Plato says, “The synoptical man, the man who has a conspectus
of knowledge, is the philosopher; and the man who is not synoptical,
who cannot see two subjects in their relation, is no philosopher.”
By all means read good logical books; but also and more especially
read good and thorough systematic books on science, or history, or
politics, or fine art--I do not mean on all of these subjects, but on
some, wherever your interest leads you. You cannot learn the nature of
inference, of systematic necessity, of the construction of reality,
by reading logic exclusively; you must {167} feel it and possess it
by working in the world of concrete knowledge. I give one example in
passing. If you study social questions, test for yourselves the value
of statistics--_i.e._ sets of enumerative judgments. Consider what the
causal analysis of any problem demands; remember that all enumeration
implies a ground or whole, on which its value depends; and contrast
the exhaustive examination of an instance thoroughly known, with the
enumeration of thousands of cases lumped under a general predicate.
Determine always to know the truth; welcome all information and all
suggestion, but remember that truth is always systematic, and that
every judgment, when you scrutinise it, demands a fuller and fuller
connection with the structure of life. It is not cleverness or learning
that makes the philosopher; it is a certain spirit; openness of mind,
thoroughness of work, and hatred of superficiality. Each of us,
whatever his opportunities, can become in a true sense, if he has the
real philosophic spirit, in Plato’s magnificent words, “The spectator
of all time and of all existence.”
THE END
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